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2 Georgia Math Teacher Guide

Grade 2 Teacher Guide

STEMscopes.com ISBN: 979-8-88826-716-5

ISBN: 979-8-88826-661-8

2 GEORGIA

MATH G2

GEORGIA

Teacher Guide: Grade 2 ISBN: 979-8-88826-661-8 Published by Accelerate Learning Inc., 5177 Richmond Ave, Suite 800, Houston, TX 77056. Copyright © 2023, by Accelerate Learning Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written consent of Accelerate Learning Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. To learn more, visit us at www. www.stemscopes stemscopes.com.

USING THE TEACHER GUIDE

Using the Teacher Guide Plan and Strategize In the Teacher Guide,, you’ll ﬁnd details about each element in our curriculum. Use these summaries to guide what you’ll integrate into your lessons based on the needs of your students and your teaching style. Throughout each scope, facilitation focuses primarily on understanding Vertical Alignment along with core Engage and Explore elements. Please note that all other elements are still available online.

Discover and Facilitate As you move through each scope, find STEMscopes Tips that explain how to use and where to find many of the aligned resources that are included throughout the curriculum. In each Explore lesson, you’ll also find Facilitation Tips to assist you in this critical part of the learning process.

Journal and Record The Teacher Guide includes areas throughout its pages for you to write notes about lessons, your students, and more. There are also areas to sketch out long-range plans, make observations, and coordinate smallgroup sessions.

Reﬂect and Enhance Trying to remember what you did last year when teaching a lesson? Use the notes and plans you write here to remind you. Find out what works, what doesn’t, and how to do it better from year to year with our product to help you along the way. When it’s time for a new year, it’s also time for a new Teacher Guide. Guide. Keep them to reference or share them with a colleague.

Using STEMscopes ............................................................................................... 4

SCOPE 1

Represent Numbers to 1,000 ............................................................................... 20

SCOPE 2

Compare and Order Numbers .............................................................................. 46

SCOPE 3

Addition and Subtraction Strategies .................................................................... 62

SCOPE 4

Addition and Subtraction Problem Solving ........................................................... 82

SCOPE 5

Arrays ................................................................................................................ 96

SCOPE 6

Two-Dimensional Shapes.................................................................................. 112

SCOPE 7

Three-Dimensional Solids ................................................................................. 134

SCOPE 8

Fractions .......................................................................................................... 152

SCOPE 9

Length ............................................................................................................. 168

TABLE OF CONTENTS

Table of Contents

SCOPE 10 Time ................................................................................................................ 194

SCOPE 11 Money.............................................................................................................. 214

8 6 4 2 0

SCOPE 12 Data Analysis ................................................................................................... 228

SCOPE 13 Patterns ........................................................................................................... 246

YEAR AT A GLANCE 2

Year at a Glance JULY

AUGUST

SEPTEMBER

OCTOBER

NOVEMBER

DECEMBER

JANUARY

FEBRUARY

MARCH

APRIL

MAY

JUNE

YEAR AT A GLANCE

Year at a Glance

USING STEMSCOPES

Using STEMscopes Utilizing the Home Section In the Home section, build your own content knowledge, analyze the standards, and gain an understanding of everything the scope has to offer. This is where you will ﬁnd all your lesson-planning materials so you can facilitate fun, purposeful experiences for your students. CONTENT SUPPORT • The standard(s) being addressed in the scope • The mathematical thinking and reasoning standards addressed in the scope • An overview of related concepts students have learned in pre-kindergarten • Student misconceptions and obstacles teachers may face • Detailed description of the content • Extensive list of terms and deﬁnitions students should know • Sample student responses to example questions • An overview of related concepts students will learn in future grades

Use Content Support to gain background knowledge to fully support the students’ understanding. • Includes the reasons a concept is being taught a certain way, examples that can be used to help teach the concepts, and sample student questions and answers • Explains what the students have already learned and gives insight to the concepts students will learn next • Provides known misconceptions students have about the content and obstacles teachers may face when teaching the content • Includes vocabulary and deﬁnitions students should learn throughout the scope Ideas for using this element: • Use it as a resource to understand why math concepts are taught a certain way and how the concepts should be taught. • Use it to understand what students should know before you teach the content, what they should learn, and what they will need to know to be successful in future grades.

STANDARDS EXPLAINED • The standard(s) being addressed in the scope • The verbs used in the standard that highlight what students should be doing • Concrete words and deﬁnitions students should know • A brief summary of the implications for instruction, including what students should understand by the end of the scope

Use the Standards Explained to fully understand the standard(s) that are being addressed in the scope. • Includes what students should be doing and what words they should know • Explains what the students must know to meet the standard • Shows the vertical alignment of relevant standards throughout the grade levels Ideas for using this element: • Use it to become familiar with the standard(s) being addressed and fully understand the concepts students need to know.

• A vertical alignment of related standards 4

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MATERIALS LIST • The ability to generate the total quantity of materials needed based on your class • A list of all the supplies that are needed for the Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration sections • A breakdown of each material, including the quantity per use; the item; whether the item is used per student, per pair, per group, or per class; whether the item is printed, reusable, or consumable; and the total quantity needed

Use the Materials List to plan for the materials that will be needed throughout the scope.

USING STEMSCOPES

Home

• Includes the ability to individualize the number of materials needed based on the total number of students, number of groups and stations, maximum class size, and total number of classes • Lists the materials needed for all the activities throughout the scope Ideas for using this element: • Use it to plan the materials you will need throughout the scope.

SCOPE OVERVIEW Use the Scope Overview to see every component of the scope. • Provides an easy-to-read, color-coded graphic showing the activities included in each element • Shows the sequential path students will take as they move throughout the scope • Includes the standard(s) and suggestions of how to use certain elements Ideas for using this element:

• The standard(s) addressed in the scope • Each element in the scope • The title of each part of an element • The order in which the scope should be taught

• Use it to quickly see the parts of the scope and how they interconnect. • Use it to plan how you will move through the scope.

PARENT LETTER • A description of the content of the Parent Letter • Procedure and facilitation points that provide a time frame for distributing the Parent Letter and suggestions for encouraging parent participation in the at-home activity

Use the Parent Letter to explain math concepts to parents. • Has a brief overview of the concepts being taught • Includes vocabulary terms and deﬁnitions students need to know • Provides resources and activities students and parents can do together to practice the concepts Ideas for using this element: • Use it to keep parents informed about what their children are studying in math. • Send home a copy of the Parent Letter the week before to notify parents of upcoming concepts and ways to help at home. • Be prepared to explain activities as questions arise from parents.

USING STEMSCOPES

Using STEMscopes Introducing Content with the Engage Section The Engage section is all about laying the foundation for learning. You begin this section by pre-assessing students using the APK (Accessing Prior Knowledge) and ﬁlling knowledge gaps using the Foundation Builder. The Hook then lays out a storyline narrative to establish a purpose for learning and captures students’ attention with real-world connections. ACCESSING PRIOR KNOWLEDGE • A general description of the activity and how it relates to what is being taught in the scope • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Sample student responses to embedded discussion prompts • A handout students use to complete the activity, if needed

Use the APK activity to help determine what students already know about the content as well as any misconceptions they have before beginning the scope. • Activates students’ thinking about the concept and how it’s been presented to them previously • Gives students opportunities to display what they know • Identifies the need to use the Foundation Builder to fill any knowledge gaps • Reveals possible misconceptions Ideas for using this element: • Due to the nature of this element, it is suggested that you complete this activity before the Hook activity. • Students typically complete and discuss the activities in small groups. • Student misconceptions identified here can be addressed and corrected as students progress through the scope.

FOUNDATION BUILDER • A general description of the activity • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Sample student responses to embedded discussion prompts • Handouts, Slideshows, and any other printed materials students will use to complete the activity

Use the Foundation Builder to help ﬁll learning gaps and review and reinforce previously taught content before beginning the scope. • Reteaches content previously taught • Uses concrete materials students can manipulate to explore mathematical concepts and develop proﬁciency • Addresses vocabulary with multiple meanings to eliminate confusion Ideas for using this element: • This activity is intended to be a short teacher-guided intervention for use in small groups. • Student preconceptions are addressed and corrected during this activity. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

HOOK • A general description of the activity • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Pre- and Post-Explore sections • A video showing a real-world situation • Sample student responses to embedded discussion prompts • Handouts, videos, and any other printed materials students will use to complete the activity

Use the Hook to engage students using real-world contexts where speciﬁc math skills are needed. Here, students have their ﬁrst experience with the new content.

USING STEMSCOPES

Home

• Introduces a real-world problem that requires use of the skills that will be taught in the scope • Uses media to show the real-world situation in action • Give students the opportunity to see how math is used in a real-world situation • Is revisited and the problem is solved after students complete the Explore activities from the next section Ideas for using this element: • Explain the real-world situation while showing the video. • Facilitate a discussion about how the scope’s math concepts are used in the situation. • Return to the Post-Explore section to solve the problem after completing the Explore activities. • Students typically complete and discuss the Post-Explore activities in pairs or small groups.

USING STEMSCOPES

Using STEMscopes Student Learning Using the Explore Section This is where students dig into the meat of the content. The Explore section provides scaffolded hands-on activities that build toward mastery of the standards. Each Explore supplies prompts for rich discussion and student reasoning, a Student Journal, and an Exit Ticket. The Explore section also gives students access to Virtual Manipulatives and teachers access to Skill Basics lessons designed to reinforce basic concepts before introducing the Explores. EXPLORES • A suggestion of which Skill Basics to use before completing the Explore, if applicable • A general description of the activity • The Mathematical Thinking and Reasoning Standards addressed in the Explores • A brief setup video showing the materials and preparation needed and explaining the activity • Materials and preparation needed to complete the Explores • Procedure and facilitation points that take you step by step through the activity • A scenario involving a realworld situation students need to solve • Sample student responses to embedded discussion prompts • Math Chat questions at the end of each Explore

Use the Explores to focus on developing students’ conceptual understanding of speciﬁc math skills using relevant situations and manipulatives. As students work through the activities, they will develop more abstract thinking and better number sense. • Provides real-world problems to motivate students to ﬁnd solutions using the math skills covered in the scope • Involves hands-on learning, rich discussions, and collaboration that encourage students to use thinking and reasoning skills • Reduces dependence on manipulatives as students progress through the activities • Helps students acquire new mathematical vocabulary through academic language embedded in the activities Ideas for using this element: • Read and discuss the real-world situations. • Provide an opportunity for students to work through the activities with partners or in small groups. • As students collaborate, monitor and assess their understanding by asking guiding questions. • Guide and correct students through any misconceptions noted during discussions or on their Student Journals. • Provide a Math Chat time at the end of the activity for students to share their observations and learning. • Have students complete the Exit Ticket to formatively assess their understanding of the concepts. • Use students’ responses from the discussions, Student Journals, and Exit Tickets to guide future instruction. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

VIRTUAL MANIPULATIVES • The Virtual Manipulatives include components such as these: • Place Value Disks • Base Ten Blocks • Number Lines • Pattern Blocks • Fraction Circles • Fraction Tiles • Two-Color Counters • Color Tiles • Linking Cubes • Geoboard • Clock • XY Coordinate Board

Use the Virtual Manipulatives to provide each student with a limitless supply of manipulatives.

USING STEMSCOPES

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• Helps students explore mathematical concepts • Makes learning engaging and meaningful • Leads to more complex understanding of math concepts • Allows students to make visual connections between math concepts and the virtual manipulatives • Helps students develop mental models and abstract thinking Ideas for using this element: • Use the Virtual Manipulatives in the classroom or remotely in place of concrete objects. • Encourage students to use the Virtual Manipulatives to develop proﬁciency in math concepts. • Differentiate instruction by using the Virtual Manipulatives for Englishlanguage learners and for students who are struggling with the concepts. Students can also beneﬁt from visual models when learning new concepts. • Use the Virtual Manipulatives to help address and clarify student misconceptions.

SKILL BASICS Use Skill Basics to pre-teach simple skills needed to complete the Explore activities. • Is designed to reinforce basic concepts before introducing the Explores • Uses manipulatives to make learning engaging and meaningful Ideas for using this element: • Teach a Skill Basics lesson before completing an Explore so students can apply the skill in the Explore. • Use the Skill Basics lesson to help students build a solid foundation of the skills they will use. • Use the Skill Basics lesson to help address and clarify student misconceptions. • Differentiate instruction by using Skill Basics lessons for students who are struggling with math concepts.

• A general description of the activity • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Sample student responses to embedded discussion prompts • Handouts and any other printed materials students will use to complete the activity • Instructions for the Explore to use after completing the lesson

USING STEMSCOPES

Using STEMscopes Guiding Students Using the Explain Section The Explain section offers a variety of resources that help connect the experiences of the Explore activities to the academic content students need to know. These resources include Anchor Charts, Picture Vocabulary, My Math Thoughts, Show What You Know, and, in some scopes, an Interactive Notebook that can be used to support the Explore activities and solidify student learning. ANCHOR CHARTS • A general description of each activity • An Anchor Chart for each Explore • Sample student responses to embedded discussion prompts • A printable sample Anchor Chart

Use the Anchor Charts during or after the Explore activities as a tool to anchor student learning of the concepts addressed in the scopes. • Provides large, poster-sized visuals of the most important content strategies • Helps students achieve mastery of skills and reinforce concepts throughout the year • Gives students access to the charts to use as resources when needed Ideas for using this element: • Create Anchor Charts during instruction or after the Explore activities. • Ask students guiding questions while interacting with the Anchor Chart to help reinforce students’ understanding of concepts. • Display Anchor Charts during instruction or throughout the year to review learning.

PICTURE VOCABULARY • A slideshow of each relevant vocabulary word • Starting in Grade 2, a ﬂash card option with either the picture and word or the picture and deﬁnition for each word • A printable copy

The Picture Vocabulary presents new vocabulary with pictures and studentfriendly definitions. • Includes a slideshow with a picture and written or visual definition for each vocabulary word • Clarifies the meaning of words used throughout the scopes • Gives students access to the vocabulary words to use as a resource when needed Ideas for using this element: • Directly teach math vocabulary using the Picture Vocabulary. • Refer to the Picture Vocabulary throughout the scope to reinforce students’ understanding of vocabulary terms. • If available, encourage students to use the flash card feature to learn relevant math vocabulary. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MY MATH THOUGHTS • A general description of the activity • Preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • A printable Student Handout and Answer Key

Use My Math Thoughts to allow students to write out their mathematical thoughts and ideas using several different avenues to ensure that a balanced approach to writing in mathematics is attained.

USING STEMSCOPES

Home

• Focuses students’ writing on problem solving, strategies, and procedures • Allows students to identify how they feel they are progressing in attaining targeted math skills Ideas for using this element: • Allow students to discuss their thinking with their neighbors before writing their thoughts on paper. • Encourage students to persevere through their thinking and to use mathematical tools and models as necessary.

SHOW WHAT YOU KNOW Use the Show What You Know to allow students to independently demonstrate their understanding and practice new skills after exploring concepts.

• A different Show What You Know activity to correspond with each Explore

• Allows students to apply the knowledge and skills they learned in the Explore activities to new situations

• A general description of the activity

• Correlates each activity piece with the same-number Explore. For example, Show What You Know – Part 1 allows students to practice the skills they developed in Explore 1.

• Materials and preparation needed to complete the activity

Ideas for using this element: • Assign the activity for students to complete independently after ﬁnishing the corresponding Explore. • Provide reading assistance if needed.

• Procedure and facilitation points that identify how to use the activity • A printable Student Handout and Answer Key

• Provide manipulatives, especially those used in the Explore, as needed. • Identify whether instruction needs to be adjusted based on student misconceptions before proceeding to the next Explore.

INTERACTIVE NOTEBOOK • A general description of the Interactive Notebook

Use the Interactive Notebook to allow students to take notes, express ideas,

• Materials and preparation needed to complete the activity

and/or process the information presented in class.

• Procedure and facilitation points that identify how to use the activity

Ideas for using this element:

• A printable Student Handout

• Provides students with the opportunity to solidify their learning

• Prepare an Interactive Notebook using a spiral or composition notebook for each student. • Precut or allow students to cut the pieces for each Student Handout according to the instructions. • Allow time for students to complete the activity and then glue the pieces in their Interactive Notebook.

USING STEMSCOPES

Using STEMscopes Extending Learning with the Elaborate Section Workstations are a go! The Elaborate section makes differentiation a cinch with readymade activities—digital and paper-based games, Spiraled Review, Life Connections, and more—that are perfect for rotations! These activities allow students to continue learning while you make time for small-group interventions, reteaching, and independent projects to help both struggling and advanced learners. FLUENCY BUILDER • A description of the activity • Materials and preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Printable Instruction Sheets and game materials

Use the Fluency Builder games to give students the opportunity to practice the skills they learned during the Explore activities. • Involves games designed to be motivating and entertaining • Increases focus and collaboration skills as students play with partners or in small groups • Allows students to continue to practice skills throughout the year using the games • Develops ﬂuency as students become more eﬃcient and accurate when using their math skills during game play Ideas for using this element: • Place students with partners or in small groups. • Read the game directions, and model the game if needed. • While students are playing the game, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

SPIRALED REVIEW • A general description of a Spiraled Review • Preparation needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Multiple real-world questions that cover previously taught math concepts • Printable Student Handout and Answer Key

Use the Spiraled Review to allow students to continue to practice skills throughout the year. • Motivates students to use the math skills to find solutions for real-world problems • Allows students to review previous or current grade-level content based on the focal points set for each grade • Gives students the flexibility to use different processes and strategies to reach solutions • Develops fluency as the students become more efficient and accurate in solving problems Ideas for using this element: • Read the story to engage student interest before moving on to the questions. • Use the Spiraled Review as a warm-up in class or send it home for homework, but be sure to discuss answers and strategies with the class as a whole group. • Refer to the standard in the lower right-hand corner of each question box to assess the students’ content knowledge or need for further intervention.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MATH STORY • A Lexile reading level for each passage, starting in Grade 2

Use the Math Story to give students an opportunity to practice ﬁnding the information they need to solve a problem while performing a new skill.

• A real-world story students can relate to

• Uses real-world engaging stories to support real-world application of math skills and concepts

• Multiple real-world questions that cover not only math concepts taught in the scope but also reading comprehension

• Offers questions covering both math concepts and reading comprehension

• Printable story in Kindergarten and Grade 1; Student Handout and Answer Key starting in Grade 2

USING STEMSCOPES

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• Develops ﬂuency as the students become more eﬃcient and accurate in solving problems • Allows students to improve reading comprehension skills and use reading strategies to answer questions Ideas for using this element: • Use the Math Story as a workstation activity, or assign it as homework. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects. Notes

USING STEMSCOPES

Using STEMscopes Extending Learning with the Elaborate Section PROBLEM-BASED TASK • A general description of a Problem-Based Task • Procedure and facilitation points that provide details on how to use the activity • Multiple real-world problems with multiple solutions or responses • Printable Student Handout and Rubric

Use the Problem-Based Task to provide a more rigorous opportunity for students to practice within a real-world context. • Allows students to work collaboratively to apply the knowledge and skills they have learned to an open-ended, real-world challenge • Engages students throughout the learning process in relevant situations where the math skill is needed • Enables students to use different processes and strategies to reach a solution • Allows students to communicate their understanding and evaluate others’ reasoning • Develops ﬂuency as the students become more eﬃcient and accurate in solving problems Ideas for using this element: • Allow students to work in groups. • Encourage students to look back at their Student Journals from the Explore activities if they need to review the skills they have learned. • If students are stuck, use guiding questions to help them think through the issue without telling them what steps to take next. • Allow each group to share its solution with the class. • Discuss how different groups tackled the challenge in different ways. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LIFE CONNECTIONS • A short description of the focus of the Life Connections • Materials and preparation needed to complete the activity • Procedure and facilitation points that provide details on how to use the activity • Video about the topic • Additional topic-related activities that students can complete • Printable Student Handout

Use the Life Connections to introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom.

USING STEMSCOPES

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• Includes creativity and innovation, critical thinking, problem solving, and technology skills • Gives students the opportunity to learn about life events and careers that highlight where math is used Ideas for using this element: • Group the students for rich collaboration and discourse. • Play the video, and use the provided in-depth guiding questions to help students think about the topic from multiple angles. • Ask guiding questions as students complete the activity.

INTERACTIVE PRACTICE Use the Interactive Practice to engage students in practice using technology. • Increases student participation and focus through graphics, sound, point accumulation, and engaging content • Develops ﬂuency as the students become more eﬃcient and accurate in solving problems

• An interactive online game • A “Show Answer” button • A feature that reads the questions • Sound and music that can be muted

Ideas for using this element: • Use the Interactive Practice as a workstation activity, or assign it as homework. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

USING STEMSCOPES

Using STEMscopes Assessing Using the Evaluate Section Get the data you need from the assessment tools provided in the Evaluate section. From performance-based assessments to Skills Quizzes and Observation Checklists, there are multiple evaluations to ensure students have mastered the standards. DECIDE AND DEFEND • A real-world prompt • Printable Student Handout and Answer Key

Use the Decide and Defend reasoning assessment to evaluate students’ ability to use mathematical evidence and reasoning. • Allows students to write out an argument in response to a relatable real-world prompt and provide support for their response • Focuses on real-world applications in new situations where complex reasoning and planning are necessary • Enhances critical thinking involved in problem solving and heightens students’ ability to make connections among mathematical ideas Ideas for using this element: • Review students’ responses to determine student mastery of math concepts. • Use students’ responses to determine whether students would beneﬁt from Intervention or Acceleration activities. Notes

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

SKILLS QUIZ • Multiple skills-based questions • Printable Student Handout and Answer Key

Use the Skills Quiz to identify which skills addressed throughout the scope students have mastered.

USING STEMSCOPES

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• Focuses on facts, details, deﬁnitions, and procedures with one correct answer Ideas for using this element: • Review students’ responses to determine student mastery of math skills. • Use students’ responses to determine whether students would beneﬁt from Intervention or Acceleration activities.

STANDARDS-BASED ASSESSMENT Use the Standards-Based Assessment to identify which concepts and skills presented throughout the scope students have mastered. • Focuses on applying skills and concepts in addition to answering how or why with one correct answer

• Multiple skills- and reasoning-based questions • Printable Student Handout and Answer Key

Ideas for using this element: • Review students’ responses to determine student mastery of math skills and concepts. • Use students’ responses to determine whether students would beneﬁt from Intervention or Acceleration activities.

USING STEMSCOPES

Using STEMscopes Using the Intervention and Acceleration Sections Useful during Elaborate or as an after-school support, Intervention contains a small handson activity designed to target students’ conceptual misunderstanding while building their math skills. The Intervention activities can also be used as a reteach or test-prep tool. In addition, the Intervention section includes information about how Supplemental Aids like base ten grids and number lines can be used during instruction. SMALL-GROUP INTERVENTION • A general description of the activity • Materials and preparation needed to complete the activity

Use the Small-Group Intervention to revisit concepts to build student understanding. • Allows small groups of students to meet for 20–30 minutes to complete activities focused on the concepts and skills addressed in the scopes

• Procedure and facilitation points that take you step by step through the activity

• Provides more hands-on experience with concrete objects

• Sample student responses to embedded discussion prompts

• Reinforces mathematical vocabulary through academic language embedded in the activities

• Teacher Checklist to monitor students’ mastery • Depending on the scope, a Checkup and Answer Key, Student Handout, and other printed materials students will use to complete the activity

• Gives students the opportunity to use thinking and reasoning skills during rich discussions and collaboration

• Provides an opportunity to take notes about each student’s progress during the activity Ideas for using this element: • Select small groups of students who need more support to develop mastery of math skills and concepts. • Provide ample opportunities for students to use manipulatives to explore mathematical concepts. • Ask guiding questions throughout the activity to assess students’ understanding and address misconceptions. • Take notes on the Teacher Checklist for each student to monitor his or her progress toward mastery of the skills. • If provided, have students complete the Checkup to formatively assess their mastery of math skills and concepts. • Use students’ responses from the discussions, notes on the Teacher Checklist, and the Checkup to guide future instruction.

SUPPLEMENTAL AIDS • A general description of the activity • Grade levels where the Supplemental Aids would typically be used • Materials needed to complete the activity • Procedure and facilitation points that take you step by step through the activity • Printable Supplemental Aids 18

Use the Supplemental Aids to help students become familiar with the tools they can use during classroom instruction and assessments. • Provides paper resources to help students, particularly those with disabilities, comprehend content Ideas for using this element: • Provide Supplemental Aids to students who meet eligibility criteria for their use during assessments. • Model how to use the Supplemental Aids. • Consistently incorporate the use of Supplemental Aids into your instruction and student activities. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Are your students ready to go above and beyond what they’ve just learned? In the Acceleration section, students connect the mathematical concepts to either science or engineering or relate what they’re learning to current events around the world. These activities prompt them to think more deeply about the content and its applications.

USING STEMSCOPES

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MATH TODAY • A general description of Math Today

Use Math Today to connect mathematical content to real-world events.

• Media provided by the Associated Press

• Allows students to explore connections and applications of math and other cross-curricular content through interactions with authentic, real-world media

• Procedure and facilitation points that take you step by step through the activity

• Focuses on real-world applications in new situations where complex reasoning is necessary

• Sample student responses to embedded discussion prompts

• Uses media to engage students and motivate them to understand how math is involved in various events around the world Ideas for using this element:

• Problems that connect the media with math concepts

• Provide opportunities for students who have mastered the content to complete the Math Today activity.

• Printable Student Handout and Answer Key

• Encourage students to discuss how mathematical concepts are used in the real world.

CONNECTION STATION Use Connection Station as a cross-curricular connection between science and math. • Provides a way for students to connect the math concepts they learned with science and engineering • Gives students an opportunity to communicate their ideas with their peers and teachers using academic language • Is designed so that students can work independently with low teacher involvement Ideas for using this element: • Provide opportunities for students who have mastered the content to complete the Connection Station.

• A general description of the Connection Station • The science standard aligned with the activity • Materials and preparation needed to complete the activity • General procedure and facilitation points • Printable Student Handout and Answer Key

• Allow students to complete the activities in pairs or groups. • While students are working on the activity, pull students for small-group intervention, for reteaching, or for supporting their work on independent projects.

SCOPE 1

Represent Numbers to 1,000 Scope Introduction SCOPE SUMMARY

2.NR.1.2 Count forward and backward by ones from any number within 1000. Count forward by ﬁves from multiples of 5 within 1000. Count forward and backward by 10s and 100s from any number within 1000. Count forward by 25s from 0. 2.NR.1.3 Represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality. Use >, =, and < symbols to record the results of comparisons. 2.NR.3.1 Determine whether a group (up to 20) has an odd or even number of objects. Write an equation to express an even number as a sum of two equal addends.

VERTICAL ALIGNMENT Background Knowledge First-grade students develop and discuss eﬃcient strategies for counting by bundling 10 ones to form a set of ten. They use mental math strategies to ﬁnd 10 more or 10 less than a number, and they use concrete and pictorial models to develop strategies to add within 100.

Future Expectations In third grade, students will use place value reasoning to represent, read, write, and compare numerical values up to 10,000 and round whole numbers up to 1,000. They will use place value reasoning to add, subtract, and multiply whole numbers.

ENGAGE ACTIVITIES Before beginning the lesson, students’ prior knowledge is assessed to address any missing student needs and skills required for content mastery. Students are assessed to determine if they can: •

compose and decompose two-digit numbers using tens and ones.

•

demonstrate each composition or decomposition with objects, drawings, expressions or equations.

•

use centimeter cubes and ten frames to compose and decompose two-digit numbers up to 100.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

2.NR.1.1 Explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

Accessing Prior Knowledge

Student Expectations

Students begin by using concrete models to form bundles of 100s, with or without leftovers. Once bundling units called hundreds is established, students use concrete models and pictorial representations to investigate how three-digit numbers can be decomposed into hundreds, tens, and ones, and then into several different combinations within those place values. Students use a place value mat alongside these models to represent the quantities with corresponding written numerals, and they interpret the place value of each digit’s position within a written numeral. Students read and write numbers to 1,000 by using baseten numerals, number names, and expanded form. Students count within 1,000 and skip count by 5s, 10s, 25s, and 100s. Finally, students apply what they know about the sums of doubles (to 20) to reason about odd and even numbers.

For the Hook, students are presented with a scenario about counting potato chips in a bag. Students will: •

use concrete and pictorial models to compose numbers in two different ways up to 1,000.

•

use concrete and pictorial models to decompose numbers in two different ways up to 1,000.

•

write numbers in expanded form

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 20

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Grouping Hundreds and Tens to Count Collections In this exploration, student groups will help a coffee shop determine the amount of straws in containers to determine the order for the next week. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

count a collection up to 1,000 by grouping objects into 100s and 10s.

•

represent numbers using standard, word, and expanded forms.

Explore 4

Explore 3

In this exploration, student groups are tasked with solving a scenario about a building contest. Students will:

After students complete the activity, they will discuss their learning and complete an Exit Ticket for assessment.

Explore 5

In this exploration, students will solve a scenario involving count seeds bought at a garden center. Students will: •

count a collection up to 1,000 by grouping objects into 100s, 10s, and 1s.

After students have solved the scenario, they discuss their learning with the class and complete an Exit Ticket.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment. Representing Numbers in Different Ways

Grouping Hundreds, Tens, and Ones to Count Collections

REPRESENT NUMBERS TO 1,000

Home

Counting and Place Value Patterns In this exploration, student partners will solve a scenario to help a high school label seats that are missing numbers in the auditorium. Students will: •

skip count by 5s, 10s, and 100s.

•

determine patterns when counting within 1,000.

After completing the activity, students share their learning and complete an Exit Ticket.

Even and Odd In this exploration, students will help solve a scenario involving a zoo in which they must help give animals the same amount of food. Students will: •

determine whether a number is odd or even.

•

write a doubles’ fact to represent an even number.

At the end of the scope, students complete an Exit Ticket and revisit the Hook to solve. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students represent two-digit numbers up to 100 as groups of tens and ones. This activity is intended to assess mastery of the following standard(s): 1.NR.1.2 Explain that the two digits of a 2-digit number represent the amounts of tens and ones.

Materials

Preparation

Printed •

•

1 Ten Frames Mat (per group)

Reusable • • • •

•

Print a Ten Frames Mat for each group, and place it in a sheet protector for use with a dry-erase marker. Place 100 centimeter cubes in a resealable bag for each group.

100 Centimeter cubes (per group) 1 Plastic sheet protector (per group) 1 Resealable bag (per group) 1 Dry-erase marker (per group)

Procedure and Facilitation Points 1. 2. 3. 4.

REPRESENT NUMBERS TO 1,000

Home

Divide the class into groups of 3 or 4. You may also have students do this activity individually. Give each group a Ten Frames Mat, a set of centimeter cubes, and a dry-erase marker. Tell students not to open their bags or touch the mats until you have explained the activity. Read the following scenario to the class: We are going to be building numbers today using centimeter cubes and the Ten Frames Mats. Let’s go over the value of the ten frame. Discuss the following questions: a. How much is one ten frame worth? Ten ones

STEMscopes Tip The Standards list is located along the menu bar. Here, a keyword can be entered to locate each standard. The search will result in a list of standards and direct links to the scopes where those standards appear. The standards are organized by grade level as well. Clicking on a standard within a grade level will also provide direct links to the scopes.

b. How many ones make one ten frame? Ten 5. 6.

Call out random numbers from 1 to 100, and have students discuss and build each number by using the ten frames and centimeter cubes. Numbers you call out may include the following examples: 10, 42, 78, 100, 36, 51, 80. Facilitate a class discussion about how students built each number. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a. How many tens are in this number? How do you know? Answers will vary. There are 4 tens in the number 42. I ﬁlled up 4 ten frames and this equals 40. b. How many ones are in this number? How do you know? Answers will vary. There are 2 ones in the number 42. There are only 2 spaces ﬁlled in the last ten frame.

What does each digit in this number tell us? The digits tell us how many groups of tens and ones are in the number.

What is the value of the digit in the tens place in this number? Answers will vary. The value of the tens place in the number 78 is 70.

What is the value of the digit in the ones place in this number? Answers will vary. The value of the digit in the ones place in the number 78 is 8.

FACILITATION TIP Project or record each number for a visual reference. FACILITATION TIP Invite students to share their composition strategies under a document camera. Have them verbally explain each step of the process as they move the cubes into ten frames.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Hook – Chips in a bag ACTIVITY PREPARATION Students use concrete and pictorial models to compose and decompose numbers in two different ways up to 1,000. Students also write numbers in expanded form.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

•

Reusable • • •

Plan to show the Phenomena Video. Part II

1 Set of base ten blocks: 5 hundreds, 50 tens, and 90 ones (per pair) 1 Resealable bag (per pair) 1 Phenomena Video (per teacher)

•

Plan to divide the class into groups of two to complete this activity. Place a set of base ten blocks in a resealable bag for each pair of students. A set includes the following blocks: ◊ 5 ﬂats (hundreds) ◊ 50 rods (tens) ◊ 90 units (ones) ◊ Print a Student Handout for each student.

PROCEDURE AND FACILITATION STEMscopes Tip STEMcoach in Action, located under the Scopes tab, provides teachers with professional development on these and many other STEM-centered classroom topics. Here you will find a variety of resources on the topics of Creating an Environment for Learning, Building Scientific and Mathematical Understanding, Engaging Students in Scientific and Engineering Practices, Designing the Learning Experience, and Developing Leadership Skills. Within each of these topics are 3–6 subtopics. Each subtopic includes an overview describing teacher, classroom, and student expectations; FAQs and resources; and/or a video library.

Part I: Pre-Explore 1.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Students in Ms. Rogers’s class compared different brands of potato chips. They counted how many chips were in 4 different brands’ bags. Each group of students received one family-sized bag to count the number of chips in the bag. Build the number of chips in each bag with base ten blocks two different ways, and record your models. Then, write the numbers in expanded form. Here are their results: Bag 1 had 318 chips. Bag 2 had 507 chips. Bag 3 had 490 chips. Bag 4 had 258 chips. Discuss the following questions: a. DOK-1 What information do we know? There are 4 bags of potato chips. Bag 1 has 318 chips. Bag 2 has 507 chips. Bag 3 has 490 chips. Bag 4 has 258 chips. b.

5. 6. 24

DOK-1 What information do we need to ﬁnd out? How can we use base ten blocks to build each number two different ways? What is each number in expanded form?

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a. DOK-1 What information do we know? There are 4 bags of potato chips. Bag 1 has 318 chips. Bag 2 has 507 chips. Bag 3 has 490 chips. Bag 4 has 258 chips. b. DOK-1 What information do we need to ﬁnd out? How can we use base ten blocks to build each number two different ways? What is each number in expanded form?

3. 4. 5.

6. 7.

Give each student a Student Handout. Divide the class into groups of two. Give each student student pair a bag of base ten blocks. Instruct students to build each number two different ways using base ten blocks. Once their concrete models are created, ask students to write each number and draw two different pictorial models on their Student Handouts. Then, have students write each number in expanded form. Allow students to share all the different ways they built each number with base ten blocks. Discuss the following questions:

FACILITATION TIP Practice as a class how to say three-digit numbers, such as 507, as “ﬁve hundred seven.”

REPRESENT NUMBERS TO 1,000

Home

FACILITATION TIP Have each partner create their own pictorial model and then share it.

a. DOK-3 What strategies did you use to build the numbers? Answers will vary. I drew a place value chart and then wrote the number under each place. Then, I got out the correct numbers of hundreds, tens, and ones to put on the chart. b. DOK-2 What do you do if there is a zero in the number? Answers will vary. You do not need to include it. 507 = 500 + 7 c.

DOK-2 What is another way to build the number 318? Answers will vary. 2 hundreds, 11 tens, and 8 ones

DOK-2 How do you say the number 507? Five hundred seven (Make sure students do NOT say, “Five hundred and seven.”)

DOK-2 How do you write a number in expanded form? Answers will vary. 318 is written 300 + 10 + 8.

FACILITATION TIP Challenge students to create a variety of ways to build each number.

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 1 – Grouping Hundreds and Tens to Count Collections ACTIVITY PREPARATION Students count a collection up to 1,000 by grouping objects into hundreds and tens.

Standards for Mathematical Practice • •

MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • •

•

1 Student Journal (per student) 1 Exit Ticket (per student)

•

Reusable •

1 Set of straws (per station) • • • • • •

•

• • • • • •

Station 1 – 130 straws Station 2 – 610 straws Station 3 – 390 straws Station 4 – 850 straws Station 5 – 570 straws Station 6 – 240 straws

• •

10 Rubber bands (per station)

Consumable •

Plan to divide the class into 6 groups to complete this activity. Set up the following stations with the speciﬁed number of straws in a tissue box (or other small container) and a set of 10 rubber bands: Station 1 – 130 straws Station 2 – 610 straws Station 3 – 390 straws Station 4 – 850 straws Station 5 – 570 straws Station 6 – 240 straws

Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Place Value Mat Supplemental Aids elements in the Intervention section.

6 Tissue boxes, or other small containers (per class)

PROCEDURE AND FACILITATION 1.

2. 3. FACILITATION TIP

Have students focus on the most eﬃcient way to count the number of straws. Have students share their ideas and try them out.

Read the following scenario to the class: STEMscopes Coffee Shop is taking an inventory of their supplies. You have been assigned to inventory the supply of straws. Your boss needs to know how many straws are in each container to determine how many more straws need to be ordered next week. Can you help ﬁnd the total number of straws in each container from the coffee shop’s supply room? Divide the class into 6 groups, and place one group at each station. Direct students’ attention to the container of straws and rubber bands. Allow students a few moments to discover the manipulatives and experience how they work with their group. Instruct students to count the straws in the container at their stations. Encourage students to think about the most eﬃcient way to count the straws using the rubber bands provided. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 How are you grouping the straws from your container? Answers will vary. I counted groups of 10. Then, I grouped groups of 10 to make 100. b. DOK-2 How are you using the rubber bands? Answers will vary. I am putting a rubber band around ten groups of ten to represent one hundred.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-2 What are you counting by to ﬁnd the total number of straws? Answers will vary. I am counting ones. I am counting by tens. I am counting by hundreds.

d. DOK-3 Is there another way to group the straws to make counting more eﬃcient? Answers will vary. I could count groups of ten and then make ten groups of ten to equal one hundred. Counting by hundreds will make counting more eﬃcient. 6.

Give each student a Student Journal and ask students to record a pictorial model and the number of hundreds and tens for their number of straws. They will record the number of groups of ten in the total number of straws. Have students rotate to each station and repeat steps 4 through 6. When students have completed each station and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Discuss as a class how to represent hundreds and tens in the pictorial model. A variety of shapes can be used.

REPRESENT NUMBERS TO 1,000

Home

Math Chat DOK-3 Explain how you drew a pictorial model of your total straw counts. We drew a large square to represent one hundred. We drew a line to represent ten. • DOK-1 How many straws were at each station? •

• • • • • • • •

•

• • • • •

•

Station 1 – 130 straws Station 2 – 610 straws Station 3 – 390 straws Station 4 – 850 straws Station 5 – 570 straws Station 6 – 240 straws

DOK-2 How many hundreds of straws were at station 3? 3 DOK-3 How did you count your straws to find this number? We counted 39 groups of ten. Then we grouped ten groups of ten to make one hundred. We did that three times until we could not make any more groups of one hundred. DOK-2 How many groups of ten did you make at station 5? 57; students might initially say 7 tens when looking at the Student Journal, but guide them to the understanding that there were 57 groups of ten to begin with, and then they used those to make five hundreds. DOK-2 How many groups of ten are in 610? 61 DOK-2 How many hundreds are in 43 groups of ten? 4 DOK-2 What number is equal to 75 groups of ten? 750 DOK-2 What number is equal to 5 hundreds and 9 tens? 590 DOK-3 What was the most efficient way to count the straws? Counting groups of ten to form groups of one hundred made counting easier and quicker. Once we made as many groups of ten as possible, we could put ten groups together to make one hundred. DOK-2 What did you skip count by to make counting the straws more efficient? Why is this more efficient than counting by ones? We skip counted by tens. This is more efficient than counting by ones because it takes less time to count a large number/amount of objects.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Use the Math Chat Print Files to project questions 6—11 to facilitate the discussion and record student responses.

STEMscopes Tip Each scope includes a Home section accessed along the scope’s menu bar. Here you will see student expectations as well as key concepts and fundamental questions. Each Home tab includes drop-down options to access the Scope Overview, Content Support, Content Unwrapped, Materials List, and Parent Letter pages.

FACILITATION TIP When previewing this Exit Ticket with students, be sure they have a solid method to carefully count and circle. This array of straws may be overwhelming for some struggling students. Consider modifying it appropriately (color or provide adult support while counting and grouping). 27

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 2 – Grouping Hundreds, Tens, and Ones to Count Collections ACTIVITY PREPARATION Students count a collection up to 1,000 by grouping objects into hundreds, tens, and ones.

Standards for Mathematical Practice • •

MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

• •

1 Student Journal (per student) 1 Set of Station Seed Cards (per class) 6 Place Value Charts (per class) 1 Exit Ticket (per student)

•

Reusable • • •

29 Resealable bags (per class) 6 Dry-erase markers (per class) 18 Sheet protectors (per class, optional)

• • • • • •

Consumable • •

Plan to divide the class into 6 groups to complete this activity. Print a set of Station Seed Cards. Be careful not to mix up the pages after printing. Cut apart the cards, and place each station’s set into an envelope for safekeeping. Laminate for future use, if desired. The images all have groups of ten except the last seed packet image for each set. Label each envelope with the correct station number. Prepare 6 stations. Each station needs an envelope with the Station Seed Cards and the following number of resealable bags:

6 Envelopes (per class) 1 Roll of tape (per class) •

•

Station 1 – 4 bags Station 2 – 6 bags Station 3 – 2 bags Station 4 – 7 bags Station 5 – 1 bag Station 6 – 9 bags

Print 6 sets of Place Value Charts, and place each page into a sheet protector or laminate. Tape the hundreds, tens, and ones page together horizontally. Place a complete Place Value Chart and a dry-erase marker at each station. Print a Student Journal and an Exit ticket for each student.

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Direct attention to how some of the seed packs have different amounts of seeds. FACILITATION TIP Skip counting by tens could be used to regroup seed packages as a set of one hundred.

2. 3.

Read the following scenario to the class: The second graders at Cliffside Elementary are going to plant a garden in front of their school. The 6 second-grade teachers went to the local garden center to buy seeds to plant in the garden. When it was time to pay, the cashier gave them large bags to hold groups of 100 seeds. Can you help count how many seeds each teacher bought? Divide the class into 6 groups, and place one group at each station. Direct students’ attention to the envelope containing the Station Seed Cards and the resealable bags. Allow students a few moments to discover the manipulatives and experience how they work with their groups. Instruct students to observe each image and count the seeds. Most images will have 10 seeds, but there will be one image at each station with fewer than 10 seeds. Encourage students to think about the scenario and how the cashier gave the teachers bags to hold groups of 100 seeds. Have students determine the most eﬃcient way to count the seeds using the bags and images of seeds provided. The Place Value Chart can be used to organize their counts and show how they are moving groups of tens from one place to another.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-2 What do you notice about the images of seed packets? They all have ten seeds except one. b.

DOK-2 How are you grouping the seed packets? We are putting 10 seed packets showing 10 seeds into a group because that will equal 100.

DOK-2 How can you use the Place Value Chart to help you group your seeds? Answers will vary. We are putting the seed packet with fewer than ten seeds in the ones place. We are putting all of the packets with ten seeds in the tens place. We are counting ten groups of ten seeds and moving them over to the hundreds place.

DOK-2 How are you moving groups of seeds from one place to the other? Answers will vary. We are counting ten groups of ten seeds and moving them over to the hundreds place.

DOK-2 How are you using the bags? We are putting 10 pictures of 10 sets of ten seeds into each bag to equal 100 seeds in the bag.

FACILITATION TIP Model with the class how to place numbers in the Place Value Chart using pictorial models.

REPRESENT NUMBERS TO 1,000

Home

f. DOK-3 Do all of the packets containing 10 seeds ﬁt into the bag? Why or why not? No, we can only put groups of 100 into the bag. Once we made as many groups of 100 as possible, there were still some groups of 10 left over. g. DOK-2 What are you counting by to ﬁnd the total number of seeds? We are counting groups of ten and hundreds. 6.

Give each student a Student Journal, and ask students to record a pictorial model within the Place Value Chart, and the number of hundreds, tens, and ones for their numbers of seeds. They will write how many groups of ten are in the total number of seeds. In addition, challenge students to draw a pictorial model of the same number decomposed in another way. Students will rotate to each station and repeat steps 4 through 6. When students have completed each station and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Increase engagement by having groups compete with one another for a set amount of time.

Math Chat •

DOK-1 How many seeds were at each station? • • • • • •

•

• • •

Station 1: 467 seeds Station 2: 623 seeds Station 3: 299 seeds Station 4: 706 seeds Station 5: 184 seeds Station 6: 937 seeds

DOK-3 Explain how you decomposed one of the numbers in another way. I decomposed the number into only groups of tens and ones. You could decompose one of the hundreds into groups of ten or one of the tens into ones. DOK-3 Compare several students’ methods for decomposing one of the numbers. Discuss similarities and differences. DOK-2 How many hundreds of seeds were at station 2? 6 DOK-2 How did you count your seeds to ﬁnd this number? We counted 62 groups of ten. Then we grouped ten groups of ten to make one hundred. We did that six times until we could not make any more groups of one hundred.

STEMscopes Tip The Engage section, located along the scope menu, is designed to activate student interest in the learning topic. Within the Engage section, activities to access students’ prior knowledge about the topic, to build a strong foundation to bridge any gaps in understanding before diving into the new content, and to set the purpose for learning a new skill are included.

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 2 – Grouping Hundreds, Tens, and Ones to Count Collections •

•

DOK-2 How many groups of ten did you make at station 4? 70; students might initially say 0 tens when looking at the Student Journal, but guide them to the understanding that there were 70 groups of ten to begin with, and then they used those to make seven hundreds. DOK-3 What was the most eﬃcient way to count the seeds? Counting groups of ten to form groups of one hundred made counting easier and quicker.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

REPRESENT NUMBERS TO 1,000

Home

_________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 3 – Representing Numbers in Different Ways ACTIVITY PREPARATION Students represent numbers using standard form, word form, and expanded form.

Standards for Mathematical Practice • •

MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Place Value Chart (per group) 1 Exit Ticket (per student)

•

Reusable •

1 Set of base ten blocks (per group) • • • • • •

• • •

Group 1 – 6 flats, 12 rods, and 9 units = 729 Group 2 – 8 flats, 15 rods, and 8 units = 958 Group 3 – 4 flats, 26 rods, and 5 units = 665 Group 4 – 3 flats, 10 rods, and 23 units = 423 Group 5 – 7 flats, 13 rods, and 32 units = 862 6 extra flats and 5 extra rods for regrouping

3 Sheet protectors (per group, optional) 1 Large resealable bag (per group) 1 Dry-erase marker (per group)

•

• • • • • • • •

Consumable

•

1 Roll of tape (per teacher)

Plan to divide the class into 5 groups to complete this activity. Print the Place Value Chart for each group. The pages will need to be taped together and laminated for durability, or each sheet can be placed into its own sheet protector and taped together. Gather the following numbers of base ten blocks, and place each set into a large resealable bag. Place one bag of blocks, one complete Place Value Chart, and a dry-erase marker at each group’s table. 6 flats, 12 rods, and 9 units = 729 8 flats, 15 rods, and 8 units = 958 4 flats, 26 rods, and 5 units = 665 3 flats, 10 rods, and 23 units = 423 7 flats, 13 rods, and 32 units = 862

Gather 6 extra ﬂats and 5 extra rods, and place them in a central location for students to borrow when regrouping. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Base Tens Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Give students a few minutes to build a structure using the ﬂats, base ten blocks, and units. 32

Read the following scenario to the class: You have been chosen to enter a building contest. Given a set of blocks, you have to build a structure that will stand on its own and use all of the blocks. Are you up for the challenge? Divide the class into 5 groups and assign each group a number 1–5. These numbers will help students record their work in the appropriate sections on their Student Journals. Direct students’ attention to the base ten blocks and Place Value Chart at their group’s table. Allow students a few moments to discover the manipulatives and experience how they work with their group. Instruct students to work cooperatively to build a structure that will stand on its own and use all of the blocks. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Monitor and talk with students as needed to check for understanding by using guiding questions. a.

DOK-1 What is the value of one base ten ﬂat? 100

DOK-1 What is the value of one base ten rod? 10

DOK-1 What is the value of one base ten unit? 1

DOK-2 How many ﬂats are used to build your structure? Answers will vary. 6, 8, 4, 3, or 7

e. DOK-2 How many rods are used to build your structure? Answers will vary. 12, 15, 26, 10, or 13 f. 6. 7. 8.

DOK-2 How many units are used to build your structure? Answers will vary. 9, 8, 5, 23, or 32

Once structures have been assembled, take a quick gallery walk as a class so students can observe the other groups’ standing structures. Have students return to their stations and disassemble their structures. Ask students to use the Place Value Chart to help determine the total number of blocks they used for their structures. Ask the following guiding questions as students are organizing their blocks: a. DOK-3 What do you notice about your amount of blocks? Answers will vary. Our tens group has more than ten groups of ten. b. DOK-2 If one place value has more than ten blocks, what do you need to do to that amount? Answers will vary. We need to regroup groups of ten.

10.

11.

12. 13.

REPRESENT NUMBERS TO 1,000

Home

FACILITATION TIP Have students observe how the structures are different from and similar to one another. Note similarities and differences on chart paper. STEMscopes Tip The Intervention section of each scope is found along the scope menu. If the assessments revealed that some students have not reached mastery of the content, the Intervention section has Small-Group Intervention and Supplemental Aid resources to help those students who need reteaching and additional support.

Encourage students to borrow what they need from the extra blocks available to regroup their blocks. Once all of the blocks have been regrouped, students should ﬁnd the total hundreds, tens, and ones and write this number at the bottom of their Place Value Charts. Give each student a Student Journal, and ask students to write their numbers in four ways: standard form, pictorial model (of their original blocks or the regrouped version), expanded form, and word form in their group number’s section of the handout. Allow the groups to share their total numbers. As they share their numbers, FACILITATION TIP pause and allow the rest of the students to complete their Student Journals in Each group can present its standard form, the appropriate group number’s section with their groups. pictorial model, expanded form, and word When students have completed their Student Journals, bring the class together form to the class. as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • • • • • • •

DOK-2 What numbers were built in this activity? 729, 958, 665, 423, and 862. DOK-1 What is standard form? A number written with a single digit in each place value. DOK-1 What is expanded form? The sum of the value of each place value DOK-1 What is word form? A number written in words DOK-2 What is the expanded form for this number? Ask the groups to share the expanded forms of their numbers. Answers will vary. DOK-3 Explain how you regrouped some of your blocks. We had 26 groups of ten, so we had to regroup 20 groups of ten to make two more hundreds. DOK-2 What do you notice when writing the expanded form for the numbers 100, 200, 300, 400, 500, 600, 700, 800, or 900? The value of the hundreds place is written as 100, 200, 300, 400, 500, 600, 700, 800, or 900. The value of the tens and ones place is zero.

FACILITATION TIP Post or project the large print ﬁle versions of questions 2–4. Add students’ responses and examples and post them on your word wall. Fluency with math phrases will be essential for students in later grades.

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 3 – Representing Numbers in Different Ways Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

REPRESENT NUMBERS TO 1,000

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REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 4 – Counting and Place Value Patterns ACTIVITY PREPARATION Students skip count by ﬁves, tens, twenty-ﬁves, and hundreds to determine patterns when counting within 1,000.

Standards for Mathematical Practice •

MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Hundreds Charts (per pair) 1 Exit Ticket (per student)

• •

Reusable • •

1 Colored dry-erase marker (per pair) 3 Plastic sheet protectors (per pair, optional)

Plan to divide the class into groups of two to complete this activity. Print one set of Hundreds Charts for each pair of students. Laminate or place each sheet into a plastic sheet protector to be used with a dryerase marker. Print a Student Journal and an Exit Ticket for each student. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Hundreds Chart)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP

Practice as a whole class skip counting by 5s. Begin with different variables of 5 then challenge students by beginning with different numbers. For example start with 5, 15, 35, 6 or 21

FACILITATION TIP Project the Hundreds Chart on the board and model how to skip count and color the chart. STEMscopes Tip Located along the scope menu is the Explore section. One to ﬁve inquirybased Explore activities are designed to be hands-on, teacher-facilitated lessons in which students collaborate to build conceptual understanding and reason mathematically. This section also contains Skill Basics lessons in Kindergarten through Grade 2 and Virtual Manipulatives. 36

Read the following scenario to the class: The high school needs help labeling the seats in the auditorium because some of the numbers have worn away. The seats are arranged using certain patterns, so you will need to use your place value skills to determine the missing numbers. Can you help label the seats that are missing numbers? Divide the class into groups of two. Distribute a set of Hundreds Charts and a colored dry-erase marker to each pair of students. Give a Student Journal to each student. Instruct students to think about what patterns are and how they can be related to numbers. Students start with the first box on their Student Journals. They start at the given number and skip count by fives. They should color in the given number using the dry-erase marker on the Hundreds Chart. Then, they skip count by fives and color in every 5th number on the chart. As they do this, they record the numbers they colored in on the seat images with missing numbers on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What is the starting number in this set of seats? Answers will vary. Box 1 – 65, Box 2 – 103, Box 3 – 119, Box 4 – 50, Box 5 – 32, Box 6 – 25

DOK-1 What are you skip counting by? Answers will vary. I am skip counting by ﬁves, tens, twenty-ﬁves, or hundreds.

DOK-2 What number comes after the starting number when skip counting by ___? Answers will vary. 70 comes after 65 when skip counting by ﬁves.

Engage

Explore

Explain

Elaborate

Evaluate

e. DOK-3 What patterns are you noticing as you skip count on the Hundreds Chart? Answers will vary. When I start at 65 and skip count by ﬁves, I see that the next numbers have either a 0 or 5 in the ones place and the tens place increases by 1 every two numbers. 5. 6.

Encourage students to answer the questions for each set of seats on their Student Journals. Students repeat steps 3–5 for the remaining sets of seats and answer the reﬂection question on the last page of their Student Journals. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

DOK-2 What are the missing seat numbers in the set that started with this given number? • • • • • •

• •

• • •

• •

•

Box 1: 70, 75, 80, 85, 90 Box 2: 203, 303, 403, 503, 603 Box 3: 129, 139, 149, 159, 169 Box 4: 55, 60, 65, 70, 75 Box 5: 132, 232, 332, 432, 532 Box 6: 50, 75, 100, 125, 150

DOK-1 What did you skip count by to determine these missing numbers? I skip counted by fives/tens/twenty-fives/hundreds. DOK-3 What patterns did you notice when starting at the number ___ and skip counting by ___? I noticed when we skip counted by fives starting at the number 65, the missing numbers had either a 0 or 5 in the ones place and the tens place increased by 1 every two numbers. DOK-2 What place value(s) changed when skip counting by fives? The ones place changed. The tens place increased by 1 every two numbers. DOK-2 What place value(s) changed when skip counting by tens? The tens place increased by 1. DOK-2 What place value(s) changed when skip counting by twenty-fives? The ones place changed back and forth from 5 to 0. The tens and hundreds place changed. DOK-2 What place value(s) changed when skip counting by hundreds? The hundreds place increased by 1. DOK-3 How did figuring out the place value pattern in each set help you figure out the missing digit in the second question for each box? I looked at the pattern and could see which place values changed and which ones stayed the same. DOK-3 How can you use place value patterns to help you count backward? I can see what the pattern is when counting forward and use that to count backward. If I see which place values change and which place values stay the same, I can count backward using the same rules. DOK-2 What do you notice about each place value when skip counting 100, 200, 300, 400, 500, 600, 700, 800, 900? The digits in the number represent one, two, three, four, five, six, seven, eight, nine hundreds with zero tens and zero ones.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Intervention

Acceleration

FACILITATION TIP Informally assess each students ability to ﬁnd patterns while monitoring groups. Finding patterns is a critical thinking skill used in all content areas.

FACILITATION TIP

REPRESENT NUMBERS TO 1,000

Home

In the Math Chat, challenge students to explain the patterns in several other examples. FACILITATION TIP During the Math Chat, provide opportunities for the class to chorally skip count by each grouping. Counting can occur in groups of two, small groups, and as a whole class Use this as a chance to spot check and quickly assess students.

STEMscopes Tip Each scope includes a Home section along the scope’s menu bar. Home is where student expectations for each scope are located. In addition, it lists key concepts that students will understand after they have completed the scope and provides fundamental questions to help guide instruction and assess students’ understanding. Each Home tab includes drop-down options to access the Scope Overview, Content Support, Content Unwrapped, Materials List, and Parent Letter pages. These pages can also be accessed by clicking on the links to the right of the screen, under Essentials.

FACILITATION TIP When previewing this Exit Ticket, consider having students underline the words ﬁves, tens and hundreds in the directions to clarify for students who may be struggling with reading. 37

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 5 – Even and Odd ACTIVITY PREPARATION Students determine whether a number is odd or even and write a doubles fact to represent an even number.

Standards for Mathematical Practice •

MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Station Story Mats (per class) 1 Exit Ticket (per student)

Reusable • • • • • •

Plan to divide the class into 6 groups to complete this activity. Print a set of Station Story Mats. Prepare six stations with a story mat and linking cubes. Each Station Story Mat will need the corresponding number and color of linking cubes listed below: • • • • • •

13 Yellow linking cubes (per class) 20 Blue linking cubes (per class) 19 Red linking cubes (per class) 17 Green linking cubes (per class) 18 Brown linking cubes (per class) 12 Orange linking cubes (per class)

• •

Station 1 – 13 yellow linking cubes Station 2 – 20 blue linking cubes Station 3 – 19 red linking cubes Station 4 – 17 green linking cubes Station 5 – 18 brown linking cubes Station 6 – 12 orange linking cubes

Print a Student Journal and an Exit Ticket for each student. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Linking Cubes)

PROCEDURE AND FACILITATION 1.

2. 3. FACILITATION TIP Engage students with the concept of sharing equally with a snack. You can have students discuss how they could share a certain number of snacks equally among all students

Read the following scenario to the class: You are a zookeeper, and it is time to feed the animals. Each animal will get the same amount of food. You do not want to overfeed or underfeed any of the animals. When you prepare the food for each animal, you have to make sure to have an even amount. Are you ready to feed the animals? Divide the class into 6 groups, and place one group at each station. Direct students’ attention to the linking cubes and Station Story Mat. Allow students a few moments to discover the manipulatives and experience how they work with their group. Instruct students to begin by counting the total number of pieces of food (linking cubes). Have students share the pieces of food equally by lining up the linking cubes in pairs on the story mat. Tell students that if there is a piece of food left over, they will place it in the bottom square. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 How many total pieces of food are there? Answers will vary. 13, 20, 19, 17, 18, 12 b.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 How many leftover pieces of food are there? Answers will vary. For even numbers, there will be 0 left over. For odd numbers, there will be 1 left over.

DOK-2 Is the total number odd or even? Answers will vary.

e. DOK-3 How do you know? Even numbers make equal pairs. They can be partnered up. Odd numbers will always have 1 left over after making equal pairs. f.

DOK-2 What number sentence could you write to show the pieces of food each animal will eat? Answers will vary. 6 + 6 + 1 = 13; 10 + 10 = 20; 9 + 9 + 1 = 19; 8 + 8 + 1 = 17; 9 + 9 = 18; 6 + 6 = 12

Give each student a Student Journal, and ask students to complete the table and questions for each station. They will write a number sentence to show the pieces of food eaten by each animal and a possible leftover piece of food to equal the total pieces of food. Have students rotate to each station and repeat steps 4 through 6. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

DOK-2 How many pieces of food were at each station? Are these numbers odd or even? • • • • • •

• •

• • •

• • • •

Station 1: 13, odd Station 2: 20, even Station 3: 19, odd Station 4: 17, odd Station 5: 18, even Station 6: 12, even

DOK-3 What did you notice about the odd numbers when sharing the pieces of food between the animals? There was always 1 piece of food left over. DOK-3 What did you notice about the number sentences you wrote for the odd numbers? There is always a plus one. If we add one to one of the numbers, we will not be adding doubles. DOK-3 What did you notice about the even numbers when sharing the pieces of food between the animals? There were 0 pieces of food left over. DOK-3 What did you notice about the number sentences for the even numbers? We added doubles to equal the even number. DOK-3 What rule can be applied to even numbers? They skip count by twos. Even numbers have partners. There is a set of doubles that can be added together to equal the even number. DOK-2 What place value in a number determines if the number is odd or even? The ones place. DOK-1 What digits are even? 0, 2, 4, 6, or 8. DOK-1 What digits are odd? 1, 3, 5, 7, 9. DOK-3 Give students different numbers between 0 and 20, and ask them to decide if they are odd or even and explain how they know. Answers will vary.

Intervention

Acceleration

FACILITATION TIP As you monitor groups, intervene as needed with other manipulatives that model the number being even and odd. FACILITATION TIP

REPRESENT NUMBERS TO 1,000

Home

A number sentence is being used to compose the numbers. Have students label the number as odd or even.

STEMscopes Tip Located along the scope menu, the Engage section is designed to assess students’ current understanding about a mathematical concept and spark their interest in the learning topic. Three activities work together to prepare students for their study. Accessing Prior Knowledge is a brief probing activity used to gauge students’ prior knowledge about a topic. The Foundation Builder is an early-intervention activity built to ﬁll gaps in understanding. The Hook is an engaging real-world activity meant to motivate students and set a purpose for learning a new skill. These activities help the teacher determine how the scope will be introduced and which parts of the scope will be most useful for students. STEMscopes Tip The Explain section, located along the scope menu, has a variety of elements designed to solidify students’ understanding of the content presented in the Explore section. Each scope’s Explain section includes a Picture Vocabulary, independent practice assignments, anchor charts, journal prompts, and interactive notebook activities.

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Explore 5 – Even and Odd •

DOK-4 When might we use even and odd numbers in real life? We would use even numbers to form equal groups to play a game when we need the same number of people on a team.

Post-Explore 1. FACILITATION TIP Be prepared with some additional realworld relevant examples for your students. Older students will use the concepts of even and odd frequently when factoring and multiplying during their math careers.

2. 3. 4.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Return to the Hook and instruct students to use their newly acquired skills to successfully complete the activity.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

REPRESENT NUMBERS TO 1,000

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REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000 Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Grouping Hundreds and Tens to Count Collections Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Grouping Hundreds, Tens, and Ones to Count Collections Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Representing Numbers in Different Ways

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Counting and Place Value Patterns

Independent practice assignment that gives students an opportunity to demonstrate their learning

Show What You Know, Part 5 Even and Odd Independent practice assignment that gives students an opportunity to demonstrate their learning

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Zoo Field Trip A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Riverwalk Pet Shop

Even or Odd

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Base-Ten Buildings

Represent Numbers to 1000 in Different Ways

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

REPRESENT NUMBERS TO 1,000

Home

Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.) Resources

Students who are still acquiring the concept and need remediation

REPRESENT NUMBERS TO 1,000

Represent Numbers to 1,000

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Key Concepts I can explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

What prompts will be used?

What does mastery look like?

REPRESENT NUMBERS TO 1,000

Home

I can count forward and backward by ones from any number within 1,000.

I can count forward by ﬁves from multiples of 5 within 1,000.

I can count forward and backward by 10s and 100s from any number with 1,000.

I can count forward by 25s from 0.

I can represent whole numbers to 1,000 with an emphasis on place value and equality.

I can determine whether a group (up to 20) has an odd or even number of objects.

I can write any equation to express an even number as a sum of two equal addends.

SCOPE 1

Compare and Order Numbers Scope Introduction SCOPE SUMMARY Students represent, compare, and order whole numbers up to 1,000 with an emphasis on place value and equality. Students use comparative language, numbers, and comparison symbols <, >, and =. In addition, students ﬁnd 10 more or 10 less than a given three-digit number and ﬁnd 100 more or 100 less than a given three-digit number by using tools such as a hundreds chart and number line. Student Expectations

2.NR.1.3 Represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality. Use >, =, and < symbols to record the results of comparisons. 2.NR.2.2 Find 10 more or 10 less than a given three-digit number and ﬁnd 100 more or 100 less than a given three-digit number.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In kindergarten, students compare sets of objects up to at least 10 in each set by using comparative language. They can also identify a number that is one more or one less than a given number 1–20. In ﬁrst grade, students learn to compare and order numbers up to 100 with place value and models such as number lines by using comparative language like greater than, less than, and equal to. In addition to using comparative language, students learn to use the comparative symbols >, <, and = to represent their comparisons. First graders can also ﬁnd 10 more or 10 less than a given two-digit number and explain their reasoning.

Third-grade students will compare whole numbers up to 10,000, and they will represent comparisons by using the symbols >, <, or =. They will also compare unit fractions.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

compare two randomly selected numbers using the symbols >, <, or =.

At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope. If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK.

compare and order whole numbers up to 1,000 by using comparative language, numbers, and symbols (>, <, or =).

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Identifying Numbers Greater Than or Less Than In this exploration, students will ﬁnd 10 more or 10 less and 100 more or 100 less than a given three-digit number. Students will:

Explore 2

Explore 1

EXPLORE ACTIVITIES Comparing and Ordering Numbers In this exploration, students will use number lines and place value to compare and order whole numbers up to 1,000. Students will:

•

build numbers for the discounted price and competitor’s price.

•

build numbers using their blocks that represent scores.

•

write the totals in each place value.

•

compare the two scores.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

COMPARE AND ORDER NUMBERS

Home

After completing the activity, students share their learning, complete an Exit Ticket, and then revisit the Hook to solve.

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students use comparing mats to compare two randomly selected numbers using the symbols >, <, or =. This activity is intended to assess mastery of the following standard(s): 1.NR.1.3 Compare and order whole numbers up to 100 using concrete models, drawings, and the symbols >, =, and <.

Materials

Preparation

Printed • •

•

1 Comparing Mat (per student) 1 Number Fish (per group)

•

Reusable • •

Print a Comparing Mat for each student. Laminate it, or place it in a sheet protector for use with a dry-erase marker. Print and cut one set of Number Fish, and place them in a container for each group.

COMPARE AND ORDER NUMBERS

Home

1 Dry-erase marker (per student) 1 Small opaque container (per group)

Procedure and Facilitation Points 1. 2.

Give each group of students a container filled with one set of Number Fish. Tell students not to touch the container until you have given instructions. Tell students that they will be going fishing for numbers today. Each time they reach into the bin, they will catch two fish. They will place their fish on the hooks located on opposite sides of the comparing circle. They will look at the numbers and compare them by using >, <, or = by writing the symbol in the comparing circle. Students will clear the Comparing Mat prior to catching new fish. Encourage students to read the sentence aloud—for example, “Sixty-four is less than 100.” Encourage students to explain to their table groups why that is the case. Facilitate a class discussion about their comparisons. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a.

What does each comparison symbol mean? > means “greater than,” < means “less than,” and = means “equal to/same as.”

How do you know this number is less than/greater than this number? Answers will vary. I know 100 is greater than 7 because it has a hundred.

c. 5.

Can you write a different comparison statement using the same numbers? Answers will vary. 100 > 7 or 7 < 100

FACILITATION TIP Depending on your students, consider drawing the Number Fish together as a class. You could do it yourself or have volunteers come up front and “fish.” Conducting this activity as a whole group may provide more opportunities to gather prior student knowledge. FACILITATION TIP Provide opportunities for students to read these sentences aloud chorally as a whole class, with a partner, and individually . Students often just want to say the greater number aloud; speaking the complete phrases will support fluency with comparison statements. FACILITATION TIP Use physical responses (arms, hands) to reinforce the meanings of these symbols. Students often identify that the “alligator” that wants to “eat” the bigger fish.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope. Notes

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Hook – Laser Tag Scores ACTIVITY PREPARATION Students compare and order whole numbers up to 1,000 by using comparative language, numbers, and symbols (>, <, or =).

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Plan to show the video. For Part II, print the Student Handout for each student.

Reusable •

1 Phenomena Video (per teacher)

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

4. FACILITATION TIP

Have students use dry-erase boards to record the information from the scenario.

DOK-1 What information do we know? I earned 617 points. My friend’s score uses the same digits but is a larger number.

DOK-1 What information do we need to ﬁnd out? What are the possible numbers that could have been your friend’s score?

STEMscopes Tip Located along the scope menu is the Elaborate section, where engaging activities that extend student learning and solidify their understanding of math concepts are found. Included are hands-on and virtual games; a math review and math story; a problembased task; proﬁles of careers and everyday life situations where math is used, and in the primary grades, a discussion of a data set. FACILITATION TIP Have students rearrange the number 617 on their dry-erase boards. 50

5. 6.

Give students time to discuss what they know about comparing numbers to determine which is larger. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What information do we know? I earned 617 points. My friend’s score uses the same digits but is a larger number.

DOK-1 What information do we need to ﬁnd out? What are the possible numbers that could have been my friend’s score?

Give each student the Student Handout. Have students determine three possible scores that are larger than 617 but have the same digits (6, 1, and 7) as the given score in the scenario. Finally, they will write a comparison statement using symbols to compare the given score and one of the possible other scores. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions: a.

DOK-2 When you have a three-digit number such as the number that was given in the scenario and you want to create a larger number, which place value do you look at ﬁrst? You look at the hundreds place.

DOK-2 Can you create a larger number than 617 while keeping a 6 in the hundreds place? If so, how? Yes, we can switch the 7 to the tens place and the 1 to the ones place. 671 is larger than/greater than/more than 617.

DOK-2 Are there other possible ways to create a number greater than 617 while keeping the 6 in the hundreds place? No.

DOK-3 How did you rearrange the digits to ﬁnd the last two possible scores that would be greater than 617? We moved the 7 to the hundreds place. Then, we put the 6 in the tens place and the 1 in the ones place. Finally, we kept the 7 in the hundreds place and moved the 1 to the tens place and the 6 to the ones place.

FACILITATION TIP Have students label the hundreds place, tens place, and ones place using sticky notes.

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e. DOK-2 What are all the possible scores your friend could have earned that would be greater than yours but still have the same digits? 671, 761, or 716 f.

DOK-3 Why couldn’t you move the 1 to the hundreds place? Because that would give us a score that is less than mine

DOK-2 Name the different statements using symbols that could be used to compare your score and your friend’s possible score. 617 < 671, 617 < 761, 617 < 716, 671 > 617, 761 > 617, 716 > 617

h. DOK-1 How do you read the symbol >? Greater than i. DOK-1 How do you read the symbol < ? Less than

FACILITATION TIP Project the symbols with examples for students to refer to. Have students circle the correct number sentences that address the scenario.

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Explore 1 – Identifying Numbers Greater Than or Less Than ACTIVITY PREPARATION Students ﬁnd 10 more or 10 less and 100 more or 100 less than a given three-digit number.

Standards for Mathematical Practice • • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

• •

1 Student Journal (per student) 1 Set of Store Ads (per class) 1 Place Value Chart (per station) 1 Exit Ticket (per student)

• •

Reusable • • • •

• •

1 Set of base ten blocks: 9 ones, 9 tens, and 9 hundreds (per station) 1 Resealable bag (per station) 3 Sheet protectors (per station) 1 Dry-erase marker (per station)

•

Plan to have students work in 6 groups to complete this activity. Prepare a resealable bag of base ten blocks for each station (9 ones, 9 tens, and 9 hundreds). Print the Store Ads and place one at each station. Print the Place Value Chart for each station. Place each sheet in its own sheet protector, and tape sheets together in order of value. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Open Number Line Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students (Base Ten Blocks).

PROCEDURE AND FACILITATION FACILITATION TIP

Review as necessary with the Foundation Builder in the Engage section.

2. 3.

FACILITATION TIP Have students circle the original price, the discounted price, and the competitor’s price with different colors of dry-erase markers.

4. 5.

FACILITATION TIP Students may need to use number lines for assistance. These are located in the Intervention section. 52

Read the following scenario to the class: The local electronics store is creating a new ad for the week. It wants the original price of the item displayed, but it also wants to show customers the discounted price and the price a local competitor is offering for the same item. The store needs our help ﬁnding those two prices so they can be added to the store ad. Can we help the electronics store identify those prices? Divide the class into 6 groups, and place one group at each station. Direct students’ attention to the base ten blocks and Store Ads. Allow students a few moments to discover the blocks and experience how they work with their groups. Give each student a Student Journal. They will be recording as they build numbers at their stations. Challenge students to build the numbers for both the discounted price and competitor’s price and write the totals in each place value. Include the totals from the Place Value Chart and also the pictorial models on their Student Journals. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-3 What patterns are you noticing? Answers will vary. When we add one ten/hundred, the tens/hundreds place increases by one digit.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 Is this number less than or greater than the original price? Less than

DOK-3 How do you know? The digit in the tens/hundreds place is less than the digit in the tens/hundreds place in the original price.

e. DOK-3 How did you determine the competitor’s price? We added the amount to the original price.

7. 8.

DOK-2 Is this number less than or greater than the original price? Greater than

DOK-3 How do you know? The digit in the tens/hundreds place is greater than the digit in the tens/hundreds place in the original price.

Intervention

Acceleration

FACILITATION TIP Monitor student groups and model for students how to calculate the discounted price and competitor’s price as needed.

Have students rotate to each station and repeat steps 5 and 6. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

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Math Chat •

•

• • •

DOK-3 When you add a ten/hundred or take away a ten/hundred, what digit changes? Why? The tens/hundreds place will change because you are adding or taking away one ten/hundred. The digit will increase or decrease by one. DOK-3 How do you know if a number is greater than or less than another number? You start at the place value farthest to the left. If the numbers both have digits in the same place value, the largest digit will be the greater number. If one number has a digit in a place value that is greater than the other number, then it is the larger number. DOK-2 What happens if you add ten to a number with a 9 in the tens place? The 9 has to be regrouped because you can’t have 10 in the tens place. So the digit in the tens place will become a 0, and 1 will be added to the digit in the hundreds place. DOK-3 Discuss the strategies used to regroup the numbers in Store Ads 3, 4, and 5. I used my base ten blocks to add/subtract the amount asked. DOK-2 Practice several examples of adding an amount to a number that would cause a place value to have to be regrouped. 295 + 10 = 305. Answers will vary. DOK-2 Given the digits 3, 0, and 9, what is the largest number you can make? What is the smallest number you can make? 930; 39

FACILITATION TIP This concept is a key standard. Slow down to ensure that students can clearly state how to determine if a number is greater or less than. Students will be ordering and comparing decimals, fractions, and integers later.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP When you preview this Exit Ticket, encourage careful reading. Students can underline the words “less” and “more” before they complete the assessment.

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Explore 2 – Comparing and Ordering Numbers ACTIVITY PREPARATION Students use number lines and place value to compare and order whole numbers up to 1,000.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Spelling Bee Scorecards (per pair) 1 Exit Ticket (per student)

•

Reusable • •

Plan to have students work in groups of two to complete this activity. Print one set of Spelling Bee Scorecards for each pair of students. If printing this many copies is an issue, the scorecards can be projected onto the board one at a time for students to view while working with their partner. Prepare a resealable bag of base ten blocks for each pair. Each set should include the following: • • •

1 Set of base ten blocks (per pair) 1 Resealable bag (per pair) • • •

18 ﬂats (hundreds) 15 rods (tens) 15 units (ones)

Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Open Number Line Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION FACILITATION TIP

Students should complete the Skill Builder before completing Explore 2. 2. 3.

5. FACILITATION TIP Practice reading numbers as a class. Provide various examples that students can build with the base ten blocks. 54

Read the following scenario to the class: The school’s spelling bee is complete, and the scores are in! The principal needs our help deciding the winner of each round and determining the overall winner of the contest. Can we help the principal ﬁnd the winner of the spelling bee? Divide the class into groups of two. Give each student pair a bag of base ten blocks and a set of Spelling Bee Scorecards. Direct students’ attention to the Spelling Bee Scorecards and base ten blocks. Give students a few moments to discover the manipulatives and experience how they could build the scores with their partner. Instruct students to look at each scorecard from each round of the spelling bee. Challenge students to build each number using their blocks and then compare the two scores. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 How many words did each student in this round spell correctly? Answers will vary. Students should say the numbers listed on the scorecard.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 Show me how you built this number. What base ten blocks did you use? Answers will vary. The number 976 could be built using 9 ﬂats, 7 rods, and 6 units.

DOK-2 How could a number line help you compare the numbers? Answers will vary. I could plot the numbers and see that the number closer to 0 is less than the other number.

DOK-2 If you had a number line with the ends marked with 0 and 1,000, where would you plot these numbers on a number line? Answers will vary. I will put the number 278 closer to 0 and 976 closer to 1,000.

e. DOK-2 Which student spelled more words correctly? Answers will vary. Round 1 – Tony, round 2 – Gia, round 3 – Imari, round 4 – Max, round 5 – Adhira f.

DOK-3 How do you know? We compared the place value of each digit. We started with the largest place value of each number. We started with the place value farthest to the left.

DOK-2 What number is the least? Answers will vary. Round 1 – 559, round 2 – 278, round 3 – 895, round 4 – 726, round 5 – 297

h. DOK-1 What symbol are you using to show greater than? > i. DOK-1 What symbol are you using to show less than? < 6.

Give each student a Student Journal, and ask students to use each Spelling Bee Scorecard to complete Part I. Explain to students that benchmarks are provided on the number lines and will assist them in plotting the numbers. When they are ﬁnished, they will use their comparisons from Part I to list and order each score from greatest to least and then plot the scores on the number line in Part II on their Student Journals. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • • • • • • • • • •

•

DOK-2 Who won each round of the spelling bee? Round 1 – Tony, round 2 – Gia, round 3 – Imari, round 4 – Max, round 5 – Adhira. DOK-2 Who spelled the most words correctly overall and won the spelling bee? Imari DOK-2 Who spelled the fewest words correctly? Shreya DOK-2 Who spelled more words correctly than Ellyn but fewer than Max? Rodney DOK-2 Which students spelled more than 600 words correctly? Gia, Max, Rodney, Imari, Ellyn, and Tony DOK-2 Which students spelled between 500 and 600 words correctly? AJ and Adhira DOK-1 What does the < symbol mean? (Draw it on the board for students.) Less than DOK-1 What does the = symbol mean? (Draw it on the board for students.) Equals or is equal to DOK-1 What does the > symbol mean? (Draw it on the board for students.) Greater than DOK-3 How did plotting the numbers on the number line help you compare the numbers? I knew the number I plotted farther to the left was smaller than the number farther to the right. DOK-3 When comparing the two scores on each scorecard, what was the same/ different? The numbers were the same for both comparisons, but our symbols and comparison statements were different because the numbers were ﬂipped.

Intervention

Acceleration

FACILITATION TIP Students should use their Student Journals to answer the question. Write all of the numbers and have students sequence them on a number line.

COMPARE AND ORDER NUMBERS

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FACILITATION TIP Have students use their arms to show which way the alligator’s mouth is open. FACILITATION TIP Use the alligator trick to help students determine which symbol to use. The symbol is the alligator with the mouth open toward the direction of the larger number. FACILITATION TIP Use the first page of Math Chat questions in the Print File to model looking for the math language in the scenarios. Go through the first five questions and have students find the comparison words as you underline them (won, most, fewest, more, between). FACILITATION TIP Encourage students to use the word phrase in between the numbers when they respond aloud to these questions. For example have them say, “15 is less than 20,” rather than just saying one of the numbers or the phrase.

STEMscopes Tip The Evaluate section, found along the scope menu, contains assessment tools designed to help teachers gather the data they need to determine whether intervention or acceleration is warranted. From standards-based assessments to an open-ended reasoning prompt, there is an evaluation for every student’s learning style.

COMPARE AND ORDER NUMBERS

Compare and Order Numbers Explore 2 – Comparing and Ordering Numbers Post-Explore 1. FACILITATION TIP When you preview this Exit Ticket with students, take time to help them underline the phrases “least to greatest” and “greatest to least.” Be sure to clarify how they are to place the numbers on the number line vs. the blank spaces below.

2. 3. 4.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

COMPARE AND ORDER NUMBERS

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COMPARE AND ORDER NUMBERS

Compare and Order Numbers Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Identifying Numbers Greater Than or Less Than Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Comparing and Ordering Numbers Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Can be done independently

Spiraled Review

Life Connections

Family Game Night

Guitar-Maker Craftsman

A quick story to engage student interest along with four problems covering previously learned skills

A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

Math Story

Fluency Builder

Building Contest

Match Greater Than or Less Than

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Zoo Food Facts

More or Less

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

COMPARE AND ORDER NUMBERS

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Students who are still acquiring the concept and need remediation

COMPARE AND ORDER NUMBERS

Compare and Order Numbers

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Key Concepts I can represent, compare, and order whole numbers up to 1,000.

What prompts will be used?

What does mastery look like?

COMPARE AND ORDER NUMBERS

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I can use the place value of the hundreds, tens, and ones digits to compare whole numbers up to 1,000.

I can order whole numbers up to 1,000 using a number line.

I can use the terms less than, greater than, between, or equal to and the symbols <, >, or = when comparing whole numbers up to 1,000.

I can identify the number that is 10 or 100 more or less than a given three-digit number using place value.

SCOPE 1

Addition and Subtraction Strategies Scope Introduction SCOPE SUMMARY Students ﬂuently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction. These strategies are also applied to add a string of up to 4 two-digit numbers. Students use concrete models and drawings to add and subtract 2 two-digit numbers within 1,000. Students explain their reasoning by using concrete objects, pictures, words, and equations. Student Expectations

VERTICAL ALIGNMENT

2.NR.2.3 Solve problems involving the addition and subtraction of two-digit numbers using part-whole strategies. 2.NR.2.4 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/ or the relationship between addition and subtraction.

Background Knowledge

Future Expectations

In ﬁrst grade, students use addition and subtraction within 20 to solve authentic problems. Students represent problem situations involving joining, separating, part-part-whole, and comparing using objects, drawings, and equations with symbols (with unknowns in all positions). They apply properties of operations (commutative, associative, and identity properties) to solve addition and subtraction problems within 20. Students use the meaning of the equal sign to determine whether equations involving addition and subtraction are true or false. They begin to recognize the inverse relationship between addition and subtraction and use this relationship to solve problems.

In third grade, students ﬁnd eﬃcient strategies for adding and subtracting within 1,000. They apply strategies based on place value, properties of operations, and the relationship between addition and subtraction to solve problems involving addition and subtraction within 10,000. Third-grade students investigate the properties of multiplication and the relationship between multiplication and division.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

apply various strategies to solve addition and subtraction problems up to 20.

For the Hook, students are presented with a scenario totalling the amount of recyclables that were collected. Students will: •

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

add four two-digit numbers by using mental math strategies involving place value and/or properties of operations.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. Notes _____________________________________________________________________________________________________________ _____________________________________________________________________________________________________________ _____________________________________________________________________________________________________________

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Addition and Subtraction with Two 2-Digit Numbers In this exploration, student partners will solve a scenario involving tracking how much they are spending on groceries. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

use addition and subtraction strategies with two 2-digit numbers.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Addition with More Than Two 2-Digit Numbers In this exploration, student groups will solve a scenario about helping a museum ﬁnd the value of bags of gems to make sure that they were all returned after they were stolen. Students will: •

add up to four 2-digit numbers using mental math strategies.

•

add up to four 2-digit numbers using algorithms

•

use knowledge of place value and properties of operation.

Explore 3

After students have solved the scenario, they discuss their learning with the class and complete an Exit Ticket.

ADDITION AND SUBTRACTION STRATEGIES

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Explaining Addition and Subtraction Strategies In this exploration, student partners will solve a scenario involving helping two girls ﬁgure out the costs of items to stay within budget. Students will: •

solve addition and subtraction problems within 100 using various strategies.

•

explain the effectiveness of different strategies for solving problems.

After completing the activity, students share their learning, complete an Exit Ticket, and then revisit the Hook to solve.

ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students apply various strategies to solve addition and subtraction problems up to 20. This activity is intended to assess mastery of the following standard(s): 1.NR.2.1 Use a variety of strategies to solve addition and subtraction problems within 20.

Materials

Preparation

Printed •

1 Student Handout (per student)

Reusable •

• •

Print the Student Handout for each student. Prepare manipulatives for students to access if they choose for each table.

30–40 Counting manipulatives, such as cubes or counters (per table)

ADDITION AND SUBTRACTION STRATEGIES

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Procedure and Facilitation Points 1. 2.

Give each student the Student Handout. Read the following scenario to the class: Josiah bought some crickets to feed to his pet lizard. There are already 4 crickets in a jar at home, and Josiah is bringing 12 more from the pet store. Josiah wants to know how many crickets he has to feed his lizard now. You have some counting manipulatives on your table if you need them. I’d like you to use the room on your paper to show me two strategies you would use to solve this problem. Circulate around the room to observe student work. Students might use any of the following strategies: a.

Counting out cubes to represent the crickets and ﬁnding the total

Drawing a picture to show how many crickets there are altogether

Using a number sentence and counting on to put 4 and 12 together

Applying mental math to add the ones place together and then combining that with the tens place

Look for students who are simply writing the answer, and encourage them to show you how they are arriving at that answer. Students can also be encouraged to show more than two strategies if they finish quickly. Once most students have finished, read the next scenario to the class: Mona is helping her mom plant tomato seeds in their garden. Mona started with 18 seeds and planted 6 of them before taking a break to get some water. How many seeds does Mona have left to plant? Use your workspace to show me two strategies you would use to find out the number of seeds Mona has left to plant. Circulate around the room to observe student thinking. Watch for the following strategies: a.

Using cubes to represent the beginning total and removing the 6 to ﬁnd out how many are left. Students can show this on paper as the number sentence 18 – 6 = 12.

Drawing out 6 seeds and counting up to 18 to see how many would be left over

Drawing 18 seeds and crossing off 6 to determine how many would be left over

Using ﬁngers to count up from 6 to 18 or down from 18 to 6. Watch for errors in counting here to note the need for further support later.

FACILITATION TIP Project the scenario and read it with students. Guide them through more than one read aloud and model how to locate the essential math phrases (more, how many, already has, wants to know) and values.

FACILITATION TIP Continue to encourage students to show their answers with physical representations. Remind them that even though they may already know the solution, using manipulatives will support visual problem solving later in more complex math scenarios. FACILITATION TIP Rather than distributing the Student Handout, project the scenarios to the whole class.

ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Lesson Calendar and Accessing Prior Knowledge 7.

Look for students who are simply giving the answer, and encourage them to show how they are arriving at that answer. If students have a number sentence, encourage them to show you what the number sentence represents by using manipulatives. Facilitate a class discussion about their strategies. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a.

What strategies did you use to solve these two problems? Answers will vary. I counted up, or I drew a picture.

Is there another way to solve this problem? Answers will vary. Instead of subtracting, I can add up.

FACILITATION TIP

Use question c. to help students create a list of math phrases that will help them decide whether to add or subtract in a variety of problems.

How did you know to add or subtract? Answers will vary. The action or what was happening in the problem helped me decide to add/subtract.

Is there another number sentence for that problem? How did you know that? Answers will vary. 18 – 6 = 12 or 6 + 12 = 18. I know this because I know how addition and subtraction are related. So I know if 6 + 12 = 18, then I know that 18 – 12 = 6 or 18 – 6 = 12.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ADDITION AND SUBTRACTION STRATEGIES

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ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Hook – Recycling ACTIVITY PREPARATION Students add four two-digit numbers by using mental math strategies involving place value and/or properties of operations.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Reusable • •

•

Plan to show the video. Bring in cans and plastic bottles for students to use as a discussion point. For Part II, print the Student Handout for each student.

1 Collection of cans and plastic bottles for recycling (per teacher) 1 Phenomena Video (per teacher)

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

2. FACILITATION TIP Project a printed version of the scenario so students can read along with you while they record the numbers.

FACILITATION TIP Write the numbers of collected items as you are reading the scenario to provide students with a visual representation of the problem.

STEMscopes Tip The Acceleration section of each scope, located along the scope menu, provides resources for students who have mastered the concepts from the scope to extend their mathematical knowledge. The Acceleration section offers real-world activities to help students further explore concepts, reinforce their learning, and demonstrate math concepts creatively.

DOK-1 What information do we know? 28 items were collected on Monday, 32 items were collected on Tuesday, 17 items were collected on Wednesday, and 23 items were collected on Thursday. They added to ﬁnd the total.

DOK-1 What information do we need to ﬁnd out? What mental math strategy could be used to ﬁnd the sum of the items they collected?

Inform students that they are not to solve the problem right now, but they are to discuss what mental strategies could be used to ﬁnd the total number of items they collected. Also allow students to discuss their experiences with collecting items to recycle. They might list plastic bottles, cans, glass, etc. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

b. 3.

4. 5.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-1 What information do we need to ﬁnd out? What mental math strategy could be used to ﬁnd the sum of the items they collected?

Give each student a Student Handout. Instruct students to ﬁnd the sum of the total items collected by Mr. Cobb’s class by using mental math strategies. Ask students to record and explain their strategies on the Student Handout. Mental math strategies can be modeled by groups of students on chart paper to share with the whole class. Discuss the following questions: a.

DOK-2 What mental math strategies will you use to add all 4 two-digit numbers? Answers will vary. Make a ten, use place value to add (tens ﬁrst and then ones), count up on an open number line, separate the problem into two problems (add two of the numbers ﬁrst), or partial sums.

DOK-1 What do you do when the tens place equals more than 9 tens? We have to regroup and make a hundred.

DOK-2 What are all the different ways you could solve this problem? Answers will vary. Add all of them up with an algorithm, use place value to ﬁnd the partial sums, or split the problem into 2 problems.

DOK-3 Which strategy did you choose to use and why? Answers will vary. I chose to make a ten because I noticed that out of the 4 numbers there were 2 sets of numbers that each made a ten, so it seemed easy to do.

FACILITATION TIP Have students share their strategies with a partner or in small groups. Students can discuss which strategy they felt was most eﬃcient when ﬁnding the sum.

FACILITATION TIP Demonstrate for or provide manipulatives to students who need extra support.

ADDITION AND SUBTRACTION STRATEGIES

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e. DOK-2 How many items did Mr. Cobb’s class collect? Mr. Cobb’s class collected 100 items to be recycled.

ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Explore 1 – Addition and Subtraction with Two 2-Digit Numbers ACTIVITY PREPARATION Students solve problems involving the addition and subtraction of two-digit numbers using part-whole strategies.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.6 Attend to precision. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • •

• •

1 Student Journal (per student) 1 Set of Grocery Shopping Task Cards (per teacher) 1 Place Value Chart (per pair) 1 Exit Ticket (per student)

• •

Reusable • • • •

• • •

2 Plastic sheet protectors (per pair) 1 Dry-erase marker (per pair) 1 Set of base ten blocks – 20 rods and 20 units (per pair) 1 Resealable bag (per pair)

•

Consumable •

Plan to have students work in groups of two to complete this activity. Plan to project the Grocery Shopping Task Cards one at a time during the lesson.

1 Roll of tape (per teacher)

Optionally, print one set of cards for each student pair.

Print a Place Value Chart for each pair of students. Place each page in a plastic sheet protector for use with a dry-erase marker. Tape the two pages together horizontally. Place 20 rods and 20 units in a resealable bag for each pair of students. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Base Tens Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base ten blocks)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Allow students to share their estimation strategies with the class. Reassure students that estimating is a critical thinking skill, and it’s OK to be way off or wrong. In fact, sometimes we learn more when we estimate incorrectly.

FACILITATION TIP

As you observe the different strategies students use, create an ongoing list of strategies on a piece of chart paper for students to reference. 70

3. 4.

Read the following scenario to the class: Carlos and Santos went to the grocery store with their grandma. As they were placing groceries into the cart, Grandma asked them to calculate how much they were spending by adding the price of each item. The boys asked Grandma if she had a calculator. Grandma’s eyes got wide, and she replied, “We didn’t have calculators when I was your age. We just used our brains.” Can you use your mental math strategies to help Carlos and Santos keep track of how much they are spending on groceries? Divide the class into groups of two, and distribute a bag of base ten blocks to each student pair. Project the ﬁrst Grocery Shopping Task Card. Read the card aloud to students. Ask students how they can use different estimation strategies before they solve a problem so they have an idea if their solution is reasonable. Instruct students to estimate solutions before solving the problem. Instruct students to solve the problem using mental math strategies. Encourage students to listen to their partners explain the strategy they would use and compare strategies to see if both partners get the same answer. Students may use the base ten blocks if they are struggling to solve mentally.

Engage

Explore

Explain

Elaborate

Evaluate

9. 10.

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 What strategy did you use to estimate the solution to the problem? Answers will vary. I used friendly numbers and changed 52 to 50 and 29 to 30. Then, I subtracted 30 from 50 and my estimation was 20.

Intervention

DOK-3 Why did you choose to use this estimation strategy? Answers will vary. Finding friendly numbers helps me because it is easier to do mental math to estimate.

DOK-1 What strategy did you use to solve the problem? Answers will vary. Adding tens, then adding ones, then combining; adding on tens and then adding on ones

FACILITATION TIP Encourage students to also discuss the beneﬁts of each strategy and the strategy they feel is most eﬃcient in solving the problem. FACILITATION TIP

Allow students to demonstrate the strategy they used to estimate the solution to the problem and to reﬂect on whether d. DOK-3 Why did you use this strategy? Answers will vary. I used the jump or not they used the same strategies. strategy for adding because it is easier for me to ﬁnd the answer by Ask students to consider if any of these making the jumps. strategies work better than others and Give each student a Student Journal, and ask students to record their estimations discuss why. and mental math strategies. Students should use base ten blocks to reenact the mental math and demonstrate their strategies to their partners. Ask students to draw pictorial models representing the concrete model of base ten blocks they used. Students will also describe the strategy they used in words. Project the remaining Grocery Shopping Task Cards one by one, and repeat FACILITATION TIP steps 3–7. Each new card begins by stating the answer from the previous card. Encourage students to use different Students can use this to check their work. strategies to help them become more When students have completed their Student Journals, bring the class together familiar and comfortable with each as a whole group. strategy. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

ADDITION AND SUBTRACTION STRATEGIES

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Math Chat • •

• •

•

DOK-1 How much money did the boys end up spending at the grocery store? $52 DOK-2 Can you describe how another student used a different strategy than you on the same problem? When I used the number line to make jumps, my friend used the split strategy. She decomposed the numbers into expanded form. She added the tens and then the ones, and then she added the tens and ones together. DOK-2 Can you think of another strategy that was not used in solving the problems today? Yes, I could use skip counting or draw a picture. DOK-3 Do you have a favorite strategy for solving problems, and why do you like that strategy? I like the number line strategy because it is easier for me to solve by making the jumps. DOK-3 Do you believe there is a best strategy for every problem? Why or why not? No, I do not, because everyone is different. Some strategies work better for different people. But everyone should know how to use many strategies so they have many ways to solve a problem. I like to use different strategies for different problems—like the larger the numbers are, the more I like to use the split strategy. DOK-3 How did estimating your solution before solving the problem help you? It helped me to know if I thought my answer was correct. If my answer was close to my estimation, then I felt conﬁdent. If my solution was not close to my estimation, it was a clue to redo the problem. Then, I could ﬁnd my mistake and solve it correctly. If I still had a problem, it was a clue that I needed more help to understand what I was doing and could ask for help. DOK-3 How do you think having a solid understanding of place value helps you use strategies to solve addition and subtraction problems? Understanding place value helps me add large numbers because I can separate numbers into tens and ones using expanded form, and then I can add up the tens and then add up the ones and then add them together.

STEMscopes Tip The Explore section, located along the scope menu, includes one to ﬁve inquiry-based Explore lessons where the most important teaching and learning take place. Each Explore lesson includes a setup video showing how to prepare and facilitate the lesson, a description of the activity, a materials list, preparation steps, procedure and facilitation points for each part of the activity, a Math Chat, Instructional Supports, and ELL teaching strategies. Print ﬁles and Answer Keys for the lesson are also provided. In addition to the Explores, this section also includes Skill Basics lessons in Kindergarten through Grade 2 that prepare students with the skills that they need to complete the Explore activities and Virtual Manipulatives that can be accessed anytime, anywhere.

ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Explore 1 – Addition and Subtraction with Two 2-Digit Numbers Post-Explore 1. FACILITATION TIP When you preview this Exit Ticket with students, support careful reading and help them locate the math words: given, gave, altogether, have left.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ADDITION AND SUBTRACTION STRATEGIES

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ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Explore 2 – Addition with More Than Two 2-Digit Numbers ACTIVITY PREPARATION Students ﬂuently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • • •

1 Student Journal (per student) 1 Place Value Chart (per group) 1 Set of Gem Bags (per group) 1 Gem Cost Evaluation Sheet (per group) 1 Exit Ticket (per student)

Reusable • • • • • •

10 Base-ten rods (per group) 25 Base-ten units (per group) 2 Plastic sheet protectors (per group, optional) 1 Dry-erase marker (per group) 1 Gallon-sized resealable bag (per group) 1 Small resealable bag (per group)

• • • • • •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Make group sets of base ten blocks and place them in a gallon-sized resealable bag so they are accessible to students. Print the Place Value Chart for each group. Place each sheet in a plastic sheet protector, or laminate it for use with a dry-erase marker. Print the Gem Bags and Gem Cost Evaluation Sheet for each group. Cut out the Gem Bags, and place them in a small resealable bag. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Open Number Line and Base Tens Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION FACILITATION TIP

Prior to the Explore activity, students could complete the Skill Basics: Mental Math Strategies as a scaffold. FACILITATION TIP Assign roles for each group member. For example, one student determines the value of the gems, one student estimates the total value, one student completes the mental math, and the other student creates a pictorial model. Students can then rotate through the roles.

4. 5.

Read the following scenario to the class: While the museum was closed over the holidays, someone came in and stole 6 bags of gems. Luckily, the person was caught just in time, and all the gems were found. The museum needs us to help find the value of the gems in each bag so the museum can make sure all the gems were returned. Can you help the museum find the value of each bag of gems? Divide the class into groups of 3 or 4. Distribute a Place Value Chart, a dry-erase marker, a set of Gem Bags, base ten blocks, and a Gem Cost Evaluation Sheet to each group. Give each student a Student Journal. Direct students’ attention to the Gem Bags and Gem Cost Evaluation Sheet. Encourage students to notice the gems in each bag and understand how to find each gem’s value using the Gem Cost Evaluation Sheet. Ask students to begin by looking at the value of each gem in the Gem Bag and estimating the sum of the values using compatible numbers. Instruct students to find the total value of each Gem Bag. Explain that they will use the Gem Cost Evaluation Sheet to write a number sentence and show a strategy for how to find the Gem Bag’s total on their Student Journals. Strategies should use mental math. Encourage students to use the base ten blocks and Place Value Chart to check their mental math strategies and solutions. Have students draw pictorial models of their base ten blocks. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What compatible numbers are you using in your estimation? Answers will vary. We are using friendly numbers close to 5 and 10.

DOK-1 What does each number represent in your number sentence? The cost of each gem in the gem bag

DOK-3 What strategy did your group decide to use to ﬁnd the sum? Answers will vary. We used place value to add the tens, then the ones, and then the tens and ones combined; or we added the tens and then the ones on a number line; or we added tens to get close and then added the ones.

DOK-3 Can you think of a different strategy from the one you used that could still give you the same answer? Answers will vary. We could use a number line.

DOK-3 How are you using base ten blocks to check your mental math strategy? Answers will vary. We are making each number using the rods and units. Then, we can make a group of ten units and trade it for another rod. Then, we can count how many total rods and units there are to see if the total is the same total we got when we used mental math.

DOK-2 What is the total for this gem bag? Answers will vary. $86

When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

• •

DOK-2 Describe some of the different strategies you could use to solve similar problems to the ones in this activity. Creating number lines to count forward, decomposing numbers into tens and ones, using base ten blocks to add and regroup, etc. DOK-2 How can you use place value to help you add two or more numbers mentally? We can add the tens place in all numbers ﬁrst. Then, we can add the ones place in all numbers. We can add the totals to determine the actual sum. DOK-2 Which strategy did you ﬁnd yourself using more? Decomposing the numbers into their place values because I like to add all the 10s and then add all the 1s. DOK-2 How is estimating using compatible numbers helpful when solving addition problems? We can compare our estimated total to the actual total. If the answers are close, then we know the actual answer is correct. If the answers are not close, then we might need to check our work to see if we made a mistake. DOK-3 How are these problems different from the problems we looked at in Explore 1? We were adding more than two numbers at a time. DOK-4 When might you need to use the skill of being able to add more than two numbers at a time in your everyday life? Adding money, completing a reading log with the number of minutes read in a week, adding the costs of items at a restaurant, etc.

Post-Explore 1. 2. 3.

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions:

e. DOK-3 Can you explain how you got your answer? Answers will vary. We added the tens together, and then we added the ones together. Then, we combined the total of the tens and ones.

Intervention

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Provide number lines or a Hundreds Chart for students to use if needed.

ADDITION AND SUBTRACTION STRATEGIES

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FACILITATION TIP In the Math Chat, students should share the different stategies they used to solve the problems. FACILITATION TIP During this Math Chat, create a list of effective strategies and post them where students can see them. These strategies for mental math will be used frequently in later grades and even more often in the real world.

FACILITATION TIP To simplify, project this colorful Exit Ticket for students using a document camera. They can solve on their own paper.

ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Explore 3 – Explaining Addition and Subtraction Strategies ACTIVITY PREPARATION Students solve addition and subtraction problems within 100 using various strategies and then explain the effectiveness of different strategies for solving problems.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Party Purchase Task Cards (per group) 1 Exit Ticket (per student)

• •

Reusable • • • • •

• •

1 Set of base ten blocks (per group) 1 Gallon-sized resealable bag (per group) 1 Whiteboard (per group) 1 Dry-erase marker (per group) 1 Paper clip (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Place a set of base ten blocks in a gallon-sized resealable bag for each group. Each set consists of 10 rods and 20 units. Print and cut out a set of Party Purchase Task Cards. Paper clip and place the cards in the resealable bag with the base ten blocks. Gather enough whiteboards and dry-erase markers for each group to have one of each. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Base Tens Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION 1. STEMscopes Tip The STEMscopes Teacher Toolbox, located under the Scopes tab on the menu bar, features a variety of resources and tools to help teachers get the get most out of their STEMscopes experience, including essentials like lesson-planning documents, intervention strategies, monitoring tools, mathematical discourse strategies, and data resources.

2. 3.

Read the following scenario to the class: Raquel and her sister Katrina are helping her family get ready for their annual family reunion party at the lake. It is a big cookout with music, food, swimming, and fun. The girls’ parents are in charge of all the food. Raquel and Katrina agree to go with their mother to purchase food and party items for the cookout. On the way to the store, their mother tells the girls she will need them to help her ﬁgure out the costs of items so they can stay within the budget she has made. Can you help Raquel and Katrina with this task? Divide the class into groups of 3 or 4. Give a dry-erase marker, whiteboard, set of base ten blocks, and set of Party Purchase Task Cards to each group. Direct students’ attention to the base ten blocks and Party Purchase Task Cards. Allow students a few moments to discover the manipulatives and experience how they work with their group. Instruct students to read each Party Purchase Task Card together as a group and then estimate and solve the problem using the whiteboard and dry-erase marker. Encourage students to use the base ten blocks if needed. Ask students to look at the strategies on the Party Purchase Task Card two different students used to solve the problem. Students will decide which strategy would not correctly solve the problem and explain why the strategy is incorrect. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What strategy did you use to estimate the solution to the problem? Answers will vary. I used friendly numbers and then added.

DOK-3 Why did you choose to use this estimation strategy? Answers will vary. Since both of the numbers were close to ten, I knew my estimation would be close to the actual answer.

DOK-1 What strategy did you use to solve the problem? Answers will vary. I added the numbers in a different order to make it easier to add.

DOK-3 Why did you use this strategy? Answers will vary. I know I will still get the same answer if I add the numbers in an easier order.

When students are ﬁnished with all of the Party Purchase Task Cards and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

DOK-3 How did estimating your solution before solving the problem help you? It helped me to know if my answer was reasonable or if I needed to try another strategy to check my answer. DOK-3 What did you notice about strategies and solving many types of addition and subtraction problems? There are many different strategies you can use that will work. There is more than one way to solve a problem. DOK-3 Did you and the members of your group all solve the problems in the same way? What did this tell you? Different people like different strategies better because the strategies make more sense to them. Also, sometimes, different types of problems work better with different strategies. DOK-3 Do you prefer to solve a problem using base ten blocks, pictorial models, or mental math? Why? I like to use mental math strategies because I understand them well and they are faster; or I like to use base ten blocks because when I do the problem with a concrete model, I know I did it correctly because I can see it. DOK-3 Besides going to a store, how might you use different addition and subtraction strategies in real life? I might use them when I am ﬁguring out points for who wins a game, when I am changing a recipe, when I am ﬁguring out how many minutes something takes, or when I want to see how many more things I have than someone else.

Post-Explore 1. 2. 3. 4.

Acceleration

Give each student a Student Journal, and ask students to record their own estimations and solutions for each Party Purchase Task Card. Students will write the number of the incorrect strategy and explain why it would not work. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

e. DOK-3 How did you know which of the two strategies was incorrect? Answers will vary. The student added the extra information. The answer was not close to my estimation. 8.

Intervention

STEMscopes Tip Found along the scope menu, the Explain section has a variety of elements designed to help students develop a more in-depth understanding of the skills and concepts covered in the Explore. These elements include a Picture Vocabulary of important math terms, independent practice assignments that correspond with the Explore lessons, anchor charts that provide visual representations of concepts addressed in the scope, journal prompts that give students opportunities to write their mathematical ideas, and interactive notebooks for organizing information.

ADDITION AND SUBTRACTION STRATEGIES

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STEMscopes Tip The Elaborate section, found along the scope menu, includes activities that assist students in extending their understanding of the concepts in each scope. Fluency Builders are engaging games and other learning activities where students can practice new skills and concepts. Spiraled Review provides an opportunity for students to work on previously taught content. The Math Story strengthens crosscurricular learning. Problem-Based Tasks engage students with real-world problem solving. Life Connections introduce students to real-world math use, and the Interactive Practice games give students a digital venue to practice math skills. Primary students work with data sets in a Data Science activity.

ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Addition and Subtraction with Two 2-Digit Numbers Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Addition with More Than Two 2-Digit Numbers Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Explaining Addition and Subtraction Strategies Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Harper and Julian’s Camping Trip A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Beads, Beads, Beads

Add and Subtract within 100

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Shopping Spree

Solve Two-Digit Addition and Subtraction Problems

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

ADDITION AND SUBTRACTION STRATEGIES

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Fluency Builder Two-Digit Addition Mental Math Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Students who are still acquiring the concept and need remediation

ADDITION AND SUBTRACTION STRATEGIES

Addition and Subtraction Strategies

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Key Concepts I can solve problems involving the addition of two-digit numbers using part-whole strategies.

What prompts will be used?

What does mastery look like?

ADDITION AND SUBTRACTION STRATEGIES

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I can solve problems involving the subtraction of two-digit numbers using part-whole strategies.

I can ﬂuently add and subtract within 100 using strategies based on place value.

I can ﬂuently add and subtract within 100 using strategies based on properties of operations.

I can ﬂuently add and subtract within 100 using strategies based on the relationship between addition and subtraction.

SCOPE 1

Addition and Subtraction Problem Solving Scope Introduction SCOPE SUMMARY

Student Expectations

2.NR.2.3 Solve problems involving the addition and subtraction of two-digit numbers using part-whole strategies.

Students apply and communicate their knowledge of problem types, such as joining, separating, partpart-whole, and comparing within unknowns in all positions. Students represent their mathematical thinking as they solve one- and two-step problems through a progression of concrete, pictorial, and abstract representations. Students add and subtract two-digit numbers (within 1,000) using concrete models, such as base ten blocks and linking cubes. They represent the problems by using concrete materials, drawings, and equations with a symbol for the unknown number. They also use pictorial models that include drawings and the use of number lines and bar models. Students extend their understanding of addition and subtraction, using strategies based on place value, properties of operation, and the relationship between addition and subtraction. Composing and decomposing a ten is referenced so students can use strategies that involve making a 10, making a 100, and breaking apart a 10. Students are not expected to use the standard algorithm in second grade.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students demonstrate fact ﬂuency as they use strategies such as counting on, making ten, decomposing a number leading to ten, using the relationship between addition and subtraction, and creating equivalent but easier sums to solve addition and subtraction problems within 20. Firstgrade students represent problem situations involving joining, separating, part-part-whole, and comparing using objects, drawings, and equations with symbols (with unknowns in all positions). Students use concrete models such as linking cubes and counters. They progress to pictorial models such as ten frames, part-part-whole models, number paths, number lines, number bonds, and bar models to help deepen their understanding of how to use the correct procedures to solve problems.

Third-grade students will ﬁnd eﬃcient strategies for adding and subtracting within 1,000. They will apply strategies based on place value, properties of operations, and the relationship between addition and subtraction. Third-grade students solve multistep problems involving all four operations, and they represent the problems using an equation with a variable. Students assess the reasonableness of answers using mental computation and estimation strategies, including rounding.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

solve addition and subtraction problems and record their thinking with pictures and number sentences.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

represent and solve a subtraction problem where the unknown may be any one of the terms in the problem.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Represent and Solve One-Step Problems In this exploration, students will represent and solve onestep problems pictorially. Students will: •

identify models that represent addition and subtraction word problems.

Explore 2

Explore 1

EXPLORE ACTIVITIES

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Represent and Solve Multistep Word Problems In this exploration, students will solve a scenario about helping a water park manager ﬁnd missing information for each ride. Students will learn how to create real-world situations based on an equation. Students will: •

represent and solve multistep addition and subtraction word problems with unknowns using number lines.

•

represent and solve multistep addition and subtraction word problems with unknowns using tape diagram models.

•

check their answers with base ten blocks.

After completing the activity, students share their learning, complete an Exit Ticket, then revisit the Hook to solve.

ADDITION AND SUBTRACTION PROBLEM SOLVING

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ADDITION AND SUBTRACTION PROBLEM SOLVING

Addition and Subtraction Problem Solving Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students solve addition and subtraction problems and record their thinking with pictures and number sentences. This activity is intended to assess mastery of the following standard(s): 1.NR.2.2 Use pictures, drawings, and equations to develop strategies for addition and subtraction within 20 by exploring strings of related problems.

Materials

Preparation

Printed •

1 Student Handout (per student)

Reusable •

• •

Print the Student Handout for each student. Prepare counters or cubes to be available for students who need them.

20 Counters or cubes as needed (per student)

Procedure and Facilitation Points 1. 2. 3.

Give each student the Student Handout. Read the following scenario to the class, and ask them to record their thinking by using pictures and number sentences. Danny had 20 cars. She gave some of them to her friend. Danny now has 13 cars. How many cars did Danny give to her friend? Once students have ﬁnished recording their thinking for the ﬁrst problem, read the second scenario aloud, and have students follow the same process of recording their thinking by using pictures and number sentences. Jake had 6 trading cards. He got some more for his birthday. Now Jake has 19 trading cards. How many cards did Jake get for his birthday? Facilitate a class discussion about the problems solved. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a.

Which problem was addition and which problem was subtraction? Danny’s problem was subtraction. Jake’s problem was addition.

How do you know? Answers will vary. I knew Danny’s problem was subtraction because she gave some of her cars away. I knew Jake’s problem was addition because he got more cards.

c. What strategies did you use to solve the addition problem? Answers will vary. To solve the addition problem, I used a counting on strategy; I used my ﬁngers; I drew a picture of the cards and marked the ones he already had. d. What strategies did you use to solve the subtraction problem? Answers will vary. To solve the subtraction problem, I drew the total amount and then crossed off the number of cars she gave away; I used my ﬁngers to show how many cars she has and how many she gave away; I counted back.

FACILITATION TIP

ADDITION AND SUBTRACTION PROBLEM SOLVING

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Consider projecting the Student Handout and conducting a class read aloud for each scenario. Guide students to find the key math phrases and values in each story. Model by reading more than once, highlighting words, and underlining or circling values. FACILITATION TIP Ask students, “What do we know?” and, “What do we need to find out?” FACILITATION TIP Use guiding questions a. and b. to embelish or create your class list of math words and phrases that indicate addition or subtraction. Consider a two column chart. FACILITATION TIP Model counting on with hands and fingers. For example, first make a fist on 13 and pound into hand. Next, use fingers to count on to 20. Hands will show 7 fingers.

e. What is the difference between how you used pictorial models to solve the addition and subtraction problem? Answers will vary. When I represented the addition problem, I started with the amount of cards he had and drew more cards until I got to 19. When I represented the subtraction problem, I drew the total number of cars and then crossed off the ones that Danny gave away.

What happens to the total when two numbers are added? When two numbers are added, the total increases.

What happens to the total when two numbers are subtracted? When two numbers are subtracted, the amount decreases.

FACILITATION TIP Check for understanding of the word total and use the Picture Vocabulary to connect the word total to sum and difference.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

ADDITION AND SUBTRACTION PROBLEM SOLVING

Addition and Subtraction Problem Solving Hook – Roll-and-Score-Game Scores ACTIVITY PREPARATION Students represent and solve a subtraction problem where the unknown may be any one of the terms in the problem.

Materials

Preparation

Printed •

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1 Student Handout (per student)

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Reusable • • •

Plan to show the video. Part II

1 Phenomena Video (per teacher) 1 Set of base ten blocks, including 10 ﬂats, 10 rods, and 10 units (per pair) 1 Resealable bag (per pair)

•

Plan to divide the class into pairs. Place 10 ﬂats, 10 rods, and 10 units into a resealable bag for each pair of students. Print the Student Handout for each student.

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

2. FACILITATION TIP

Project a print version of the scenario. Write the numbers of points scored as you are reading the scenario to provide students with a visual representation of the problem.

FACILITATION TIP Invite students to consider if any of the strategies discussed would work better than others for this problem and discuss why.

DOK-1 What information do we know? Kayla scored 26 points in her ﬁrst game. She scored a total of 93 points in both games combined.

DOK-1 What information do we need to ﬁnd out? How many points did she score in her second game?

Inform students that they are not to solve the problem right now, but they are to discuss what strategies they could use to ﬁnd how many points Kayla scored in her second game. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

3. 86

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What information do we know? Kayla scored 26 points in her ﬁrst game. She scored a total of 93 points in both games combined.

DOK-1 What information do we need to ﬁnd out? How many points did she score in her second game?

Divide the class into groups of two, and give each student pair a bag of base ten blocks. Encourage students to use the base ten blocks to solve the problem. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Give students the Student Handout. Students will represent the problem by using either a bar model or number line. Encourage partners to try different approaches. Then, have them compare their answers with their partners. Discuss the following questions: a.

DOK-1 What is a bar model? A bar model is a pictorial model of a word problem using rectangles to represent the parts and total of the problem.

DOK-1 What do the rectangles in a bar model represent? The rectangles represent two amounts that are combined to equal a total amount.

DOK-1 What pieces of information did you use to solve using a bar model? I used the total, which was 93, and her ﬁrst score, which was 26.

DOK-2 What does the ? represent in your bar model? It represents the number of points she scored in her second game, which is the amount we are looking for.

e. DOK-1 How many points did she score in her second game? 67 points f.

DOK-1 What is a number line? A number line is a line where numbers and marks are added as a result of information from the problem. Arrows are drawn to indicate the actions of the problem.

DOK-2 What pieces of information did you use to solve using a number line? I used the total, which was 93, and her ﬁrst score, which was 26.

h. DOK-3 Which way did your arrow point on your number line? Why? Answers will vary. The arrow pointed to the left to show subtraction, or the arrow pointed to the right to show addition. i. DOK-2 What does the ? represent on your number line? It represents the number of points she scored in her second game, which is the amount we are looking for, the unknown. j. DOK-3 How are both of these representations similar? Answers will vary. They both have the ﬁrst score and total score. The missing score (the second score) is represented with a ? in both models. Both models lead us to subtract to ﬁnd the second score. They both give us the same answer. k.

DOK-3 Which is easier for you to use and understand: concrete models (like the place value blocks) or pictorial models (like the number line or bar model)? Why? Answers will vary. I prefer the concrete model because I can count everything out and see that I am correct. I prefer a pictorial model because it is faster.

Intervention

Acceleration

FACILITATION TIP Model each of these strategies for students. FACILITATION TIP If students don’t arrive at the same answers, have them look at one another’s work to determine whether the solutions are correct. Alternatively, students can discuss the processes they used to arrive at their solutions to help find mathematical errors. STEMscopes Tip The Evaluate section, found along the scope menu, contains assessment tools designed to help teachers gather the data they need to determine whether intervention or acceleration is warranted. Several assessment tools for measuring student performance accommodate students’ varied learning styles. Kindergarten and Grade 1 evaluations include a handson Observation Checklist and Showand-Tell assessment. Assessments in Grades 2–5 include open-ended and multiple-choice questions. A Skills Quiz focused on computational fluency can be found in all grades. Each assessment is aligned to the specific scope’s standards and can be used formatively or summatively.

ADDITION AND SUBTRACTION PROBLEM SOLVING

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FACILITATION TIP Also discuss how these two strategies are different and which strategy students felt was more eﬃcient or easier to use when solving this problem.

ADDITION AND SUBTRACTION PROBLEM SOLVING

Addition and Subtraction Problem Solving Explore 1 – Represent and Solve One-Step Problems ACTIVITY PREPARATION Students represent and solve one-step problems pictorially and then identify models that represent addition and subtraction word problems.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • • •

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1 Student Journal (per student) 1 Set of Zoo Problem Cards (per group) 1 Place Value Chart (per group) 1 Exit Ticket (per student)

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Reusable • • • • • •

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1 Dry-erase marker (per group) 2 Plastic sheet protectors (per group, optional) 9 Base-ten rods (per group) 20 Base-ten units (per group) 1 Small resealable bag (per group) 1 Large resealable bag (per group)

• •

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print a set of Zoo Problem Cards for each group. Cut off the bottom portion of each Zoo Problem Card, and place them in a small resealable bag. Students will not use the bottom portion of each card until Part II of the activity. Put the base-ten rods and units and a set of Zoo Problem Cards into a large resealable bag for each group. Print one Place Value Chart for each group, and place each page in a separate plastic sheet protector or laminate for use with a dry-erase marker. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Open Number Line and Base Tens Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION Part I 1.

FACILITATION TIP Have each student in the group take a different role (reader, base ten block user, writer) to keep students engaged. Have students rotate roles when solving a new problem.

2. 3.

Read the following scenario to the class: Today, we are going to have a Zoofari day. You will be walking around the zoo to learn different facts about the animals who live there. You will read each problem and decide how to solve it using the provided manipulatives. Can you use the base ten blocks to solve and then draw a pictorial model of your solution? Divide the class into groups of 3 or 4, and direct students’ attention to the Zoo Problem Cards, Place Value Chart, dry-erase marker, and base ten blocks. Instruct students to read each problem and solve using the base ten blocks. Students can place their blocks on the Place Value Chart and write each digit in the space provided at the bottom of the chart as they work. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What information do you know? Answers will vary. The zoo has 27 venomous snakes. Some more were donated. Now there are 46 venomous snakes.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-3 How will you use the base ten blocks to model this problem? Answers will vary. I will show the number 27 using two rods and seven units. Then, I will keep adding rods and units until I get to the total, 46. DOK-2 What number sentence will you write to describe this problem? Answers will vary. 27 + ? = 46

e. DOK-2 Where is the unknown in the number sentence? Answers will vary. The unknown is the second number in the number sentence.

DOK-2 How will you represent the unknown in your number sentence? Answers will vary. I will write a question mark for the unknown.

DOK-3 Is this an addition or subtraction problem? How do you know? Answers will vary. This is an addition problem because we have to put together two numbers to equal the total that is given.

Give each student a Student Journal, and ask students to draw a pictorial model of the base ten blocks they used to solve. Students will write two number sentences: one number sentence using a symbol for the unknown and another number sentence with the solution.

Intervention

Acceleration

FACILITATION TIP Ask students what other strategies they could use to solve the problem.

STEMscopes Tip A link to the list of standards is located on the menu bar. Here, standards can be accessed using two methods: click on the expandable list to see standards organized by grade level, or locate speciﬁc standards using the key word search. Either method will result in locating standards with direct links to the scopes in which they appear.

Part II 1.

2. 3.

4. 5.

Continue the scenario from Part I: Each problem has 4 choices of models to represent the problem. Can you decide which model works best to help the zookeeper solve each problem? Give a bag that contains the bottom portion of the Zoo Problem Cards to each group. Instruct students to use the pictorial models and number sentences they created in Part I to determine which bar model and number line model best represent each Zoo Problem Card. Ask students to complete Part II of their Student Journals and answer the reﬂection question, and then bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat

ADDITION AND SUBTRACTION PROBLEM SOLVING

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FACILITATION TIP Model how to use tape diagrams and number lines to solve problems. FACILITATION TIP Allow student volunteers to read their story problems and show the strategies they used to solve them.

DOK-3 Why do you think there were different representations that worked better for certain kinds of problems? If the problem was talking about something that happens in a straight line, I would use a number line. If we were comparing something, I would use a bar model. • DOK-3 How did you use your pictorial model and number sentences to help you choose the bar model and number line that best described each problem? I looked at the numbers and operations I used in my pictorial model to help me choose the best bar model and number line model. • DOK-2 What is wrong with the other models? The other models have the numbers in the wrong places, or they have the wrong operation. • DOK-3 Which representation do you feel most conﬁdent in using? I like to use the number line because it helps me ﬁnd the answer by counting forward or backward. •

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP When you preview this Exit Ticket with students, support careful reading; encourage them to underline the math words: more, how many, some, only. FACILITATION TIP Model for students the four parts required for success on this assessment: Two models and two number sentences.

ADDITION AND SUBTRACTION PROBLEM SOLVING

Addition and Subtraction Problem Solving Explore 2 – Represent and Solve Multistep Problems ACTIVITY PREPARATION Students represent and solve multistep addition and subtraction problems where unknowns may be any one of the terms in the problem by using number lines or bar models and checking answers with base ten blocks.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Water Park Ride Cards (per class) 1 Exit Ticket (per student)

Reusable • • • •

1 Base-ten ﬂat (per group) 10 Base-ten rods (per group) 20 Base-ten units (per group) 1 Resealable bag (per group)

• • • • •

•

Plan to have students work in 6 groups to complete this activity. Print a set of Water Park Ride Cards, and hang them around the classroom. Prepare a resealable bag with 1 ﬂat, 10 rods, and 20 units for each group. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Open Number Line and Base Tens Supplemental Aids elements in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Base Ten Blocks)

PROCEDURE AND FACILITATION 1.

2. 3. FACILITATION TIP Allow students to write their own word problems or use different pictorial models than others in their group. Encourage students to share how they solved the problem differently but arrived at the same solution. FACILITATION TIP

Read the following scenario to the class: Today, you will be taking a trip to a water park. Every student needs to visit every ride before leaving the water park. Something interesting happened at each ride, but not all of the information was recorded for the park. Can you help the water park managers ﬁnd the missing information at each ride? Divide the class into 6 groups, and place each group at a Water Park Ride Card. Direct students’ attention to the ride and the problem presented. Instruct students to read the problem together and then discuss what information is given and what information is missing. Encourage students to discuss what pictorial model or number sentence including an unknown would ﬁt the problem at each ride. Give each student a Student Journal, and ask students to record either the pictorial model or number sentence with unknown for each ride. Have students work with their groups to solve each problem. Encourage students to use base ten blocks if needed. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-3 How did you decide which strategy to use when you were only given the number sentence? Answers will vary. I chose the one that was the easiest for me to solve. When I compare, I like to see the two different bars to remind me to ﬁnd the difference.

DOK-3 Did you always use the number sentence given to ﬁnd the answer or did you prefer a different one? Answers will vary. Sometimes I had to move the numbers around to make a new number sentence to help me solve it.

Discuss the advantages and disadvantages of each strategy. FACILITATION TIP Have student volunteers demonstrate how and why they changed the location of the numbers in the number sentence. 90

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-3 What were the differences in the types of problems when you saw the number line used and when you saw a bar model used? Answers will vary. The number line problems were talking about something that could be put in a line. I like to use the bar model when there are two groups and a whole.

When students complete all the Water Park Ride Cards and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

•

• •

•

• •

DOK-3 What type of problem do you solve using a bar model? Why? When information is broken up into parts and you are missing either a part or total, a bar model can be used to display that information. DOK-3 What type of problem do you solve using a number line? Why? When you are ﬁnding the distance between two numbers or numbers are being added together, a number line can be used to solve the problem. DOK-2 Do you always have to subtract when given a subtraction number sentence? No, you can add up to the total. DOK-3 How did using the base ten blocks to check your answers help? For addition, I would build each number, add the blocks together, and regroup to ﬁnd my answer. For subtraction, I would build the total and take blocks away, regrouping if needed. Then I would see if my answer matched the answer I got using a bar model or number line. DOK-2 What do you have to remember when solving multistep problems? You have to pay attention to the action of each step and make sure you complete all of the steps. DOK-3 Do you have to solve a multistep addition problem in a certain order? Explain. No, you can move the numbers around and still get the same answer. DOK-3 When might you need to solve addition and subtraction problems in real life? When you are paying bills, when you are adding up grocery costs, when you are counting your collection of baseball cards.

FACILITATION TIP When conducting this Math Chat emphasize to students that they will be asked to use a bar model and a number line in all the upper grades. These tools will become very helpful when students need to think through fractions, percents, and integer problems FACILITATION TIP

ADDITION AND SUBTRACTION PROBLEM SOLVING

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When conducting this Math Chat emphasize to students that they will be asked to use a bar model and a number line in all the upper grades. These tools will become very helpful when students need to think through fractions, percents, and integer problems

Post-Explore 1. 2. 3. 4.

ADDITION AND SUBTRACTION PROBLEM SOLVING

Addition and Subtraction Problem Solving Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Represent and Solve One-Step Problems Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Represent and Solve Multistep Problems Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Pizza Party A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Serving Others

Addition and Subtraction Problems and Representations

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Travel Agency

Match a Two-Digit Addition or Subtraction Problem with a Model

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

ADDITION AND SUBTRACTION PROBLEM SOLVING

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Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Students who are still acquiring the concept and need remediation

ADDITION AND SUBTRACTION PROBLEM SOLVING

Addition and Subtraction Problem Solving

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Key Concepts I can solve problems involving the addition and subtraction of two-digit numbers using diagrams.

What prompts will be used?

What does mastery look like?

ADDITION AND SUBTRACTION PROBLEM SOLVING

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I can solve problems involving the addition and subtraction of two-digit numbers using number lines or paths.

I can represent the problem using an equation with a symbol for the unknown.

SCOPE 1

Arrays Scope Introduction SCOPE SUMMARY

Student Expectations

Students use repeated addition to work with rectangular arrays. Students explore this concept by using concrete models (counters, square tiles, and linking cubes) and by creating pictorial representations on grid paper. Based on the commutative property of addition, which was explored in ﬁrst grade, students can add either the rows or the columns to ﬁnd the total amount within an array. Students express the array using equations. Arrays at this grade level are composed of up to 5 rows and up to 5 columns. This concept is a building block toward multiplication.

2.NR.3.2 Use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

First-grade students solve problems within 20 by using pictures, drawings, and equations. They determine the unknown whole number in addition or subtraction equations relating to three whole numbers. First graders use and explain a variety of counting strategies, reason about the sums and differences of basic facts through sums of 10, and explore the properties of operations. They also identify, describe, and create growing, shrinking, and repeating patterns based on the repeated addition or subtraction of 1s, 2s, 5s, and 10s.

In third grade, students use a variety of strategies, such as repeated addition, skip counting, arrays, area models, and jumps on a number line, to solve contextual problems involving multiplication. Students make connections between multiplication and division and apply this knowledge to problems. Third graders work with plane ﬁgures, covering rectangular shapes with square tiles, and develop an understanding of square units.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

use and explain a variety of counting strategies in order to add equal addends with sums up to 20.

For the Hook, students are presented with a scenario about Fiona, a girl who needs help ﬁnding the total number of each color bead using addition. Students will: •

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK.

use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ARRAYS

Home

Arrays with Concrete Objects In this exploration, students will participate in solving a scenario about a toy factory that needs help preparing the distribution of toys by its deadline. Students will: •

observe and manipulate objects in arrays.

•

explore concrete objects to count.

•

build rectangular arrays with up to 5 rows and up to 5 columns.

Explore 2

Explore 1

EXPLORE ACTIVITIES Arrays with Pictorial Models In this exploration, students will solve a scenario about helping planting magic beans. Students will: •

use pictorial models to count.

•

build rectangular arrays with up to 5 rows and up to 5 columns.

•

use story mats.

After completing the activity, students share their learning, complete an Exit Ticket, then revisit the Hook to solve.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

ARRAYS

Arrays Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ARRAYS

Home

ACCESSING PRIOR KNOWLEDGE Students use and explain a variety of counting strategies in order to add equal addends with sums up to 20. This activity is intended to assess mastery of the following standard(s): 1.NR.2.2 Use pictures, drawings, and equations to develop strategies for addition and subtraction within 20 by exploring strings of related problems.

Materials

Preparation

Printed •

•

1 Student Handout (per student)

•

Reusable • • •

•

12 Counters (per student) 3 Paper plates (per student) 1 Resealable bag (per student)

Put a set of 12 counters into a resealable bag for each student. Prepare 3 plates for each student, or provide the Student Handout. Label a corner of the room with each of the following numbers: 3, 4, 12, and 7.

Procedure and Facilitation Points 1. 2. 3. 4.

FACILITATION TIP

Give a bag of counters and 3 paper plates to each student. Provide the Student Handout if paper plates are not available. Read the following scenario to the class: Isabella had 3 plates of cookies. Each plate had 4 cookies on it. How many cookies did Isabella have in all? Instruct students to use the paper plates and counters to act out the problem. Then have students move to the corner that represents their answer: 3, 4, 12, or 7. Facilitate a class discussion about their strategies. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a.

How did you model the word problem using the plates and counters? I laid out 3 plates and placed 4 counters on each plate.

What did you notice about the number of cookies on each plate? The number of cookies on each plate was the same number, 4.

What strategy did you use to solve the problem? Answers will vary. I skip counted by 4. I added 4 + 4 + 4 to get 12.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

Project this scenario and conduct a guided read aloud. Model reading the scenario more than once and coach students to locate the key phrases and values. FACILITATION TIP Prior to having students move to the corners, clarify your expectations about the paper plates and counters at their desks. Alternatively, have students vote for their answers. FACILITATION TIP Take time to address the phrase in all in this scenario. Add the phrase to your class list for math phrases that help students determine appropriate strategies. FACILITATION TIP If students are ready for a challenge, encourage them to create scenarios that use the three plates and the twelve counters.

ARRAYS

Arrays Hook – Making Bracelets ACTIVITY PREPARATION Students use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

•

Reusable • • • • •

Plan to show the video. Part II

9 Red plastic beads (per student) 10 Blue plastic beads (per student) 12 Yellow plastic beads (per student) 1 Resealable bag (per student) 1 Phenomena Video (per teacher)

•

Place 9 red, 10 blue, and 12 yellow plastic beads in a resealable bag for each student. Print a Student Handout for each student.

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

2. FACILITATION TIP Project this scenario so students can read it along with you. Have some students read it a second time and allow students to take notes. Emphasize the math words and phrases: pattern, sort, no more than, rectangular array, rows and columns, total, addition.

5. 6.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Fiona is making bracelets. She wants to organize her beads by color to make creating patterns easier. Fiona also needs to know how many of each color bead she has available. She has a bag of red, blue, and yellow beads. In order to count the beads, she will need to sort by color and arrange each color in a rectangular array with no more than 5 rows and 5 columns. Can you help Fiona ﬁnd the total number of each color bead using addition? Discuss the following questions: a.

DOK-1 What information do we know? Fiona has a bag of red, blue, and yellow beads. She needs to sort by color and then arrange each color in an array with no more than 5 rows and 5 columns.

DOK-1 What information do we need to ﬁnd out? What is the total number of each color bead?

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities. Notes

100

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ARRAYS

Home

Part II: Post-Explore 1. 2.

4. 5.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What information do we know? Fiona has a bag of red, blue, and yellow beads. She needs to sort by color and then arrange each color in an array with no more than 5 rows and 5 columns.

DOK-1 What information do we need to ﬁnd out? What is the total number of each color bead?

FACILITATION TIP Print and project these directions so students can see them as they work.

Give each student a copy of the Student Handout and a bag of beads. Instruct students to sort the beads by color and then arrange each color into a rectangular array with no more than 5 rows or 5 columns. Ask students to draw a pictorial model of each array and write an equation to ﬁnd the total number of each color bead on their copies of the Student Handout. Discuss the following questions: a.

DOK-3 What strategy did you use to make counting each color of bead easier? I sorted by color and then arranged the beads in equal rows and columns.

DOK-1 What are you trying to ﬁnd? The total number of each color bead

DOK-3 How did you make your model? Red = 3 rows of 3; blue = 5 rows of 2 or 2 rows of 5; yellow = 3 rows of 4 or 4 rows of 3.

DOK-3 How can we use addition to create a number sentence to describe your model? Answers will vary depending on the color of the beads. For example, blue = 2 + 2 + 2 + 2 + 2 or 5 + 5

FACILITATION TIP Compare the strategies for ﬁnding the total number of beads and discuss the advantages and disadvantages of each strategy.

e. DOK-3 Is there another strategy you can use to ﬁnd the total number of beads? I can skip count or just count the beads one at a time. f.

DOK-2 How many beads of each color are there in all? There are 9 red beads, 10 blue beads, and 12 yellow beads.

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Arrays Explore 1 – Arrays with Concrete Objects ACTIVITY PREPARATION Students use concrete objects to count and build rectangular arrays with up to 5 rows and up to 5 columns.

Standards for Mathematical Practices • • •

MP.4 Model with mathematics. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Story Mats (per class) 1 Set of Direction Cards (per class) 1 Exit Ticket (per student)

Preparation • • •

• • • • •

Reusable Part I • • • • •

10 Buttons (per class) 8 Stickers (per class) 15 Linking cubes (per class) 6 Square color tiles (per class) 12 Bear counters (per class)

• •

15 Buttons (per class) 10 Stickers (per class) 5 Linking cubes (per class) 12 Square color tiles (per class) 20 Bear counters (per class) 5 Baskets (per class)

• • •

Station 1 – 2 rows of 5 buttons Station 2 – 4 rows of 2 stickers Station 3 – 5 rows of 3 linking cubes Station 4 – 3 rows of 2 square tiles Station 5 – 4 rows of 3 bear counters

Print and cut out a set of Direction Cards. Prepare the following station materials by placing the objects in a basket with the Direction Card for Part II: • • • • •

Part II • • • •

Plan to have students work in groups of 3 or 4 to complete this activity. Print a set of Story Mats, and place one at each station. Part I materials are already placed on the Story Mat for the students. Part II materials are in a basket, and students place materials on the Story Mat. Prepare the following station materials by laying objects in an array on the Story Mat for Part I:

Station 1 – Package 1 card and 15 buttons Station 2 – Package 2 card and 10 stickers Station 3 – Package 3 card and 5 linking cubes Station 4 – Package 4 card and 12 square tiles Station 5 – Package 5 card and 20 bear counters

Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore dropdown menu and can be digitally assigned to students. (Color Tiles, Linking Cubes) Notes

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PROCEDURE AND FACILITATION Part I 1.

2. 3. 4. 5.

Read the following scenario to the class: The STEMscopes Toy Factory needs to package up the toys to distribute to all the local toy stores in the next week. They noticed that some of the packages don’t have labels that tell the customer how many toys are in each package. Can you help the toy factory prepare to distribute all the toys and meet its deadline? Divide students into groups of 3 or 4 and place each group at a station. Direct students’ attention to the arrays at their stations. Allow students a few moments to discuss the manipulatives without touching or moving the arrays. Instruct students to count the objects in the arrays. Encourage students to discuss the different counting strategies that can be used with their groups. Monitor and talk with students as needed to check for understanding using the following guiding questions: a.

DOK-1 How many objects make up your array? Answers will vary. There are 10 buttons.

DOK-2 How did you count the objects? Answers will vary. We skip counted by twos.

DOK-3 Is there another way to count the objects? Answers will vary. We could add 5 + 5 to get 10.

FACILITATION TIP It will be tempting for students to touch the manipulatives, especially when counting. You might consider placing pictures of each array at the stations instead, so the arrangements don’t alter as groups rotate through the stations.

Give each student a Student Journal, and direct students’ attention to Part I. Ask students to write an equation to represent how many total objects are in the array. Remind students to label the package of toys with the total on their Student Journals. Rotate students through each station, and remind students to complete their Student Journals for Part I.

Part II 1. 2.

3. 4.

Clear off the Part I Story Mats. Leave the Story Mat at each station. Distribute the Part II baskets to the stations around the room. Read the following scenario to the class: The STEMscopes Toy Factory just found baskets of toys that haven’t been packaged yet, and the deadline to get them shipped is fast approaching. These toys need to be packaged, counted, and labeled. Can you help the toy factory meet its deadline? Keep students in groups of 3 or 4 and place each group at a station. Direct students’ attention to the baskets of objects, Direction Cards, and Story Mats at their stations. Allow students a few minutes to discover the manipulatives and experience how they work with their groups. Instruct students to read the Direction Cards and build arrays on the Story Mats using all of the objects in the baskets. Encourage students to discuss all of the different ways to build the arrays. Monitor and talk with students as needed to check for understanding using the following guiding questions: a.

DOK-1 What directions were you given on the Direction Card? Answers will vary. Build an array of 5 rows of 3 buttons.

DOK-2 How did you arrange your objects into an array? Answers will vary. We put 3 buttons in each row until we had 5 rows.

DOK-3 Is there another way to build the array? Answers will vary. We could do 3 rows with 5 buttons in each row.

DOK-1 How many objects were in the package? Answers will vary. There were 15 buttons.

STEMscopes Tip If the assessments reveal that some students have not yet reached mastery of the content, use the resources in the Intervention section, found along the scope menu. These are designed to support students who need help building their understanding of the skills and concepts in the scopes. This section includes a Small-Group Intervention activity that reviews previous skills or reteaches new skills, Supplemental Aids that can be used to assist with assignments, and a short assessment to determine students’ level of mastery after intervention. These materials can also be used in conjunction with the Elaborate activities, as afterschool support, or as a test-prep tool.

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Arrays Explore 1 – Arrays with Concrete Objects 7.

FACILITATION TIP Keep a list of the different equations used to represent the fruit snack arrays and which students used each one. This will assist while facilitating the Math Chat later on.

8. 9. 10.

Direct students’ attention to Part II in their Student Journals. Ask students to draw models of their arrays and write equations to represent the total number of objects. Remind students to label the packages of toys with the totals on their Student Journals. Rotate students through each station, and remind students to complete their Student Journals for Part II. After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

• •

•

DOK-3 What strategy did you ﬁnd worked the best for counting the objects? Why? I just counted one by one. I skip counted by twos and ﬁves. I added each row together using repeated addition. DOK-3 Was there more than one way to build an array using the objects? Explain. Yes. I built an array with 2 rows of 5 stickers and 5 rows of 2 stickers. DOK-3 Are the equations the same for both arrays? Explain. No. I wrote 5 + 5 = 10 and 2 + 2 + 2 + 2 + 2 = 10. I got the same answer, but the equations were different. DOK-4 When would you need to arrange objects into an array in order to count them at home? I arrange my toy cars into an array when I put them in the carrying case. It makes it easier to count to see how many toy cars I have.

Post-Explore FACILITATION TIP

On this Exit Ticket, allow students the option to sketch a model of the Fruit Snack Boxes on the shelves rather than cutting and gluing.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

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Intervention

Acceleration

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Arrays Explore 2 – Arrays with Pictorial Models ACTIVITY PREPARATION Students use pictorial models to count and build rectangular arrays with up to 5 rows and up to 5 columns.

Standards for Mathematical Practice • • •

MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • • •

• •

1 Student Journal (per student) 1 Story Mat (per group) 1 Set of Task Cards (per group) 1 Exit Ticket (per student)

• • •

Reusable • • •

1 Plastic sheet protector (per group) 1 Dry-erase marker (per group) 1 Resealable bag (per group)

Plan to have students work in groups of 3 or 4 to complete this activity. Print and cut the Task Cards, and place them in a resealable bag for each group. Print a Story Mat for each group, and place it in a plastic sheet protector for use with a dry-erase marker. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids elements in the Intervention section.

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Before giving students the Task Cards, check for clear understanding of the terms rows and columns. This vocabulary will be used repeatedly throughout their math career.

2. 3.

FACILITATION TIP Although the grid paper has plenty of space to form each array, students need to be selective about where to start drawing each array. Prompt students to plan accordingly by tracing the array with their ﬁngers before drawing it in pencil. This will ensure that they have enough space and that their arrays do not stretch outside of the provided grid space.

Read the following scenario to the class: A farmer named Jane wants to plant magic beans to grow in her garden. She knows these magic beans can grow magical discoveries. Can you help Jane plant all the magic beans? Give a Story Mat, set of Task Cards, and dry-erase marker to each group. Instruct students to read each Task Card and use the Story Mat to draw a pictorial model of the array. Point out the ﬁve rows already printed on the Story Mat, and discuss if they think they will use every row for every Task Card. Monitor and talk with students as needed to check for understanding using the following guiding questions: a.

DOK-1 How many objects make up your array? Answers will vary. There are 8 beans.

DOK-2 How did you count the objects? Answers will vary. We skip counted by twos.

DOK-3 Is there another way to count the objects? Answers will vary. We could add 5 + 5 to get 10.

Give each student a Student Journal. Ask students to draw pictorial models using the grid paper and write equations to show the total number of objects. Notes

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6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

•

DOK-3 What strategy did you find worked the best for arranging the magic beans? Why? I put them in rows of 3 and made 4 rows with 3 in each row. DOK-3 What strategy did you find worked the best for counting the magic beans? Why? I just counted one by one. I skip counted by twos and fives. I added each row together using repeated addition. DOK-3 Was there more than one way to build an array using the magic beans? Explain. Yes. I built an array with 2 rows of 5 magic beans and 5 rows of 2 magic beans. DOK-3 Are the equations the same for both arrays? Explain. No. I wrote 5 + 5 = 10 and 2 + 2 + 2 + 2 + 2 = 10. I got the same answer, but the equations were different. DOK-4 When would you need to draw an array in order to count objects at home? When I helped my dad put new tile down on the bathroom floor, he had me draw out the rows and columns of tile so we knew how many tiles to buy at the store.

Post-Explore 1. 2. 3. 4.

Intervention

Acceleration

ARRAYS

Home

FACILITATION TIP Challenge students who ﬁnish early to use at least two equations for each Task Card response. Although repeated addition is the content focus at this level, some students may notice that multiplication can be used. Acknowledge this discovery, but don’t require the whole class to use multiplication.

STEMscopes Tip The Home section of each scope contains a Scope Overview. Here, teachers can access a colorful flowchart to see the overall flow of the scope. Each of the 5E lessons and their activities are listed. In addition, the flowchart shows paths to take for students needing more support as well as for students who have mastered the content.

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Arrays Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Arrays with Concrete Objects Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Arrays with Pictorial Models Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

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Explain

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Acceleration

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ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

A Trip to the Doll Store A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Watch Them Grow!

Array Questions and Answers

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

The Party Planners

Solve Array Problems

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

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Arrays Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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What prompts will be used?

What does mastery look like?

I can use addition to ﬁnd the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns.

I can write an equation to express the total as a sum of equal addends.

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SCOPE 1

Two-Dimensional Shapes Scope Introduction SCOPE SUMMARY Students describe, compare, and sort two-dimensional shapes based on a given set of attributes. They also identify at least one line of symmetry through exploration with realworld objects. Shapes include polygons, triangles, quadrilaterals (squares, rectangles, rhombuses, parallelograms, and trapezoids), pentagons, and hexagons.

Student Expectations

2.GSR.7.1 Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes. 2.GSR.7.2 Identify at least one line of symmetry in everyday objects to describe each object as a whole.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In first grade, students distinguish between defining attributes and nondefining attributes, and they draw shapes that possess defining attributes. Students identify squares, circles, triangles, rectangles, hexagons, half-circles, and quartercircles.

In third grade, students use precise language to identify and describe the properties of two-dimensional shapes as they make generalizations about properties that are shared between categories of shapes. Properties are used to determine whether a shape is a quadrilateral, and within that category, students classify and draw subcategories, such as parallelograms, rectangles, squares, rhombuses, trapezoids, and kites.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

identify common two-dimensional shapes and three-dimensional ﬁgures.

•

sort and classify the shapes by their attributes.

•

build and draw shapes that possess deﬁning attributes.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES For the Hook, students are presented with a scenario of helping determine what the cover of a math journal will look like. Students will: •

draw 2-D shapes based on attributes provided.

•

name the shapes and the number of sides, vertices, and angles.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope. If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. Notes

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Explain

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Evaluate

Intervention

Acceleration

Sorting 2-D Shapes In this exploration, students will solve a scenario in their Math Journals that involves students helping sort shapes seen at the City Zoo. Students will: •

sort shapes according to their attributes.

•

identify the number of sides and the number of vertices.

Explore 2

Explore 1

EXPLORE ACTIVITIES Classifying 2-D Shapes In this exploration, students will solve a scenario about helping to guess which two-dimensional ﬁgures are in a bag without looking. Students will: •

classify 2-D shapes according to their attributes.

TWO-DIMENSIONAL SHAPES

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Once students have solved the scenario, they discuss their learning with the class and complete an Exit Ticket.

Drawing 2-D Shapes In this exploration, students will solve a scenario about a math manipulative company that has asked them to draw shapes based on attributes given to them for other students to use. Students will: •

identify different 2-D shapes based on different attributes.

•

draw different 2-D shapes based on different attributes.

Explore 4

Explore 3

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment. Identifying Lines of Symmetry In this exploration, students will identify line(s) of symmetry for two-dimensional shapes. Students will: •

identify a line of symmetry for each shape by tracing the fold.

The teacher will bring the class together for a discussion of learning and conclude the lesson with an Exit Ticket before returning to the Hook to apply learning and solve.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

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TWO-DIMENSIONAL SHAPES

Two-Dimensional Shapes Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

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Acceleration

ACCESSING PRIOR KNOWLEDGE Students use wax craft sticks or chenille stems to build two-dimensional shapes. This activity is intended to assess mastery of the following standard(s): 1.GSR.4.1 Identify common two-dimensional shapes and three-dimensional figures, sort and classify them by their attributes and build and draw shapes that possess defining attributes. 1.GSR.4.2 Compose two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter-circles) and three-dimensional figures (cubes, rectangular prisms, cones, and cylinders) to create a shape formed of two or more common shapes and compose new shapes from the composite shape.

Materials

Preparation

Reusable • • 1.

•

3 Different-colored wax craft sticks or chenille stems (per student) 1 Resealable bag (per student)

Gather enough different-colored wax craft sticks or chenille stems for each student to have 3. Place the materials in a resealable bag for each student.

Explain to students that you will be reviewing different types of shapes and building models of them to show attributes that help name a shape and attributes that do not help name a shape. Remind them that each 2-D shape is special and has speciﬁc attributes. Read the following scenario to the class: I’m going to call out a shape by its name. As fast as you can, I need you to build three of that shape using your materials. You’re only going to get 1 minute to build three examples of the shape I name. Are you ready? Let’s go! One by one, give students the italicized directions listed below for building. Make sure to look at their shapes carefully to see that they have a clear understanding of the attributes that each shape has. Discuss how students are building the twodimensional shapes by using the questions that follow each direction. a.

TWO-DIMENSIONAL SHAPES

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Build a small, medium, and large circle. i. How are these shapes the same? They are all closed shapes. They are all circles.

FACILITATION TIP Before reading this scenario, allow students time to manipulate the materials. Set a timer to give students some exploration time. Consider suggesting that they “make a few shapes” if they need some guidance. FACILITATION TIP Students may need fresh sticks or stems as they progress through making the many shapes. FACILITATION TIP To help monitor students’ shapes, consider having students hold up their “best” shape for each set.

ii. How are these shapes different? They are different sizes. iii. How many sides do these shapes have? 0

iv.

How many vertices do these shapes have? 0

What attribute of these shapes would not help a person build or draw a circle? Their sizes would not help a person build or draw a circle.

Build three triangles that face different directions. i. How are these shapes the same? They are all closed shapes. They are all triangles.

FACILITATION TIP Be prepared to clarify what “face different directions” means.

ii. How are these shapes different? They are facing different directions. iii. How many sides do these shapes have? Three iv.

How many vertices do these shapes have? Three

What attribute of these shapes would not help a person build or draw a triangle? The direction they are facing would not help a person build or draw a triangle.

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TWO-DIMENSIONAL SHAPES

Two-Dimensional Shapes Lesson Calendar and Accessing Prior Knowledge c.

Build three squares that are the same size. i. How are these shapes the same? They are all closed shapes. They are all squares. ii.

How are these shapes different? They are different colors.

iii. How many sides do these shapes have? Four

FACILITATION TIP Successfully creating a hexagon may be diﬃcult for some students with limited ﬁne motor skills. Provide support or alternatives.

iv.

How many vertices do these shapes have? Four

What attribute of these shapes would not help a person build or draw a square? Their color would not help a person build or draw a square.

Build three hexagons. i. How are these shapes the same? They are all closed shapes. They are all hexagons. ii.

How are these shapes different? Answers may vary. They are different colors/sizes.

iii. How many sides do these shapes have? Six STEMscopes Tip Located along the scope menu, the Acceleration section contains activities for students who have demonstrated they have mastered the skills and concepts of the scope. Enrichment options for all grades include an opportunity to explore ways math is connected and applied in real-world events. In Kindergarten through Grade 2, students make connections between math, science, and social studies through a hands-on activity. In Grades 3–5, students have the opportunity to express their creativity in an openended task. All activities are designed to help students reinforce their learning and extend their mathematical knowledge.

How many vertices do these shapes have? Six

What attribute of these shapes would not help a person build or draw a hexagon? Answers may vary. Their color/size would not help a person build or draw a hexagon.

e. Build three rectangles that are turned in different ways. i. How are these shapes the same? They are all closed shapes. They are all rectangles. ii.

How are these shapes different? They are facing different directions.

iii. How many sides do these shapes have? Four

FACILITATION TIP Use this class discussion to begin a posted class list of essential vocabulary to use during the upcoming scope. Refer to Picture Vocabulary.

iv.

How many vertices do these shapes have? Four

What attribute of these shapes would not help a person build or draw a rectangle? The direction they are facing would not help a person build or draw a rectangle.

Facilitate a class discussion about building two-dimensional shapes. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a.

What attributes help name a shape? Closed/open shape, number of sides, number of vertices

What attributes do not help name a shape? Color, size, direction it is facing

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

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Two-Dimensional Shapes Hook – Designing a Math Journal Cover ACTIVITY PREPARATION Students draw two-dimensional shapes based on given attributes. Students also name the shapes and the numbers of sides, vertices, and angles.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

•

Reusable • •

Plan to show the video. Part II

1 Pack of crayons or colored pencils (per student) 1 Phenomena Video (per teacher)

•

Gather enough packs of crayons or colored pencils for each student to have one pack. Print the Student Handout for each student.

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

2. FACILITATION TIP

Project this scenario for students to read along with you. After reading it aloud, ask students to locate and share the math words they notice.

4. FACILITATION TIP

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Lacy wanted to design the cover of her math journal with different two-dimensional shapes. She planned out her journal cover by drawing it on a piece of paper. Lacy drew three different shapes with 4 sides, 4 vertices, and 4 angles. Then, she drew three more shapes: one shape with 5 sides, 5 vertices, and 5 angles; one shape with 6 sides, 6 vertices, and 6 angles; and one shape with 3 sides, 3 vertices, and 3 angles. After she drew them all, she labeled them with their names and the numbers of sides, vertices, and angles. What might the cover of her math journal look like? Discuss the following questions: a.

DOK-1 What information do we know? Lacy drew 2-D shapes on a piece of paper. She drew three different shapes with 4 sides, 4 vertices, and 4 angles. Then she drew three more shapes: one shape with 5 sides, 5 vertices, and 5 angles; one shape with 6 sides, 6 vertices, and 6 angles; and one shape with 3 sides, 3 vertices, and 3 angles. She labeled them with their names and the numbers of sides/vertices/angles.

DOK-1 What information do we need to ﬁnd out? What shapes did she draw in her math journal?

Take time to review the terms sides, vertices, and 2-D with students. If angles is a new vocabulary word, take time to use the visual dictionary and teach it.

FACILITATION TIP

Select students to share how they might solve the problem with the class.

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities.

Part II: Post-Explore 1. 118

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Discuss the following questions: a.

DOK-1 What information do we know? Lacy drew 2-D shapes on a piece of paper. She drew three different shapes with 4 sides, 4 vertices, and 4 angles. Then, she drew three more shapes: one shape with 5 sides, 5 vertices, and 5 angles; one shape with 6 sides, 6 vertices, and 6 angles; and one shape with 3 sides, 3 vertices, and 3 angles. She labeled them with their names and the numbers of sides, vertices, and angles.

DOK-1 What information do we need to ﬁnd out? What shapes did she draw in her math journal?

Give each student the Student Handout and a pack of crayons or colored pencils. Instruct students to draw and label the two-dimensional shapes Lacy drew in the box on the Student Handout. Remind students to label the shapes with the name, the number of sides, the number of vertices, and the number of angles. Discuss the following questions: a.

DOK-1 What shapes did Lacy draw? Answers will vary. Rectangle, square, parallelogram, trapezoid, rhombus, pentagon, hexagon, and triangle

DOK-1 How many sides, vertices, and angles does a hexagon have? 6 sides, 6 vertices, and 6 angles

DOK-1 How many sides, vertices, and angles does a pentagon have? 5 sides, 5 vertices, and 5 angles

DOK-2 Do any of these shapes have more than one name? Answers will vary. The square is also called a rectangle and a rhombus. The rectangle, square, rhombus, and trapezoid are all called quadrilaterals because they have 4 sides.

e. DOK-3 How are the square and rectangle the same, and how are they different? Answers will vary. They both have 4 sides and 4 vertices. The square has 4 equal-length sides. f.

DOK-3 How can you classify the shapes that you drew? Answers will vary. I could draw all the quadrilaterals on one side of the paper and the other 3 shapes on the other side.

TWO-DIMENSIONAL SHAPES

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FACILITATION TIP Provide rulers or other straight edges to help students draw the figures. For students with fine-motor difficulties, provide cutouts from the Supplemental Aids – Math Shapes in the Intervention section. Students can select the shapes based on their attributes and trace around them. FACILITATION TIP Provide students with a word bank of the two-dimensional figure names or display an anchor chart if needed.

FACILITATION TIP Have students compare and contrast other ﬁgures. FACILITATION TIP Challenge students to classify the ﬁgures a different way.

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TWO-DIMENSIONAL SHAPES

Two-Dimensional Shapes Explore 1 – Sorting 2-D Shapes ACTIVITY PREPARATION Students sort shapes according to attributes, including identifying the number of sides and the number of vertices.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

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1 Student Journal (per student) 1 Set of Shape Cutouts (per group) 1 Exit Ticket (per student)

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Reusable • •

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1 Pair of scissors (per student) 1 Resealable bag (per group)

Consumable •

Plan to have students work in groups of 2 or 3 to complete this activity. Gather scissors and glue for each student. Print and cut the Shape Cutouts for each group, and place them in a resealable bag. Laminate them for future use, if desired. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Math Shapes Supplemental Aids element in the Intervention section.

1 Glue stick (per student)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Let students know that as they sort the shapes, you will record a list of all the different categories you see being used. Record attributes for students to reference. This visual reference can be used to help students who are reluctant to start and it may also encourage students to refine their chosen categories and/or to consider other attributes. FACILITATION TIP Review the term attribute. Come up with a class definition and post it on the board for students to reference. (An attribute is a characteristic used to identify or define a specific type of shape.)

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Read the following scenario to the class: Mrs. Jones’s class went on a ﬁeld trip to the City Zoo. They saw a lot of shapes around them as they traveled to the zoo and also once they got to the zoo. When they got back to school, they drew the shapes they saw and sorted them in their math journals. What do you think their shape sorts looked like? Divide the class into groups of 2 or 3, and direct students’ attention to the Shape Cutouts. Allow students a few moments to discover the manipulatives and experience how they work with their groups. Instruct students to work together to sort the shapes. Students get to decide how they want to complete their sorts. If they sort by color, prompt them to sort another way. They can sort into however many groups they wish. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 What helped you decide how to group the shapes? Answers will vary. These shapes all had 4 sides, and these shapes did not have 4 sides.

DOK-2 How did you label your groups? Answers will vary. Quadrilaterals/ nonquadrilaterals; 4 sides, more than 4 sides, fewer than 4 sides; rectangles, nonrectangles

DOK-3 How are these shapes the same? How are they different? Answers will vary. All of these shapes are 2-D, but some have more than/fewer than/exactly four sides or vertices.

DOK-2 What are some attributes of these shapes? Answers will vary. These all have at least 3 straight sides and 3 vertices. These shapes have 6 sides and 6 vertices. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

e. DOK-1 How many sides does this shape have? Answers will vary. 0, 2, 3, 4, 5, 6 f.

DOK-1 How many vertices does this shape have? Answers will vary. 0, 1, 3, 4, 5, 6

DOK-3 What do you notice about the number of sides compared to the number of vertices of each shape? The number of sides is the same as the number of vertices.

h. DOK-3 How would we sort these shapes into polygons vs. nonpolygons? Answers will vary. I could sort the quadrilaterals to polygons because they have all straight sides. All other shapes with curves would be non-polygons. 5. 6. 7.

Give ive each student a Student Journal, and ask students to draw a picture of their sort. Students will work together to answer the reﬂection questions. After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

TWO-DIMENSIONAL SHAPES

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FACILITATION TIP Provide students who have ﬁne-motor diﬃculties with extra cut shape sets so they can glue them directly into the Student Journal.

Math Chat • • •

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DOK-3 What attributes do shapes ___ and ___ have in common? (Insert letters A–T.) L and T are both hexagons because they have 6 sides. DOK-3 What attributes do shapes ___ and ___ have that are different? (Insert letters A–T.) C has 5 sides, and E has 4 sides. DOK-2 Which shapes would be classiﬁed as polygons? Why? Triangles, quadrilaterals, pentagons, and hexagons. Each of these shapes have all straight sides with no curve. DOK-1 What makes a shape a quadrilateral? Quadrilaterals are 2-D shapes that have four sides and four vertices. DOK-2 Which shapes are quadrilaterals? A, D, E, G, I , O, and S. DOK-1 What attributes make a shape a rectangle? Rectangles have four sides, four vertices, and opposite sides that are the same length. DOK-2 Which shapes are rectangles? G and I. DOK-3 What do you notice about shapes J, M, P, and R? These shapes are not circles, triangles, squares, rectangles, rhombuses, trapezoids, pentagons, or hexagons. DOK-3 Describe the different ways your group sorted the shapes. We sorted quadrilateral/nonquadrilateral, straight sides/curved sides, and fewer than 3 sides/more than 3 sides.

STEMscopes Tip The STEMscopes Teacher Toolbox, found under the Scopes tab on the menu bar, features a wide variety of resources and tools to support teachers with instruction. Resources include essentials like lesson-planning documents, blackline masters, a parent letter, and more. Monitoring Tools are provided to help students selfevaluate. Intervention strategies for a wide variety of developmental issues are also included. Communicate Math consists of strategies to help facilitate math discussions. The toolbox also includes tools to help understand and disaggregate student data.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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Two-Dimensional Shapes Explore 2 – Classifying 2-D Shapes ACTIVITY PREPARATION Students classify two-dimensional shapes according to attributes.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

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1 Student Journal (per student) 1 Set of Shape Cutouts (per group) 1 Exit Ticket (per student)

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Consumable • •

Plan to have students work in groups of 4 to complete this activity. Print a set of Shape Cutouts on card stock for each group. Cut out the shapes along the dashed lines. Laminate them for future use, if desired. Create 3 bags per group so that each group has all the Shape Cutouts. Label the outside of each bag with “Mystery Bag” and the bag number. • • •

3 Brown paper bags (per group) 3 Pieces of card stock (per group) • •

Bag 1 – square, rectangle, rhombus Bag 2 – 2 triangles, hexagon, pentagon Bag 3 – circle, crescent, cloud, heart

Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Math Shapes Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION FACILITATION TIP Model this process with one shape. Emphasize the importance of students taking their time to feel around the entire border of the shape. Name deﬁning attributes, such being a 2-D closed shape with or without a certain amount of straight sides and with or without a certain amount of vertices.

2. 3.

FACILITATION TIP All of the cutouts are closed figures. It may be beneficial to draw a large example of an open figure for students to consider in determining whether or not a figure is closed.

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Read the following scenario to the class: As I was walking into class, I saw that someone had left these Mystery Bags on the tables, and this note was on my desk: “Guess what shapes are in the bag without looking.” Now, what does that mean? I could guess and guess and guess and never guess correctly. How am I supposed to guess without looking? Divide the class into groups of 4, and distribute 3 Mystery Bags to each group. Instruct students to take turns placing their hands in the bag and feeling one shape. Since these are card stock cutouts, students will gently need to rub their ﬁngers along the borders of the shape. They will describe the shape to their groups. Encourage students to list the attributes and the name if they know it. After describing the shape, students will pull it out of the bag for everyone to see. Once the shape has been shown and identiﬁed, encourage students to discuss how many angles they see on the shape and how this number relates to the shape’s number of sides and vertices. Each student will keep the shape and pass the bag to the next person in the group. Monitor and talk with students as needed to check for understanding using the following guiding questions: a.

DOK-2 What attributes does your shape have? Answers will vary. My shape has four sides with all the same length. It also has four vertices and four angles.

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

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Give each student a Student Journal, and ask students to record the names and attributes of the shapes in each bag. Encourage students to discuss what the shapes have in common, record their answers, and answer the reﬂection question. After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

DOK-2 What attributes did your shape have? The square had 4 sides, 4 vertices, and 4 angles. DOK-1 What are the names of the shapes in bag 1? Square, rectangle, and rhombus. DOK-1 What special name do we call all shapes with 4 sides, 4 vertices, and 4 angles? Quadrilaterals DOK-3 How do you think I chose the shapes to go in bag 1? Bag 2? Bag 3? I think you put all the shapes with 4 sides, 4 vertices, and 4 angles in bag 1. Shapes in bag 2 do not have 4 sides, 4 vertices, or 4 angles. Shapes in bag 3 have no sides. DOK-3 Which shapes could not be put in a group with any of the others? Why? The circle, heart, crescent, and cloud cannot be put in a group with all of the others. These shapes do not have straight sides. DOK-3 How are the shapes in bag 1 different from the shapes in bag 2? They all have 4 sides, 4 vertices, and 4 angles. They are all quadrilaterals. DOK-3 How are the shapes in bag 1 and bag 2 different from the shapes in bag 3? They are all shapes with straight sides. Bag 3 shapes do not have straight sides. Each shape in bag 1 and bag 2 has an equal number of sides, vertices, and angles. DOK-3 How would you sort the bags into polygons vs. non-polygons? Bag 1 and bag 2 are all polygons; they all have straight sides and are closed shapes. Bag 3 shapes do not have straight sides; they are non-polygons.

Post-Explore 1. 2. 3.

Acceleration

DOK-1 Does your shape have another name? If so, what is that name? Answers will vary. The square can also be called a rectangle. The square can also be called a rhombus or a quadrilateral.

Math Chat •

Intervention

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Provide a word bank for students to use to record the names of the shapes. Some students may need a copy of the word bank printed and on their desk. FACILITATION TIP

TWO-DIMENSIONAL SHAPES

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During the Math Chat, several vocabulary words are featured: triangle, pentagon, hexagon, and octagon.

STEMscopes Tip Daily Numeracy, located in each grade level under the Scopes tab, provides short activities focused on developing students’ mental math strategies and number sense. These activities are designed to increase students’ ability to reason with numbers and build their thinking and reasoning skills. A Daily Numeracy overview, a description of what it looks like in the classroom, and an example of a daily numeracy plan give teachers the tools to implement the program. In addition, links in a Daily Numeracy Teacher Toolbox provide teachers with resources they can use alongside the activities to help students develop an understanding of the relationships and connections in math. FACILITATION TIP Before students complete this Exit Ticket, check to see if they can read and spell the required math words.

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Two-Dimensional Shapes Explore 3 – Drawing 2-D Shapes ACTIVITY PREPARATION Students draw different shapes based on attributes.

Standards for Mathematical Practice • •

MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

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1 Student Journal (per student) 1 Set of Task Cards (per group) 1 Exit Ticket (per student)

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Reusable • •

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1 Set of markers/crayons/colored pencils (per group) 1 Resealable bag (per group)

Plan to have students work in 4 groups to complete this activity. Print and cut out a set of Task Cards, and place them in a resealable bag for each group. Prepare a set of markers, crayons, or colored pencils for each group. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Math Shapes and Geoboard Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Provide access to rulers that students can use as a straight edge. FACILITATION TIP Prompt students to highlight or underline deﬁning attributes. This will help them keep track of all necessary information. FACILITATION TIP

2. 3. 4.

Prompt students to make sure that the sections labeled by letters on the Student Journal correspond with the letters on the Task Cards.

Read the following scenario to the class: Today, we are going to be shape artists. A math manipulative company has asked us to draw shapes for other students to use. You are tasked with drawing shapes from the given attributes. Can you help the company draw new shapes? Direct students’ attention to the Task Cards and set of markers, crayons, or colored pencils. Give each student a Student Journal. Instruct students to select a Task Card. Students will draw a shape using a pencil to include the attributes described on the card. Encourage students to color the shape. When ﬁnished drawing the shape, students will list the attributes, write the name of the shape, and then select a new Task Card. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-3 What are the attributes of your shape? Answers will vary. It is a quadrilateral with 4 equal sides and 4 vertices.

DOK-2 How will you draw this shape? Answers will vary. I will draw 4 equal lines and 4 right angles.

DOK-1 What is the name of your shape? Answers will vary. Square

FACILITATION TIP Students with fine motor difficulties may also benefit from Supplemental Aids – Math Shapes. Provide cut shape sets that students can trace or glue into the Student Journal instead of drawing the shapes freehand.

6. 7.

After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Ask students who ﬁnish early to compare Student Journals to see if they are in agreement about each shape drawing. 124

Engage

Explore

Explain

Elaborate

Evaluate

Math Chat •

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DOK-3 How did you draw your shapes? I thought of all the attributes. Then, I sketched the shape with a pencil ﬁrst, checked that I had included all the attributes, and then colored the shape in with a marker. DOK-3 Could you have drawn more than one shape with the given attributes? When it said 4 sides, 4 angles, and 4 vertices with opposite sides equal, I could have created a rectangle, square, or rhombus. DOK-3 What do you notice about your shape compared to the other shapes in your group? All of our shapes had 4 sides, 4 angles, and 4 vertices, but the shapes looked different. They were different sizes or were turned different ways. I drew a square, while someone else drew a rectangle. They all correctly included the attributes. DOK-3 Do all the shapes in this table look the exact same? Why do you think they all look the same or different? We drew the shapes with different colors. Also, since many shapes have similar attributes, different shapes could ﬁt for the same Task Card.

Intervention

Acceleration

STEMscopes Tip Within the Engage section, Accessing Prior Knowledge is designed to determine what students have learned in the past about a concept before moving on. Activities are designed to assess students’ proﬁciency levels and ﬁnd learning gaps, which can be addressed using the Foundation Builder, also found in the Engage section.

TWO-DIMENSIONAL SHAPES

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Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. When you preview this Exit Ticket, clarify Complete the Anchor Chart as a class. your criteria for success. Provide a word bank for students and allow some students Have each student complete their Interactive Notebook. to draw fewer shapes than required. Challenge some students to draw more than the required ﬁve shapes. Notes

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Two-Dimensional Shapes Explore 4 – Identifying Lines of Symmetry ACTIVITY PREPARATION Students identify line(s) of symmetry for two-dimensional shapes.

Standards for Mathematical Practice • • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials Printed • • • •

1 Student Journal (per student) 1 Set of Party Invitations (per group) 1 Set of Thank-You Notes (per group) 1 Exit Ticket (per student)

Preparation • • •

• • • • • •

Reusable • • •

2 Quart-size resealable bags (per group) 2 Markers (per group) 6 Envelopes, 4.125” × 9.5” (per group)

Plan for students to work in groups of 4 to complete this activity. Print one set of Party Invitations for each group. Cut out the outlined shapes, and place them and a marker in a resealable bag. Print one set of Thank-You Notes for each group. Cut out the outlined shapes. Fold each shape in one way that either shows one line of symmetry or does not show one line of symmetry:

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Hexagon – line of symmetry Square – no line of symmetry Triangle – no line of symmetry Rectangle – line of symmetry Pentagon – line of symmetry Octagon – no line of symmetry

Place each of the folded Thank-You Notes in their own separate envelope. Do not seal the envelopes. Place all of the envelopes and one marker in a resealable bag for each group. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Math Shapes and Geoboard Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION Part I FACILITATION TIP

Print and project this scenario; read it with students. Underline the math words; fold, half, lines, symmetry, shape. 2.

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Read the following scenario to the class: Priscilla is about to turn nine! Her mom picked up some invitations that were shaped like different two-dimensional ﬁgures. Priscilla ﬁlled in the important information on each invitation all by herself. Before she put them in their envelopes and mailed them to her friends, she wanted to fold them in half along one of the lines of symmetry for the shape. Can you help Priscilla fold her party invitations along a line of symmetry for each shape? Divide students into groups of 4. Give a bag of Party Invitations and a marker to each group. Allow students a few moments to discover the manipulatives and experience how they work with their group. Instruct students to take out each party invitation and fold it in half while making sure the halves that are created are equal. They should identify a line of symmetry for each shape by tracing the fold they created with the marker. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What two-dimensional shape is this party invitation shaped like? Answers will vary. Hexagon, square, triangle, rectangle, pentagon, or octagon

DOK-2 How are you folding the party invitation? In half

DOK-3 How do you know you folded the party invitation in half? We created two pieces that are equal.

DOK-1 What does the fold you created represent? A line of symmetry

e. DOK-3 What do you notice about the traced line of symmetry you created? The two halves are equal. The pieces on either side of the fold/ traced line of symmetry are equal. f.

DOK-3 Can you fold the party invitation in a different way to show a different line of symmetry? Each ﬁgure should have more than one line of symmetry. Students should model various lines of symmetry.

Give each student a Student Journal, and ask students to draw the line of symmetry they created for each ﬁgure in Part I. Students should work together to answer the Part I question. After students have completed Part I, bring the class together as a whole group.

Part II 1.

6. 7.

Acceleration

Monitor and talk with students as needed to check for understanding using the following guiding questions: a.

Intervention

Read the following scenario to the class: Priscilla had an awesome ninth birthday party! Her friends gave her some fun gifts. She wrote her thank-you notes and decided to let her little brother fold them and put them in the envelopes. Before she sealed each envelope, she took out the notes and noticed her brother folded some of them along a line of symmetry, and some were not folded along a line of symmetry. Can you identify which thank-you notes were folded along a line of symmetry and which ones were not folded along a line of symmetry? Students should continue working with their groups from Part I. Give each group a set of envelopes containing the Thank-You Notes and a marker. Allow students a few moments to discover the manipulatives and experience how they work with their groups. Instruct students to take out each Thank-You Note from each envelope. They should notice that each note has already been folded. Using a marker, they should trace the line on the pre-folded notes. Monitor and talk with students as needed to check for understanding using the following guiding questions: a.

DOK-3 How many folds do you see on this thank-you note? One

DOK-3 What did you notice about the fold once you traced it? Answers will vary. I see there are two pieces. I see that the pieces are/are not equal.

DOK-3 Is this a line of symmetry? Explain how you know. Answers will vary. Yes, this is a line of symmetry because the two halves are equal in size. No, this is not a line of symmetry because the two halves are not equal in size.

Students should draw lines on each shape on Part II of their Student Journals to show how the ﬁgure was folded. They should write “yes” or “no” to tell whether the line they drew was or was not a line of symmetry, and then they should explain their reasoning. Instruct them to answer the Part II question. After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP It may be challenging for students to realize that there are several different ways to form lines of symmetry in a particular shape. Take pictures of all the lines of symmetry that students generate using the square (there are 4) or octagon (there are 10). Share these pictures during the Math Chat and/or post them onto a piece of chart paper for students to reference moving forward.

TWO-DIMENSIONAL SHAPES

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FACILITATION TIP Challenge early finishers to write a definition for the term “line of symmetry” and invite them to share their definitions during the math chat. FACILITATION TIP Print and project this scenario. Read it with students. Underline the math words; fold, lines, symmetry, shape.

STEMscopes Tip Content Support, located in the Home section of each scope, is primarily for teachers who need additional background knowledge to fully support student understanding. This element includes the reasons a concept is being taught a certain way by explaining what the students have already learned; misconceptions students may have about the concepts being taught; obstacles teachers might encounter throughout the scope; what students will be learning, including the mathematical vocabulary; and detailed strategies for instruction that include examples and assessment questions. Finally, teachers are given insight to the concepts students will learn next.

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Two-Dimensional Shapes Explore 4 – Identifying Lines of Symmetry Math Chat • • •

• STEMscopes Tip The Math Chat provides a forum for students to collaboratively discuss the concepts taught in the Explore lesson. This rich discussion helps students develop their number sense, mathematical vocabulary, and math thinking skills. A Math Chat is located at the end of each part of the Explore lesson and is also available in printable form.

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DOK-1 What is a line of symmetry? A line of symmetry is an imaginary line that creates two equal halves on a figure. DOK-2 How can you identify a line of symmetry on a two-dimensional shape? You can fold the figure in half to create two equal or identical pieces. DOK-2 How do you know if a line of symmetry was created? You have to look at the halves on either side of the line of symmetry to see if they are equal or identical. DOK-3 What do you notice about how your group folded the shapes to create lines of symmetry and how other groups folded theirs? What does this tell you about a shape? Our line of symmetry looks different than the other group’s. This tells us that figures can have more than one line of symmetry. DOK-2 Can a shape have more than one line of symmetry? It depends on the figure, but yes, some figures can have more than one line of symmetry. DOK-2 Which shape in Part I only had one line of symmetry? All shapes in Part I had more than one line of symmetry. DOK-2 Which shapes in Part II did have a line of symmetry once you traced the folds? Hexagon, rectangle, pentagon. DOK-3 How do you know these were lines of symmetry? The halves on either side of the fold/traced line were equal. DOK-2 Which shapes in Part II did not have a line of symmetry once you traced the folds? Square, triangle, and octagon DOK-3 How do you know these were not lines of symmetry? The halves on either side of the fold/traced line were not equal. DOK-4 When might you need to identify lines of symmetry at home? When I am cutting a cake to make sure people get equal-sized pieces.

Post-Explore FACILITATION TIP This Exit Ticket could be used as a pretest and again as a post test to see how to focus the instruction.

1. 2. 3. 4.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

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Two-Dimensional Shapes Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Sorting 2-D Shapes Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Classifying 2-D Shapes Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Drawing 2-D Shapes

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Identifying Lines of Symmetry

Independent practice assignment that gives students an opportunity to demonstrate their learning

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Student Council A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Carlos’s Global Coin Collection

2-D Shape Attributes

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Designing a Recreation Center

Match a Shape to Attributes

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

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Students who are still acquiring the concept and need remediation

TWO-DIMENSIONAL SHAPES

Two-Dimensional Shapes

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

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 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

What prompts will be used?

What does mastery look like?

TWO-DIMENSIONAL SHAPES

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I can describe two-dimensional shapes having speciﬁed attributes such as sides, vertices, and/or angles.

I can compare two-dimensional shapes having speciﬁed attributes such as sides, vertices, and/or angles.

I can sort two-dimensional shapes having speciﬁed attributes such as sides, vertices, and/or angles.

I can identify at least one line of symmetry in everyday objects to describe each object as a whole.

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SCOPE 1

Three-Dimensional Solids Scope Introduction SCOPE SUMMARY Students describe, compare, and sort 3-D solids, including rectangular prisms, cubes, cylinders, spheres, and cones given a set of attributes. They explore the relationships between cubes and rectangular prisms by observing the similarities and differences of their attributes. Additionally, students draw 3-D solids with given speciﬁed attributes.

Student Expectations

2.GSR.7.1 Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In first grade, students distinguish between defining attributes and nondefining attributes, and they build and draw shapes that possess defining attributes. Students compose three-dimensional solids (cubes, rectangular prisms, cones, and cylinders) to create composite solids.

In third grade, students use precise language to identify and describe the properties of threedimensional solids as they make generalizations about properties that are shared among categories of solids.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

identify common two-dimensional shapes and three-dimensional ﬁgures.

•

sort and classify the shapes by their attributes.

•

build and draw shapes that possess deﬁning attributes.

For the Hook, students are presented with a scenario involving their school and competing to see which class will have their 3-D structure showcased in the foyer. Students will: •

create a structure with speciﬁc attributes.

•

classify, draw, and design a structure a 3-D solids.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

In this exploration, students will solve a real-world scenario involving helping their mom organize birthday party supplies that have been purchased. Students will:

Explore 3

•

Explore 2

Sorting 3-D Solids

sort 3-D solids based on attributes.

Classifying 3-D Solids In this exploration, students will continue their learning of 3-D solids with a scenario involving a local museum needing students to help group shapes based on attributes for an exhibit. Students will: •

classify solids based on speciﬁc attributes.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

After students have solved the scenario, they discuss their learning with the class and complete an Exit Ticket.

Relationships between Cubes and Rectangular Prisms

Drawing 3-D Solids

In this exploration, students will explore the relationships between cubes and rectangular prisms by observing the similarities and differences of their attributes. Students will: •

complete a Venn diagram to compare two solids.

•

decide which block would work the best to make a die for a board game.

Explore 4

Explore 1

EXPLORE ACTIVITIES

THREE-DIMENSIONAL SOLIDS

Home

In this exploration, students will learn through solving a real-world scenario about the STEMscopes Toy Factory who needs help designing new blocks. Students will: •

draw 3-D solids with given speciﬁed attributes.

After completing the activity, the teacher will bring the class together for a discussion of their learning, have students complete an Exit Ticket for assessment, and have students revisit the Hook to solve.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

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Three-Dimensional Solids Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

136

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students play a game in order to distinguish between defining and nondefining attributes of a three-dimensional solid. This activity is intended to assess mastery of the following standard(s): 1.GSR.4.1 Identify common two-dimensional shapes and three-dimensional figures, sort and classify them by their attributes and build and draw shapes that possess defining attributes.

Materials

Preparation

Printed •

1 Set of Three-Dimensional Solid Cards (per class)

• •

Consumable • • •

1 Deﬁning Attributes sign (per class) 1 Nondeﬁning Attributes sign (per class) 1 Roll of tape (per teacher)

•

THREE-DIMENSIONAL SOLIDS

Home

Print the Three-Dimensional Solid Cards. Create and hang a Deﬁning Attributes sign and a Nondeﬁning Attributes sign at two separate, easily accessible locations in the classroom. Prepare music to play while students are moving around the room.

Procedure and Facilitation Points 1. 2.

3. 4.

Inform students that they will be playing Musical Attributes today. They will have 10 seconds to find and stand on the correct side of the room—the Defining Attributes side or the Nondefining Attributes side. Ask students to stand up and start walking as the music is playing. When the music stops, show one of the Three-Dimensional Solid Cards, and call out an attribute. Mix up the attributes called so both defining attributes and nondefining attributes are called randomly. Give students 10 seconds to find their way to the correct gathering spot. Repeat until all cards with solids have been shown and various attributes have been announced. Facilitate a class discussion after each attribute to discuss why some attributes are defining and others are nondefining. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers and to check for understanding and misconceptions. Ask the following questions: a.

What are some examples of deﬁning attributes of a sphere? Round like a ball; 0 faces, 0 edges, 0 vertices

What are some examples of nondeﬁning attributes of a sphere? It’s blue; it’s large; it’s bouncy.

What are some deﬁning attributes of a cone? 1 apex, 1 face, 0 edges

What are some nondeﬁning attributes of a cone? It’s tall; it’s orange; it’s ﬂexible; it’s upside down.

e. What are some deﬁning attributes of a cylinder? 2 faces, 0 edges, 0 vertices f.

What are some nondeﬁning attributes of a cylinder? It’s tall or short; it’s metal, it’s shiny; it’s silver; it’s sideways or right side up.

What are some deﬁning attributes of a cube? 6 faces, 12 edges, and 8 vertices; 24 right angles (4 angles per face)

FACILITATION TIP Take time to determine whether students understand the word attributes. FACILITATION TIP If space is limited, consider having students use hand signals for defining and non-defining attributes. FACILITATION TIP Create a class two-column chart or list of defining and non-defining attributes and post it in the classroom.

STEMscopes Tip The Show What You Know activities, located in the Explain section, allow students to independently demonstrate understanding and practice new skills after exploring the concepts presented in each Explore lesson. These assignments provide insight into student learning and help guide teachers’ future instruction.

h. What are some nondefining attributes of a cube? It’s colorful; it’s small; it’s hard. i. What are some defining attributes of a rectangular prism? 6 faces, 12 edges, and 8 vertices; 24 right angles (4 per face) j. What are some nondefining attributes of a rectangular prism? It’s brown; it’s made of paper; it’s right side up; it’s large. 5.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP This Foundation Builder provides a good review of deﬁning attributes. Consider using it with the whole class either before or after this section. 137

THREE-DIMENSIONAL SOLIDS

Three-Dimensional Solids Hook – Building a Structure ACTIVITY PREPARATION Students draw designs of structures that include three-dimensional solids, and students also classify the solids.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

•

Reusable • •

Plan to show the video. Part II

1 Set of three-dimensional solid manipulatives (per group) 1 Phenomena Video (per teacher)

• •

Plan to divide the class into groups of 3 or 4 to complete this activity. Gather a set of three-dimensional solids and other items students can use to design their structure for each group. Print the Student Handout for each student.

Consumable • • • •

1 Toilet paper roll (per group) 1 Paper towel roll (per group) 1 Tissue box (per group) 1 Cone-shaped party hat (per group)

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

FACILITATION TIP

Research and project some art examples made of 3-D objects to generate ideas to lead the discussion.

4. FACILITATION TIP

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: The principal asked our class to draw a design of a structure to be placed in the foyer of the school for others to learn more about three-dimensional solids. Each group in our class will need to turn in a sketch of their structure. The structures will be judged to decide which one will be showcased in the foyer. Work with your group to draw a design of a structure that includes the following three-dimensional solids: a solid with 1 apex and 1 circular face, a solid with 2 circular faces and a curved surface, and two different solids with six faces. You may also add any other solids you wish. The attributes of each solid must be labeled with the numbers of faces, edges, and vertices. Discuss the following questions: a.

DOK-1 What information do we know? We have to draw a structure using 3-D solids. We must draw a solid with 1 apex and 1 circular face, a solid with 2 circular faces and a curved surface, and two different solids with six faces each. We can also add any other solids we want. We have to label the numbers of faces, edges, and vertices for each solid.

DOK-1 What information do we need to ﬁnd out? What will our structure look like? What are the names of the solids will we use? How many faces, edges, and vertices does each solid have?

Students can discuss their initial ideas with a partner and write them on sticky notes/dry erase boards. After the Explore activities, revisit their initial ideas.

5. 6. 138

Engage

Explore

Explain

Elaborate

Evaluate

Part II: Post-Explore 1. 2.

3. 4.

Acceleration

STEMscopes Tip

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What information do we know? We have to draw a structure by using 3-D solids. We must draw a solid with 1 apex and 1 circular face, a solid with 2 circular faces and a curved surface, and two different solids with six faces each. We can also add any other solids we want. We have to label the numbers of faces, edges, and vertices for each solid.

DOK-1 What information do we need to ﬁnd out? What will our structure look like? What are the names of the solids will we use? How many faces, edges, and vertices does each solid have?

Divide the class into groups of 3 or 4. Distribute a set of three-dimensional solids and other materials you have gathered (paper towel rolls, toilet paper rolls, and tissue boxes) to help each group as they are drawing their designs. Give each student the Student Handout. Allow time for students to explore the materials to create structures. They may build their structures and then sketch the designs on the Student Handout. Remind students to label each solid with the number of faces, edges, and vertices. Discuss the following questions: a.

DOK-1 What is a three-dimensional solid? A ﬁgure that has three dimensions, such as length, width, and height

DOK-1 What three-dimensional solids did you use? Cube, rectangular prism, cylinder, and cone

DOK-3 How can you classify the solids you used? Answers will vary. I can put the cube and rectangular prism together because a cube is a rectangular prism. I can put the cone and cylinder together because they each have at least 1 circular face. I can put the cylinder, cube, cone, and rectangular prisms together because they have faces.

Intervention

DOK-1 How many vertices, faces, and edges does each of your solids have? Answers will vary. See below for examples.

Cube

Cone

Cylinder

6 faces

1 face

2 faces

8 vertices

1 apex

0 vertices

12 edges

0 edges

Sphere

Rectangular prism

0 faces

6 faces

0 vertices

8 vertices

0 edges

12 edges

Fluency Builders are hands-on games that motivate students to practice the concepts from the scope. Located in the Elaborate section, these studentled games include printable studentfriendly instruction sheets detailing how the games are played as well as all the materials needed for game play.

THREE-DIMENSIONAL SOLIDS

Home

FACILITATION TIP Students can bring in objects from home. Provide a checklist for students to use as they compare their ideas to the structure requirements. FACILITATION TIP Provide sticky notes to label the attributes and their solids on their sketch. Students can take a Gallery Walk and provide feedback to other groups.

STEMscopes Tip In Grades 2–5, a Standards-Based Assessment can be found in the Evaluate section. This assessment is designed to allow students to demonstrate their mastery of the standards. Multiple-choice and gridded response questions reﬂect the formats found on state tests. The assessment can be administered and scored multiple ways: digitally, printed, or edited to meet students’ needs.

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Three-Dimensional Solids Explore 1 – Sorting 3-D Solids ACTIVITY PREPARATION Students sort three-dimensional solids based on attributes.

Standards for Mathematical Practice • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Real-World Solid Cutouts (per group, optional) 1 Exit Ticket (per student)

• • • • •

Reusable • • •

Plan to have students work in groups of 3 or 4 to complete this activity. Prepare a container with the following real-world three-dimensional solids (or solids of your choice):

1 Set of real-world three-dimensional solids (per group) 1 Container (per group) 1 Resealable bag (per group, optional)

•

• •

Party hat, traﬃc cone, and ice-cream cone (cone) Candle and soda can (cylinder) Die (cube) Present (rectangular prism) Soccer ball and marble (sphere)

If real-world solids are not available, print and cut out a set of Real-World Solid Cutouts for each group. Place them in a resealable bag. Laminate them for durability, if desired. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our 3-D Objects and 3-D Nets Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION 1.

140

FACILITATION TIP

Each group can sort the 3-D objects differently and share their ideas in the Math Chat.

Read the following scenario to the class: It’s your birthday! Mom has purchased everything for your party, but she needs help organizing it. She wants every item with similar attributes or characteristics together. Can you help mom get ready for your party? Divide the class into groups of 3 or 4 and direct students’ attention to the realworld three-dimensional solids in the container. Allow students a few moments to discover the manipulatives and experience how they work with their group. Instruct students to sort the three-dimensional solids based on their attributes. Students get to decide how to sort the solids with their groups. Encourage students to sort in many different ways. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP

As you monitor the groups, check for students’ understanding by asking different guiding questions.

DOK-2 How did you sort the solids? Answers will vary. These solids roll, and these solids do not roll.

DOK-2 What attributes does this group of 3-D solids have in common? Answers will vary. These solids have at least one circle-shaped face.

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Give each student a Student Journal, and ask students to record how they sorted the three-dimensional solids in two different ways. Students will discuss and answer the reﬂection question. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the students to a Math Chat to share their observations and learning.

Math Chat • • • • • • •

DOK-2 How did another group sort the 3-D solids? This group sorted by number of faces. DOK-2 What attributes does this group of 3-D solids have in common? These solids have points or vertices. DOK-1 What is another name for point/line/flat side? A point is called a “vertex”; a line is called an “edge”; a flat side is called a “face.” DOK-3 Is there another way to sort these 3-D solids? We could sort by the number of vertices. DOK-2 What can you say about the 3-D solids that roll and their number of angles? The 3-D solids that roll do not have any angles. DOK-2 Can you think of other real-world solids similar to this one? The orange cone in the hallway is like this party hat. DOK-4 Why would you ever need to sort three-dimensional solids at home or other places outside of school? The grocery bagger puts all the rectangular prisms together so they fit into the bag; my mom puts all the cans together in the pantry so they can be stacked.

Intervention

Acceleration

STEMscopes Tip Small-Group Intervention is found in the Intervention section. This handson lesson is used to build student understanding of the concepts covered throughout the scope. The lesson includes Teacher Checklists to help monitor students’ progress and Student Handouts. A short assessment to determine whether students have attained mastery of the skills and concepts being retaught is available in Grades 2-5.

THREE-DIMENSIONAL SOLIDS

Home

FACILITATION TIP Gather some scenes from video games or other real-world examples of how 3-D solids are used in design.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Use your projector to display this Exit Ticket for students and them respond on their own paper.

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Three-Dimensional Solids Explore 2 – Classifying 3-D Solids ACTIVITY PREPARATION Students classify solids based on speciﬁed attributes.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Solid Cutouts (per class) 1 Exit Ticket (per student)

• •

Reusable •

• • • • • •

• •

1 Set of three-dimensional solid manipulatives (per class) Spheres, multiple sizes Cones, multiple sizes Cylinders, multiple sizes Rectangular prisms, multiple sizes Cubes, multiple sizes

Plan to have students work in 5 groups to complete this activity. Print and cut out a set of Solid Cutouts for the class. Laminate them for future use, if desired. Gather several sizes of each three-dimensional solid manipulative for the class. Set up 5 stations by placing cutouts and manipulatives in a container arranged by solid name. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our 3-D Nets Supplemental Aids element in the Intervention section.

5 Containers (per class)

PROCEDURE AND FACILITATION 1.

2. 3.

142

FACILITATION TIP

Have students give an example of each attribute and solid as a review.

Read the following scenario to the class: The local museum has created a new shape exhibit. They grouped the shapes based on attributes but forgot to label the groups with facts for patrons to read as they walk through the exhibit. Can you help the museum label each group before the exhibit opens? Divide the class into 5 groups and place each group at a station. Direct students’ attention to the Solid Cutouts and solid manipulatives at their stations. Allow students a few moments to discover the manipulatives and experience how they work with their groups. Instruct students to discuss the attributes of the solids at their stations and the names of the groups. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-3 What do you notice about these solids? Answers will vary. This group of solids is round. They all roll.

6. 7. 8.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What is this attribute called? Answers will vary. This ﬂat surface is called a face; this line is called an edge; this point is called a vertex; this corner on a face is called an angle.

DOK-2 Based on the attributes that you notice, what would you call this solid? Answers will vary. This solid is called a sphere.

Give each student a Student Journal and ask students to record the names and attributes of the solids at their stations and draw an example of each solid. When students have completed all stations and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the students to a Math Chat to share their observations and learning.

Intervention

Acceleration

FACILITATION TIP Challenge students to ﬁnd real-world examples of each solid from the school, classroom, or home.

THREE-DIMENSIONAL SOLIDS

Home

Math Chat • •

•

• • •

DOK-3 Why do you think the solids were grouped this way? Each group of solids has the same attributes and name. DOK-3 What did you notice about the three-dimensional solids? Threedimensional solids have edges instead of sides like 2-D shapes; they have faces that are made of 2-D shapes that have different types of angles. DOK-3 Why do some solids have angles as an attribute and some do not? Some solids do not have faces, so they cannot have angles. A sphere does not have a face, so it cannot have angles. A cube has 6 faces that are all in the shape of a square, so each face has 4 right angles. DOK-3 How are the cylinder and cone similar? They both have 0 edges. They both roll. DOK-3 What is similar among all of the solids? Solids stand up on their own. They are not flat. DOK-3 Is it more challenging to draw a three-dimensional solid than a twodimensional shape? Why? Yes, it is more challenging because a 3-D solid is not flat, so it is difficult to make it look like it is standing up.

STEMscopes Tip Math Today, found in the Acceleration section, is designed to engage students using real-world videos, photos, or articles provided by the Associated Press in exploring the connections between the current events and math as well as other cross-curricular content. Used as a review or a formative assessment, this activity includes a printable Student Handout and Answer Key.

Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. For this Exit Ticket, be prepared to read Complete the Anchor Chart as a class. the clues aloud to some (or all) students. Underline or highlight the key words with Have each student complete their Interactive Notebook. them as needed. Notes

143

THREE-DIMENSIONAL SOLIDS

Three-Dimensional Solids Explore 3 – Relationships between Cubes and Rectangular Prisms ACTIVITY PREPARATION Students explore the relationships between cubes and rectangular prisms by observing the similarities and differences of their attributes.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Block Pictures (per pair, optional) 1 Exit Ticket (per student)

Reusable • • •

• • • • •

1 Cube-shaped block (per pair) 1 Rectangular prism-shaped block (per pair) 1 Resealable bag (per pair)

Plan to have students work in groups of two to complete this activity. Gather two differently shaped blocks (cube and rectangular prism), and place them in a resealable bag for each pair of students. Print Block Pictures for each pair of students if blocks are not available. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our 3-D Nets Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION FACILITATION TIP Have a collection of dice to show students. Help them count the faces with you as you display each one. FACILITATION TIP Print and project this scenario so students can read it along with you.

STEMscopes Tip The Visual Glossary, located under the Scopes tab, provides a variety of instructional resources. Browse topics alphabetically in English or Spanish. Each topic includes a visual and/or video featuring key vocabulary and concepts. The visuals include text and a speech button with narration. The videos, featuring real-world examples, are 3–15 seconds in length.

144

2. 3. 4.

Read the following scenario to the class: Joseph decides to make his own board game to practice his math facts. He needs one die, but he only has two differently shaped blocks to use instead. Joseph cannot decide which block would work best as a die. Can you help him decide which shape to use? Divide the class into groups of two, and direct students’ attention to the two different blocks or Block Pictures. Allow students a few moments to discover the blocks and experience how they work with their partners. Instruct students to discuss what they notice about the two blocks. Encourage students to compare the attributes of each one as they are deciding which one would work better. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-3 What do you notice about each block? Answers will vary. Both blocks are composed of rectangles. The cube rolls better than the rectangular prism.

b. DOK-2 What three-dimensional solid is this block? Answers will vary. This block is a rectangular prism. This block is a rectangular prism and a cube. c.

DOK-3 How are they the same? Answers will vary. They have the same numbers of edges, vertices, and faces. They are both rectangular prisms. They both have rectangular faces. They both have 4 right angles on each face.

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Give each student a Student Journal, and ask students to complete the Venn diagram to compare the two solids. Instruct students to discuss and decide which block would work the best to make a die for the board game. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the students to a Math Chat to share their observations and learning.

Math Chat •

• • •

•

DOK-3 What similarities and differences did you list when comparing the solids? They are both three-dimensional. They both have the same numbers of edges, vertices, and faces. They both have 4 right angles on each face. The shapes of the faces are not identical. DOK-3 What do you notice about the faces of each prism? The faces are all rectangles, but the cube’s faces are also squares. DOK-3 Is a cube always a rectangular prism? Yes because a square is a special rectangle in which all sides are the same length. DOK-3 Is a rectangular prism always a cube? No, a rectangular prism is not always a cube because the cube’s edges are all equal length and its faces are always squares. Unless the rectangular prism has all edges the same length, it is not a cube. DOK-3 Which block do you think would work best as a die? Why? We think the cube-shaped block will work the best because it rolls better when thrown across the desk. Because all the edges and faces are the same, it seems to roll better. Joseph would want the die to roll well.

Intervention

Acceleration

FACILITATION TIP Depending on your students’ proﬁciency and experience with Venn Diagrams, you may need to take some time to teach them how to use one. If you do, start with some very simple things to compare: soccer ball vs basketball, ice cream sundae vs ice cream in a cone, cafeteria pizza vs restaurant pizza.

THREE-DIMENSIONAL SOLIDS

Home

STEMscopes Tip Fact Fluency activities, located in each grade level under the Scopes tab, help develop students’ addition and subtraction fact fluency in all grades and multiplication and division fact fluency in grades 3–5. Activities include mini-lessons, stations, games, and assessments to help address common fact-fluency groupings and strategies.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP During this Exit Ticket, allow students to use the physical solids while they record their answers. Some students may need support to determine all of the angles. Consider modifying to the problem require students to count fewer of the attributes.

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THREE-DIMENSIONAL SOLIDS

Three-Dimensional Solids Explore 4 – Drawing 3-D Solids ACTIVITY PREPARATION Students draw three-dimensional solids with given speciﬁed attributes.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Set of Direction Cards (per group) 1 Exit Ticket (per student)

•

• •

Reusable •

1 Small resealable bag (per group)

Plan to have students work in 6 groups to complete this activity. Print and cut out the Direction Cards, and place them in a resealable bag for each group. Laminate for future use, if desired. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our 3-D Objects and 3-D Nets Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Depending on your students’ ﬁne motor skills and your criteria for success for the drawings, you could conduct a whole class lesson and support step-by-step instruction on drawing some or every ﬁgure. FACILITATION TIP Each group member can take turns reading the Direction Cards, describing the attributes to draw the new block, and then drawing the new block. Students will need to listen to one another to complete the task. FACILITATION TIP

3. 4.

Using a dry-erase board will allow students to make and correct mistakes on their models.

6. 146

Read the following scenario to the class: Today, the STEMscopes Toy Factory wants you to design new blocks. You will have to read the directions for each block and draw a design to create each one. Your drawings will help the building design team bring the blocks to life. Are you up for the challenge? Divide the class into 6 groups, and direct students’ attention to the Direction Cards. Allow students a few moments to discover the cards and experience how they work with their groups. Give each student a Student Journal. Instruct students to read, discuss, and follow the directions on each Direction Card. Encourage students to think about the attributes as they plan to draw each block. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What information is on the Direction Card? Answers will vary. Draw a block with 8 vertices, 12 edges, and 6 faces. All of the faces are squares.

DOK-2 What attributes are you using to help you draw this block? Answers will vary. This block has 8 vertices and 12 edges.

DOK-2 What three-dimensional solid are you drawing? Answers will vary. We are drawing a cube.

DOK-2 Could you draw a different 3-D solid that has these same attributes? Answers will vary. Yes, a rectangular prism has the same attributes as a cube.

Engage

Explore

Explain

Elaborate

Evaluate

After the Explore activity, invite the students to a Math Chat to share their observations and learning.

Math Chat DOK-3 How did you represent the edges of each block in your drawing? We drew straight lines. • DOK-3 How did you represent the vertices of each block in your drawing? We drew dots on the corners. • DOK-3 How did you represent the faces of each block in your drawing? We represented the faces as open spaces. • DOK-4 Imagine you were on the building team for the toy company. What are some materials you could use to create models of the blocks you drew today? We could use candy. We could use toothpicks and marshmallows. We could use construction paper and tape. •

Intervention

Acceleration

FACILITATION TIP Have students share and compare their drawings for each Direction Card. Students can then modify, add to, or redraw their 3-D models.

THREE-DIMENSIONAL SOLIDS

Home

Post-Explore 1. 2. 3. 4.

FACILITATION TIP For this Exit Ticket, plan to read the clues aloud for some ( or all) students.

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THREE-DIMENSIONAL SOLIDS

Three-Dimensional Solids Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Sorting 3-D Solids Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Classifying 3-D Solids Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Relationships between Cubes and Rectangular Prisms Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Drawing 3-D Solids Independent practice assignment that gives students an opportunity to demonstrate their learning

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Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Lemonade for Sale! A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Playground Geometry

Match 3-D Solids to Attributes

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

My Classroom Model

Three-Dimensional Solid Names and Attributes

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

THREE-DIMENSIONAL SOLIDS

Home

149

Students who are still acquiring the concept and need remediation

THREE-DIMENSIONAL SOLIDS

Three-Dimensional Solids

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

150

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ASSESSMENT PLANNER Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Key Concepts I can describe threedimensional solids given a set of attributes such as faces, bases, edges, and vertices.

What prompts will be used?

What does mastery look like?

THREE-DIMENSIONAL SOLIDS

Home

I can compare threedimensional solids given a set of attributes such as faces, bases, edges, and vertices.

I can sort three-dimensional solids given a set of attributes such as faces, bases, edges, and vertices.

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SCOPE 1

Fractions Scope Introduction SCOPE SUMMARY Students continue their learning of fractions using circles and rectangles partitioned into two, three, or four equal shares. Students describe the shares using the words halves, thirds, and fourths. Students recognize that a whole is composed of two halves, three thirds, or four fourths, and they recognize that equal shares of identical wholes may not have the same shape. Fraction notation (1/2, 1/3, 1/4) is not introduced until third grade. Student Expectations

2.GSR.7.3 Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (halves, thirds, fourths, half of, third of, quarter of, etc.). 2.GSR.7.4 Recognize that equal shares of identical wholes may be different shapes within the same whole.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students partitioned circles and rectangles into two and four equal shares, and they reasoned about the size of the shares.

Third-grade students will compare two unit fractions by ﬂexibly using a variety of tools and strategies. They will represent fractions, including fractions greater than one, in multiple ways. Students will recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8.

Before beginning the lesson, students’ prior knowledge is assessed to address any missing student needs and skills required for content mastery. Students are assessed to determine if they can:

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

•

partition circles and rectangles into two and four equal-sized parts.

•

explain how partitioning is an example of decomposing.

For the Hook, students are presented with a scenario involving students manipulating paper to partition a rectangular chocolate cake. Students will: •

ﬁnd the ways a girl can cut or partition into four equal shares.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

152

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

FRACTIONS

Home

Partitioning Objects In this exploration, student groups will work together to cut and manipulate paper to help a grade 2 class create a quilt for their school spirit week. Students will: •

partition rectangular sheets of paper into equal shares.

•

describe the shares using the words halves, thirds, or fourths.

Explore 2

Explore 1

EXPLORE ACTIVITIES

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

Examples and Nonexamples In this exploration, student groups will solve a scenario about helping a candy shop look their chocolate candy over to make sure they are divided into equal shares before they are wrapped and boxed. Students will: •

identify examples and nonexamples of halves, thirds, and fourths by examining a series of illustrations of partitioned circles.

•

identify examples and nonexamples of halves, thirds, and fourths by examining a series of illustrations of partitioned rectangles.

After completing the activity, students share their learning, complete an Exit Ticket, then revisit the Hook to solve.

153

FRACTIONS

Fractions Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

154

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

FRACTIONS

Home

ACCESSING PRIOR KNOWLEDGE Students partition pizzas into halves and fourths. Students also describe how many pieces make one whole pizza. This activity is intended to assess mastery of the following standard(s): 1.GSR.4.3 Partition circles and rectangles into two and four equal shares.

Materials

Preparation

Printed •

•

Print and cut a set of Pizza Cutouts for each student.

1 Pizza Cutouts (per student)

Reusable • •

1 Pair of scissors (per student) 1 Marker (per student)

Procedure and Facilitation Points 1. 2.

3. 4.

5. 6. 7. 8. 9.

10.

11.

12.

13.

Give each student a set of Pizza Cutouts, a pair of scissors, and a marker. Read the following scenario to the class: Jocelyn ordered a pepperoni pizza to share with her best friend. Each person will get half of the pizza. Fold the pepperoni pizza to show how much of the pizza Jocelyn and her friend will get. Give students time to fold the pepperoni pizza cutout. Each student should fold the pizza into two equal pieces by making one fold. Instruct students to use a marker to trace the fold on the pepperoni pizza. Once they have equal shares, students can cut on the line or fold. When they are ﬁnished, ask students to hold up the pizza to show it partitioned into halves. Discuss the following questions: What 2-D shape is the pizza? Circle How many people are going to be sharing this pizza? 2 How many pieces did you need to partition the pizza into? 2 Are the pieces the same size? Yes Did you fold your pizza the same way someone around you did? If not, what do you notice about your pieces? I folded mine across and my neighbor folded hers up and down. Even though we folded it different ways, we still made two equalsized pieces of pizza. Ask students to count and write the number of each piece directly onto their pizza. In addition, they will label each equal share as one-half. Explain that no matter which way the pizza is folded, the two halves will always be the same size. Read the following scenario to the class: A different pizzeria is known for their delicious supreme pizzas. The Henson family has decided to order one of these specialty pizzas to share equally between the four family members. Fold the supreme pizza to show how much pizza each family member will get. Give students time to fold the supreme pizza. They should fold the pizza into four equal pieces by making one fold vertically and one fold horizontally, three vertical folds, or three horizontal folds. Ask students to use their markers to trace the folds they made on the supreme pizza. Once they have equal shares, students can cut on the line or fold. When they are ﬁnished, ask students to hold up the pizza to show their pizza partitioned into fourths. Discuss the following questions: a.

What 2-D shape is the pizza? Rectangle or square

How many people are going to be sharing this pizza? 4

FACILITATION TIP Make sure students understand that partition means to separate into pieces of equal size. When a shape is partitioned, the pieces within it are the same shape and the same size.

FACILITATION TIP Many schools have fraction kits that include equivalent pieces. Consider adding these manipulatives to your lessons in this scope. FACILITATION TIP Take a digital picture of each type of fold. Make a display labeled “Ways to Partition a Rectangle into Fourths” for students to reference throughout this scope. 155

FRACTIONS

Fractions Accessing Prior Knowledge

14.

15.

STEMscopes Tip The Scope Overview, located in the Home section of each scope, provides a colorful ﬂowchart that maps out the overall ﬂow of the scope. Activities contained in each of the 5E lessons are included, as well as the path for students who need additional support and acceleration activities for those who mastered the content.

How many pieces did you need to partition the pizza into? 4

Are the pieces the same size? Yes

e. Did you fold your pizza the same way someone around you did? If not, what do you notice about your pieces? Some students might have made one vertical fold and one horizontal fold. Some students might have made 3 vertical folds. Some students might have made 3 horizontal folds. All folds made should have resulted in 4 equal-sized pieces.

FACILITATION TIP If students have diﬃculty seeing that different folds result in equal pieces, have them cut along the folds and overlap them to prove that they are the same size. Challenge students to consider if there is a limit to the number of ways a circle can be folded to form two equal parts. (There are an inﬁnite number of possibilities.)

16.

Tell students to count and write the number of each piece directly onto their pizza. In addition, they will label each equal share as one-fourth. Explain that no matter which way the pizza was folded, the fourths will always be the same size. Facilitate a class discussion about partitioning into halves and fourths. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: f.

How many pieces made up the whole pepperoni pizza? 2

What is one piece of the pepperoni pizza called? One-half

How many pieces made up the whole supreme pizza? 4

What is one piece of the supreme pizza called? One-fourth

How do you know your halves or fourths are equal shares? Answers will vary. I know I have equal shares because each piece is the same size; I can lay one on top of the other to see if they are the same.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

156

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes

FRACTIONS

Home

157

FRACTIONS

Fractions Hook – Making a Chocolate Cake ACTIVITY PREPARATION Students partition rectangles into three equal shares and describe each share appropriately.

Materials

Preparation

Reusable • • •

• •

1 Phenomena Video (per teacher) 1 Projector (per teacher) 1 Pair of scissors (per student)

•

Consumable •

Plan to show the Phenomena Video. Part II Gather enough brown construction paper and pairs of scissors for each student to have 2 sheets of paper and 1 pair of scissors.

2 Sheets of brown construction paper (per student)

PROCEDURE AND FACILITATION Part I: Pre-Explore FACILITATION TIP Students could bring a snack from home that they have to share with a partner. Have students ﬁgure out how to share the snacks equally with their partner.

STEMscopes Tip Within the Engage section, Accessing Prior Knowledge is designed to assess whether students have the skills and strategies they need to continue in the inquiry process. If learning gaps are identiﬁed, teachers can use the Foundation Builder to bridge students’ learning to the current concept by addressing the foundational knowledge from previous grade levels. The Accessing Prior Knowledge and Foundation Builder are written from foundational standards and include activities that use manipulatives to help students gain the knowledge they need before beginning their exploration into a new concept.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Katy wanted to make a chocolate cake for her mom and dad. She poured the gooey batter into a rectangular cake pan. She put it in the oven and tried to wait patiently for the timer to go off as the kitchen started to smell like her yummy dessert. When the cake had cooled, she decided to cut it into thirds. She will get one-third, her mom will get one-third, and her dad will get one-third of the cake. What are two ways Katy could cut the delicious chocolate cake into three equal shares? Cut the construction paper to show your thinking. Discuss the following questions: a.

DOK-1 What information do we know? Katy is going to cut a cake into three equal shares.

DOK-1 What information do we need to ﬁnd out? What are two ways Katy could cut the delicious chocolate cake into three equal shares?

Allow time for students to discuss their experiences with baking cakes or watching someone bake a cake and then cutting it into pieces. Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

158

b. 3.

Engage

Explore

Explain

Elaborate

Evaluate

Acceleration

DOK-1 What information do we need to ﬁnd out? What are two ways Katy could cut the delicious chocolate cake into three equal shares?

Give each student two sheets of brown construction paper and a pair of scissors. Explain to students that the brown construction paper represents the chocolate cake. Instruct students to cut each sheet of brown paper into thirds. Have them cut the two sheets of paper to show thirds in two different ways. Encourage students to fold the construction paper before cutting it to make sure they have equal shares. Discuss the following questions: a.

DOK-2 What does one sheet of construction paper represent? One whole

DOK-2 How many equal shares will Katy cut the cake into? She will cut the cake into three equal shares.

DOK-2 What is one way you cut your construction paper into three equal shares? Answers will vary but may include the following idea: I can cut the paper horizontally into three parts.

Intervention

DOK-2 What is another way you cut your other sheet of construction paper into three equal shares? Answers will vary but may include the following idea: I can cut the paper vertically into three parts.

e. DOK-1 What is the fractional name for each equal share in Katy’s cake? One-third f.

DOK-2 How many of these fractional parts equal one whole cake? Three thirds

DOK-3 What do you notice about the thirds from one of your models compared to the thirds from your other model? Answers will vary but may include the following idea: the thirds in one of my models seem thinner than the thirds in my other model.

FRACTIONS

Home

FACILITATION TIP Support students by showing them how to easily fold the paper into thirds by ﬁrst rolling it into a cylinder, aligning the edges and then compressing the cylinder to create folds. (Decide if you want to show them how to do this both vertically and horizontally or let them problem solve the other way on their own). FACILITATION TIP During this discussion, encourage students to use the directional vocabulary (horizontal and vertical) correctly.

FACILITATION TIP During the discussion, write down the fractional names in word form and number form to support students’ comprehension.

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FRACTIONS

Fractions Explore 1 – Partitioning Objects ACTIVITY PREPARATION Students partition rectangles into equal shares and describe the shares using the words halves, thirds, and fourths.

Standards for Mathematical Practice • •

MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • •

•

1 Student Journal (per student) 1 Exit Ticket (per student)

•

Reusable • • • • • • • •

1 Sheet of red construction paper (per group) 1 Sheet of blue construction paper (per group) 1 Sheet of green construction paper (per group) 1 Sheet of yellow construction paper (per group) 1 Sheet of black construction paper (per group) 1 Sheet of orange construction paper (per group) 1 Pair of scissors (per group) 1 Set of markers or crayons (per group)

• •

Plan to divide the class into groups of 4 to complete this activity. Prepare a set of construction paper (all colors), and gather enough pairs of scissors, markers or crayons, and tape for each group to have some of each. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Grid Paper Supplemental Aids element in the Intervention section.

Consumable •

1 Roll of tape (per group)

PROCEDURE AND FACILITATION 1. FACILITATION TIP Project some images of quilts and other tangrams for students to develop some ideas.

FACILITATION TIP

Using this rectangular model now (rather than using circles) for fractions will help students as they progress through more complex fraction operations. FACILITATION TIP

4. 5.

Take time to model some folding methods before students begin working independently on cutting. 6.

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Read the following scenario to the class: Each 2nd-grade class has been asked to make a quilt for school spirit week. We have been given fabric and instructions, and it is our job to cut and put the quilt together. It is time to get creative! Are you ready? Divide the class into groups of 4, and give each group a set of construction paper, scissors, markers or crayons, and tape. Direct students’ attention to the sheets of construction paper. Explain to students that the sheets of paper will represent fabric from the scenario. Allow students a few moments to discover the manipulatives and experience how they can be pieced together to create a quilt. Give a Student Journal to each student. Instruct students to read the instructions on their Student Journals to find out how they will be cutting each sheet of construction paper. Explain that they will be cutting each sheet into halves, thirds, or fourths. Remind students that the pieces they cut must be equal in size. Suggest folding the paper first to see if all group members agree on the partitioning before cutting the paper. Ask students to record their partitioning by drawing lines on the rectangle on their Student Journals and answer the questions before moving on to the next colored sheet of paper. When students get to the yellow, black, and orange pieces of paper, they will cut them into halves, thirds, and fourths in different ways from the first three sheets of paper. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Monitor and talk with students as needed to check for understanding by using guiding questions. a.

DOK-1 How many pieces are you cutting your paper into? Answers will vary. 2, 3, or 4

DOK-1 What does the one sheet of paper represent? One whole

DOK-1 How many parts make one whole? Answers will vary. 2, 3, or 4

DOK-1 What do you call one part of this whole? Answers will vary. Onehalf, one-third, one-fourth

After students have completed their Student Journals and cut all of their sheets of construction paper, instruct students to use tape to piece together all of the pieces to form a quilt. They can decorate the quilt using markers or crayons. Display each group’s quilt, and allow students to do a gallery walk to view all of the quilts. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

FACILITATION TIP

FRACTIONS

Home

Focus students’ attention on the fact that the fabric or paper is the whole. How many parts the whole is equally divided into will determine the name of each part. FACILITATION TIP Print and post these guiding questions for students and teaching assistants to refer to as students work and collaborate. FACILITATION TIP Consider having students color the quilt pieces before taping.

Math Chat •

• • • • • • • • • •

DOK-3 Ask students to observe each group’s quilt. What do you notice about the red pieces of fabric? Everyone cut their papers into halves, but some groups cut horizontally and some cut vertically. (Discuss the differences in what the pieces look like but that they still represent halves, thirds, or fourths.) DOK-1 How many halves equal one whole? Two DOK-1 How many thirds equal one whole? Three DOK-1 How many fourths equal one whole? Four DOK-4 How do we use fractions in everyday life? When we share something equally with friends and family, to be fair, etc. DOK-2 What do you notice about the size of each part as you partition your object into more and more parts? The individual parts get smaller. DOK-1 What is a new vocabulary word for the whole thing that you are cutting into equal shares? The whole or unit DOK-1 What do we call a whole that is partitioned into two equal shares? Two halves DOK-1 What do we call a whole that is partitioned into three equal shares? Three thirds DOK-1 What do we call a whole that is partitioned into four equal shares? Four fourths DOK-2 Is there more than one way a rectangle can be partitioned into 4 equal parts? What are the different shapes that can be made from these fourths? Yes, it can be divided into 4 squares or 4 triangles or 4 equal long rectangles.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

STEMscopes Tip The Picture Vocabulary, located in the Explain section, presents key vocabulary terms in a slide presentation. Each term is featured with a student-friendly definition as well as a colorful image that reflects the vocabulary. Using activities that include the Picture Vocabulary helps develop students’ fluency in mathspecific terminology, conventions, and language used when discussing math concepts. The Picture Vocabulary can be assigned to students or downloaded and printed for use on an interactive word wall, in student resource handouts, or as study flash cards.

FACILITATION TIP This Exit Ticket provides a good opportunity to assess students’ understanding before the next Explore. Adjust instruction as needed and then use the Exit Ticket after the Explore to measure students’ growth.

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FRACTIONS

Fractions Explore 2 – Examples and Nonexamples ACTIVITY PREPARATION Students identify examples and nonexamples of halves, thirds, and fourths through examining a series of illustrations of partitioned circles and rectangles.

Standards for Mathematical Practice • •

MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 2 Sets of Chocolate Candy Images (per class) 1 Exit Ticket (per student)

Reusable •

• •

10 Resealable bags (per class)

Plan to divide the class into groups of 2 or 3 to complete this activity. Print two sets of Chocolate Candy Images. Hang one set around the room. Cut apart each chocolate candy in the second set, and place each set of candy pieces into its own resealable bag. Place each cut-apart chocolate candy near its corresponding hanging image. Students will use the hanging image to see what the whole looks like but can use the cut-apart pieces to compare the size of the pieces. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Grid Paper and Fraction Circles Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION 1.

2. FACILITATION TIP

Consider printing each set of images on a different color of paper. This will help students distinguish the whole from the parts.

4. 5.

Read the following scenario to the class: The STEMscopes Candy Shop just hired a new chocolate candymaker. He has been working for a few days and has already divided lots of candy into pieces. Some of the chocolate candy are bars shaped like rectangles, and some are candy cups shaped like circles. The shop supervisor needs us to look the chocolate candy over to make sure they are divided into equal shares before they are wrapped and boxed. Can you look at the chocolate candy and identify equal shares? Divide the class into groups of 2 or 3 and place one group in each area of the room with a hanging Chocolate Candy Image. Direct students’ attention to the hanging Chocolate Candy Image, as well as the resealable bag containing the same image cut into pieces. Allow students a few moments to discover the manipulatives and experience how they work with their group. Give a Student Journal to each student. Encourage students to record their thinking as they observe each image. Instruct students to count how many pieces make up the whole candy bar (rectangles) or candy cup (circles). Encourage students to use the cut-apart pieces to determine if the pieces are equal in size. a.

6. 162

Note that candy bars 2 and 9 may appear to have parts that are unequal in size. Students should use the pieces to help them compare. For candy bar 9, students should visualize cutting apart the thin fourths in half to equal the fatter fourths. If students are still struggling to see this concept, cut the thin fourths into halves, and put them on top of the fatter fourths so students can see that they are equal.

Engage

Explore

Explain

Elaborate

Evaluate

10.

DOK-1 How many parts are in this whole candy bar/cup? Answers will vary. 2, 3, or 4

DOK-2 Are the pieces equal in size? Answers will vary. Yes – candy bars/cups 1, 2, 4, 6, 8, 9, and 10; no – candy bars/cups 3, 5, 7

DOK-2 Do the pieces have to look exactly the same to be equal in size? No, candy bars 2 and 9 have pieces that do not look the same, but they are the same size.

DOK-2 Is this an example of halves, thirds, or fourths? Answers will vary. Halves – candy bars/cups 6 and 10; thirds – 1 and 8; and fourths – 2, 4, and 9

Have students rotate to each Candy Bar Image and repeat steps 5–7. When students have completed each image and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • • •

•

DOK-2 Which candy bars/cups are examples of fractions? Chocolate Candy 1, 2, 4, 6, 8, 9, and 10. DOK-2 Which candy bars/cups are nonexamples of fractions? Candy bars 3, 5, and 7. DOK-2 What characteristic makes candy bars/cups 3, 5, and 7 nonexamples? The parts of these candy bars are not equal in size. To be a fraction, all parts must be equal. DOK-2 Does a shape have to be partitioned in the exact same way to make the parts equal? No, you can partition a shape in half and then partition the same shape in half a different way. DOK-3 What do you notice about fourths? There are a lot of different ways to divide a shape into fourths. You can trick people by partitioning a square into halves and then halves again in two different ways, etc. DOK-4 What was a surprise or new learning that you want to share about examples and nonexamples of fractions based on our activities and exploration today? There are tricky fourths that are partitioned equally but do not look like it at ﬁrst; fourths are smaller even though the number 4 is bigger than the number 3 (thirds), etc.

Post-Explore 1. 2. 3. 4.

Acceleration

Monitor and talk with students as needed to check for understanding by using guiding questions.

e. DOK-3 Is this an example or nonexample of a fraction? Explain how you know. Answers will vary. This is an example of a fraction because the size of the parts is the same. This is a nonexample of a fraction because the size of the parts is not the same. 8. 9.

Intervention

FRACTIONS

Home

FACILITATION TIP As you monitor the groups, model with manipulatives for students who may be struggling how candy bars 2 and 9 are equal parts.

FACILITATION TIP Students should be able to explain that fractions are about equal parts of a whole. The term fraction should have context with the Explore activities.

FACILITATION TIP Follow up this Math Chat with how understanding fractions will help students get their fair share in the real world. Consider some questions about your class’s favorite treats, prizes, or game pieces/cards. Students are often very concerned about fairness.

STEMscopes Tip Each Explore activity includes a Student Journal that students complete collaboratively while participating in group work. Students use the journal to develop metacognitive skills by reﬂecting on how and what they are learning. Communicating mathematical thinking leads to a deeper conceptual understanding of the skills at hand.

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FRACTIONS

Fractions Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Partitioning Objects Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Examples and Nonexamples Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

164

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

FRACTIONS

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Arcade Party A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Baking Treats with Grandma

Fraction Models of Halves, Thirds, and Fourths with Names

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Party Time!

Match Halves, Thirds, and Fourths

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

165

FRACTIONS

Fractions Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

166

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

FRACTIONS

Home

What prompts will be used?

What does mastery look like?

I can partition circles and rectangles into two, three, or four equal shares.

I can identify and describe equal-sized parts of the whole using fractional names.

I can describe the shares using the words halves, thirds, fourths, half of, third of, and quarter of.

I can describe the whole using the words two halves, three thirds, and four fourths.

I can recognize that equal shares of identical wholes may be different shapes within the same whole.

167

SCOPE 1

Length Scope Introduction SCOPE SUMMARY

Student Expectations

2.MDR.5.1 Construct simple measuring instruments using unit models. Compare unit models to rulers.

Students construct simple measuring instruments using unit models and compare those models to rulers. This is the ﬁrst time students are introduced to a standard-length unit such as an inch. After estimating the length of an object, students identify appropriate measurement tools and units for obtaining accurate measurements. When measuring objects with two different units, students recognize that fewer of the larger units are required. They measure the lengths of two objects using the same unit, and they determine how much longer or shorter one object is than another. Students also represent sums and differences on a number line. Students are not expected to convert measurements.

2.MDR.5.2 Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools. 2.MDR.5.3 Measure to determine how much longer one object is than another and express the length difference in terms of a standard-length unit. 2.MDR.5.5 Represent whole-number sums and differences within a standard unit of measurement on a number line diagram.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students measure the length of objects by laying nonstandard measuring tools end to end with no gaps or overlaps. They compare and order the length of up to three objects.

Third-grade students select and use appropriate tools to measure the length and weight of an object and the volume of a liquid by using customary units. Students use a ruler to measure to the nearest half, fourth, or whole inch. Students also use containers of various sizes to measure liquid volumes, and they use a platform scale to measure weight. Students apply what they know about measurement to model and solve real-world problems involving whole-number lengths, weights, or liquid volumes. Students are not expected to convert measurements.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

estimate, measure, and record lengths of objects using nonstandard units, and compare and order up to three objects using the recorded measurements.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

measure their height to the nearest inch and centimeter by using various tools.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 168

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

Construct Measuring Instruments In this exploration, students will construct simple measuring instruments using unit models and compare them to rulers. Students will: •

measure books in order to know how they will ﬁt on shelves.

•

decide which measuring instruments would be best to use.

Explore 2

Explore 1

EXPLORE ACTIVITIES

•

model what the centimeters and inches looked like on foot measurements by drawing two number lines.

Solving Problems with Length In this exploration, students will solve one- and two-step real-world measurement problems involving addition and subtraction of lengths given in the same units. Students will: •

After students solve the scenario, they discuss their learning with the class and complete an Exit Ticket for assessment.

Explore 5

measure six items selected around the classroom using various measurement tools.

After students have solved the scenario, the teacher guides students in color coding, sharing, and discussing their ﬁndings. Students discuss their learning and then complete an Exit Ticket.

Explore 4

Explore 3

In this exploration, students will explore the inverse relationship between the size of the unit and the number of units needed to equal the length of an object. Students will:

In this exploration, students will estimate lengths and use appropriate measuring tools to measure to the nearest inch, foot, yard, centimeter, and meter. Students will: •

As students are working, the teacher monitors and adjusts, leads a discussion about the students’ ﬁndings, and has students complete an Exit Ticket to assess their learning. Inverse Relationships

Length Using Formal Measuring Tools

use a ruler to solve a word problem involving length or estimation of length.

After students have solved the scenario, they share and discuss their ﬁndings. Then they complete an Exit Ticket for assessment.

Representing Addition and Subtraction on a Number Line In this exploration, students will use number lines to solve all types of addition and subtraction word problems within 100 with unknowns in various places. Students will: •

add intervals to open number lines, evenly spaced and marked with numbers.

•

write a number sentence reﬂecting the strategies used on the number line.

After solving the scenario, students discuss their learning with the class, complete an Exit Ticket, then revisit the Hook to solve.

169

LENGTH

Length Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

170

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

ACCESSING PRIOR KNOWLEDGE Students measure objects in the classroom to the closest unit and order them from longest to shortest. This activity is intended to assess mastery of the following standard(s): 1.MDR.6.1 Estimate, measure, and record lengths of objects using non-standard units, and compare and order up to three objects using the recorded measurements. Describe the objects compared.

Materials

Preparation

Printed •

1 Student Handout (per student)

Reusable • • • •

• • •

15 Inch tiles (per student) 15 Small paper clips (per student) 4–5 Commonly found classroom objects (per teacher) 1 Resealable bag (per student)

• •

Plan to have students work in groups of 3 or 4 to complete this activity. Prepare a resealable bag with 15 inch tiles and 15 small paper clips for each student. Identify 4 or 5 commonly found classroom items such as a pencil, binder, journal, book, etc. Measure the items ahead of time to ensure proper measurement for students. List the objects on the Student Handout for students, or have the names available for students to use. Place items on the tables for students to easily rotate through. Print the Student Handout for each student.

Procedure and Facilitation Points 1. 2. 3.

6. 7. 8.

Divide the class into groups of 3 or 4. Instruct students to work with their group to measure objects from around the room. Distribute the Student Handouts, bags of inch tiles, and bags of paper clips to students. Students rotate around to measure individual items. They need to measure 3 items. Instruct students to write down an estimate for the length of each item before they measure the items. Instruct students to then use the inch tiles or paper clips to measure the items. Pay close attention to see how students are lining up the units. Students should be lining up the item with the end of the units. The units should be placed end to end with no gaps. Allow students to share their measurements with the class to compare their measurements with everyone else’s. Have students order the items at the bottom of the page. Facilitate a class discussion about measuring. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a.

What do you need to remember when using inch tiles or paper clips to measure an object? We need to start measuring the object by lining up the object with the end of the units. The units should be placed end to end with no gaps.

How close were your estimates to your actual measurement? Answers will vary.

How can we make closer estimates? Answers will vary. Measure different objects with measuring tools.

FACILITATION TIP Before instructing students to measure objects around the room, be sure your selected objects (pencil, binder, journal, book, desk, etc) are listed on the Student Handout. FACILITATION TIP Before distributing the paper clips, model expectations for how to manipulate them without bending their shapes. FACILITATION TIP Consider guiding students to record their estimates before they leave their seats to measure the items. Students are often hesitant to approximate because they don’t like being wrong. Reassure them that estimating is a good thinking tool and that we often learn more when we are wrong. FACILITATION TIP Continue to reassure students that estimating is an excellent way to learn and that it is OK to be way off. Learning to measure accurately with tools later will be easier if they practice approximation now.

d. How could you tell which item was longer? How could you tell which item was shorter? Answers will vary. The longer items had a higher number. 9.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

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Length Hook – How Tall Am I ACTIVITY PREPARATION Students measure their height to the nearest inch and centimeter by using various tools. These can include rulers, yardsticks, metersticks, and measuring tapes.

Materials

Preparation

Reusable • • • • •

• •

1 Ruler (per group) 1 Yardstick (per group) 1 Meterstick (per group) 1 Measuring tape (per group) 1 Phenomena Video (per teacher)

Plan to show the video. Part II • •

Consumable • • •

1 Sheet of butcher paper two meters in length (per group) 1 Roll of tape (per teacher) 1 Marker (per group)

• •

Divide the class into groups of 3 or 4 to complete this activity. Gather enough butcher paper sheets for each group of students to have one. Tape the bottom of the butcher paper to the bottom of a wall in the classroom. Make sure the edge of the paper lines up against the ﬂoor. Tape the top of the paper to the wall. The paper should be secured against the wall lengthwise so that the longer sides are perpendicular to the ﬂoor. Gather various measuring tools for each group of students to use when measuring their height. Gather enough markers for each group to have one.

PROCEDURE AND FACILITATION Part I: Pre-Explore 1. STEMscopes Tip In the Elaborate section, the Spiraled Review activity begins with a short real-world story to peak students’ interest. Students are then presented with four problems based on the story that cover previous and current grade-level content. Completing the Spiraled Review helps students maintain essential knowledge, see how mathematical skills connect from one topic to the next, and experience real-world applications of previously learned skills. On the right side of the screen are a printable Student Handout and Answer Key. The Student Handout can also be downloaded and differentiated to address the needs of students.

5. 6.

DOK-1 What information do we know? We are measuring one another’s height in inches and centimeters.

DOK-1 What information do we need to ﬁnd out? What will we use to measure height? How tall am I?

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities.

Part II: Post-Explore FACILITATION TIP To simplify this activity, consider choosing either inches or centimeters for this Hook. Choose the other measurement unit for something smaller during another lesson. 172

1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

b. 3.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

DOK-1 What information do we need to ﬁnd out? What will we use to measure height? How tall am I?

Divide the class into groups of 3 or 4. Give each group a set of measuring tools including a ruler, a yardstick, a meterstick, and a measuring tape. Direct their attention to the butcher paper hanging on the wall. Instruct students to stand against the paper, one at a time, and have a group member mark the height of each student in the group. Each mark should be labeled with the appropriate student’s name. Ask students to use the measuring tools to measure each student’s height in inches and centimeters. Students can take the butcher paper off of the wall and lay it on the ﬂoor to make measuring easier. Remind students to write the measurements on the butcher paper. Discuss the following questions: a.

DOK-1 How many inches tall are you? Answers will vary. 48 inches

DOK-1 How many centimeters tall are you? Answers will vary. 122 centimeters

DOK-3 Are we all the same height? How do you know? We know we are not all the same height because our measurements are different.

DOK-3 What can you say about the relationship between the size of a unit of measurement and using this unit to measure the length of an object? The smaller the unit is, the more units it will take to measure the length of the object. The larger the unit is, the fewer units it will take to measure its length.

FACILITATION TIP Alternatively, place the butcher paper on the ﬂoor. Have students lie down on the paper, making sure their feet are at the bottom. FACILITATION TIP First, have students estimate one another’s height in inches and centimeters to help them visualize the concept of length. Have students write their estimations on the butcher paper. FACILITATION TIP This activity might work best if small groups of students are supported by an adult to help facilitate. Have small groups go in the hallway with a grown up to help them learn now to use the tools skillfully.

e. DOK-1 Which tool did you use to measure in inches? Ruler, yardstick, measuring tape f.

DOK-1 Which tool did you use to measure in centimeters? Ruler, meterstick, measuring tape

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LENGTH

Length Explore 1 – Construct Measuring Instruments ACTIVITY PREPARATION Students construct simple measuring instruments using unit models and compare them to rulers.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • •

•

1 Student Journal (per student) 1 Exit Ticket (per student)

•

Reusable • • • • • • • •

1 Ruler, centimeters and inches (per station) 24 Inch tiles (per class) 24 Small paper clips (per class) 30 Centimeter cubes (per class) 12 Linking cubes (per class) 15 Pennies (per class) 5 Resealable plastic bags (per class) 2 Books of varying sizes (per station)

•

• • • • • •

• •

Consumable 1 Roll of tape (per station)

Plan to have students work in groups of 4 or 5 to complete this activity. Gather 2 books, a roll of tape, and a ruler for each station. Place the following materials listed below in a resealable bag at stations indicated: Station 1 – 12 inch tiles Station 2 – 12 small paper clips Station 3 – 30 centimeter cubes Station 4 – 12 linking cubes Station 5 – 15 pennies

For Part II, prepare a simple measuring instrument using 12 small paper clips or 12 inch tiles by taping them together. Print a Student Journal and an Exit Ticket for each student. For the Exit Ticket, prepare bins of small paper clips and inch tiles for the class to share.

PROCEDURE AND FACILITATION Part I 1.

FACILITATION TIP Students may need adult help taping the items together in a line. 174

3. 4.

Read the following scenario to the class: The school library just got a lot of new books! I’m so excited to read them, but the librarian says we can’t check them out until she ﬁnds a place to put them. She needs our help to measure the books in order to know how they will ﬁt on the shelves. I have several measuring instruments we could use to measure the books. Can you help me decide which measuring instruments would be best to use? Divide students into groups of 4 or 5, and assign each group to one of the 5 stations. They will work at this station for Part I. Give students time to explore the materials. Instruct students to set the items found at their stations next to one another end to end to construct a measuring instrument. Ask students to use the tape to tape the items together in a line. Then, have students place the line next to the ruler. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

After students have had suﬃcient time to compare their instruments with rulers, have them measure the books at their stations. (Note that students may not realize they need to place the end of the object on 0 when using a ruler. They will explore this further in the next Explore.) Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 What do you notice about the measuring instrument you constructed? Answers will vary. The 12 tiles seem to be about the length of the ruler. I can use it to measure the book.

DOK-2 How is your instrument similar to a ruler? Answers will vary. It is about the same length as the ruler. It can be used to measure something.

DOK-2 How is your instrument different from a ruler? Answers will vary. It is a little longer/shorter than a ruler. It is hard to keep the (tiles, pennies, etc.) together when measuring an object.

DOK-2 Which do you think will be more eﬃcient to use to measure a book? Answers will vary. I think a ruler would be more eﬃcient.

2. 3.

6. 7.

Acceleration

FACILITATION TIP Before having students visit the stations, consider where you want students to keep their “constructed measurement instruments” before moving on to Part II with the Student Journals.

After students have had suﬃcient time to work with the materials at their station, move on to Part II. Students will use the same materials as in Part I.

Part II 1.

Intervention

LENGTH

Home

FACILITATION TIP

Display your simple measuring instrument you made out of inch tiles or paper clips. Ask a student to show you how they would measure a book using this instrument. If needed, model how to place the end of the instrument with the end of the object measuring. Then, show students the ruler and have another student model how to measure the book by placing the end of the book next to 0. Give each student a Student Journal. Instruct students to measure the books at their stations using the measuring instruments they constructed and the rulers again. They will record their work on their Student Journals. Give students 5 to 7 minutes at each station. Make sure students are taking turns with the units and ruler to practice measuring. Students rotate from station to station. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-3 Which do you think will be more eﬃcient to use to measure a book? Why? Answers will vary. I think a ruler would be more eﬃcient because it is easier and more accurate.

DOK-1 What is the length of your book using the instrument you constructed? Answers will vary. It is ___ (tiles, paper clips, centimeter cubes, linking cubes, pennies) long.

DOK-1 What is the length of your book using the ruler? Answers will vary. It is ___ inches long.

After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Before Part II, determine how you want students to transport and display their “simple measuring instruments.” FACILITATION TIP Model the steps for accurately measuring with the ruler. If you have a set of rulers that are not all the same, take time to model how to use each type. If the rulers have both inches and centimeters on them, be sure each student is clear on how to speciﬁcally use the tool for today’s lesson.

STEMscopes Tip The Accessing Prior Knowledge activity, located in the Engage section, helps teachers determine students’ prior knowledge about a concept before engaging in the inquiry process. If students struggle with the task, the Foundation Builder, also found in the Engage section, helps to ﬁll the gaps in prior knowledge.

175

LENGTH

Length Explore 1 – Construct Measuring Instruments Math Chat DOK-2 What items can you use to measure the length of objects if you don’t have a ruler? I can use tiles, cubes, my foot, etc. • DOK-3 How does measuring with cubes or pennies compare to measuring with a ruler? A cube and penny are not as close to an inch as a ruler, so I did not get the exact same measurement as I did with the ruler. • DOK-3 How does measuring with inch tiles compare to measuring with a ruler? The inch tiles were an inch long, but they were hard to keep next to one another without leaving gaps. The ruler is easier to use to measure an object that is longer than 1 inch. • DOK-2 Which measuring tool was easier to use to get an accurate measurement? Explain why. The ruler gave the most accurate measurement because it is marked with exact inches from 0 to 12 inches. The unit models were not exactly one inch, or they were diﬃcult to keep together without leaving any gaps. • FACILITATION TIP Before or after this Explore, provide students with some real-world uses for measurement skills. Older students get to use rulers in wood shop, measuring cups in life skills classes, and many careers require accurate measurement skills. FACILITATION TIP For this Exit Ticket, students need access to the shared bins of paper clips and tiles. Consider letting students choose one or the other to use as a tool.

Post-Explore

FACILITATION TIP

When you preview this Exit Ticket with students, draw their attention to the ends of the images. Some students may need to be shown how to measure the parallelogram eraser and how to be careful to include the full length of the pencil.

2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

176

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

177

LENGTH

Length Explore 2 – Length Using Formal Measuring Tools ACTIVITY PREPARATION Students estimate lengths and use appropriate measuring tools to measure to the nearest inch, foot, yard, centimeter, and meter.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • •

• •

1 Student Journal (per student) 1 Exit Ticket (per student)

•

Reusable • • • • • • • • • • •

1 Ruler with inches and centimeters (per group) 1 Yardstick (per group) 1 Meterstick (per group) 1 Measuring tape (per group) 6 Items for students to measure around the classroom (per class) 1 Packing box (per class) 1 Stapler (per class) 1 Sticky note pad (per class) 1 Pen (per class) 1 Pair of teacher scissors (per class) 1 Spiral notebook (per class)

Plan to have students work in 6 groups to complete this activity. Gather a ruler, a yardstick, a meterstick, and measuring tape for each group. Select 6 items around the classroom for students to measure in Part I of the activity. Items might include the following: • •

• • •

Rug, lamp, chair, desk, shelf, trash can Pencil, book, markers, tissue box, poster, ﬁle folder

Have a packing box available to show students what the items need to ﬁt into when placed in the cabinet. Gather a stapler, pen, spiral notebook, sticky note pad, and pair of teacher scissors for Part II. Print a Student Journal and an Exit Ticket for each student.

PROCEDURE AND FACILITATION

178

FACILITATION TIP

Part I

Explain that students should estimate the length of an object in inches before measuring it. Ask students to identify personal benchmarks for an inch, foot, yard, and meter. For example, the distance from the tip of your thumb to the knuckle joint is about one inch, the length of a football is about a foot, the distance from a person’s chest to their ﬁngertips is about a yard, and the distance from an adult’s hip to the ﬂoor is about a meter. Having personal benchmarks or anchoring units of measure is helpful when estimating.

Read the following scenario to the class: On the last day of school, I have to pack up my classroom and fit everything into the cabinets. If something doesn’t fit, I have to take it home. I need help measuring some of the items in the classroom to see if they will fit into boxes to be stored in the cabinets. Can you help me decide what can stay here and what needs to go home? Divide the class into 6 groups, and direct students’ attention to the ruler, yardstick, meterstick, and measuring tape. Allow students a few moments to discover the manipulatives and experience how they work with their group. Instruct students to choose a measuring tool to measure the 6 items you selected around the classroom. Encourage students to discuss if they would fit in the box or the cabinet.

Engage

Explore

Explain

Elaborate

Evaluate

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 Which measuring tool did you choose to measure this item? Answers will vary. We used the meterstick to measure the rug.

b. DOK-2 Is there a different measuring tool you could have used to measure this item? Answers will vary. Yes, we could have used a yardstick to measure the rug because that tool is similar in size to a meterstick.

DOK-2 What was your estimation for this item? Answers will vary. We think the rug is going to be 3 meters long.

DOK-3 How do you use the measurement tools to measure? I begin with the 0 and place the end of the object next to the 0.

Intervention

Acceleration

LENGTH

Home

FACILITATION TIP Prompt students to identify each measuring tool and to locate inches and centimeters on each. FACILITATION TIP Choose an additional object and ask a student to help you demonstrate how to obtain an accurate measure of length. Emphasize the importance of lining up the measuring tool at zero along the end of the object and making sure that the measuring tool is straight.

Give each student a Student Journal, and ask students to record the name of the item being measured, the measurement tool used, the estimation, the actual length, and if the item ﬁts in the box or cabinet. Remind students to use benchmarks they previously learned about in the Skill Basics activity when estimating lengths. When writing their estimations and actual lengths, students should include a number and units.

Part II 1.

2. 3.

5. 6. 7.

Read the following scenario to the class: I have some room left over in the box to pack some items from my desk. I will pack my stapler, scissors, pen, sticky note pad, and notebook. Measure each of these items, and compare their lengths. Students continue working in their groups from Part I. Give each group one of the objects (stapler, scissors, pen, sticky note pad, and spiral notebook) and a ruler. Instruct students to use their rulers to measure using the speciﬁed units in the table in Part II of their Student Journals. Remind students to measure to the nearest unit. Rotate objects until each group has had an opportunity to measure each object and record its length in the table. Students answer each question by writing a number sentence using subtraction to determine how much shorter one object is than another and express the length difference in terms of a standard length unit. Encourage students to discuss and answer the reﬂection question. When students have completed both parts of their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP Next to each object, post a sheet of chart paper for students to record their measurements. If there is a discrepancy in recorded measurements, have the class meet to decide which measurement is most accurate. Invite a student to demonstrate how they measured, and have students ﬁx their errors and discuss what may have caused errors.

Math Chat • • •

DOK-1 What tool did you use to measure this item? We used the ruler to measure the pencils. DOK-3 Why did you choose that tool? I thought that the yardstick and meterstick were too long, and it was easier with a ruler. DOK-4 What benchmarks could help you measure an item if you do not have a measuring tool on hand? • • • • •

Inch – the distance from one knuckle to the next, width of a quarter, thickness of a book Centimeter – the width of a pinky, the width of a large paper clip Foot – the length of a square tile on the floor, length of a football Yard – the distance from the doorknob to the floor, the distance from the tip of my nose to my middle finger Meter – the distance from my hip to the floor, the height of a chair, length of a baseball bat

FACILITATION TIP Use some time during this Math Chat to connect students to real-world applications of being able to measure accurately. Some examples are purchasing items for construction or landscaping jobs, building things in wood shop, and sewing. Think about your students’ interests.

179

LENGTH

Length Explore 2 – Length Using Formal Measuring Tools •

•

• STEMscopes Tip Located in the Acceleration section, Math Today is an activity in which students in all grades explore connections and applications of mathematics and other crosscurricular content through interactions with videos, photos, or articles provided by the Associated Press. This engaging activity can be used as a review or as a formative assessment.

• • • • •

DOK-2 What benchmark helped you estimate the length of the ____ (name one of the objects)? I used the length of one of my knuckles to the next to estimate the length of the ____ in inches. DOK-3 Can you explain how to use a ruler? When using a ruler, we have to make sure we count the spaces, not the ticks, and we have to see if it’s starting at 0 or 1. Rulers are very similar to number lines. DOK-3 Can the whiteboard be measured using centimeters? Explain your thinking. Using centimeters to measure the length of the whiteboard would take too long; instead, we could use the yardstick or the meterstick. DOK-2 What is the difference between a ruler and measuring tape? A ruler only goes to 12 inches (1 foot), and a measuring tape can go to several feet. DOK-4 When might you need to use a measuring tape instead of a ruler? If an object is longer, then I would use a measuring tape. DOK-3 What were some items that fit in the box? The books, pencils, markers, and posters can stay here. They will fit in the box or cabinet. DOK-3 What items have to go home with me? You will have to take home the rug, shelf, and trash can. They will not fit in the box or cabinet. DOK-2 How did you determine how much longer one object was than another in Part II? I subtracted the length of the shorter object from the length of the longer object.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

180

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

181

LENGTH

Length Explore 3 – Inverse Relationships ACTIVITY PREPARATION Students explore the inverse relationship between the size of the unit and the number of units needed to equal the length of an object.

Standards for Mathematical Practice • • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • •

•

1 Student Journal (per student) 1 Exit Ticket (per student)

•

Reusable •

•

1 Ruler, centimeters and inches (per pair)

•

Consumable •

Plan to have students work with a partner to complete this activity. Collect a ruler with centimeters marked on one side and inches marked on the other side for each pair of students. Each pair of students needs one piece of construction paper to trace a foot. Print a Student Journal and an Exit Ticket for each student.

1 Piece of construction paper (per pair)

PROCEDURE AND FACILITATION 1.

2. FACILITATION TIP It is easy for inaccuracies to occur when measuring. To ensure that measurements are accurate, have both students measure each traced foot so they can compare lengths and adjust as needed.

FACILITATION TIP

182

While all students have a ruler, have them measure the widths and lengths of some ﬁngers. Helping them ﬁnd a body part that is about an inch or about a centimeter will help them with estimation.

Read the following scenario to the class: You need new shoes for school. In order to ﬁnd shoes that ﬁt your foot, you need to know the length of your foot from toe to heel. You have a ruler that is marked with centimeters on one side and inches on the other side. You are not sure if you will buy shoes from a company that sizes shoes in centimeters or from a company that sizes shoes in inches. Can you measure your foot using both units? Divide the class into groups of two, and direct students’ attention to the rulers marked with both centimeters and inches. Allow students a few moments to discover the manipulatives and experience how they work with their partner. Instruct students to trace one person’s foot onto the construction paper and use the ruler to measure it in both centimeters and inches. Encourage students to discuss the relationship between the two sides of the ruler and the two different measurements. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How are you measuring your foot using the centimeter side of the ruler? How are you measuring your foot using the inch side of the ruler? Answers will vary. We are lining up the end of the foot with the 0 mark and laying the ruler next to the foot to see where on the ruler it ends, marking the number, and noting the unit used.

DOK-3 What do you notice about the size of each unit on the ruler? The centimeter marks are smaller/shorter than the inch marks.

DOK-3 What do you notice about the two different measurements and how many of each were required to measure your foot? It did not take as many inches to measure our foot as it did centimeters. © Accelerate Learning Inc. - All Rights Reserved

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Give each student a Student Journal, and ask students to model what the centimeters and inches looked like on their foot measurements by drawing two number lines—one representing centimeters and the other representing inches. Ask students to record their measurements and answer the reﬂection question. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the students to a Math Chat to share their observations and learning.

Intervention

Acceleration

LENGTH

Home

FACILITATION TIP If students struggle with drawing the number lines, demonstrate how to use the straight edge of the ruler to draw a line, and then use the increments on the ruler to form tick marks along the drawn line.

Math Chat •

•

DOK-3 What did you notice when you measured your foot using both units? The number of centimeters and inches required to measure were different. It took more centimeters than inches to measure our foot. DOK-3 What is the relationship between the size of the unit and the number of units needed? The shorter the unit is, the more units are needed to measure an object. The longer the unit is, the fewer units are needed to measure an object. DOK-3 What is another unit longer than centimeters or inches you could use to measure your foot? Would this be an effective way to measure your foot? Why? We could use meters, but it would not work as well because our feet are not even 1 meter long. DOK-3 What is something that would be reasonable to measure using meters? The length of a swimming pool, the width of a backyard, the length of a school bus DOK-3 Why would measuring these items in meters be better than measuring them in centimeters? These are all objects that are much larger than a centimeter. It would take too many centimeters to measure them. It would take too much time, and the number would be very large. DOK-3 When you are trying to decide what measuring unit to use, do you want to use more or less of the unit to measure the object? You want to use less of the unit because it saves time and uses smaller numbers. DOK-3 When would knowing which units to use to measure something be helpful at home? If I want to measure how long my neighborhood pool is before a race, I don’t want to end up with a really big number or take a long time ﬁguring it out by adding many numbers together.

STEMscopes Tip If students are not ready to move on to the next concept, use Small-Group Intervention, located in the Intervention section, to revisit the conceptual foundation of the scope’s concepts and to build student understanding. Here, you will ﬁnd a hands-on reteach activity, Teacher Checklists for monitoring student progress, and supplemental Student Handouts. A student Checkup is provided in Grades 2-5.

Post-Explore 1. 2. 3.

FACILITATION TIP Have students complete the Exit Ticket to formatively assess their understanding of the concept. When previewing this Exit Ticket with students, encourage them to draw a line Complete the Anchor Chart as a class. from the end of the objects down to the Have each student complete their Interactive Notebook. ruler. Notes

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LENGTH

Length Explore 4 – Solving Problems with Length ACTIVITY PREPARATION Students solve one- and two-step real-world measurement problems involving addition and subtraction of lengths given in the same units.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Set of Task Cards (per pair) 1 Exit Ticket (per student)

• • •

Reusable • •

Plan to have the students work with a partner to complete this activity. Print and cut out a set of Task Cards, and place them in a resealable bag for each pair of students. Print a Student Journal and an Exit Ticket for each student. For the Exit Ticket, gather a ruler for each student.

1 Resealable bag (per pair) 1 Ruler (per student)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Consider including at least one strong reader in each pair. Reading comprehension is an important part of the problem-solving process. FACILITATION TIP Students may beneﬁt from highlighting or underlining important information. Numbers and words such as total, together, and sum are helpful to keep track of when problem solving.

184

2. 3.

Read the following scenario to the class: Martina is planning a birthday party for her nephews Carter and Grayson. She keeps running into problems when it comes to the lengths of certain items. Martina has written everything down, but she needs our help to solve her problems. Do you think you can use your knowledge of length and addition and subtraction to help Martina? Divide the class into groups of two, and direct students’ attention to the bag of Task Cards. Instruct students to read through each Task Card and discuss it with their partners. Encourage students to predict how they might answer each one of Martina’s problems. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What is the problem asking you to ﬁnd? Answers will vary. How much longer the birthday candle is when it is lit than when it is not lit.

DOK-1 What information is given? Answers will vary. The picture of the candle and ﬂame with a centimeter ruler.

DOK-2 How do you estimate the length of an object? Answers will vary. You can use the information or unit given to make a close guess. You can use benchmark measurements.

DOK-3 How can you use a ruler to help solve a word problem involving length or estimation of length? Answers will vary. A ruler can help you estimate lengths. Those lengths can be used to add or subtract and solve word problems. © Accelerate Learning Inc. - All Rights Reserved

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Give each student a Student Journal, and ask students to record the answer to each problem. Encourage students to discuss and answer the reﬂection question with their partners. When students have completed the Task Cards and their Student Journals, bring the class together as a whole group. After the Explore activity, invite students to a Math Chat to share their observations and learning.

Intervention

Acceleration

LENGTH

Home

FACILITATION TIP Challenge students to write an equation representing each answer. Explain that an equation communicates the steps used to solve the problem and will be helpful in explaining their mathematical thinking during the upcoming Math Chat.

Math Chat •

• •

•

DOK-3 When solving a problem using length, what do you need to know? You need to know what information is given and what the problem is asking you to find. DOK-2 What operation would you use when comparing lengths? I could use subtraction, or I could count up to find the difference. DOK-3 When might you use addition to solve a measurement problem? I might use addition when I know the length of an item but need to know the length of 3 of those items. So I would add the length 3 times—like 10 inches + 10 inches + 10 inches = 30 inches long. DOK-3 When might you use subtraction to solve a measurement problem? I might use subtraction when I measure the length of something, but then I cut part of it off and I want to know how long the leftover part is. DOK-4 What types of real-world problems involve measuring or estimating length? Framing a picture; fitting a TV into an entertainment center; measuring a foot for shoe size

2. 3.

Take some time to gather some images of people measuring in the real-world to share with students.

FACILITATION TIP

Post-Explore 1.

FACILITATION TIP

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

This Exit Ticket provides a good opportunity to discuss perimeter with students. In addition, some students may be distracted by the measurements of the bulletin board. Pre-read the scenario with them and reassure students that this is a just model for a bulletin board. The measurements are quite small for the real world.

185

LENGTH

Length Explore 5 – Representing Addition and Subtraction on a Number Line ACTIVITY PREPARATION Students use number lines to solve all types of addition and subtraction word problems within 100 with unknowns in various places.

Standards for Mathematical Practice • •

MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Frog Problem-Solving Cards (per group) 1 Exit Ticket (per student)

Reusable • • •

1 Black permanent marker (per teacher) 1 Counter, green if available (per student) 1 Resealable bag (per group)

• • •

Plan to have students work in groups of 3 or 4 to complete this activity. Draw an open number line on a poster board with a permanent marker for each group. Print and cut the Frog Problem-Solving Cards, and place them into a resealable bag for each group along with a set of sticky notes. Laminate them for future use, if desired. Gather enough counters (green, if possible) for each student to have one. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Assorted Number Lines and 1–120 Number Chart Supplemental Aids elements in the Intervention section.

Consumable • •

1 Poster board (per group) 1 Set of sticky notes (per group)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Have each group make a number line with different intervals using sticky notes.

FACILITATION TIP Depending on your students, you may want to read some of the cards together as a class. Make time to model ﬁnding the math words in the stories by underlining or highlighting them while you read. 186

Read the following scenario to the class: Jamaal and his sister Imani spend summer vacations in the country. Their backyard contains a large pond, and many frogs live there. Jamaal and Imani decide to build the frogs a line of lily pads from one side of the pond to the other, like a footbridge. Then, they try to keep track of how many lily pads the frogs hop across. Can you use a number line and make jumps on it like the frogs make jumps on the lily pads to help Jamaal and Imani keep track of how the frogs use the lily pads? Divide the class into groups of 3 or 4. Distribute and direct students’ attention to the open number lines, counters, and sticky notes. Allow students a few moments to think about the open number lines, discover the manipulatives, and experience how they work with their group. Tell students they will add intervals to their open number lines, evenly spaced and marked with numbers, by using a pencil to write the numbers on sticky notes and attaching the sticky notes to the number line for each problem. Ask the following questions: a.

DOK-3 What intervals do you think work best on a number line to solve problems within 100? Why? Answers will vary. It depends on the problem, but usually intervals of 1s, 2s, 5s, or 10s work best. If the problem was 28 – 16, 2s might be the best interval. If the problem was 98 – 80, 10s might work best.

7. 8.

Explore

Explain

Elaborate

Evaluate

DOK-2 Is there another way to mark your number line so it still helps you solve addition and subtraction problems within 100? Yes, there is always more than one way to mark a number line. Instead of using 10s, you could use 5s, but it will just be more crowded and have more jumps. If you use intervals of 2, you would need to make a longer number line and include a lot more jumps. DOK-2 After looking at your group’s number line, what measuring tool does it remind you of? Why? Answers will vary. It reminds me of a ruler because now that we have the intervals on it, it has the same-sized spaces in between and marks at regular intervals, and the numbers increase in value from left to right. It is used to measure the distance from one point to another—just like a ruler.

Intervention

Acceleration

FACILITATION TIP Model for students how to determine the interval, place intervals on a number line, solve an addition problem, and solve a subtraction problem. FACILITATION TIP Acting out each card allows students to determine if the solution requires addition or subtraction.

Give a bag of Frog Problem-Solving Cards to each group. Challenge students to take turns acting out each problem using the counters to jump to the left or to the right on the number line to reﬂect the addition or subtraction problem being solved. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

Engage

LENGTH

Home

DOK-3 Which way do you jump on the number line to show addition? Why? To the right because you are adding to or putting together numbers, so you will have a greater number as a solution. Values increase from left to right. DOK-3 Which way do you jump on the number line to show subtraction? Why? To the left because you are taking from, taking apart, or comparing numbers and will have a lesser number as a solution. Values decrease from right to left.

Give each student a Student Journal, and ask students to draw what was acted out with counters on the number line on their Student Journals for each Frog Problem-Solving Card. Students should write intervals (in 1s, 2s, 5s, and/or 10s) on sticky notes and attach them equally spaced to the open number line. Remind students to then write a number sentence reﬂecting the strategies used on the number line. When students have completed each Frog Problem-Solving Card and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the students to a Math Chat to share their observations and learning.

Math Chat DOK-3 What strategy did you use to solve this problem using the open number line? First I decided what the intervals should be to best solve this problem. I drew them on the open number line, and then I labeled each interval with the correct number. I started at one number from the problem and added the other number by jumping the correct number of intervals to the right, counting as I jumped until I landed on the correct answer. • DOK-2 What do you think is the most challenging part of using an open number line? I think the most challenging part is looking at the numbers in the problem, deciding what intervals to use, and marking them carefully on the number line. • DOK-3 How was the number line helpful in solving addition and subtraction problems? I like using a number line because it is a pictorial model and tool that helps me see my answers and lets me count up or count back easily. I can ﬁnd the distance between numbers. • DOK-3 Did you and your group members always use the same strategies for solving the Frog Problem-Solving Cards? Why? On card 6, my classmate did addition and added 18 + unknown = 78. I did subtraction and subtracted 78 – 18 = 60. We both got the correct answer but used different strategies. •

STEMscopes Tip The Kindergarten through Grade 5 Vertical Alignment Chart is found in the Teacher Toolbox Essentials Section. This printable document explains that standards are organized by the six domains: Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations Fractions, Measurement and Data, and Geometry. A Grade Level Focus page shows the progression of emphasized content areas across grade levels. Vertical alignments are separated by color-coded domains, and each domain contains the clusters and standards showing the curriculum progression across grade levels.

187

LENGTH

Length Explore 5 – Representing Addition and Subtraction on a Number Line Post-Explore 1. FACILITATION TIP On this Exit Ticket, students who are struggling may need the starting number and intervals marked for them to begin. Support students by reading the story problem aloud with them and underline the key math words.

2. 3. 4.

Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

188

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

189

LENGTH

Length Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Construct Measuring Instruments Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Length Using Formal Measuring Tools Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Inverse Relationships

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Solving Problems with Length

Independent practice assignment that gives students an opportunity to demonstrate their learning

Show What You Know, Part 5 Representing Addition and Subtraction on a Number Line Independent practice assignment that gives students an opportunity to demonstrate their learning

190

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Art Camp A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Creating a Study

Length Problem Solving

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Measure Up

Length with Formal Measurement Tools

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

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LENGTH

Length Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

192

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

LENGTH

Home

What prompts will be used?

What does mastery look like?

I can construct simple measuring instruments using unit models.

I can compare unit models to rulers.

I can estimate the length of an object or distance to the nearest whole unit.

I can measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools.

I can measure to determine how much longer one object is than another.

I can express the length difference in terms of a standard-length unit.

I can represent whole-number sums and differences within a standard unit of measurement on a number line diagram.

193

SCOPE 1

Time Scope Introduction SCOPE SUMMARY

Student Expectations

Students continue to make connections between number lines and clocks to help them learn to read and write time to the nearest ﬁve minutes. Using a number line helps students understand that the numerals on clocks are divided into increments of 5, which represent ﬁve minutes. Students also identify activities that occur from midnight to right before noon as a.m. activities, and they identify activities that occur from noon to right before midnight as p.m. activities. They use both analog and digital clocks to read and write time. Students also measure elapsed time using a time line to the hour or half hour while avoiding crossing over a.m. and p.m.

2.MDR.6.1 Tell and write time from analog and digital clocks to the nearest ﬁve minutes, and estimate and measure elapsed time using a timeline, to the hour or half hour on the hour or half hour.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students use both analog and digital clocks to identify time to the nearest hour and half hour. They also measure elapsed time to the hour on the hour using a predetermined number line.

Third-grade students tell and write time from analog and digital clocks to the nearest minute. They solve problems involving elapsed time to the hour, half hour, and quarter hour.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

tell and write time in hours and half-hours using analog and digital clocks.

•

measure elapsed time to the hour on the hour using a predetermined number line.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES For the Hook, students are presented with a scenario to solve using clocks to write the time a class goes to and comes back from recess. Students will: •

read and write time to the nearest 5 minutes.

•

use analog and digital clocks.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

194

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

A.M. and P.M. In this exploration, student groups will create a timeline to complete helping a family member keep track of their school schedule. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

create a timeline of their day using a.m. and p.m.

Hour- and Minute-Hand Clocks In this exploration, student pairs will solve a scenario in which they help an airport read analog clocks and write the time to update the Arrival and Departure board before people arrive at the airport. Students will: •

•

estimate time based on where the hour hand is located solely.

•

use a clock to add the estimated time by hour.

Digital and Analog Clocks In this exploration, students will solve a scenario about helping read and write jump-rope contest times using analog and digital clocks. Students will: •

read and write time on an analog clock to the nearest 5 minutes.

read and write time on digital and analog clocks to the nearest 5 minutes.

After students have solved the scenario, they will share and discuss their ﬁndings and then complete an Exit Ticket for assessment.

As students solve the scenario, they discuss their learning with the class and complete an Exit Ticket for assessment.

Explore 5

In this exploration, students will continue the scenario from the previous exploration by adding estimated time to their timeline Students will:

After students have solved the scenario, the teacher guides students in color coding, sharing, and discussing their ﬁndings. Then students discuss their learning and complete an Exit Ticket.

Explore 4

Explore 3

As students are working, the teacher monitors and adjusts, leads a discussion about the students’ ﬁndings, and has students complete an Exit Ticket to assess learning.

Hour-Hand Clocks

Elapsed Time In this exploration, students will estimate and measure elapsed time using a timeline, to the hour or half hour. Students will: •

read the time on the analog or digital clock and decide if the time is a.m. or p.m.

•

use a timeline to help measure how long each event will last or the ending time by labeling the time by the hour or half hour.

After solving the scenario, students discuss their learning with the class, complete an Exit Ticket for assessment, and then revisit the Hook to solve.

195

TIME

Time Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

196

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE Students show a given time to the half hour on an analog clock. They write this time to show what it would look like on a digital clock. This activity is intended to assess mastery of the following standard(s): 1.MDR.6.2 Tell and write time in hours and half-hours using analog and digital clocks, and measure elapsed time to the hour on the hour using a predetermined number line.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Reusable •

1 Geared clock, optional (per student)

Print the Student Handout for each student. Students will be writing times on both analog and digital clocks. Another option would be to provide geared clocks for students and allow them to manipulate the hands on the clock to show the time.

Procedure and Facilitation Points 1. 2. 3. 4. 5.

Give each student the Student Handout. Read the following scenario to the class: Josh and Manny are planning on leaving their houses at 2:30 p.m. to meet up at their neighborhood swimming pool. Have students draw hands on the analog clock to show the time, and then have them write the time on the digital clock. Have students check their work with a partner. Facilitate a class discussion about time to the half hour. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers, and check for understanding and misconceptions. Ask the following discussion questions: a.

Which hand on an analog clock tells us the hour? The short hand

Which hand on an analog clock tells us the minutes? The long hand

Describe where the hour hand needs to be if the time is 2:30. The short hand will be in between the 2 and 3 because it is 30 minutes past the hour.

Describe where the minute hand needs to be if the time is 2:30. The long hand will be on the 6 because the numbers shown on a clock are counting by ﬁves.

FACILITATION TIP Before giving each student a Student Handout, project this scenario and conduct a guided read aloud of it.

STEMscopes Tip Depth of Knowledge (DoK) Levels are found on the Lesson Planning Resources page in the Essentials section of the Teacher Toolbox. A printable document lists the DoK levels for all elements of the scope. This resource gives teachers the ability to choose the appropriate DoK-leveled assignments to help students expand and deepen their mathematical thinking and reasoning.

e. What does the number before the colon symbol tell us? The hour

What does the number after the colon symbol tell us? The minutes

What is the difference between analog clocks and digital clocks? Analog clocks show tick marks with numbers 1–12 and small tick marks. They have short hands and long hands. Digital clocks have the time printed out in number form with the hour ﬁrst before the colon and then the minutes second after the colon.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

FACILITATION TIP The clock images on this Foundation Builder are a good resource for some extra whole class review. This section provides only one opportunity to gather understanding of prior knowledge. Consider using the Foundation Builder clock images with the whole class.

197

TIME

Time Hook – Recess Times ACTIVITY PREPARATION Students read and write time to the nearest ﬁve minutes.

Materials

Preparation

Printed •

• •

1 Recess Times (per pair)

Reusable • • • • •

•

1 Geared clock (per student) 1 Whiteboard (per student) 1 Dry-erase marker (per student) 1 Projector or document camera (per teacher) 1 Phenomena Video (per teacher)

Plan to show the video. Plan to display Recess Times on the board, and print Recess Times for each pair of students. Part II • •

Gather a geared clock, a whiteboard, and a dry-erase marker for each student. Plan to divide the class into pairs so that each pair can share one Recess Times.

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

FACILITATION TIP

3. 4.

Remind students that this type of clock is called an analog clock. FACILITATION TIP Have a discussion about what students notice about the two clocks. How are they alike? How are they different?

STEMscopes Tip Located under the Scopes tab, the Visual Glossary is an alphabetical list that provides learners with visuals of the key vocabulary and concepts in English and Spanish. Each visual includes the term, a written deﬁnition, and a speech button with narration. Some vocabulary also includes a 3- to 15-second video featuring real-world examples.

6. 7.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Display the Recess Times on the board. Read the following scenario to the class: Mrs. Moore’s class goes outside for recess every afternoon at the same time. The time on the ﬁrst clock shows what time the class goes outside for recess. They stay outside on the playground for 25 minutes. The time on the second clock shows what time they come inside from recess. Look at the clocks, and write the times Mrs. Moore’s class goes to recess and comes in from recess. Discuss the following questions: a.

DOK-1 What information do we know? The ﬁrst clock shows what time the class goes outside for recess. The second clock shows what time they come inside from recess.

DOK-1 What information do we need to ﬁnd out? What time do the two clocks show?

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

198

DOK-1 What information do we know? The ﬁrst clock shows what time the class goes outside for recess. The second clock shows what time they come inside from recess. © Accelerate Learning Inc. - All Rights Reserved

TIME

Home

b. 3.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-1 What information do we need to ﬁnd out? What time do the two clocks show?

Divide the class into groups of two. Give each pair of students a Recess Times. Provide each student with a geared clock, a whiteboard, and a dry-erase marker. Allow time for students to use their strategies to ﬁgure out what times Mrs. Moore’s class goes to recess and comes in from recess. Have students write the times on their whiteboards and make sure to label each time with a.m. or p.m. Discuss the following questions:

FACILITATION TIP

DOK-1 What is an analog clock? A clock or watch that has moving hands Use a large analog clock and point to each hand as students respond. to show the time

DOK-1 What does the short hand tell us? The hour

DOK-1 What does the long hand tell us? The minutes

DOK-3 What strategy did you use to read the time on the analog clock? Answers will vary. I looked at the hour hand ﬁrst to see what the hour was. I knew it was 12 o’clock because the short hand is between 12 and 1. Then I counted by 5s from 12 to 2, so I knew the minute hand read 10.

e. DOK-2 What time does Mrs. Moore’s class go outside for recess every afternoon? 12:10 p.m. f.

DOK-2 What time do they come back inside from recess? 12:35 p.m.

DOK-3 How do you know these times are p.m.? Because they are in the afternoon; if it was 12:10 a.m., it would be in the middle of the night.

h. DOK-2 If their school gets out at 3:50 p.m., where would the hour hand be at this time? It would be between the 3 and 4 but closer to the 4.

FACILITATION TIP Discuss the times of other events that occur throughout the school day, and have students model the times on their geared clocks.

199

TIME

Time Explore 1 – A.M. and P.M ACTIVITY PREPARATION Students explore the concept of a.m. and p.m. through creating time lines of their day.

Standards for Mathematical Practice • •

MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Activity Cards (per pair) 1 Exit Ticket (per student)

• •

Reusable • •

1 Stapler (per class) 1 Resealable bag (per pair)

Consumable • • •

Plan to have students work in groups of two to complete this activity. Print and cut a set of Activity Cards, and place them in a resealable bag for each pair of students. If desired, laminate them for future use. Gather a glue stick for each pair of students. Prepare a time line for each pair of students by stapling a red and a blue sentence strip together as shown here:

• •

1 Red sentence strip (per pair) 1 Blue sentence strip (per pair) 1 Glue stick (per pair)

Print a Student Journal and an Exit Ticket for each student. Note: Please allow students to keep time lines to use with Explore 2.

PROCEDURE AND FACILITATION 1.

FACILITATION TIP Not all student pairs will agree on the time at which they complete each activity. Encourage students to compromise on the placement of the activities on the time line. Allow students to write when they complete the activities in their Student Journals, even if it doesn’t match the time line. FACILITATION TIP Students may not be familiar with the terms midnight and noon. Explain that midnight is considered the middle of the night and noon is considered the middle of the day.

200

Read the following scenario to the class: Your mom is super busy with her job and cannot keep up with everyone’s schedule. She wants you to create a time line of all the daily activities that she can hang on the refrigerator. Can you help Mom keep track of your schedule? Divide the class into groups of two, and direct students’ attention to the sentence strip time lines, bags of Activity Cards, and glue sticks. Allow students a few moments to discover the manipulatives and experience how they work with their partner. Instruct students to read or create each Activity Card and place it on the time line, either on the red, which represents a.m., or blue, which represents p.m. Encourage students to discuss the activities and make decisions with their partners. Ask students to glue the Activity Cards onto their time lines. Monitor and talk with students as needed to check for understanding by using the following guiding questions. a.

DOK-1 What do a.m. and p.m. mean? Answers will vary; time periods of a day

DOK-1 When is a.m.? Answers will vary. It is the half of the day between midnight and noon; morning and lunchtime.

DOK-1 When is p.m.? Answers will vary. It is the half of the day between noon and midnight; afternoon and night.

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

e. DOK-3 What activities can you and your partner add to the time line? Answers will vary. We are adding when I have basketball practice in the afternoon; we are adding when I ride the bus to school in the morning. 5.

6. 7.

Give each student a Student Journal, and ask students to complete the table with a.m. and p.m. activities from their time lines. Encourage students to discuss and respond to the reﬂection questions with their partner. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

FACILITATION TIP If students have diﬃculty thinking of additional activities they do each day, ask them guiding questions about their activities to activate their thinking. For example, what do you do after dinner? Are you in any after-school activities?

Math Chat •

•

• • • • • • •

DOK-3 What is the ﬁrst thing you do when you wake up? What time of day is that, a.m. or p.m.? I make my bed/brush my teeth/eat breakfast, etc. I do this in the a.m. DOK-3 What is the last thing you do before you go to bed? What time of day is that, a.m or p.m.? I put on my pajamas/brush my teeth/read a book, etc. I do this in the p.m. DOK-1 What part of the day is midnight? In the middle of the night; it is the beginning of a.m. DOK-1 What part of the day is noon? In the middle of the day; it is the beginning of p.m. DOK-1 Are there certain activities you only do in the a.m.? I only eat breakfast in the a.m., but sometimes we eat breakfast for dinner. DOK-1 Are there certain activities you only do in the p.m.? I only have basketball practice in the p.m., but sometimes we have games in the a.m. DOK-1 How many hours are in a day? There are 24 hours in a day. DOK-1 How many days are in a month? There are 30 or 31 days in a month, depending on the month. February has 28 days, unless it is a leap year. DOK-1 How many weeks are in a year? There are 52 or 53 weeks in a year, depending on the year.

STEMscopes Tip Housed in the Home section, the Content Unwrapped element provides a clariﬁcation of the instructional expectations. Each student expectation is dissected into what students should be doing and what they should know, as well as the implications for instruction. A vertical alignment shows how the topic progresses through applicable grade levels.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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TIME

Time Explore 2 – Hour-Hand Clocks ACTIVITY PREPARATION Students estimate time based only on the location of the hour hand.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Reusable • • •

1 a.m. and p.m. time line from Explore 1 (per pair) 1 Geared clock (per student) 1 Projector (per class)

• Plan to have students work with the same partner from Explore 1 to complete this activity. • Plan to use the a.m. and p.m. time lines that students created in Explore 1. • Gather geared clocks for all students, or plan to project the digital manipulative so students can focus on the hour hand only. • Print a Student Journal and an Exit Ticket for each student. • For students who need more support in recalling information, please see our Analog Clock Supplemental Aids element in the Intervention section. • Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Clock – Hour Hand only)

PROCEDURE AND FACILITATION 1.

2. FACILITATION TIP If students are having diﬃculty estimating time, ask them to identify the actual time any of their activities take place. For example, they may know exactly when they get out of bed and when they get to school. Then, guide them to understand that the times of the activities between these known events will fall between these times.

FACILITATION TIP As students draw, remind them that the hour hand is shorter than the minute hand and does not reach the clock numbers. 202

Read the following scenario to the class: Your mom is so excited about the time line you made to hang on the refrigerator. But something is missing! She wants to know about what time each of the a.m. and p.m. activities happen by placing the hour with each card. Can you estimate what hour each activity occurs? Divide the class into the same pairs of students as with Explore 1, and direct students’ attention to the time line and geared clock. Give students a few moments to discover the manipulatives and experience how they work with their partner. Instruct students to estimate the hour of each activity on the time line. Encourage students to discuss where the hour hand would be on the clock based on the actual hour each activity occurs. Monitor and talk with students as needed to check for understanding using the following guiding questions: a.

DOK-2 What is the actual time of this activity? Answers will vary. I wake up and get out of bed at 7:00 a.m.

DOK-2 Where is the hour hand on the clock when it is that time? Answers will vary. The hour hand should be pointing at the 7 when it is 7:00.

DOK-2 What hour are you writing for this activity? Answers will vary. I am writing 7 a.m. for this activity.

Give each student a Student Journal, and ask students to draw the hour hand on the analog clock and write the hour for each a.m. and p.m. activity on their time lines. Encourage students to discuss and respond to the reﬂection question with their partner. © Accelerate Learning Inc. - All Rights Reserved

TIME

Home

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

• • •

DOK-2 If I place my hour hand between the 2 and the 3 on the clock, what is the approximate time shown? How do you know? It is around 2:30 because half of an hour is 30 minutes. DOK-2 What time do you wake up? Can you show me how to represent that time on the clock? I wake up at 7:00. The hour hand should be pointing to the 7. DOK-2 What time do you eat lunch? How would you draw that on the clock? I eat lunch at 11:30. The hour hand should be between the 11 and 12. DOK-2 If I place my hour hand where it is almost touching the 9, what hour would it be? How do you know? The hour would still be 8 because the hour hand is still before the 9.

Intervention

Acceleration

STEMscopes Tip Found in the Engage section, the Foundation Builder is used to ﬁll the learning gaps identiﬁed in the Accessing Prior Knowledge activities and bridge students’ learning to the current scope. These activities use manipulatives to review prerequisite student knowledge. Also included are possible student preconceptions about a topic and suggestions on how to overcome those preconceptions.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP On this Exit Ticket, allow students to draw the minute hand if they are able.

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TIME

Time Explore 3 – Hour- and Minute-Hand Clocks ACTIVITY PREPARATION Students practice reading and writing time to the nearest ﬁve minutes on an analog clock.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Arrivals and Departures (per pair) 1 Exit Ticket (per student)

Reusable •

• • • • •

1 Geared clock (per student) •

Plan to have students work in groups of two to complete this activity. Gather geared clocks for all students, or plan to use the digital manipulative. Print a set of Arrivals and Departures for each pair of students. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Analog Clock Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Clock)

PROCEDURE AND FACILITATION FACILITATION TIP

Clarify what arrivals and departures are at an airport, bus stop, and train station.

2. FACILITATION TIP For students who are having diﬃculty reading the time on the analog clock, have number lines available and allow them to ﬁrst show the time on a number line.

204

Read the following scenario to the class: You are in charge of keeping track of the arrival and departure times for the local airport. Someone accidentally posted clocks on the display board instead of the digital time. Your supervisor has asked that you read each clock and write the time to update the arrival and departure board before people arrive at the airport. Can you read the clocks and write the times? Divide the class into groups of two, and direct students’ attention to the Arrivals and Departures and geared clock. Allow students a few moments to discover the manipulatives and experience how they work with their partner. Instruct students to read the clocks for each flight and find the time on their own geared clocks. Encourage students to discuss how to read the time with their partners. Give each student a Student Journal, and ask students to write the time for each arrival and departure. Encourage students to discuss and respond to the reflection questions with their partner. Monitor and talk with students as needed to check for understanding by using the following guiding question:s a.

DOK-3 What do you notice about the clock for this ﬂight? Answers will vary. The hour hand is between the 4 and 5; the minute hand is pointing to the 9.

FACILITATION TIP

Have students use their arms to show some different times in imitation of an analog clock.

DOK-1 Where is the hour hand? Minute hand? Answers will vary. The hour hand is closer to 5, but it is still 4 o’clock. The minute hand is pointing at the 9. When I count by 5s around the clock, it is 45 minutes.

DOK-3 What do you notice about the hour hand when you are turning the clock hands to a certain time? The hour hand moves slowly from one number to the next as the minute hand moves around the whole clock. © Accelerate Learning Inc. - All Rights Reserved

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

DOK-1 How many minutes are in one hour? 60 minutes

e. DOK-2 When we measure the distance the minute hand moves around the clock one time, how many intervals are there? (Intervals are the spaces from tick mark to tick mark.) 60 intervals or 60 minutes f.

DOK-2 If there are 60 minutes in an hour, how many minutes are in half an hour? 30 minutes

DOK-3 What would be an example of a time to the half hour? Answers will vary. 2:30 or 4:30 or half-past 10

FACILITATION TIP Use the Math Chat Print Files to record answers visually for some of these questions so students can refer to them as they learn about time.

h. DOK-2 If there are 60 minutes in an hour, how many minutes are in a quarter of an hour? 15 minutes i. DOK-3 What does “a quarter past” mean? What would be an example of time referred to as “a quarter past”? Answers will vary. It means a quarter of an hour (or 15 minutes) past the hour mark. Examples include 3:15 and 9:15. j. DOK-3 What does “a quarter ’til” mean? What would be an example of time referred to as “a quarter ’til”? It means a quarter of an hour (or 15 minutes) until the next hour. 8:45 or 1:45 are examples 6. 7.

When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • •

• • • • •

DOK-3 How did you know the time for this ﬂight? I looked at where the hour hand was pointing and then looked at where the minute hand was pointing. DOK-2 How can you tell the time with only the hour hand? I look at the position of the hour hand to help me know. If it is pointing exactly to the number, then it is that hour. DOK-1 Where will the hour hand be if it is half past the hour? It will be halfway between the two numbers. DOK-2 If the time is 15 minutes past 3, what is another way to say this time? Three-ﬁfteen or a quarter past 3 DOK-2 If the time is half past 7, what is another way to say this time? Seven-thirty DOK-2 If the time is a quarter ’til 11, what time is it? 10:45 DOK-3 When would you need to know how to read a clock outside of school? Waiting for a doctor’s appointment; knowing when gymnastics is over; being ready for a parent to pick you up from a friend’s house

STEMscopes Tip Interactive Practice, found in the Elaborate section, includes interactive games that can be utilized on almost any device. The engaging games focus on the skills and concepts established by the standards in the scope. They can be assigned as practice throughout the scope or as a review throughout the year. These games give students another opportunity to see the concepts they have learned in action. While students are playing the games, teachers can facilitate smallgroup interventions and reteaching for struggling students as well as independent projects assigned to advanced learners.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP On this Exit Ticket, an accommodation might include highlighting the hour hand for students who can’t quite see which hand is longer.

205

TIME

Time Explore 4 – Digital and Analog Clocks ACTIVITY PREPARATION Students read and write time to the nearest ﬁve-minute increment using analog and digital clocks.

Standards for Mathematical Practice • • •

MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Time Task Cards (per group) 1 Exit Ticket (per student)

•

Reusable • •

• •

1 Geared clock (per group) 1 Resealable bag (per group)

•

Plan to have students work in groups of 4 to complete this activity. Gather enough geared clocks for each group, or plan to use the digital manipulatives. Print and cut out a set of Time Task Cards, and place them in a resealable bag for each group. If desired, laminate them for future use. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Analog Clock Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Clock)

PROCEDURE AND FACILITATION 1.

2. FACILITATION TIP For students needing extra support, allow them to show the times on number lines ﬁrst and then show the time on the geared clock.

FACILITATION TIP

a. DOK-2 What is the start time for this grade level? End time? Answers will vary. Kindergarten’s start time is half past 9, or 9:30, and its end time is a quarter ’til 10:00, or 9:45.

Encourage students to say the times on the cards another way. For example, half past 9 is also 9:30.

b. DOK-2 Can you show me that time using the geared clock? Answers will vary. I would move the minute hand around the clock until the hour hand was between the 9 and 10 and the minute hand was pointing at 30 minutes. c.

FACILITATION TIP Remind students to accurately draw the lengths of the hour and minute hands on the clocks. 206

Read the following scenario to the class: The school jump-rope contest is complete, and the times have been recorded. Not all the students can read the times because the teachers wrote in words instead of using clocks or numbers. Can you read the times and create clocks that all the students can read? Divide the class into groups of 4, and direct students’ attention to the geared clocks and bag of Time Task Cards. Allow students a few moments to discover the manipulatives and experience how they work with their groups. Instruct students to read the start and end times for each grade level on the Time Task Cards and ﬁnd the time on their geared clocks. Encourage students to discuss the time on their clocks with their groups. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

DOK-2 How would you write that time? Answers will vary. 9:30 or half past nine o’clock

Give each student a Student Journal, and ask students to draw the hands on the analog clock and write the digital time for each grade level. Encourage students to discuss and respond to the reﬂection question with their groups. © Accelerate Learning Inc. - All Rights Reserved

TIME

Home

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

When students have completed the Time Task Cards and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat • • •

• • •

•

DOK-3 How do you know what time it is on an analog clock? I look at the hour hand ﬁrst, and then I count by 5s to see how many minutes past the hour it is. DOK-1 How many minutes are there in an hour? 60 minutes DOK-3 What does it mean if we say it is a quarter ’til 4? Why? It means it is 15 minutes before 4 o’clock, or 3:45. 15 minutes is a quarter of an hour because an hour has 60 minutes. DOK-3 What is another way you can write the time 5:20? 20 minutes past 5 DOK-3 What happens to the hour hand as the minute hand moves forward on the clock? It moves slowly—one tick mark every 12 minutes. DOK-3 When is using a digital clock more appropriate for telling time? When kids are little and do not understand how an analog clock works; when you need to tell time quickly on an alarm clock or stopwatch DOK-3 When is using an analog clock more appropriate for telling time? When kids are older and can tell time on an analog clock, to hang on a wall, or as a watch to wear on your wrist

Intervention

Acceleration

STEMscopes Tip Under the Communicate Math tab of the Teacher Toolbox is the Communicate Math – Questioning page. Here, purposeful questioning strategies are grouped for Kindergarten through Grade 2, Grades 3–5, and Secondary. These strategies include modeling question techniques, allowing wait time, and using different questioning approaches. Teachers can use the questioning strategies to challenge and stimulate students’ ability to clarify and extend their mathematical thinking. Also included are tips to help walk students through appropriate mathematical discourse and communication of their ideas. Examples of questioning types are provided.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP This Exit Ticket can also be used prior to this Explore to assess prior knowledge to inform your instruction.

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Time Explore 5 – Elapsed Time ACTIVITY PREPARATION Students estimate and measure elapsed time using a time line, to the hour or half hour.

Standards for Mathematical Practices • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.

Materials

Preparation

Printed • • • •

• • •

1 Student Journal (per student) 1 Time Line (per student) 1 Carnival Schedule (per group) 1 Exit Ticket (per student)

• •

Reusable • • •

1 Geared analog clock (per student) 1 Sheet protector (per student) 1 Dry-erase marker (per student)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print the Carnival Schedule for each group. Print the Time Line for each student, and place it in a sheet protector for use with a dry-erase marker. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our Analog Clock and Open Number Line Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Analog Clock, Hundreds Chart, and Number Line)

PROCEDURE AND FACILITATION FACILITATION TIP

Be sure students are aware that this is an imaginary scenario. FACILITATION TIP If time and geared clocks are limited, this Explore could be completed as a whole class activity. Project the Carnival Schedule to the whole group and use the guiding questions.

2. 3.

FACILITATION TIP Another way to help students with counting elapsed time is to use fist, palm, and fingers to count up. Say the start time while pounding a closed fist into an open palm, then open the fist to count up saying the elapsing times aloud. For example (the first one in the Student Journal), pound fist while saying “7:30”, then raise thumb and say “8:30” and stop. Finally, add on the half hour. 208

Read the following scenario to the class: STEMscopes Elementary School is having a school carnival in a few days. The parents have volunteered to work at the carnival for speciﬁc time periods. The principal gave your teacher the schedule of each activity so you can ask your parents if they can work. Some of the information is missing. You need to determine when each event will begin or end or how long it will last. Can you help your teacher so your class can get enough parents to volunteer on the day of the carnival? Divide students into groups of 3 or 4. Distribute the Carnival Schedule and geared clocks to each group. Direct students’ attention to the ﬁrst activity on the Carnival Schedule. Discuss whether the activity time is a.m. or p.m., and have students read the time on the analog or digital clock. Allow time for students to talk with their groups about how to measure the elapsed time for the Go Fish activity. Give each student a Student Journal, dry-erase marker, and Time Line. Discuss how they will use the time line to help measure how long each event will last or the ending time by labeling the time by the hour or half hour. Instruct students to work with their groups to determine the elapsed time for each activity. Remind students that the elapsed time will either be to the hour or half hour. Students will determine the elapsed time by using jumps on the Time Line and record their work on their Student Journals. © Accelerate Learning Inc. - All Rights Reserved

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What time does the activity begin? Answers will vary. The activity begins at _____.

DOK-1 What time does the activity end? Answers will vary. The activity ends at _____.

DOK-2 Is the activity in the a.m. or p.m.? Answers will vary. The activity is in the morning, so it is a.m.

DOK-2 How can you use the time line to measure elapsed time? Answers will vary. I write the start time on the far left of the time line and then jump by the hour or half hour until I reach the end time. I will record each time on the time line.

DOK-2 How much time will a parent need to volunteer at the activity? Answers will vary. A parent will need to volunteer for __ hours.

After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

• • •

•

Acceleration

Monitor and talk with students as needed to check for understanding using the following guiding questions.

e. DOK-2 How can you use the time line to ﬁnd the ending time if you know the beginning time and the elapsed time? Answers will vary. I write the start time on the far left of the time line and then jump by the hour or half hour until I have counted the correct numbers of hours and half hours. I will write the times by the hour or half hour for my jumps.

Intervention

STEMscopes Tip The Skills Quiz, which is located in the Evaluate section, provides a means for students to demonstrate their knowledge about a topic and their computational fluency. Presented in multiple-choice, short-answer, drag-and-drop, and fill-in-the-blank formats, these standards-based assessments can be used as a formative assessment or as a review of the concepts learned throughout the scope. A printable assessment and Answer Key are found on the right-hand side of the screen. Teachers can also download and edit the assessment to provide the accommodations or modifications students require to demonstrate their ability to compute accurately and efficiently.

DOK-3 Why do we need to know how long an activity takes? We need to know how long something takes so our parents will know when to pick us up. We need to be on time for activities so we won’t be late. DOK-2 Which activity lasts the longest? Explain. The dunking booth lasts the longest. It was open for 4 hours. DOK-2 When will the sack race end? The sack race will end at 3:30 p.m. DOK-2 Explain the steps you used to measure elapsed time on the time line. I wrote the start time on the far left of the time line and then jumped by the hour or half hour until I reached the end time. I recorded each time on the time line to help me keep track. Then I added up the hours and half hours. DOK-3 What is another way you can measure elapsed time other than using a time line? I can use the analog clock or I can draw my own clock and count the hours an event lasts. I can just write the start time and then write the times in a column by the hour or half hour.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP On this Exit Ticket, provide some read aloud support for some students. Underline the key math words.

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TIME

Time Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

A.M. and P.M. Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Hour-Hand Clocks Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Hour- and Minute-Hand Clocks

Interactive Notebook

Show What You Know, Part 4

A cut-and-glue activity to process learning that can be added to a notebook for future reference

Digital and Analog Clocks

Independent practice assignment that gives students an opportunity to demonstrate their learning

Show What You Know, Part 5 Elapsed Time Independent practice assignment that gives students an opportunity to demonstrate their learning

210

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Coding Camp A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

The First Day of Second Grade

A.M. and P.M.

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

You’re in Charge

Analog and Digital Time to Five Minutes

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

211

TIME

Time Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

212

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

TIME

Home

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

What prompts will be used?

What does mastery look like?

I can tell and write time from an analog clock to the nearest ﬁve minutes.

I can tell and write time from a digital clock to the nearest ﬁve minutes.

I can estimate and measure elapsed time using a timeline, to the hour or half hour on the hour or half hour.

213

SCOPE 1

Money Scope Introduction SCOPE SUMMARY

Student Expectations

2.MDR.6.2 Find the value of a group of coins and determine combinations of coins that equal a given amount that is less than one hundred cents, and solve problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Students recognize the values of coins and count collections of coins that include quarters, dimes, nickels, and pennies that equal a given amount that is less than one hundred cents. They also learn to express values of coins with the combination of a numerical value and a cent symbol, which represents a unit of monetary measurement. Students also determine relationships of coins based on their values. They count groups of one type of coin and groups of mixed coins by using strategies such as counting by ones, twos, fives, tens, and twenty-fives. With mixed collections of coins, students count by larger values first and then by smaller values to find total values. Students also count dollar bills as they learn the relationships among the values of a penny, nickel, dime, quarter, and dollar bill. Students experience making equivalent amounts of money in coins or in bills. Students solve contextual problems involving dollars or cents.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students add quarters. Students may have informal real-world experiences involving money, such as buying school lunch or shopping with an adult, but this is the ﬁrst year that students formally work with money to solve problems with all coins. Students have only worked with whole numbers up to this point (decimals are introduced in fourth grade).

In fourth grade, students are introduced to decimals, acquiring and using decimal notation to the hundredths place. They also represent, read, and write fractions with denominators of 10 or 100 using decimal notation. Money can be an authentic context for this skill. They use the four operations to solve problems involving money.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

identify the value of quarters and compare the values of pennies, nickels, dimes, and quarters.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES For the Hook, students are presented with a scenario involving a local farmers market and paying for items. Students will: •

keep track of how much they will pay for the items.

•

check the value of change received.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

If your students are struggling with previously taught concepts, use the Foundation Builder activity in this scope to reinforce ideas presented in the APK. 214

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MONEY

Home

Value of a Collection of Bills and Coins In this exploration, students solve a real-world scenario about helping count money from customers at Bubba’s Burger Barn to determine the total value of bills and coins given to them. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

determine the value of a collection of bills and coins.

After completing the activity, students share their learning, and complete an Exit Ticket.

Solving Word Problems Involving Bills and Coins In this exploration, students will solve word problems in a scenario involving a local fruit stand to determine how much each customer paid and the change they should receive for their purchases. Students will: •

record the value using the appropriate money symbol.

•

add and subtract US coins and bills.

After completing the activity, students share their learning, complete an Exit Ticket, then revisit the Hook to solve. Notes

215

MONEY

Money Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

216

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MONEY

Home

ACCESSING PRIOR KNOWLEDGE Students identify the value of quarters and compare the values of pennies, nickels, dimes, and quarters. This activity is intended to assess mastery of the following standard(s): 1.MDR.6.3 Identify the value of quarters and compare the values of pennies, nickels, dimes, and quarters.

Materials

Preparation

Reusable • • • •

•

1 Quarter (per group) 2 Dimes (per group) 5 Nickels (per group) 25 Pennies (per group)

Consumable •

• • • •

Gather sets of coins, and place each set in a resealable bag for each group. Each set should contain the following coins: 1 Quarter 2 Dimes 5 Nickels 25 Pennies

1 Resealable bag (per group)

Procedure and Facilitation Points 1. 2. 3.

Divide the class into groups of 3 or 4. Give each group of students a set of coins. Tell students not to open the bag of coins until you have read the scenario. Read the following scenario to the class: Keegan found some change at the bottom of his backpack. He wants to separate it into different piles based on how much each coin is worth. Can you help Keegan identify and sort the coins? Ask students to take out all of the coins. Instruct students to work with their group to identify and sort the coins. Encourage students to discuss the attributes of the coins and how much each coin is worth (the value of each coin). Facilitate a class discussion about the coins. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers and to check for understanding and misconceptions. Ask the following discussion questions: a.

How did you sort the coins found in Keegan’s backpack? We sorted by quarters, dimes, nickels, and pennies.

What attributes helped you identify this coin? Answers will vary. The penny is a different color than all the other coins. The quarter is the largest and the dime is the smallest.

How much is a quarter worth? Twenty-ﬁve cents

How much is a dime worth? Ten cents

e. How much is a nickel worth? Five cents f.

How much is a penny worth? One cent

Which coin(s) could you trade for one nickel/dime/quarter? Answers will vary. I could trade two nickels or ten pennies for a dime.

h. How many pennies could you trade for one quarter? Can you show me? 25 pennies (Students should use the coins in the bag to demonstrate 25 pennies for one quarter.) 6.

FACILITATION TIP Do not distribute the coins until you have read the scenario. In addition, clarify your expectations for the coins before this activity. Be aware that some students will want to keep the coins. Consider whether you feel comfortable allowing students to keep all of or part of the seventy-ﬁve cents or not. FACILITATION TIP Project the scenario and conduct a whole class read aloud.

STEMscopes Tip The Exit Ticket, located within each Explore, gives teachers insight into student learning. This quick formative assessment helps teachers guide their future instruction. It can also be used to reinforce the skills and concepts at any time during the scope. Exit Tickets, Answer Keys, and editable ﬁles are located on the right side of the screen in the list of print ﬁles.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

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MONEY

Money Hook – A Trip to the Farmers’ Market ACTIVITY PREPARATION Students solve word problems involving coins, including quarters, dimes, nickels, and pennies, and they use the cent symbol appropriately.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

• •

Reusable • • •

Plan to show the video. Part II

1 Set of coin manipulatives (per pair) 1 Resealable bag (per pair) 1 Phenomena Video (per teacher)

•

Plan to divide the class into pairs to complete this activity. Place a set of coin manipulatives into a resealable bag for each pair of students. Print the Student Handout for each student.

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

2. FACILITATION TIP

To engage students, consider bringing in two plums and an orange to demonstrate the scenario. FACILITATION TIP Project this scenario for students to read along with you. Write the numbers of fruits and their costs as you are reading the scenario to provide students with a visual representation of the problem.

STEMscopes Tip Located under the Explain tab, Anchor Charts are designed to be used after teaching the Explore lessons. Creating anchor charts is a collaborative effort between teacher and students with each section illustrating the concepts covered in the individual Explores. A printable sample anchor chart is also included.

218

5. 6.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: It is a beautiful Saturday morning at the local farmers’ market. You see all kinds of fresh vegetables and fruits for sale. You know you will buy many different fruits and vegetables with the change in your change purse. Your mom tells you to problem solve and keep track of how you will pay for items and how you will check your change. You start by picking out 2 juicy plums for 18¢ each and an orange for 47¢. You give the vendor 2 quarters, 3 dimes, and a nickel. How much change should you receive? Discuss the following questions: a.

DOK-1 What information do we know? I bought 2 plums for 18¢ each. I bought an orange for 47¢. I paid for them with 2 quarters, 3 dimes, and a nickel.

DOK-1 What information do we need to ﬁnd out? How much change will I get?

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What information do we know? I bought 2 plums for 18¢each. I bought an orange for 47¢. I paid for them with 2 quarters, 3 dimes, and a nickel.

Engage

Explore

Explain

Elaborate

Evaluate

Divide the class into groups of two, and give each student pair a bag of coins. Give each student the Student Handout. Ask the students to determine how much change they will get from the transaction. Encourage students to use the coin manipulatives as needed. Discuss the following questions: a.

DOK-2 What strategy did you use to ﬁgure out how much the fruit cost? Answers will vary. We laid out the coins for each fruit and then added them together. We added the cents for each piece of fruit together like a regular addition problem.

DOK-2 What strategy did you use to ﬁgure out how much money you paid the vendor? Answers will vary. We just counted the coins.

DOK-2 What strategy did you use to ﬁnd the difference between what you owed and what you paid, also known as your change? Answers will vary. We solved this problem by subtracting the cents we owed from the cents we paid.

DOK-3 How did having the concrete models of coins help you to solve this problem? Answers will vary. It helped me because I could check my answers by trading the coins and seeing that I should be paid 2 pennies as change.

Intervention

Acceleration

MONEY

Home

FACILITATION TIP Have students refer to the Anchor Chart for the value of the coins and paper money if needed. FACILITATION TIP To save time, students can simply write coin initials instead of drawing circles for each coin (p = penny, n = nickel, d = dime, and q = quarter). FACILITATION TIP Allow students to discuss the advantages and disadvantages of the different strategies they used. Point out that even though different strategies were used, they all resulted in the same answers.

219

MONEY

Money Explore 1 – Value of a Collection of Bills and Coins ACTIVITY PREPARATION Students determine the value of a collection of bills and coins.

Standards for Mathematical Practice • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics.

Materials

Preparation

Printed • • •

•

1 Student Journal (per student) 1 Set of To-Go Order Cards (per pair) 1 Exit Ticket (per student)

• •

Reusable • • • • • • • • • •

•

6 Pennies (per pair) 6 Nickels (per pair) 5 Dimes (per pair) 3 Quarters (per pair) 3 One-dollar bills (per pair) 3 Five-dollar bills (per pair) 1 Ten-dollar bill (per pair) 1 Twenty-dollar bill (per pair) 1 Hundred-dollar bill (per pair) 1 Resealable bag (per pair)

Plan to have students work in groups of two to complete this activity. Print and cut out one set of To-Go Order Cards for each pair of students. Laminate them for future use, if desired. Place bill and coin manipulatives into a resealable bag for each pair of students. Print a Student Journal and an Exit Ticket for each student.

PROCEDURE AND FACILITATION 1.

FACILITATION TIP

Provide a quick review of identifying coins and bills by asking students to individually hold up each coin and bill type.

FACILITATION TIP

Review the cent and dollar symbols and write these on the board for students to reference.

220

Read the following scenario to the class: Bubba’s Burger Barn is known for its delicious hamburgers, fries, and milkshakes. You have been hired to work at their takeout window and collect money from customers. Can you count the money given to you by each customer and determine the total value of the collection of bills and coins? Direct students’ attention to the To-Go Order Cards and the bag of bill and coin manipulatives. Allow students a few moments to discover the manipulatives and experience how they work with their partner. Instruct students to read each To-Go Order Card. Students will take the bills and coins out of the bag to match what is on each card. They can use these manipulatives to help them count to ﬁnd the total value of bills and coins. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What bills did the customer give you for this order? Answers will vary. 1 twenty-dollar bill, 2 ﬁve-dollar bills, and 6 one-dollar bills

DOK-1 What coins did the customer give you for this order? Answers will vary. 3 quarters, 1 dime, 1 nickel, and 2 pennies

DOK-3 How are you ordering your bills to make skip counting easier? We are starting with the bills with the largest values and ending with the bills with the smallest values. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MONEY

Home

DOK-3 How are you ordering your coins to make skip counting easier? We are starting with the coins with the largest values and ending with the coins with the smallest values.

e. DOK-2 What is the total cost of this order? Answers will vary. 36 dollars

6. 7.

DOK-3 How are the two ways to write the total value similar? They both have the same numbers.

DOK-3 How are the two ways to write the total value different? One way uses a dollar sign or cent symbol; the other way uses only words.

Give each student a Student Journal, and ask students to draw a pictorial model of the collection of bills and coins for each To-Go Order Card. Encourage students to show their skip-counting strategies under the bills and coins. They will ﬁll in the total cost in two ways in the table on their Student Journals. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

FACILITATION TIP To save time, students can simply write coin initials instead of drawing circles for each coin (p = penny, n = nickel, d = dime, and q = quarter).

Math Chat • •

• • •

•

DOK-2 What was the total cost of this to-go order? Order 1 was $36. DOK-3 What strategy did you use to count your bills or coins? I sorted my coins and then skip counted the coins with the greatest value. I can skip count 25, 50, 60, 70, 75, 76. DOK-2 How would you count 3 quarters? 25, 50, 75 DOK-2 How many nickels does it take to make 45¢? 9 nickels equals 45¢. DOK-2 What is one way to make a collection of bills that totals twelve dollars? Two ﬁve-dollar bills and two one-dollar bills; one ten-dollar bill and two one-dollar bills DOK-1 What are the correct ways to write the values of bills and coins? We can use a dollar symbol or a cent symbol, or we can write the total number of bills and coins in words.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

FACILITATION TIP Have students skip count by 5, 10, and 25 as a whole group, in small groups, and with a partner. Use the choral responses as a quick spot check assessment for some students.

FACILITATION TIP On this Exit Ticket, extend the challenge to a few students by having them write the values using decimals.

221

MONEY

Money Explore 2 – Solving Word Problems Involving Bills and Coins ACTIVITY PREPARATION Students solve word problems involving bills and coins and record the value using the dollar sign and cent symbol appropriately.

Standards for Mathematical Practice • • •

MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.6 Attend to precision.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Task Cards (per pair) 1 Exit Ticket (per student)

•

Reusable • • • • • • • • •

•

Plan to have the students work in groups of two to complete this activity. Print and cut out one set of Task Cards for each pair of students. Laminate them for future use, if desired. Place bill and coin manipulatives into a resealable bag for each pair of students. Print a Student Journal and an Exit Ticket for each student.

10 Pennies (per pair) 10 Nickels (per pair) 10 Dimes (per pair) 4 Quarters (per pair) 5 One-dollar bills (per pair) 3 Five-dollar bills (per pair) 1 Ten-dollar bill (per pair) 1 Twenty-dollar bill (per pair) 1 Resealable bag (per pair)

PROCEDURE AND FACILITATION 1.

FACILITATION TIP

Pose a question to use as a warm-up task. For example, “I bought an apple for 25 cents and a banana for 30 cents. How much did I spend on both fruits?

3. 4.

Read the following scenario to the class: You have been hired by a local fruit stand to collect customers’ money when they buy some delicious fruit. Sometimes the customers pay using only dollar bills, and sometimes they pay using only coins. Can you solve each word problem to determine how much money each customer paid or how much change they should receive? Direct students’ attention to the Task Cards and the bags of bill and coin manipulatives. Allow students a few moments to discover the manipulatives and experience how they work with their partner. Instruct students to read each Task Card and solve using the bill and coin manipulatives. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

222

DOK-1 What information do you know? Answers will vary. Customer 1 bought an apple and a peach. She had 84 cents. She spent 3 dimes, 3 nickels, and 6 pennies on the fruit. © Accelerate Learning Inc. - All Rights Reserved

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-1 What information do you need to ﬁnd out? Answers will vary. How much money she has left

DOK-2 Which manipulatives will you use to solve? Answers will vary. I will use the coins because it talks about coins in the problem.

DOK-3 What strategy could you use to solve? Answers will vary. I will make a pile of coins from the problem. I will sort them by value and then use skip counting to ﬁnd the value of the collection of coins.

Give each student a Student Journal. Ask students to show their work in the space provided on the table and then write their solutions. Students can show their work using drawings and/or equations. When students have completed the Task Cards and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat DOK-3 How did you use the manipulatives to help you solve each problem? We used the bills to solve problems about dollars and the coins to solve problems about cents. • DOK-2 Can you think of a different combination of bills that would equal $16 than the combination you found for Task Card 2? 1 ten-dollar bill, 1 ﬁve-dollar bill, and 1 one-dollar bill; 3 ﬁve-dollar bills and 1 one-dollar bill; 16 one-dollar bills; 1 tendollar bill and 6 one-dollar bills; etc. • DOK-2 What are some possible combinations of coins that equal 37 cents? 1 quarter, 1 dime, and 2 pennies; 3 dimes, 1 nickel, and 2 pennies; 7 nickels and 2 pennies; etc. • DOK-4 When might you need to know how to solve problems related to bills and coins outside of school? Paying for an item at a store or restaurant, counting money in a piggy bank, counting money from a lemonade stand, etc. •

Post-Explore 1. 2. 3. 4.

Intervention

Acceleration

MONEY

Home

FACILITATION TIP Encourage collaboration by having partners alternate between reading aloud the Task Card and forming values with the manipulatives. Remind students that both partners must agree before recording answers in the Student Journal. Make a list of different strategies used by students and feature them during the Math Chat. (Strategies might include using letters to represent coin types, using repeated addition, or using text to describe a process.)

STEMscopes Tip Located in the Elaborate section, the Math Story supports the literacy-math connection. After reading or listening to the teacher read the real-world passage, students are tasked with ﬁnding information within the story to solve math problems that focus on the new skills learned in the scope and to answer literacy-based comprehension questions.

FACILITATION TIP

This Exit Ticket includes two excellent opportunities to support careful reading of real-world story problems. Take time to model reading the questions more than once, underlining the key words and writing down critical values before solving. Clarify your criteria for students successfully showing their work.

223

MONEY

Money Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Value of a Collection of Bills and Coins Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Solving Word Problems Involving Bills and Coins Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

224

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MONEY

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Dog Sitting A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

Change for Change

Coin Value Matching

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Money Madness

Money Names and Values

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Fluency Builder Match Coins and Bills to Values Independent and partner games and other activities that provide students with an engaging way to practice the new concept

225

MONEY

Money Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

226

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

MONEY

Home

What prompts will be used?

What does mastery look like?

I can ﬁnd the value of a group of coins.

I can determine combinations of coins that equal a given amount that is less than one hundred cents.

I can solve problems involving dollar bills using symbols appropriately.

I can solve problems involving quarters, dimes, nickels, and pennies using symbols appropriately.

227

SCOPE 1

Data Analysis Scope Introduction 8 6 4 2 0

SCOPE SUMMARY Students learn to collect, categorize, and represent data by using tally marks, tables, pictographs, and bar graphs with intervals of one. They interpret the data, including solving addition and subtraction problems.

Student Expectations

2.MDR.5.4 Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students learn to organize categories of data by using tally marks. Data is represented in picture graphs and bar-type graphs with intervals of one. First graders ask questions and answer them based on gathered information, observations, and appropriate graphical displays.

In third grade, students will create questions from authentic situations and then collect numerical and categorical data by using pictographs, bar graphs, or dot plots, using scaled intervals and multiple categories of data. They will interpret data from real situations to answer questions.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

ask questions and answer them based on gathered information, observations, and appropriate graphical displays to compare and order whole numbers.

Students who are successful will be ready to proceed to the Hook activity. Any students who need to build on prior knowledge can utilize the Foundation Builder within this scope.

At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

organize a collection of data by creating a bar graph about animals in a park.

•

draw conclusions and make predictions about the data.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

228

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Organizing Data Using Pictographs In this exploration, students will organize a collection of data with up to four categories using a pictograph with intervals of one. Students will: •

Explore 2

Explore 1

EXPLORE ACTIVITIES

collect data by creating a question they can ask the other students in the class.

Organizing Data Using Bar Graphs In this exploration, students will organize a collection of data using bar graphs with intervals of one. Students will: •

use the data and pictograph from Explore 1 to create a bar graph.

After students have solved the scenario, the teacher guides students in color coding, sharing, and discussing their ﬁndings. Then students discuss their learning and complete an Exit Ticket.

As students are working, the teacher monitors and adjusts, leads a discussion about the students’ ﬁndings, and has students complete an Exit Ticket to assess their learning.

Explore 3

DATA ANALYSIS

Home

Solving Problems by Interpreting Data In this exploration, students will solve addition and subtraction problems by interpreting data represented with tally marks, tables, pictographs, and bar graphs. Students will: •

analyze the title, intervals, and categories.

•

discuss how the data is represented.

As students solve the scenario, they discuss their learning with the class complete an Exit Ticket, and revisit the Hook to solve. Notes __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________

229

DATA ANALYSIS

Data Analysis Lesson Calendar and Accessing Prior Knowledge

8 6 4 2 0

PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

230

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ACCESSING PRIOR KNOWLEDGE

DATA ANALYSIS

Home

Students collect and represent data on a student-created picture graph about the favorite classroom colors. This activity is intended to assess mastery of the following standard(s): 1.MDR.6.4 Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to compare and order whole numbers.

Materials

Preparation

Printed •

1 Student Handout (per student)

Reusable • • • • •

• • •

1 Large resealable bag (per class) 1 Red crayon (per student) 1 Blue crayon (per student) 1 Green crayon (per student) 1 Pair of scissors (per student)

Print the Student Handout for each student. Gather enough red, blue, and green crayons for each student to have one of each color. Gather enough pairs of scissors, glue sticks, and sticky notes for each student to have one of each.

Consumable • •

1 Small sticky note (per student) 1 Glue stick (per student)

Procedure and Facilitation Points 1.

4. 5. 6.

7. 8.

Give each student one sticky note, three crayons (red, blue, and green), a pair of scissors, a glue stick, and the Student Handout. Tell students not to write on the sticky note until you have read the scenario. Read the following scenario to the class: The principal wants to paint a wall in the cafeteria red, blue, or green. She has asked each class to collect data on which of these three colors is their favorite. In order to collect data, she would like for each of you to write your favorite color (red, blue, or green) on a sticky note and place it in this bag. You will then analyze the class data by creating a picture graph and sharing your results. Ask students to write their favorite color on a sticky note, but do not share it with anyone else in the class. They will then place their sticky notes in the resealable bag. After you have collected the sticky notes, pull one sticky note out at a time, and read the color aloud. Students will use crayons to shade in the black and white crayons on page 2 of the Student Handout. Once all colors have been read, students will cut out all the colored crayon images and glue them in the correct columns on the graph on page 1 of the Student Handout. Students will work with small groups of 3 or 4 to discuss the class ﬁndings. Allow students to discuss the following questions with their small groups ﬁrst before discussing them as a whole group. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Students’ responses will provide evidence of their ability to draw conclusions and answer questions about data. Encourage students to support their answers and to check for understanding and misconceptions. Ask the following discussion questions: a.

FACILITATION TIP Read the scenario before distributing materials. Project the scenario and conduct a class read aloud. FACILITATION TIP Reassure students that for this activity they may vote for a color they “like best out of these three” rather than a favorite. FACILITATION TIP Consider conducting a secret vote using hands to determine favorite colors rather than sticky notes and baggies. FACILITATION TIP Before students shade in the crayons, they will need to know how many of each color to shade. FACILITATION TIP If time is limited, consider using already cut colored construction paper (red, green, blue) shapes for students to glue.

How many students like red? Students should respond by stating the number of red crayons on their picture charts.

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DATA ANALYSIS

Data Analysis 8 6 4 2 0

Accessing Prior Knowledge b.

How many students like blue? Students should respond by stating the number of blue crayons on their picture charts.

How many students like green? Students should respond by stating the number of green crayons on their picture charts.

What color did most of the class like? Students should respond by stating the color that has the most crayon pictures.

e. What color was least popular in the class? Students should respond by stating the color that has the least crayon pictures.

FACILITATION TIP Consider using the Foundation Builder before or after this activity. It provides clear images and readable questions that would facilitate some additional classroom discussion.

Did more students like (color) or (color)? How many more people liked (color) than (color)? Answers will vary. Encourage students to refer to their charts to support their responses.

Are there any colors that received the same number of likes? Answers will vary. If there are two colors with the same number of crayon pictures, students may respond by stating _____ is the same as _____.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope.

232

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Notes __________________________________________________________________________________________________________________________________________________

DATA ANALYSIS

Home

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233

DATA ANALYSIS

Data Analysis Hook – Animals at the Park

8 6 4 2 0

ACTIVITY PREPARATION Students organize a collection of data by creating a bar graph. They draw conclusions and make predictions about the data.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

Plan to show the video. For Part II, print the Student Handout for each student.

Reusable •

1 Phenomena Video (per teacher)

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

FACILITATION TIP

Project a visual version of the scenario so students can read it along with you.

STEMscopes Tip Found in the Evaluate section in Grades 2-5, the Decide and Defend formative assessment presents a mathematical problem. Students respond with an argument and justify it by using mathematical evidence and reasoning in the form of written text, visual models, expressions, and equations.

234

5. 6.

Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Tamera Tamera and Yolanda were at the park collecting data for a science project. They counted the number of animals they saw in one hour at the park and wrote down the data on a tally chart. After they collected the data, they represented their data on a bar graph with intervals of one. When they got to school with their data, they shared their graph showing the number of animals they saw at the park. Create a bar graph showing what their data might have looked like. Discuss the following questions: a.

DOK-1 What information do we know? The girls made a tally chart with the number of animals they saw at the park. Then they made a bar graph to represent the data.

DOK-1 What information do we need to ﬁnd out? What does their data look like on a bar graph?

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a.

DOK-1 What information do we know? The girls made a tally chart with the number of animals they saw at the park; then they made a bar graph to represent the data.

Engage

Explore

Explain

Elaborate

Evaluate

Give each student the Student Handout. Instruct students to use the data in the tally chart on page 1 of the Student Handout to help them complete the bar graph on page 2. Allow time for students to create their own bar graphs of Tamera and Yolanda’s data with intervals of one. Discuss the following questions: a.

DOK-1 What were the types of animals that were seen at the park by Tamera and Yolanda? Ducks, squirrels, butterﬂies, dogs

DOK-2 How many of each type of animal did they see? 6 ducks, 12 squirrels, 8 butterﬂies, 4 dogs

DOK-2 Which type of animal did they see the most? Squirrels

DOK-2 Which type of animal did they see the least? Dogs

Intervention

Acceleration

DATA ANALYSIS

Home

FACILITATION TIP Encourage students to explain how they were able to determine which animals were seen the most and least. Ask, “How do you know?” Ask students if there are any other strategies they could use to solve this problem.

e. DOK-2 How many more squirrels than ducks did they see? They saw 6 more squirrels than ducks because I counted 6 more tally marks for the squirrels. f.

DOK-2 How many ducks and squirrels were seen at the park? 18 ducks and squirrels

DOK-4 If they sat at the park for 2 hours, how many animals do you think they would have seen? Answers will vary. Some would say maybe the same number because they have seen all of the animals living in the park. Some might think that the number would double because it is twice the amount of time. Some might list other animals they would have seen besides these four types.

FACILITATION TIP Encourage students to explain how they were able to determine the total number of ducks and squirrels. Ask, “How do you know?” Ask students if there are any other strategies they could use to solve this problem.

235

DATA ANALYSIS

Data Analysis Explore 1 – Organizing Data Using Pictographs

8 6 4 2 0

ACTIVITY PREPARATION Students organize a collection of data with up to four categories using a pictograph with intervals of one.

Standards For Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • •

• •

1 Student Journal (per student) 1 Exit Ticket (per student)

Plan to have students work with a partner to complete this activity. Print a Student Journal and an Exit Ticket for each student. Note that Part I of the Student Journal will be used with this Explore. You will need to collect the Student Journals so that Part II can be completed as part of Explore 2.

PROCEDURE AND FACILITATION FACILITATION TIP To activate students’ thinking, discuss the types of data they could collect. FACILITATION TIP While students have had experience collecting data in previous grades, remind them that the question they ask should be based on something that can be easily measured or determined. Ask for or provide some examples. (What is your favorite color? How many brothers and sisters do you have? How many years have you gone to our school?)

2. 3. 4.

FACILITATION TIP Remind students that the categories should be something that can be quantiﬁed (for example, color, ﬂavor, sport, etc.) and are related to the question. FACILITATION TIP While students have had experience creating pictographs in previous grades, monitor and provide a review on pictographs if needed.

5. 6. 7.

Read the following scenario to the class: You are in charge of making a classroom website. The website will need to include fun facts about the students in this class. What information would other people want to know about our class? Divide the class into groups of two, and give each student a Student Journal. Instruct students to plan to collect data using a question they can ask the other students in the class and the options they will give to answer the question. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What question do you want to ask the other students? Answers will vary. I want to ask my classmates what their favorite color is.

DOK-1 What four categories will you give as choices to answer your question? My classmates will select from the color options blue, red, yellow, or green and choose one as their favorite color.

DOK-1 What will you do as students answer your question? I will collect data and graph my classmates’ votes using symbols.

Give students time to walk around, ask their questions, and collect the data they need to complete Part II of their Student Journals. When students have completed their Student Journals, collect the Student Journals to use with Explore 2, and bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

236

Engage

Explore

Explain

Elaborate

Evaluate

• • • • • • •

DOK-1 What question did you ask? What were the categories? What is your favorite color? Blue, red, yellow, and green DOK-1 What are the categories on your pictograph? The same categories I gave as options to answer the question. DOK-1 What is the title of your pictograph? Our Favorite Colors DOK-1 What symbol did you use to represent the data? Circle, triangle, square DOK-1 What is a pictograph? A graph that uses symbols to show data DOK-1 What is a legend/key? A key/legend tells what each symbol stands for. Each smiley face stands for 1 vote. DOK-2 Which option did most of your classmates choose? How do you know? This was the option with the most symbols on my graph. DOK-2 Which option had the least votes from your classmates? How do you know? This was the option with the least symbols on my graph.

Post-Explore 1. 2. 3.

Acceleration

FACILITATION TIP

Math Chat •

Intervention

Consider creating a pictograph anchor chart with students that they can use for reference.

DATA ANALYSIS

Home

FACILITATION TIP

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook.

This Exit Ticket could also be used as a way to assess prior knowledge before teaching this Explore.

237

DATA ANALYSIS

Data Analysis Explore 2 – Organizing Data Using Bar Graphs

8 6 4 2 0

ACTIVITY PREPARATION Students organize a collection of data using bar graphs with intervals of one.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • •

• • •

1 Student Journal (per student) 1 Exit Ticket (per student)

Plan to have students work with a partner to complete this activity. Plan to distribute Student Journals from Explore 1. Print a Student Journal and an Exit Ticket for each student.

Reusable •

1 Student Journal from Explore 1 (per student)

PROCEDURE AND FACILITATION FACILITATION TIP Take time to gather some real-world relevant bar graphs to show students prior to this Explore. Textbooks for other subjects may have some age appropriate graphs that have clear titles, labels, and simple intervals. FACILITATION TIP Students have not had previous experience creating bar graphs. Provide guidance as needed.

2. 3. 4.

FACILITATION TIP Ask students what strategies they used to determine the most and least votes.

FACILITATION TIP Consider creating a bar graph anchor chart with students that they can refer to.

5. 6. 7.

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Read the following scenario to the class: The principal has challenged us to present our fun facts for our class website using different types of graphs. Yesterday, you created a pictograph using data collected after asking other students a question. Today, you will use that same data to create a bar graph. Can you create a bar graph using your data? Give a Student Journal from Explore 1 and a new Student Journal for this Explore to each student. Instruct students to use the data and pictograph from Explore 1 to create a bar graph. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-2 How can we use the pictograph to create a bar graph? We can look at the number of people who liked each item and use that data on our bar graph.

DOK-2 What parts of a pictograph are also on the bar graph? The title and categories

DOK-2 What parts of a pictograph are not on the bar graph? The bars and numbers on the side of the graph; the pictograph has a key.

Encourage students to discuss and respond to the reﬂection question. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning. © Accelerate Learning Inc. - All Rights Reserved

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Math Chat •

• • • • • •

•

DOK-2 How did you create your bar graph? I drew a bar graph and labeled the numbers up the side by 1s. Then, I labeled the bottom with each category. Next, I counted the number of items in each category and made a bar to show that number. DOK-1 What is the interval scale? An interval scale is what the bar graph is counting by; for this graph, we are counting by 1s. DOK-1 What are titles/labels/categories? Titles, labels, and categories tell us what the bar graph is about. DOK-2 Does data in the bar graph change when represented horizontally or vertically? Data doesn’t change if the bar graph is turned. DOK-1 Which of your categories has the most votes? Answers will vary. DOK-1 Which has the least votes? Answers will vary. DOK-3 If you asked the same question in another class, do you think you would get the same results? Maybe, but not everyone likes the same things, so the results would probably be different. DOK-3 If you asked the same questions to adults, would your results be the same? Probably not because adults don’t like the same things as kids.

DATA ANALYSIS

Home

STEMscopes Tip In Kindergarten through Grade 2, the Connection Station, located in the Acceleration section, connects gradelevel math, science, and social studies concepts. During a hands-on activity, students have the opportunity to apply their mathematical thinking and reasoning skills to standards-based science and/or social studies subject matter.

Post-Explore 1. 2. 3.

Have students complete the Exit Ticket to formatively assess their understanding FACILITATION TIP of the concept. When previewing this Exit Ticket with Complete the Anchor Chart as a class. students, clarify your expectations for Have each student complete their Interactive Notebook. how they are to show tally marks. Some students may need a review.

239

DATA ANALYSIS

Data Analysis Explore 3 – Solving Problems by Interpreting Data

8 6 4 2 0

ACTIVITY PREPARATION Students solve addition and subtraction problems by interpreting data represented with tally marks, tables, pictographs, and bar graphs.

Standards for Mathematical Practice • • • •

MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

• • •

1 Student Journal (per student) 1 Set of Data Cards (per class) 1 Exit Ticket (per student)

Plan to have students work in 6 groups to complete this activity. Print one set of Data Cards, and hang them around the room. Print a Student Journal and an Exit Ticket for each student.

PROCEDURE AND FACILITATION 1.

2. FACILITATION TIP If anchor charts are available, have students refer to them to help them analyze the Data Cards.

Read the following scenario to the class: Each second-grade class has been working hard to present facts about their class on their class website. Today, you will look at Data Cards that show information from other second-grade classes. Classes could choose how they wanted to represent their data, either by tally marks, tables, pictographs, or bar graphs. Can you use the data presented on each card to solve problems? Divide students into 6 groups, and assign each group a Data Card to begin working. Give a Student Journal to each student. Instruct students to analyze their Data Cards and discuss how the data is represented. If the data is presented as a pictograph or bar graph, they should analyze the title, intervals, and categories. They use the information presented on each Data Card to answer the questions. Monitor and talk with students as needed to check for understanding by using the following guiding questions:

FACILITATION TIP

Discuss with students whether the way the data is represented on the card is the most appropriate way to display the data or whether the data could be better presented using another method.

DOK-1 How is the data represented on this Data Card? Answers will vary depending on the card but should include tally marks, a table, a pictograph, or a bar graph.

DOK-2 How do you know this is an example of tally marks/a table/a pictograph/a bar graph? Answers will vary. Students should describe characteristics of each type of data display.

DOK-1 What is the title of this graph? Answers will vary. Our Favorite Season

DOK-1 What are the intervals of this graph? Ones

e. DOK-1 What are the categories shown on this graph? Answers will vary. Winter, spring, summer, fall f.

240

Engage

Explore

Explain

Elaborate

Evaluate

DOK-3 How do you solve for the missing information? Answers will vary. I need to add the total votes for spring, summer, and fall. Then, I will subtract the number of votes for winter from this total.

h. DOK-3 How could you solve using a pictorial model? Answers will vary. I could draw circles, a bar model, or a number line. i. DOK-3 What number sentence could you write to solve for the missing information? Answers will vary. 5 + 9 + 4 = 18 and then 18 – 3 = 15 j. DOK-1 What operation are you using to solve? Answers will vary. I have to add and then subtract. 5.

6. 7. 8.

Have students solve the problems related to each Data Card by showing a pictorial model and writing a number sentence to show their solutions in their Student Journals. Have students rotate through each Data Card and complete their Student Journals. When students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Intervention

Acceleration

FACILITATION TIP Encourage students to use various strategies to solve for the missing information. Acknowledge different strategies and discuss which strategies are most eﬃcient when solving these types of problems.

DATA ANALYSIS

Home

FACILITATION TIP Encourage students to use a variety of pictorial models to help them become proﬁcient with multiple methods that can be used to solve problems.

Math Chat • •

•

• •

•

DOK-3 Why are the intervals on a pictograph or bar graph important? Intervals help you determine the total number of votes for a category. DOK-3 How can you determine which category has the most or least amount on a chart or graph? The category with the most will always have the tallest bar. The category with the least will always have the shortest bar. DOK-3 How could you determine the total number of students in each class using the Data Cards? I could add the total from each category. This information tells me how many total students voted. DOK-3 How are the Data Cards you saw today similar? They all have a title and categories and show data. DOK-3 How are the Data Cards you saw today different? The data was displayed in different ways. Some data was shown by tally marks, some in tables, some in pictographs, and some in bar graphs. DOK-3 What other questions could you ask from the data collected? I could ask which category had the least/most votes. I could ask the difference between two or more categories.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP

When previewing this Exit Ticket with students, you may want to support struggling students by going over the details on the graph. The single question on this Exit Ticket requires locating multiple values on the graph and performing a calculation.

241

DATA ANALYSIS

Data Analysis 8 6 4 2 0

Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Organizing Data Using Pictographs Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Organizing Data Using Bar Graphs Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Show What You Know, Part 3

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

Solving Problems by Interpreting Data Independent practice assignment that gives students an opportunity to demonstrate their learning

Interactive Notebook A cut-and-glue activity to process learning that can be added to a notebook for future reference

242

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

DATA ANALYSIS

Home

Can be done independently

Spiraled Review

Life Connections

New Shoes

Scientist

A quick story to engage student interest along with four problems covering previously learned skills

A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

Math Story

Fluency Builder

Favorite Fruits in Second Grade

Match Data to Graph

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task Class Pet Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

243

DATA ANALYSIS

Data Analysis 8 6 4 2 0

Intervention and Assessment SMALL-GROUP PLANNER

Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

244

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

ASSESSMENT PLANNER

DATA ANALYSIS

Home

Use this template to decide how to assess your students for concept mastery. Depending on the format of the assessment, you can identify prompts and intended responses that would measure student mastery of the expectation. See the beginning of this scope to identify standards and grade-level expectations. Key Concepts

What prompts will be used?

What does mastery look like?

I can generate a question to be answered by collecting, sorting, and organizing data.

I can collect data and record it by using tally marks.

I can sort information into up to four different categories.

I can organize data I have collected into a T-chart.

I can create a pictograph or bar graph using data.

I can draw conclusions and generate and answer questions by using information from pictographs or bar graphs.

245

SCOPE 1

Patterns Scope Introduction SCOPE SUMMARY Students begin by acting out patterns using a hundreds chart or number line. They identify, describe, and create a numerical pattern resulting from repeated addition or repeated subtraction. Patterns include sums within 1,000 and intervals of 1s, 2s, 5s, 10s, 25s, and 100s. Students also identify, describe, and create growing and shrinking patterns involving addition and subtraction up to 20. Student Expectations

2.PAR.4.1 Identify, describe, and create a numerical pattern resulting from repeating an operation such as addition and subtraction. 2.PAR.4.2 Identify, describe, and create growing patterns and shrinking patterns involving addition and subtraction up to 20.

VERTICAL ALIGNMENT Background Knowledge

Future Expectations

In ﬁrst grade, students investigate, create, and make predictions about repeating patterns resulting from repeating an operation, as a series of shapes, or a number string. They also create growing, shrinking, and repeating patterns based on the repeated addition or subtraction of 1s, 2s, 5s, and 10s.

In third grade, students describe, extend, and create numerical patterns related to multiplication and make predictions related to the patterns. They may use multiplication tables to discover that multiples of even numbers are always even, the products in each row and column increase by the same amount, the multiples of 4 are double the multiples of 2, and the multiples of 6 are double the multiples of 3, and so on.

Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses students’ ability to: •

Hook

Accessing Prior Knowledge

ENGAGE ACTIVITIES

identify, describe, and create growing, shrinking and repeating patterns based on the repeated addition or subtraction of 1s, 2s, 5s, and 10s.

At the beginning of the scope, students are introduced to the Hook. Through completing the Hook, students will demonstrate their ability to: •

identify and describe repeating, growing, and shrinking patterns in the context of building a brick wall.

Students move on to the Explore activities and come back at the end of the explorations to repeat the activity and discuss what they found.

246

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PATTERNS

Home

Repeated Operations In this exploration, students will identify, describe, and create numerical patterns resulting from repeated addition or subtraction. Students will: •

act out and identify the patterns.

•

record the missing numbers and describe the patterns.

Explore 2

Explore 1

EXPLORE ACTIVITIES Growing and Shrinking Patterns In this exploration, students will identify, describe, and create growing and shrinking patterns. Students will: •

describe the growing or shrinking patterns.

•

build the next two items with their pattern blocks.

After completing the activity, students share their learning, complete an Exit Ticket, and revisit the Hook to solve.

After students have had time to explore and solve the scenario, they will discuss their learning and complete an Exit Ticket for assessment.

247

PATTERNS

Patterns Lesson Calendar and Accessing Prior Knowledge PLAN YOUR LESSONS Monday

Tuesday

Wednesday

Thursday

Friday

248

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PATTERNS

Home

ACCESSING PRIOR KNOWLEDGE Students identify, describe, and create growing and shrinking patterns. This activity is intended to assess mastery of the following standard(s): 1.PAR.3.2 Identify, describe, and create growing, shrinking and repeating patterns based on the repeated addition or subtraction of 1s, 2s, 5s, and 10s.

Materials

Preparation

Printed • •

•

Print the Student Handout and 120 Chart for each student.

1 Student Handout (per student) 1 120 Chart (per student)

Procedure and Facilitation Points 1. 2. 3. 4.

5. 6. 7. 8.

Give each student the Student Handout. Read the following scenario to the class: Peter was counting while climbing on the monkey bars. I wonder what pattern he was using to count. Instruct students to look at the monkey bar pattern on their Student Handout. Have them complete the monkey bar pattern and identify whether the pattern is growing or shrinking. Discuss the following questions: a.

What number does the pattern begin with? 36

Is the pattern growing or shrinking? How do you know? It is shrinking because the numbers are getting smaller.

What comes next in the pattern? Twenty-eight comes next.

How do you know what comes next? I noticed a repeating shrinking pattern of two.

Give each student the 120 Chart. Instruct students to create their own growing or shrinking pattern by using the 120 Chart. Check patterns and address any misconceptions. Facilitate a class discussion about the students’ patterns. This provides an opportunity to gather an understanding of prior student knowledge before beginning the lessons. Encourage students to support their answers and to check for understanding and misconceptions. Ask the following discussion questions: a.

What pattern did you create? Answers will vary. I created a pattern counting by 10s beginning with 10.

Is your pattern growing or shrinking? How do you know? Answers will vary. My pattern is growing because the numbers are getting greater.

What comes next in your pattern? Answers will vary.

STEMscopes Tip Within the Intervention section are a wide variety of Supplemental Aids that can be used throughout and across scopes to help students with any assignments. Supplemental Aids include documents to help students visualize mathematical concepts or help organize the information from the scope. Each Supplemental Aid provides a description of how and when it can be used to be the most beneﬁcial to student learning, the speciﬁc mathematical concepts it reinforces, as well as detailed procedures outlining strategies teachers can use to model the aid for students. Many of the Supplemental Aids are approved for use by students who meet eligibility criteria.

If students are struggling to complete this task, do the Foundation Builder to ﬁll the gap in prior knowledge before moving on to other parts of the scope. Notes

249

PATTERNS

Patterns Hook – Brick Wall Patterns ACTIVITY PREPARATION Students identify and describe repeating, growing, and shrinking patterns in the context of building a brick wall.

Materials

Preparation

Printed •

• •

1 Student Handout (per student)

• •

Reusable •

Plan to show the video. Part II

1 Phenomena Video (per teacher)

Print the Student Handout for each student. For students who need more support in recalling information, please see our 100 Chart Supplemental Aids element in the Intervention section.

PROCEDURE AND FACILITATION Part I: Pre-Explore 1.

2. FACILITATION TIP

Project this scenario and read it aloud with students. Read through it more than once and allow students to note down the important information for questions, a and b, before the discussion. FACILITATION TIP

Some students might also notice the way the bricks are laid with mortar spaced at different equal intervals. This visual brick pattern applies to identiﬁcation and description of patterns.

a. DOK-1 What information do we know? We know Mr. Patel took water breaks after laying 25 bricks on Saturday. He took 7 water breaks. Then on Sunday, he took water breaks after laying 100 bricks and he took 5 water breaks.

STEMscopes Tip Located in the Elaborate section, the Problem-Based Task is designed to have students work together to solve an open-ended, real-world math challenge. Students apply the knowledge and skills they learned in the scope to solve the problem. They will recognize that solutions to the problem can be approached in multiple ways and with multiple responses.

Introduce this activity toward the beginning of the scope. The class revisits the activity and solves the original problem after students have completed the corresponding Explore activities. Show the Phenomena Video. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Read the following scenario to the class: Mr. Patel spent all day Saturday building a brick wall in his backyard. Since it was hot outside, he took a water break each time he had laid 25 bricks. At the end of the day on Saturday, Mr. Patel had taken 7 water breaks. On Sunday, he continued building the brick wall. It was cooler outside, so he only took a water break each time he had laid 100 bricks. He took 5 water breaks before stopping for the day. What pattern can Mr. Patel use to ﬁnd the total number of bricks he laid on Saturday and Sunday? Discuss the following questions:

5. 6.

DOK-2 What pattern can we count in to ﬁnd the total number of bricks laid Saturday? We can count by 25s.

DOK-2 What pattern can we count in to ﬁnd the total number of bricks laid Sunday? We can count by 100s beginning with the number from Saturday.

Ask students to turn and talk to share how they would solve the problem. They are not required to solve it yet. Move on to complete the Explore activities.

Part II: Post-Explore 1. 2.

After students have completed the Explore activities for this topic, show the Phenomena Video again, and repeat the scenario. Discuss the following questions: a. DOK-1 What information do we know? We know Mr. Patel took water breaks after laying 25 bricks on Saturday. He took 7 water breaks. Then on Sunday, he took water breaks after laying 100 bricks and he took 5 water breaks.

250

3. 4. 5.

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

DOK-2 What pattern can we count in to ﬁnd the total number of bricks laid Saturday? We can count by 25s.

DOK-2 What pattern can we count in to ﬁnd the total number of bricks laid Sunday? We can count by 100s beginning with the number from Saturday.

Divide the class into groups of 2 or 3. Give each student a Student Handout. Instruct students to begin with the pattern for Saturday to ﬁgure out how Mr. Patel can count by using a pattern. Students may use Hundreds Charts if needed. Discuss the following questions: a.

DOK-1 What will you be counting by? Twenty-ﬁves

DOK-2 What is the last number in the pattern after 7 water breaks? How do you know? The last number is 175 because I counted by 25s. 25, 50, 75, 100, 125, 150, 175

Intervention

Acceleration

FACILITATION TIP

PATTERNS

Home

Take time to do some choral skip counting with students with the whole group, selected small groups, and with a partner. Use the group responses to quickly check to see if students are struggling.

Instruct students to move on to ﬁguring out how Mr. Patel can count by using a pattern for Sunday. Discuss the following questions: a.

DOK-1 What number will you begin with for the pattern? Answers will vary. I will begin with the number from Saturday, 175.

DOK-1 What will you be counting by? Answers will vary. I will count by 100s.

DOK-1 Is the pattern growing or shrinking? Explain. The pattern is growing. I am adding 100 each time he takes a water break.

DOK-2 What is the last number in the pattern after the pattern grows by 100 each time? How do you know? 175, 275, 375, 475, 575, 675; The last number is 675.

FACILITATION TIP Print and project these guiding questions to facilitate student collaboration and whole class discussion. Follow-up with a question about more real-world applications for using patterns to count eﬃciently.

e. DOK-3 How did you use patterns to help you determine the total number of bricks Mr. Patel used on Saturday and Sunday? Answers will vary. It was easier to count by 25s while thinking about how to count money (quarters). Then, when I counted by 100s, all I had to do was add 100 each time he took a water break.

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PATTERNS

Patterns Explore 1 – Repeated Operations ACTIVITY PREPARATION Students identify, describe, and create numerical patterns resulting from repeated addition or subtraction.

Standards for Mathematical Practice • • •

MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

• •

1 Student Journal (per student) 1 Set of Task Cards (per group) 1 Exit Ticket (per student)

• • •

Reusable • •

1 Resealable bag (per group) 1 Jump rope (per group)

•

Plan to have students work in groups of 3 or 4 to complete this activity. Print and cut out the Task Cards, and place them in a resealable bag for each group. Gather one jump rope for each group. Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our 120 Chart, Blank 120 Chart, and Open Number Line Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Hundred Board and Number Lines)

PROCEDURE AND FACILITATION 1. FACILITATION TIP

The Task Card Activities create good practice opportunities for students. It might be best to do the Task Cards inside at desks after going outside to do some simple pattern counting practice with jump ropes, swinging, hopping and sliding in small groups.

FACILITATION TIP Encourage students to carefully examine the patterns and look for any clues about what might be happening. Some students can get overwhelmed and give up quickly when they see a string of numbers. Asking these scaffolded questions will support success.

Read the following scenario to the class: Today is a great day for our class! We get to go outside for extra recess today! But when we go out to recess, we must do all of the activities using a pattern. Can you help identify the patterns? Divide students into groups of 3 or 4. Give a set of Task Cards and a jump rope to each group. This activity can be done inside or outside depending on teacher preference. Students can pretend to do the activities listed on the Task Cards or actually do the activities outside on the playground. Ask students to ﬁnd Task Card 1. Instruct students to act out, identify, and describe the pattern using the instructions on the Task Card. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 What activity was listed on this Task Card? Answers will vary. We need to jump rope and count using the pattern.

DOK-2 What do you notice about this pattern? Answers will vary. The pattern skip counts backward. It counts by twos. The numbers are all odd numbers.

DOK-1 What tools can you use to help you identify the pattern? Answers will vary. We can use a hundreds chart or number line.

DOK-2 What is the repeated operation for this pattern? Answers will vary. The pattern is repeated subtraction by twos.

e. DOK-1 What are the missing numbers for this pattern? Answers will vary. The missing numbers are 23 and 21. 252

6. 7.

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

Give a Student Journal to each student. Ask students to work with their groups to act out and identify the patterns. They will record the missing numbers and describe the patterns on their Student Journals. After students have completed the Task Cards and their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

PATTERNS

Home

Math Chat • • •

•

DOK-2 What did you notice about the patterns? Some patterns counted forward, and some counted backward. Some used addition, and some used subtraction. DOK-2 What do you notice about the pattern on Task Card 4? The pattern is subtracting 10 each time. All the numbers are even. DOK-2 What equation can you write to complete the pattern on Task Card 3? We can write an addition problem adding 25 to each number. 100 + 25 = 125 and 125 + 25 = 150. DOK-3 What pattern did you create? Can you describe it? I created a pattern that counted (backward/forward) by ___. I used (addition/subtraction) to create the pattern. DOK-4 Can you describe a repeating addition or subtraction pattern you have seen outside of school? I use repeated addition when I add up the coins in my piggy bank. When I play video games, it either repeatedly adds points or repeatedly subtracts points.

Post-Explore 1. 2. 3.

FACILITATION TIP A good ﬁrst step for many students is just to identify if the pattern is going up, growing, going forward, adding or the going down, shrinking, going backwards or subtracting. Use a variety of different phrases and words to help students describe the patterns. FACILITATION TIP Take some time to gather some additional real world examples of uses of repeating addition and subtraction patterns. Some students might connect with a visual representation of the times tables, while others might enjoy being read a favorite picture book story that includes a repeating number pattern.

Have students complete the Exit Ticket to formatively assess their understanding of the concept. Complete the Anchor Chart as a class. Have each student complete their Interactive Notebook. Notes

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PATTERNS

Patterns Explore 2 – Growing and Shrinking Patterns ACTIVITY PREPARATION Students identify, describe, and create growing and shrinking patterns.

Standards for Mathematical Practice • •

MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Materials

Preparation

Printed • • •

1 Student Journal (per student) 1 Set of Pattern Hunt Task Cards (per class) 1 Exit Ticket (per student)

• • •

• • • •

Reusable •

Plan to have students work in 10 groups to complete this activity. Print and cut out a set of Pattern Hunt Task Cards, and place them around the room. Gather the following pattern blocks for each group:

1 Set of pattern blocks (per group)

• •

•

15 Orange squares 15 Green triangles 10 Yellow hexagons 10 Blue rhombuses

Print a Student Journal and an Exit Ticket for each student. For students who need more support in recalling information, please see our 120 Chart, Blank 120 Chart, and Open Number Line Supplemental Aids element in the Intervention section. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students. (Hundred Board and Number Lines)

PROCEDURE AND FACILITATION FACILITATION TIP This activity could easily be split into two parts. Pages 1 and 2 are hands-on with pattern blocks and pages 3 and 4 have more written story patterns. Have students complete the pattern block activities at their own tables/desks (page 1 and 2). Provide each group enough pattern blocks and have them complete the ﬁrst two pages. After students have had time and opportunity to build some patterns, complete pages 3 and 4 (Task Cards 6,7,8,9, and 10) as a whole group. FACILITATION TIP Some students may struggle with the ﬁne motor skills needed to draw the patterns on the Student Journal. Consider accommodating them by allowing them to show an adult how they built the pattern. 254

4. 5. 6.

Read the following scenario to the class: When I walked to school today, I noticed that the numbers on the houses on my street were in a pattern. Where do you see patterns in the real world? Allow time for students to respond. Answers will vary. The numbers on our classroom doors are in a pattern. One side of the hallway counts by even numbers, and the other side counts by odd numbers. My neighbors’ bushes in their front yard look like a pattern. Continue reading the following scenario to the class: Patterns are all around us. Let’s go on a pattern hunt and see what we discover! Are you ready to hunt for patterns? Divide students into 10 groups, and assign each group to the specific Pattern Hunt Task Card at which they will begin. Distribute the Student Journals and pattern blocks to students. Have students find their specific Task Card on their Student Journals. Instruct students to describe the growing or shrinking patterns and build the next 2 items with their pattern blocks. Students will record the patterns on their Student Journals. Then, they will hunt around the room to find another Task Card, paying close attention to the number on the Task Card until they have completed all the cards.

8. 9.

Engage

Explore

Explain

Elaborate

Evaluate

• • •

•

Acceleration

Monitor and talk with students as needed to check for understanding by using the following guiding questions: a.

DOK-1 Is this pattern a growing or a shrinking pattern? Answers will vary. This is a growing pattern. This is a shrinking pattern.

DOK-1 What tools can you use to help you identify the pattern? Answers will vary. I can use pattern blocks or a hundred chart.

DOK-1 How can you use the pattern blocks to identify the pattern? I can lay out each shape pattern to visually see how the pattern is growing or shrinking.

DOK-2 How can you determine what the next 2 items will be in the pattern? I can add or subtract from the previous item to determine the next item.

After students have completed their Student Journals, bring the class together as a whole group. After the Explore activity, invite the class to a Math Chat to share their observations and learning.

Math Chat •

Intervention

PATTERNS

Home

FACILITATION TIP Print the Math Chat questions from the Print Files and project them while students are working. Question a. is an excellent starter question for students to use any time they encounter a pattern problem.

STEMscopes Tip

DOK-2 What do you notice about the patterns? The patterns are either growing or shrinking. They added/subtracted ___ each time. DOK-2 What strategy did you use to determine the pattern? I laid out the pattern blocks in the pattern and added on. DOK-2 What operation can you use to complete a shrinking pattern? I can use subtraction. DOK-2 What did you notice about Mr. Green’s pattern? I noticed that his pattern was shrinking. He counted backward by twos beginning with 19. All his numbers were odd. DOK-3 3 What pattern did you create? Can you describe your pattern? My pattern is growing/shrinking. I added/subtracted ___ each time.

The Skills Quiz is housed in the Evaluate section. This assessment includes multiple question types and is designed to formatively evaluate students’ computational knowledge. Aligned to the scope’s standards, the assessments can also be used as a review of the concepts learned throughout the scope.

Post-Explore 1. 2. 3. 4.

FACILITATION TIP This Exit Ticket can be used as a preassessment as well as a formative assessment after the Explore. The second page provides good opportunities for students to show their pattern skills.

255

PATTERNS

Patterns Additional Scope Resources EXPLAIN ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Picture Vocabulary

Can be done independently

Show What You Know, Part 1

A slide presentation of important vocabulary terms along with a picture and deﬁnition

Repeated Operations Independent practice assignment that gives students an opportunity to demonstrate their learning

Anchor Chart

Show What You Know, Part 2

A guide to facilitating the creation of a chart with students for each scope

Growing and Shrinking Patterns Independent practice assignment that gives students an opportunity to demonstrate their learning

My Math Thoughts

Interactive Notebook

A collection of journal prompts designed to allow students to explain their thinking and reﬂect on their learning

A cut-and-glue activity to process learning that can be added to a notebook for future reference

256

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PATTERNS

Home

ELABORATE ELEMENTS ELEMENT USE KEY

Can be assigned digitally

Contains printable handouts

Spiraled Review

Can be done independently

Life Connections

Basketball A video and activity that introduce students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom

A quick story to engage student interest along with four problems covering previously learned skills

Math Story

Fluency Builder

The Doll Quilt

Growing and Shrinking Patterns

Reading passage that supports literacy and expands students’ ability to identify the information they need to solve problems

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

Problem-Based Task

Fluency Builder

Patio Patterns

Patterns with Repeated Operations

Independent or collaborative task that allows students to solve a challenging, meaningful problem in a real-world context

Independent and partner games and other activities that provide students with an engaging way to practice the new concept

257

PATTERNS

Patterns Intervention and Assessment SMALL-GROUP PLANNER Depending on available time and your teaching style, use the resources provided in our Explain, Elaborate, Intervention, and Acceleration sections of this scope to move forward. Use the space below to organize next steps while keeping the needs of your students in mind. Some suggested resources have been listed. (Look online to see the full menu.)

Students who are still acquiring the concept and need remediation

Resources

Students

Notes

 Fluency Builder  Small-Group Intervention

Students who have mastered the concept and need extension

Students who are approaching mastery and need review

 Life Connections

258

 Interactive Practice

 Problem-Based Task  Math Today  Connection Station

Engage

Explore

Explain

Elaborate

Evaluate

Intervention

Acceleration

PATTERNS

Home

What prompts will be used?

What does mastery look like?

I can identify a numerical pattern resulting from repeating an operation such as addition or subtraction.

I can describe a numerical pattern resulting from repeating an operation such as addition or subtraction.

I can create a numerical pattern resulting from repeating an operation such as addition or subtraction.

I can identify growing and shrinking patterns involving addition and subtraction up to 20.

I can describe growing and shrinking patterns involving addition and subtraction up to 20.

I can create growing and shrinking patterns involving addition and subtraction up to 20.

259

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2 Georgia Math Teacher Guide

Grade 2 Teacher Guide

STEMscopes.com ISBN: 979-8-88826-716-5

ISBN: 979-8-88826-661-8

2 GEORGIA

MATH G2