EM2 Teach Grade 1 Module 5 UTE by Great Minds

What does this painting have to do with math? American realist Edward Hopper painted ordinary people and places in ways that made viewers examine them more deeply. In this painting, we are in a restaurant, where a cashier and server are busily at work. What can you count here? If the server gave two of the yellow fruits to the guests at the table, how many would be left in the row? We will learn all about addition and subtraction within 10s in Units of Ten. On the cover Tables for Ladies, 1930 Edward Hopper, American, 1882–1967 Oil on canvas The Metropolitan Museum of Art, New York, NY, USA Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48 1/4, W. 60 1/4 in (122.6 x 153 cm). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists Rights Society (ARS), NY. Photo credit: Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY

Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®. Published by Great Minds PBC. greatminds.org Copyright © 2021 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Where expressly indicated, teachers may copy pages solely for use by students in their classrooms. Printed in the USA 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-63898-397-2

A Story of Units®

Units of Ten ▸ 1 TEACH

Module

1 2 3 4 5 6

Counting, Comparison, and Addition

Addition and Subtraction Relationships

Properties of Operations to Make Easier Problems

Comparison and Composition of Length Measurements

Place Value Concepts to Compare, Add, and Subtract

Attributes of Shapes · Advancing Place Value, Addition, and Subtraction

Before This Module

Overview

Kindergarten Module 6

Place Value Concepts to Compare, Add, and Subtract

Students begin to develop place value understanding when they come to see that teen numbers are composed of 10 ones and some more ones. They do not formalize the notion of “a ten” as a unit. Students also count to 100 by tens and by ones.

Grade 1 Module 3 Students rename groups of ten ones as units of ten. They come to see that all two-digit numbers are composed of tens and ones.

Grade 1 Module 4 Students use 10-centimeter sticks (tens) and centimeter cubes (ones) to measure lengths. They state total lengths in terms of tens and ones.

Topic A Grouping Units in Tens and Ones Topic A builds on work with tens and ones from modules 3 and 4. Lessons develop the idea that smaller units, such as ones, compose larger units, such as tens. The following place value models, which increase in complexity, help students to internalize the equivalence of 10 ones and 1 ten and to understand that two-digit numbers represent amounts of tens and ones. Groupable Physically group 10 ones to compose a new unit of ten. The size of the new unit is proportionally larger than the base unit.

Pre-grouped Tens are composed by trading 10 ones for a new item that represents 1 ten. The new item is proportionally larger than the base unit.

Nonproportional 10 ones are traded for a new item that represents 1 ten. However, the new item is non-proportional. Visually, it is not 10 times larger than the base unit.

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Students represent two-digit totals in different ways. For example, a total of 21 may be shown as 21 ones, 1 ten 11 ones, or 2 tens 1 one. Students see that the digits used to write a numeral, such as 2 and 1 in 21, show how many tens and ones there are when the number is expressed in its “most composed” form.

Topic B Use Place Value to Compare Students compare two-digit numbers by using the place value structure of tens and ones rather than by using size or length. They represent comparisons with number sentences that include the symbols >, =, or < and explain why the number sentences are true. Comparing numbers such as 39 and 93 helps students focus on the value of each digit. They see that if two numbers have different digits in the tens place, then they can use those digits to compare them efficiently.

tens

ones

tens

ones

Topic C Addition of One-Digit and Two-Digit Numbers Students add a one-digit number to a two-digit number by using place value to make easier problems. They solve problems with the help of a variety of tools such as cubes, drawings, number bonds, and number paths, and they explain their thinking. Students solve problems where the ones do not compose a new ten (e.g., 25 + 3 = 28) by decomposing the two-digit addend into tens and ones, combining the ones with the

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one-digit addend, and then adding the tens. They also find the total when the ones do compose a ten (e.g., 25 + 5 = 30). Students decompose an addend to make the next ten, and then add the tens. Sometimes the ones compose a ten and some ones (e.g., 25 + 7 = 32).

Topic D Addition and Subtraction of Tens Students learn three skills to complete grade 1 subtraction work and to prepare them for adding 2 two-digit numbers in topic E: tens ones tens ones • Add tens to a multiple of ten. • Add tens to any two-digit number.

• Subtract tens from a multiple of ten. To add and subtract tens, students use the Level 2 strategies of counting on and counting back with tens. They advance to using the Level 3 strategy 30 of representing an equation in unit form to find an easier one-digit fact they know. For example, rewriting 20 + 40 as 2 tens + 4 tens helps students see that they can use 2 + 4 to solve the problem. Similarly, rewriting 60 – 30 as 6 tens – 3 tens helps students see that they can use 6 – 3 to solve this problem. Then students add tens to a two-digit number by adding the tens first and recognizing that the ones-digit stays the same.

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Topic E

After This Module

Addition of Two-Digit Numbers Students use place value understanding to make easier two-digit addition problems. They practice three strategies that involve decomposing one or both addends and composing the resulting parts. Students self-select strategies and tools for solving the problems based on the numbers in the problem and their preference. Students record their reasoning using a written method and they explain their thinking. Add Like Units Decompose both addends into tens and ones, combine tens with tens and ones with ones. Then combine tens and ones.

Add Tens First Decompose an addend into tens and ones, combine the tens with the other addend, and then add the ones.

Add Ones First (May Make the Next Ten) Decompose an addend to combine some (or all) of the ones with the other addend, in many cases to make the next ten.

Grade 1 Module 6 Part 2 Students count beyond 100 to 120 and begin to understand that 10 tens compose 100. Students apply the same addition strategies they used in this module, but with addends where more than 1 or 2 new tens can be composed.

Grade 2 Module 1 Students extend their place value knowledge with larger numbers. Specifically, they learn that 10 tens make 1 hundred. They represent three-digit numbers in different ways by using place value understanding.

Grade 2 Module 2 Students continue to use place value to make easier problems when adding within 1,000. Strategies include add like units, count on with benchmark numbers, and make a ten or a hundred within 200. Students also extend place value thinking to make easier subtraction problems within 1,000.

Contents Place Value Concepts to Compare, Add, and Subtract Why. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Achievement Descriptors: Overview . . . . . . . . . . . . . . . . . . . . . 10 Topic A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Grouping Units in Tens and Ones Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Tell time to the hour and half hour by using digital and analog clocks.

Lesson 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Count a collection and record the total in units of tens and ones.

Lesson 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Recognize the place value of digits in a two-digit number.

Lesson 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Represent a number in multiple ways by trading 10 ones for a ten.

Topic C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Addition of One-Digit and Two-Digit Numbers Lesson 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Add the ones first.

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Add the ones to make the next ten.

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Decompose an addend to make the next ten.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Reason about related problems that make the next ten.

Lesson 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 Determine which equations make the next ten.

Reason about equivalent representations of a number.

Topic D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Addition and Subtraction of Tens

Lesson 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Add 10 or take 10 from a two-digit number.

Count on and back by tens to add and subtract.

Topic B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Use Place Value to Compare

Lesson 16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Lesson 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Lesson 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Use place value reasoning to compare two quantities.

Lesson 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Use related single-digit facts to add and subtract multiples of ten.

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Use tens to find an unknown part.

Lesson 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

Use place value reasoning to write and compare 2 two-digit numbers.

Determine if number sentences involving addition and subtraction are true or false.

Lesson 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Lesson 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

Compare two quantities and make them equal.

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Lesson 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Add ones and multiples of ten to any number.

Topic E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 Addition of Two-Digit Numbers Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

Module Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 Resources Achievement Descriptors: Proficiency Indicators. . . . . . . . . . . . . . . . 362 Observational Assessment Recording Sheet . . . . . . . . . . . . . . . . . . . . 370

Use varied strategies to add 2 two-digit addends.

Sample Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

Lesson 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

Decompose both addends and add like units.

Lesson 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 Decompose an addend and add tens first.

Lesson 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

Math Past. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

Decompose an addend to make the next ten.

Works Cited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Lesson 25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

Credits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

Compare equivalent expressions used to solve two-digit addition equations.

Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

Why Place Value Concepts to Compare, Add, and Subtract Why are there so many strategies and tools for adding large numbers? One concept unifies the many ways to add two-digit numbers: make an equivalent yet easier problem. Break the addends into parts and combine the parts in ways that make sense. Exposing students to more than one way to make an easier problem increases number sense, encourages flexibility, and provides choice. Presenting different strategies acknowledges that learners think about numbers in different ways. Also, the addends may lend themselves to certain strategies. For example, to solve 29 + 21 efficiently, simply add the 1 from 21 to 29 to make 30. Then add 30 and 20. However, to solve 32 + 26, it may be easier to think of 26 in terms of tens and ones, solve 32 + 20, and add 6 more to make 58. Students who develop a toolbox of strategies will begin to select them intentionally. Students also select different tools or models, such as manipulatives, drawings, number paths, number bonds, and number sentences. How they solve a problem is less important than an accurate solution, the written record of their thinking, and their explanation of their reasoning. Sharing such representations and engaging in discussion to analyze various ways to solve are critical features of instruction that deepen understanding of place value, operations, and quantity.

What skills do students need to add two-digit numbers by the end of the year? Students need several skills to add 2 two-digit numbers. As they work through module 5 topic E and module 6 part 2, they continue to develop these embedded skills through practice. However, if students are still working toward proficiency with some of the first skills in the following chart, then they may benefit from directly modeling 2-digit addition problems using concrete or pictorial tools.

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8 + 5 = 13 8 + 5 = 13 8 + 5 = 13 7 = 10 Add Break Up a Add3a+ Two-Digit Identify Know 3 + 7 = 10 One-Digit Number and a 16 One-Digit 8 + 5 =into 13 the Next Ten Partners to 10 16 Numbers Tens and Ones Number 3 + 7 = 10 10 6 16 8 + 5 = 13 3 + 7 = 10 16 10

10 6

12 + 8 = 20 14 + 9 = 23 27 + 10 = 37

8 + 5 = 13

12 + 8 = 20

3 + 7 = 10

14 + 9 = 23 27 + 10 = 37

16 10

3 + 7 = 10 Add16Tens to a10 Two-Digit 6 Number 12 + 8 = 20 14 + 9 = 23 27 + 10 = 37

12 + 8 = 20

How do students deepen and advance their understanding of the equal sign?

14 + 9 = 23 12 + 8 = 20 10 ==37 Students 20 + 30. They determine whether 14 + 9 = 23evaluate number sentences such as 9027– +40 the27number sentence is true or false by calculating the value of the expressions on either + 10 = 37 side of the equal sign. This provides practice with adding and subtracting tens while giving students opportunities to engage with uncommon and complex equation types. Students also evaluate number sentences with equivalent expressions that represent different ways to make an easier problem. For example, the expression on either side of the equals sign in 10 + 10 + 2 + 6 = 12 + 10 + 6 shows one way to break up the addends in 12 + 16. Students find the expressions have the same value and conclude that the number sentence is true. This helps confirm that there are several valid ways to solve a problem.

Why is telling time included in a module on place value? Module 5 centers on the idea that smaller units such as ones compose larger unit such as tens. Time also involves composing units. For example, minutes make up hours and half hours, and hours make up days. Work with units in various contexts (e.g., time, measurement, and shapes) develops reasoning that helps students understand numerical units such as ones, tens, and hundreds. Students revisit telling time to the half hour in module 6.

Achievement Descriptors: Overview Place Value Concepts to Compare, Add, and Subtract Achievement Descriptors (ADs) are standards-aligned descriptions that detail what students should know and be able to do based on the instruction. ADs are written by using portions of various standards to form a clear, concise description of the work covered in each module. Each module has its own set of ADs, and the number of ADs varies by module. Taken together, the sets of module-level ADs describe what students should accomplish by the end of the year. ADs and their proficiency indicators support teachers with interpreting student work on • informal classroom observations (recording sheet provided in the module resources), • data from other lesson-embedded formative assessments, • Exit Tickets, • Topic Tickets, and

Observational Assessment Recording Sheet Student Name

Grade 1 Module 5

Place Value Concepts to Compare, Add, and Subtract Achievement Descriptors

Dates and Details of Observations

1.Mod1.AD6

Determine whether addition and/or subtraction number sentences are true or false.

1.Mod5.AD1

Represent a set of up to 99 objects with a two-digit number by composing tens.

1.Mod5.AD2

Represent two-digit numbers within 99 as tens and ones.

1.Mod5.AD3

Determine the values represented by the digits of a two-digit number.

1.Mod5.AD4

Compare two-digit numbers by using the symbols >, =, and <.

1.Mod5.AD5

Add or subtract multiples of 10.

1.Mod5.AD6

Add a two-digit number and a multiple of 10 that have a sum within 100.

1.Mod5.AD7

Add a two-digit number and a one-digit number that have a sum within 50, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

1.Mod5.AD8

Add 2 two-digit numbers that have a sum within 50, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

1.Mod5.AD9

Mentally find 10 more or 10 less than a two-digit number.

1.Mod5.AD10

Tell time to the hour and half hour on analog and digital clocks. PP Partially Proficient

Notes

370

This page may be reproduced for classroom use only.

P Proficient

HP Highly Proficient

• Module Assessments. This module contains the eleven ADs listed. 1.Mod1.AD6

1.Mod5.AD1

1.Mod5.AD2

Determine whether addition and/or subtraction number sentences are true or false.

Represent a set of up to 99 objects with a two-digit number by composing tens.

Represent two-digit numbers within 99 as tens and ones.

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1.Mod5.AD3

1.Mod5.AD4

1.Mod5.AD5

Determine the values represented by the digits of a two-digit number.

Compare two-digit numbers by using the symbols >, =, and <.

Add or subtract multiples of 10.

1.Mod5.AD6

1.Mod5.AD7

1.Mod5.AD8

Add a two-digit number and a multiple of 10 that have a sum within 100.

1.Mod5.AD9

1.Mod5.AD10

Mentally find 10 more or 10 less than a two-digit number.

Tell time to the hour and half hour on analog and digital clocks.

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The first page of each lesson identifies the ADs aligned with that lesson. Each AD may have up to three indicators, each aligned to a proficiency category (i.e., Partially Proficient, Proficient, Highly Proficient). While every AD has an indicator to describe Proficient performance, only select ADs have an indicator for Partially Proficient and/or Highly Proficient performance. An example of one of these ADs, along with its proficiency indicators, is shown here for reference. The complete set of this module’s ADs with proficiency indicators can be found in the Achievement Descriptors: Proficiency Indicators resource. ADs have the following parts: • AD Code: The code indicates the grade level and the module number and then lists the ADs in no particular order. For example, the first AD for grade 1 module 5 is coded as 1.Mod5.AD1. • AD Language: The language is crafted from standards and concisely describes what will be assessed. • AD Indicators: The indicators describe the precise expectations of the AD for the given proficiency category.

AD Code Grade.Module.AD#

AD Language

1 ▸ M5

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1.Mod5.AD2 Represent two-digit numbers within 99 as tens and ones. Partially Proficient

Proficient

Highly Proficient

Represent two-digit numbers within 50 as tens and ones.

Represent two-digit numbers within 99 as tens and ones.

Represent numbers through 100–120 as tens and ones.

Draw the number with tens and ones.

Show the total with a number bond or number sentence.

AD Indicators

Draw the number with tens and ones.

114

1.Mod5.AD3 Determine the values represented by the digits of a two-digit number. Partially Proficient

Highly Proficient

Determine the number represented by given amounts of tens and ones.

Determine the values represented by the digits of a two-digit number.

Write the total.

Fill in the number bond.

6 tens and 3 ones is

Proficient

63 60

Topic A Grouping Units in Tens and Ones Topic A builds on work with tens and ones that students completed in modules 3 and 4. At first students reason about units in the context of time. They learn through experience that smaller units can compose larger units. For example, they discover that 1 hour is made of 60 minutes and 1 half hour is made of 30 minutes. Lessons build on the idea that smaller units can be used to compose larger units by considering the place value units of tens and ones. Students work with sets of objects to compose groups of 10 and represent two-digit totals in different ways. For example, 26 ones can also be represented as 1 ten 16 ones or 2 tens 6 ones. Working with numbers that have more than 9 ones prepares students for adding and subtracting with larger numbers in later grades. However, students come to understand that the digits we use to write a number, such as the 2 and the 6 in 26, show how many tens and ones there are when the number is expressed in its “most composed” form. This leads to recognition that the value of digits can be determined based on their place in the number. The value of the digit 2 can be expressed as 2 tens or 20. The value of the digit 6 can be expressed as 6 ones or simply 6. Students compose (or decompose) a total such as 26 by place value units: 20 and 6 or 2 tens 6 ones. Using different representations of the same total invites students to consider equivalence and deepens their number sense.

50 pennies 50 ones

5 dimes 5 tens

Several place value models that increase in complexity help students internalize the basic understanding that 10 ones are equivalent to 1 ten.

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Groupable Students group 10 ones to compose a new unit of ten. They may put 10 bears into 1 cup, link 10 cubes into a stick, or circle 10 donuts to represent a box of 10. Students can see and manipulate the individual units within the new larger unit. The size of the new unit is proportionally larger than the base unit.

Pregrouped Students group 10 ones and trade them for a new item that represents 1 ten. For example, given 23 centimeter cubes, students trade 10 cubes for 1 ten-centimeter stick. The new item is proportionally larger than the base unit.

Nonproportional Students trade 10 ones for a new item that represents 1 ten, but the ten looks different from the 10 ones. An example is trading 10 pennies for 1 dime. These models are nonproportional because the new unit, in this case a dime, is not visually 10 times larger than the base unit, or penny. Nonproportional models prepare students to work with place value disks in grades 2–5.

In this topic, students also add 10 and take 10 all at once from numbers. They add to and subtract from numbers in sequence: 54 + 10 = 64, 64 + 10 = 74, and so on. From this a pattern becomes visible: the digit in the tens place changes by 1, but the digit in the ones place remains the same.

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Progression of Lessons Lesson 1

Lesson 2

Lesson 3

Tell time to the hour and half hour by using digital and analog clocks.

Count a collection and record the total in units of tens and ones.

Recognize the place value of digits in a two-digit number.

4:30 The minute hand is pointing at the 6, and the hour hand is not at 5 yet, so it is 4:30. EUREKA MATH2

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bears How many do you think there are?

5 03

10 10 tens

Total

LESSON

After we composed all of the tens, there were 5 tens and 3 ones. The digits 5 and 3 make 53. The value of the digit 5 is 50 and the value of the digit 3 is 3.

10 5

ones

We composed tens by making groups of 10. We had 5 groups of ten and 2 extras. That is 52 bears. EM2_0105TE_A_L02_classwork_1_studentwork_CE.indd 2

07/04/21 3:45 PM

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Lesson 4

Lesson 5

Lesson 6

Represent a number in multiple ways by trading 10 ones for a ten.

Reason about equivalent representations of a number.

Add 10 or take 10 from a two-digit number. tens ones

30 crayons

I can trade 10 pennies for a dime and use dimes and pennies to show different ways to make 30 cents.

3 boxes of crayons

I would rather have 30 loose crayons so I can see all the colors, but both pictures have the same number of crayons. 30 ones is 30 and 3 tens is 30.

6 16 26 36 46 56 66 76 86

tens ones

96 86 76 66 56 46 36 26 16

When I add ten, the digit in the tens place is 1 more. When I subtract ten, the digit in the tens place is 1 less.

LESSON 1

Tell time to the hour and half hour by using digital and analog clocks.

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Name

Circle the time.

Lesson at a Glance Students analyze an analog clock and a digital clock that show the same time. They learn how each clock represents the hour and minutes and practice reading the time to the hour and half hour on both kinds of clocks.

Key Question • What time is it? How do you know?

Achievement Descriptor 1.Mod5.AD10 Tell time to the hour and half hour on analog and

8:00

8:30

digital clocks.

9:30

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Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Match: Time cards removables must be torn out of student books. Cut out the cards on the removable to make a set. Each student pair needs one set of cards.

Launch Learn

10 min 5 min

35 min

• Hours and Minutes • Tell Time to the Hour and Half Hour

• Computer with internet access* • Projection device* • Teach book* • 100-bead rekenrek

• Match: Time

Students

• Problem Set

• Dry-erase marker*

Land

10 min

• Prepare the digital interactive clock for the lesson.

• Pencil* • Personal whiteboard* • Personal whiteboard eraser* • Learn book* • Match: Time cards removable (1 per student pair, in the student book) * These materials are only listed in lesson 1. Ready these materials for every lesson in this module.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

Fluency

10 5

Whiteboard Exchange: 4 as an Addend 35and use the commutative property to write a related Students find a total addition sentence to build addition fluency within 20. 10

After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display 1 + 4 = .

1+4= 5

Write the equation, and then find the total. Display the completed addition sentence: 1 + 4 = 5.

4+ 1 = 5

Change the order of the addends to write a related addition sentence. (Point to the addends.) Display the related addition sentence: 4 + 1 = 5. Repeat the process with the following sequence:

3+4

2+4

7+4

5+4

0+4

9+4

4+4

6+4

8+4

5-Groups: 10 and Some More Students recognize a group of dots and say the number two ways to prepare for identifying a given set with all the tens composed in lesson 3. Display the 5-group cards that show 11. How many dots? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 11 20

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 1

We can say 11 is 1 ten 1 one. On my signal, say it with me. Ready? 11 is 1 ten 1 one. Repeat the process with the following sequence:

12 1 ten 2 ones

15 1 ten 5 ones

17 1 ten 7 ones

16 1 ten 6 ones

20 2 tens

19 1 ten 9 ones

15 1 ten 5 ones

14 1 ten 4 ones

13 1 ten 3 ones

10 1 ten

As students are ready, challenge them to recognize the groups of dots more quickly by showing each set of 5-group cards for a shorter time.

Counting on the Rekenrek by Tens and Ones Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for recording the units of tens and ones in a given set in lesson 2. Show students the rekenrek. Start with all the beads to the right side. Let’s count to 41 the Say Ten way. Say how many beads there are as I slide them over. Slide over 10 beads in each row all at once as students count to 4 ten. 1 ten, 2 ten, 3 ten, 4 ten Slide over 1 more bead as students count to 4 ten 1. 4 ten 1

Student View 21

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

Slide all the beads back to the right side.

Language Support

Let’s count to 41 the regular way. Say how many beads there are as I slide them over.

Consider using strategic, flexible grouping throughout the module.

Repeat the process as students count by tens and ones to 41. 10, 20, 30, 40, 41 Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

4 ten 6

6 ten 3

6 ten 8

• Pair students who have different levels of mathematical proficiency. • Pair students who have different levels of English language proficiency. • Join pairs of students to form small groups of four. As applicable, complement any of these groupings by pairing students who speak the same native language.

Launch

5 35

Students listen to sounds of different durations and learn that 60 minutes make an hour. 10

Tell students to prepare to listen carefully. Play the first sound, which lasts for 1 second. What do you notice? It is very short. Play the next sound, which lasts for 10 seconds. What do you notice this time? It was longer this time, so I can tell it is music. The first sound is a short part. (Show your palms facing each other, close together.) The sound we just heard is longer. (Increase the distance between your palms.) 22

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 1

Play the third sound, which is 60 seconds long.

Promoting Mathematical Practice

Is this sound shorter (show palms close together) or longer (expand the distance between palms) than the first one?

Students attend to precision when they use minutes and hours appropriately to describe lengths of time. Appropriate use of units begins with understanding that a minute is a short length of time and an hour is a longer length of time. It extends to discussing how larger units are made out of smaller ones.

Longer That last sound was a minute long! Help students recall their learning about time by asking the following questions. Which is longer, a minute or an hour? How do you know? An hour is longer. A minute goes by fast, but an hour takes more time. You are right. An hour is longer because 60 minutes go together to make an hour. Transition to the next segment by framing the work.

Reasoning with units in different contexts (e.g., time, measurement, or shapes) helps students to work with numerical units (tens, hundreds, etc.) later on.

Today, we will look at a clock and see how minutes make an hour. 10 5

Learn

35 10

Hours and Minutes Students count minutes to see how analog and digital clocks represent the time. Show students 1 o’clock on the analog clock only. (Point to the red hand.) The short hand is the hour hand. It tells the hour.

(Point to the blue hand.) The long hand is the minute hand. It tells the minutes.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

Turn on the digital clock as well. This is a different type of clock. It shows the time using only numbers. The numbers to the left of the dots tell the hour. (Point to the 1 on the digital clock.) The numbers to the right of the dots tell the number of minutes. (Point to the 00 on the digital clock.) Tell students that both clocks show 1 hour and 0 minutes. Help them read the time on each clock as 1 o’clock. Tell students that as time passes, the hands on the first clock (the analog clock) move, but the numbers on the second clock (the digital clock) just change.

1:00

Watch and see what happens on each clock as time passes. Let’s count minutes. Slowly move the minute hand from 1:01 to 1:30. Have the class chorally count the minutes. 1 minute, 2 minutes, … , 29 minutes, 30 minutes

1:01

1:30

Point to the analog clock that shows 1:30. What did the hands do on this clock as we counted? The minute hand moved a little bit at a time. It went from the top of the clock to the bottom of it. The hour hand only moved a little. Now it’s past the 1, but not to the 2. Reset the clock to 1 o’clock. As time passes, the minute hand moves forward one tick mark at a time. Each tick mark represents 1 minute. Watch the blue minute hand. Slowly move the minute hand from 1:00 to 1:05. The hour hand moves too. As minutes go by, the hour hand moves slowly from one number on the clock to the next. Watch the red hour hand. 24

1:00

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 1

Slowly move the minute hand to 1:30. Now the hour hand is between two numbers, or hours. The minute hand points straight down to the 6. When the hands are in this position, we say the first number for the hour and read the time as one thirty. Point to the digital clock that also shows 1:30. What did the numbers on this clock do as we counted? They changed. The minutes went from 00 up to 30. They went up by 1 each time.

1:30

What time does the clock show? 1:30 Both clocks started at 1 o’clock. We counted 30 minutes from 1 o’clock to 1:30. Now the clocks show 1:30. Let’s keep counting until the minute hand moves all the way around the clock. (Point to the picture of the analog clock.) Slowly move the minute hand from 1:30 to 2 o’clock. Have the class chorally count the minutes. 31 minutes, 32 minutes, … , 59 minutes, 60 minutes

2:00

What time do the clocks show now? How do you know? 2 o’clock The hour hand is pointing at the 2 and the minute hand is on the 12. There is a 2 and two zeros on the clock with only numbers. Confirm that both clocks show 2 o’clock. (Point to the digital clock.) On this clock, after the minutes show 59, they start over at 0. It shows 1:59 and then 2:00. This happens because there are 60 minutes in 1 hour. How many minutes are in an hour? 60 minutes (Point to the analog clock.) On the other clock, when the minute hand goes all the way around the clock, the hour hand arrives at the next number, or hour. Now the hour hand is pointing to 2. Copyright © Great Minds PBC

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

Tell Time to the Hour and Half Hour

Differentiation: Support

Students practice telling time to the hour and half hour by using an analog clock.

If needed, provide additional support for students with telling time to the half hour.

Have students practice telling time to the hour and half hour. Consider having students stand.

• The hour hand is between 2 and 3. When the hour hand is between two hours, or numbers, we say the first hour. The hour hand is getting closer to the next hour, but it’s not there yet.

Use only the analog clock set to 2 o’clock. What time is it? 2 o’clock

• When the minute hand points straight down at the 6, 30 minutes of the hour have passed.

Move the minute hand to show 2:30. Provide a moment of wait time. What time is it?

• This clock shows 2:30. The hour hand is still in the two o’clock hour and 30 minutes have passed.

2:30 Continue to show various times to the hour and half hour (3:00 and 3:30, 11:00 and 11:30, etc.) until students say the time to the half hour with confidence.

Match: Time Materials—S: Match: Time cards

Students match cards that use different formats of time to show time to the hour and half hour. Demonstrate and explain how to play Match: Time by using the following directions: • Place all of the Match: Time cards faceup. • One partner finds two cards that match because they show the same time. • They tell their partner how they know the cards match. • Partners take turns finding matches until all the matches have been found.

30 minutes 9 hours

3:00

8 hours 0 minutes

0 minutes 3 hours

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 1

Circulate as students play and ask the following questions:

UDL: Engagement

• (Point to a card.) Where do you see the hour? Where do you see the minutes? • Show me a match. What is the time on both cards?

Problem Set Differentiate the10set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 5 read aloud. Directions may be 35

Land Debrief

Foster collaboration and help students to engage successfully in the sorting game by assigning clear roles for each partner. Review the activity goal, directions, and group norms before groups begin. Consider embedding any socio-emotional skills students are learning in other areas of their day, such as sharing, taking turns, and disagreeing respectfully, into the activity.

5 min

Objective: Tell time to the hour and half hour by using digital and analog clocks. Show the analog clock set to 4:30. What time is it? How do you know? 4:30

The hour hand is a little past 4 and the minute hand points to 6. Show 4:30 with both clocks. Have students consider, discuss, and share the similarities and differences between the two clocks. How are the clocks the same? Both have numbers and tell the time. Both tell you the time is 4:30.

4:30

Both clocks show 4 hours and 30 minutes.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

How are the clocks different? One only has numbers. It does not have hands.

Teacher Note

One has hour and minute hands. For 30 minutes, one has the number 30. The other one shows 30 minutes at the 6. These clocks show the time in different ways. They both make a new hour every 60 minutes.

Exit Ticket

Distributed practice with telling time helps students master the skill. Each day, consider pausing periodically at the hour and half hour to ask: What time is it?

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 1

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

Name

1 ▸ M5 ▸ TA ▸ Lesson 1

2. Draw lines to match the times.

1. Fill in.

2:30

EUREKA MATH2

9 o’clock 2

5:00

7:30

hours

minutes

hours

30 0 7

minutes

3:30 minutes

8:30

hours

6 o’clock

minutes

hours

minutes

PROBLEM SET

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 1

3. Write what you do and the time you do it. Draw the time on the clock. Sample:

What You Do

Time

School

8:30

Clock

8 : 30 What You Do

Time

Recess

1 o’clock

Clock

PROBLEM SET

LESSON 2

Count a collection and record the total in units of tens and ones. Lesson at a Glance Students analyze a counting collection organized into groups of tens and ones and discuss the values of the digits in the total. Partners organize, count, and record their own collections. The class discusses student work and considers how groups of 10 and extra ones combine to make a total. The term digit is introduced in this lesson. There is no Fluency component, Exit Ticket, or Problem Set in this lesson. This allows students to spend more time completing the counting collection activity. Use student recordings to analyze their work.

Key Question • What do the digits in a number tell us?

Achievement Descriptors 1.Mod5.AD1 Represent a set of up to 99 objects with a two-digit number by composing tens. 1.Mod5.AD3 Determine the values represented by the digits of a two-digit number.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 2

Agenda

Materials

Lesson Preparation

Launch

Teacher

• Copy or print the counting collection recording page to use for demonstration.

Learn

15 min

40 min

• Chart paper

• Organize, Count, and Record

• Hide Zero® cards, demonstration set

• Share, Compare, Connect

Students

Land

• Counting collection (1 per student pair)

5 min

• Work mat (1 per student pair) • Organizing tools • Hide Zero® cards (1 set per student pair)

• Use small, everyday objects to assemble at least one counting collection per pair of students. Place each collection in a bag or box. Each collection should contain 50–100 objects. Differ the number of objects in the collections based on the needs of your students. Provide a challenge by creating collections with 101–120 objects. Save collections for future use. • Provide tools students can choose from to organize their counting. Place them in a central location. Tools may include cups, plates, number paths, or 10-frames. • Gather large pieces of construction paper or trays for students to use as work mats. Work mats help students keep track of and organize the objects in their collection. They can also make students’ work portable. • Prepare an anchor chart that will be used to keep track of tens, ones, and totals in the lesson (see image in Launch).

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 2

Launch

15 40

Materials—T: Chart paper, Hide Zero cards

Students analyze the 5 way a counting collection is organized and describe it in terms of tens and ones.

We will ... 1

Choose a collection.

If needed, briefly review the procedure of counting a collection by using the chart from module 3 lesson 15.

Make a good guess.

Display a picture of a counting collection. Give students a quiet moment to study the image.

Make a plan and count.

Record the collection.

How is the counting collection organized? The cubes are in sticks of 10. There are 5 extra cubes next to the sticks. Why do you think the collection is organized this way?

1, 2, 3, 4, …

our 5 Share work. Language Note

It is fast to count by tens. There are a lot of cubes. It’s helpful to put them into groups of 10 to make them easier to count.

Support students in reading two-digit numbers by using the rekenrek and the Say Ten way.

Organizing larger collections into tens and ones can help make counting efficient.

For example, show 75 on the rekenrek. Help students read the number the Say Ten way: 7 tens 5. Connect the Say Ten way to the standard form: 7 tens is 70, so we say seventy-five.

Have students turn and talk to estimate or make a good guess about the total. Then guide the class to chorally count by tens and ones to find the total, 75. Show 75 by using Hide Zero cards. Then separate the cards to show 70 and 5. 70 and 5 make 75. (Point to the 70 card.) Where do you see 70 in the collection? The ten-sticks equal 70. 34

7 05

7 0 5

Saying 75 as 7 ten 5, or as 7 tens 5 ones, helps students relate the number name to its place value structure, helping them connect the idea that -ty means tens.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 2

If needed, count the ten-sticks by tens to 70. (Point to 5.) Where do you see 5 in the collection? There are 5 extra cubes to the side of the tens. 70 and 5 is … 75 Put the cards back together to show 75. Numbers such as 7 and 5 are called digits. When we write digits next to each other, we make another number. For example, we write the digits 7 and 5 next to each other to make 75. In 75, the digit 7 tells us that there are 7 tens. We know that 7 tens is 70. (Separate the cards again to show 70 and 5.) The digit 5 in 75 tells us that there are 5 ones, or 5. Put the cards back together to show 75. What are the digits in 75? 7 and 5

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 2

cubes

Name

How many do you think there are? How many do you think there are?

Show the counting collection recording page from the student book. Use a combination of the following questions to interactively demonstrate how to record a collection: • What are we counting in this collection? • What was one of our good guesses about the total number of objects? tens

• What can we draw to show how the counting collection is organized? • How many groups of 10 are there? How many extra ones are there? • What is the total number of objects in the collection?

EM2_0105TE_A_L02_classwork_1_studentwork_CE V2.indd 1

ones tens

Total

ones

75 1

07/04/21 3:42 PM

Post a chart for keeping track of counting collection totals in terms of tens and ones. Record the sample on the chart.

1 ▸ M5 ▸ TA ▸ Lesson 2

EUREKA MATH2

Let’s keep track of all the counting collections we talk about today. In this collection there are 7 groups of 10 and 5 extra ones. What is the total? 75 Transition to the next segment by framing the work. Today, we will organize, count, and record a collection.

Learn

40 5

Organize, Count, and Record Materials—S: Counting collection, organizing tools, Hide Zero cards, work mat

Students organize, count, and record a collection of objects. Partner students and invite them to choose a collection, organizing tools, a work mat, and a workspace. Have them open their student book to the counting collection recording page. After you count your collection and record your work, use Hide Zero cards to represent the total. Look for the digits that show how many tens and how many ones. Circulate as students work. Use any combination of the following questions or statements to assess and advance student thinking: • Show me how many tens and ones are in your collection. • What is the total? How do you know? • What does your drawing show? How can you label it? • How can you show the total with Hide Zero cards? 36

Promoting Mathematical Practice Students model with mathematics when they record their collection. Using a symbol such as a line or a box to record a group of 10 shows that students are thinking abstractly and understand that you can represent 10 without drawing 10 distinct items. Consider asking the following questions: • How is what you wrote or drew the same as your collection? How is it different from your collection? • Why is it helpful to draw groups of 10 instead of drawing every item in your collection?

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 2

• What are the digits that make your total?

Teacher Note

• What could be a more efficient way to organize the collection? Select student work that makes use of tens and ones to share in the next segment. The following chart shows samples. If some pairs finish early, invite them to draw number bonds or write number sentences to represent their total. Corey and Kioko

EUREKA MATH2

Name

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 2

Name

bears

circles How many do you think there are?

90 + 3 = 93

How many do you think there are?

tens

Total

EM2_0105TE_A_L02_classwork_1_studentwork_CE.indd 1

10 10

1 1 1

By grouping, students see the individual units that compose the new, larger unit. For instance, one cup of 10 bears contains 10 individual bears.

Sakon and Violet

1 ▸ M5 ▸ TA ▸ Lesson 2

tens

Total 1

07/04/21 3:45 PM

EM2_0105TE_A_L02_classwork_1_studentwork_CE V1.indd 1

Grouping also allows students to see that the size of the new unit is proportionally larger than the base unit. For example, 10 disks in a 10-frame are visually about 10 times larger than a single disk. Consider providing distributed practice with groupable models during the remainder of the year. Invite students to group and count various collections. Have them label their collections with Hide Zero cards and represent them by using number bonds, unit form, and number sentences.

10 5

ones

To fully grasp place value concepts, students need ample experience with grouping, or putting together items to make a new unit.

ones

52 1

12/03/21 8:29 PM

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 2

Share, Compare, Connect Materials—T: Chart, Hide Zero cards; S: Hide Zero cards

Students share and discuss recordings of counting collections. Invite two pairs to share their work. Encourage the class to use the Talking Tool to engage in discussion by asking questions, making observations, and sharing compliments.

Corey and Kioko How did you organize and count your collection? We put 10 disks in each line, 5 red and 5 yellow. Tell us about your recording. We drew rectangles to show a group of 10. We drew 3 circles to show our extra disks. Draw attention to the unit form at the bottom of the recording page.

Teacher Note The sample student work shows common responses. Look for similar work from your students and encourage authentic classroom conversations about the key concepts. If your students do not produce similar work, choose a student’s work to share and highlight how it shows movement toward the goal of this lesson. Then select a provided sample that advances your class’s thinking. Consider presenting the work by saying, “This is how another student counted the collection. What do you think this student did?”

Class, where do you see 9 tens in the drawing? Where do you see 3 ones? The 9 rectangles are 9 tens. The 3 circles labeled with a 1 are 3 ones.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 2

Name

circles

Invite students to turn and talk to their partner.

How many do you think there are?

Do you agree this recording shows a total of 93? Why? Using the recording, guide students to count chorally by tens and ones. Show 93 by using Hide Zero cards. 9 and 3 Refer back to the recording of the collection as needed to support students with answering the following questions.

90 + 3 = 93

10 10

tens

Total

EM2_0105TE_A_L02_classwork_1_studentwork_CE.indd 1

1 1 1

What digits do you see?

ones

93 1

07/04/21 3:45 PM

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 2

What does the digit 9 tell us in the number 93? It tells there are 9 tens.

Differentiation: Challenge

How many is 9 tens? EUREKA MATH2

Name

Slide apart the cards to confirm. Then put them back together. Repeat the process for the digit 3.

cubes How many do you think there are?

9 tens is 90 and 3 ones is 3. 90 and 3 make 93. Record the pair’s work under 75 on the class chart.

103 100

ones

103

Sakon and Violet EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 2

Name

bears How many do you think there are?

At another time, invite pairs who count collections with more than 100 objects to share their work. Facilitate discussion by using the following questions: EM2_0105TE_A_L02_classwork_2_studentwork_CE.indd 1

Class, how is this recording different from the other group’s recording?

05/04/21 4:35 PM

• Do you all agree this recording shows a total of 103 cubes? Why? • How many tens and ones do you see?

• How many is 10 tens 3 ones?

10 10

They have 5 tens. Corey and Kioko had 9 tens. 10

Invite students to think–pair–share about the second recording.

10 5

tens

EM2_0105TE_A_L02_classwork_1_studentwork_CE V1.indd 1

tens

Total

They have 2 ones, not 3 ones.

What is the total?

This one has circles instead of rectangles for the groups of 10.

120

10 20 30 40 50 60 70 80 90 100 101 102 103

This collection has 9 groups of 10 and 3 more ones.

Invite a different pair to share their work. Then direct the class’s attention to the unit form.

1 ▸ M5 ▸ TA ▸ Lesson 2

ones

52 1

12/03/21 8:29 PM

1 ▸ M5 ▸ TA ▸ Lesson 2

EUREKA MATH2

Do you agree that this recording shows a total of 52? Why? Yes. 10, … , 50, 51, 52. 50 plus 2 equals 52. 5 tens and 2 ones is 52. Ask partners to show 52 by using their set of Hide Zero cards. What digits do you see? 5 and 2 In 52, what does the digit 5 tell us? 5 tens How many is 5 tens? 50 Have students slide apart the cards to confirm and then put them back together. Repeat the process for the digit 2. Record the pair’s work on the class chart. In this collection there are 5 groups of 10 and 2 ones. What is the total? 52 Allow a few minutes for cleanup. Collect students’ recordings to review as an informal assessment.

15 EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 2 40

Land Debrief

5 min

Materials—T: Chart, Hide Zero cards

Objective: Count a collection and record the total in units of tens and ones. Gather students and display the class chart. (Point to the first row.) What was the total of this collection? 75 The digits of these numbers tell us how many tens or ones there are. In the number 75, what does the digit 7 tell us? (Point to the 7 in the tens column.) There are 7 groups of 10. How many is 7 tens? 70 As needed, use Hide Zero cards to support students. In the number 75, what does the digit 5 tell us? (Point to the digit in the ones column.) There are 5 ones. How many is 5 ones?

7 05

7 0 5

5 70 and 5 is 75. Ask a pair to share a new total and add it to the chart. Repeat the process.

LESSON 3

Recognize the place value of digits in a two-digit number.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

Name

Circle all the groups of 10.

Lesson at a Glance Students work with sets of objects to compose as many groups of 10 as they can. They record their work by writing the total in both standard form and as the number of tens and ones. The terms compose, value, and place (as in place value) are introduced in this lesson.

Key Question

tens

Total

ones

• What is the value of each digit in a two-digit number? How do you know?

Achievement Descriptors

1.Mod5.AD1 Represent a set of up to 99 objects with a two-digit

number by composing tens. 1.Mod5.AD3 Determine the values represented by the digits of a

two-digit number.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 3

Agenda

Materials

Lesson Preparation

Fluency

Teacher

The Tens and Ones removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 5 min

35 min

• 100-bead rekenrek • Hide Zero® cards, demonstration set

• Place Value

Students

• Tens and Ones

• Tens and Ones removable (in the student book)

• Compose Tens • Problem Set

Land

• Hide Zero® cards (1 set per student pair)

10 min

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

Fluency

10 5

Whiteboard Exchange: 5 as an Addend 35and use the commutative property to write a related Students find a total addition sentence to build addition fluency within 20. 10

1+5= 6

Write the equation, and then find the total. Display the completed addition sentence: 1 + 5 = 6.

5+1= 6

Change the order of the addends to write a related addition sentence. (Point to the addends.) Display the related addition sentence: 5 + 1 = 6. Repeat the process with the following sequence:

2+5

4+5

8+5

5+5

0+5

9+5

6+5

3+5

7+5

5-Groups: 20 and Some More Students recognize a group of dots and say the number two ways to prepare for identifying a given set with all the tens composed. Display the 5-group cards that show 20. How many dots? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 20 44

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 3

We can say 20 is 2 tens. On my signal, say it with me. Ready? 20 is 2 tens. Repeat the process with the following sequence: 21 2 tens 1 one

25 2 tens 5 ones

29 2 tens 9 ones

30 3 tens

34 3 tens 4 ones

36 3 tens 6 ones

40 4 tens

43 4 tens 3 ones

As students are ready, challenge them to recognize the groups of dots more quickly by showing each 5-group set for a shorter time.

Counting on the Rekenrek by Tens and Ones Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for identifying a given set with all the tens composed. Show students the rekenrek. Start with all the beads to the right side. Let’s count to 52 the Say Ten way. Say how many beads there are as I slide them over. Slide over 10 beads in each row all at once as students count to 5 ten. 1 ten, 2 ten, 3 ten, 4 ten, 5 ten Copyright © Great Minds PBC

Student View 45

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

Slide over 2 more beads, one at a time, as students count to 5 ten 2. 5 ten 1, 5 ten 2 Slide all the beads back to the right side. Let’s count to 52 the regular way. Say how many beads there are as I slide them over. Repeat the process as students count by tens and ones to 52. 10, 20, 30, 40, 50, 51, 52 Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

5 ten 7 57

7 ten 4 74

7 ten 9 79 Teacher Note

Launch

5 35

Students see a group of items composed into tens and ones and discuss how they are composed. 10

Have students watch part 1 of the video, which shows a baker boxing doughnuts as they come down a conveyor belt. Invite students to discuss what they notice and wonder. I noticed he made a box of 10 donuts. Are there 50 donuts in all? I wonder if he will make more boxes of 10.

To fully grasp place value concepts, students need experience with groupable pictorial models. Although items in pictorial models cannot be physically grouped, students can still compose units. They may circle 10 items or group them in other ways to show that 10 items go together to make 1 ten. They may also rename the group by saying 1 box of doughnuts rather than 10 doughnuts, for example. They are internalizing that 10 ones are equivalent to 1 ten. Many pictorial models are proportional: The next unit is visually ten times larger than the base unit from which it is composed.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 3

Play part 2, which shows the baker making progress toward boxing all the doughnuts. The baker is making full boxes. Can he fill more boxes with the doughnuts that are left? How do you know? He can make more. He puts 10 doughnuts in a box. There are more than 10 doughnuts left. Play part 3, which shows 5 complete boxes and 3 leftover doughnuts. Why do you think the baker did not put the last 3 doughnuts in a box? Because he’s making full boxes of 10 doughnuts, and 3 doughnuts won’t fill a box.

Language Support Support understanding of the term compose by having students make ten. Ask them to lace their fingers together and say, “I composed a ten by putting together 10 ones.” Show other examples of composition, such as these: • A table group is composed of 4 desks.

The baker composed as many boxes of 10 doughnuts as he could. To compose means to put together or group. Many of us compose groups of 10 when we count a collection.

• Our class is composed of 24 students.

What did the baker compose?

• A painting can be composed of many shapes and colors.

Groups of 10 doughnuts

• A band is composed of many musical instruments.

Transition to the next segment by framing the work. Today, we will find the total number of doughnuts. We will talk about how many tens and ones are in the total.

10 EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3 5

Learn Place Value

35 10

Materials—T: Hide Zero cards

Students analyze a two-digit number and see that it is made of tens and ones. Display the image of the baker’s doughnuts as he first begins to box them. First the baker composed 1 box of 10 doughnuts. He had 43 more doughnuts, or ones, to box. Record this as 1 ten 43 ones. Display the image of the doughnuts at the end of the video. The baker composed as many tens as he could. How many boxes, or tens, did he compose? 5 tens How many extra doughnuts, or ones, did he have left? 3 ones Record this as 5 tens 3 ones. Invite students to think–pair–share about the total number of doughnuts in the video. What is the total number of doughnuts? 53

Teacher Note Unit form is a way of representing numbers in terms of place value units. For example, 48 can be written as 4 tens 8 ones or 3 tens 18 ones. Unit form is helpful for these reasons: • The unit is written to the right of the number so that students read left to right. • Units may be presented in a different order. For example, 43 can be written as 3 ones 4 tens. • When ones or tens are not fully grouped (e.g., 2 tens 43 ones), it may be easier for students to identify totals when they are written in unit form rather than shown on a place value chart. On a place value chart, students are more likely to mistake 2 in the tens and 43 in the ones as the number 243. Unit form is familiar from previous modules. However, students do not need to know it by name. The place value chart is introduced in lesson 6.

Support students as needed by chorally counting doughnuts by tens and ones. Show 53 using Hide Zero cards.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 3

Numbers with two digits have two places. This is the tens place. (Point to 5.) And this is the ones place. (Point to 3.) Tell students that the digit in the tens place tells how many tens are in the number. The digit in the ones place tells how many ones are in the number.

Language Support Consider making a chart to help students remember new terms.

What are the places in a number with two digits? The tens place and the ones place In 53, what digit is in the tens place? 5

5 03

(Point to the image of the doughnuts.) How many is 5 tens? 50

50 3

When 5 is in the tens place, it has a value of 50. Value tells how much something is worth. What digit is in the ones place? 3 3 is in the ones place. What is the value of 3 ones? 3 Display the picture of Hide Zero cards for 53 that are separated. 53 is made of 50 and 3. (Draw arms to form a number bond.) That is 5 tens and 3 ones. (Point to the digits in 53.)

5 03

50 3

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

Tens and Ones Materials—S: Tens and Ones removable, Hide Zero cards

Students find the value of digits in the tens and ones places and reason about their relationship to the total. Make sure students have inserted a Tens and Ones removable into their whiteboard. Display the picture of 35 doughnuts. The baker made this many doughnuts the next day. Invite students to think–pair–share about the number of tens shown in the picture. How many tens did he compose? How many ones are left?

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Tens and Ones

He composed 3 tens. There are 5 ones left. Have students record the number of tens and ones.

What is the total number of doughnuts? 35

Tell students to record the total in the number bond.

3 3tenstens

What are the digits in 35?

5 5 5 onesones

The tens place

EM2_0105TE_A_L03_removable_tens_and_ones_studentwork1_CE.indd 15

18/02/21 1:32 AM

What is the value of 3 in 35? How do you know? 30 There are 3 tens. 10, 20, 30. Tell students to record the value of the digit 3 in the number bond as shown.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 3

What place is 5 in?

3 05

The ones place What is the value of 5 in 35? How do you know? 5

3 0

There are 5 ones. 1, 2, 3, 4, 5. Tell students to record the value of the digit 5 in the number bond as shown.

Support students as needed by having them use Hide Zero cards to show the total. They can separate them to show the value of the digits.

Compose Tens

EUREKA MATH2

Materials—S: Tens and Ones removable

Name

Students compose groups of 10 within a set of objects and represent the total in terms of tens and ones.

Teacher Note

1 ▸ M5 ▸ TA ▸ Lesson 3

Circle all of the groups of 10.

Consider having students play Spill and Snap to provide additional practice with composing tens. Students take two big handfuls of cubes and spill them onto a surface. They snap ten cubes together to compose as many tens as possible. There are likely to be extra ones.

Tell students to turn to the ladybugs picture in their student book. What is an efficient way to find the total number of ladybugs? We could count groups of 10. We could count by fives. Copyright © Great Minds PBC

Have students circle groups to compose as many groups of 10 as they can. EM2_0105TE_A_L03_classwork_studentwork_CE.indd 17

How do you know you composed as many tens as you can? There are only 4 ladybugs left. I can’t make another group of 10. Have students use their Tens and Ones removable to record their work in unit form, and to record the total number of ladybugs in the number bond. Look at the total. What digit is in the tens place?

Students use the Tens and Ones removable to record their work. As they work, ask questions such as these:

25/01/21 10:55 PM

• How do you know you composed all of the tens? • What digit is in the tens place? • What digit is in the ones place? • What is the value of the digit ? How do you know?

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

What is the value of 2 in 24? How do you know? 20 There are 2 tens. 10, 20.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Tens and Ones

What digit is in the ones place? 4 What is the value of 4 in 24? How do you know?

4 There are 4 ones. 1, 2, 3, 4.

Ask students to complete the parts of the number bond to show the value of each digit.

2 2tenstens

4 4 4 onesones

Repeat the process for the feathers and the peanuts.

Problem Set Differentiate the10set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

EM2_0105TE_A_L03_removable_tens_and_ones_studentwork2_CE.indd 15

18/02/21 1:33 AM

10 read aloud. Directions may be 30

Land Debrief

Promoting Mathematical Practice 10

5 min

Objective: Recognize the place value of digits in a two-digit number. Display the picture of candles. State and record the number of tens and ones in the picture in unit form. Are all of the tens composed? How do you know? No, there are 11 extra candles. We could compose another ten. 52

As students relate the digits in a number to a representation of that number with all of the tens composed, they look for and make use of structure. The digits in a number always represent the number in its most composed form. Students need experience representing numbers that have different quantities of tens and ones to prepare them for adding and subtracting with larger numbers later in grade 1 and throughout grade 2.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 3

Display the second candle image. How many tens do you see now? How many extra ones do you see? 2 tens, 1 one (Write the number of tens and ones in unit form.)

tens

ones

We can write digits to represent the total as a number. When there are tens and ones, we write a digit in the tens place and a digit in the ones place. Invite students to think–pair–share about the number that shows 2 tens 1 one. What number can we write to represent 2 tens 1 one? 21 Record the total number of candles below the unit form. What is the value of each digit in 21? How do you know? The 2 means 20. We made 2 tens. The 1 in the ones place means there was 1 extra candle. Draw a number bond to record 20 and 1 as parts of 21.

Exit Ticket

Teacher Note Grouping amounts to make different units is whimsically portrayed in the picture book entitled One is a Snail, Ten is a Crab: A Counting by Feet Book, written by Sayre and Sayre. A wide range of critters on the beach have their feet counted in all sorts of combinations, including crabs with 10 legs. Consider using this book as a read-aloud to complement the lessons in this topic.

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

Name

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

2. Circle more groups of 10.

1. Circle all the groups of 10.

tens

Total

ones

tens

Total

tens

Total

tens

Total

ones

26 6

ones

tens

Total

PROBLEM SET

ones

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 3

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 3

5. Draw the number with tens and ones.

3. Circle all the groups of 10.

Show the total with a number bond or a number sentence. Sample:

44 40

10 10 10 30 + 7 = 37

4 58

tens

ones

4. Circle more groups of 10.

50 8

31 10

30 3

tens

1 60 + 4 = 64

one PROBLEM SET

PROBLEM SET

LESSON 4

Represent a number in multiple ways by trading 10 ones for a ten.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

Name

Show ways to make 25 using tens and ones.

tens

ones

Lesson at a Glance This lesson advances students from grouping objects to compose a ten to trading a group of 10 objects for an object that represents the next unit. For example, students trade 10 pennies for 1 dime. As they compose groups of 10, students record their thinking in unit form and also record the total as a two-digit number. They discuss the equivalence of various ways they can represent a given total.

Key Question

10 10

• How can we represent the same number in different ways using tens and ones?

tens

Achievement Descriptors

ones

1.Mod5.AD2 Represent two-digit numbers within 99 as tens

and ones.

1.Mod5.AD3 Determine the values represented by the digits of a

two-digit number.

tens

ones

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 4

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Consider preparing bags of coins before beginning the lesson for easy distribution. Each pair of students needs one bag of 6 dimes and 50 pennies. Save the bags of coins for use in a later lesson.

Launch Learn

10 min 10 min

30 min

• Trade Coins • Coin Combinations • Problem Set

Land

10 min

• 100-bead rekenrek • Base 10 rod • Centimeter cube • Dimes (6) • Pennies (50)

Students • Base 10 rods (5) • Centimeter cubes (25) • Dimes (6 per student pair)

• Ready the base 10 rods (ten-sticks) and cubes from module 4. Add 5 cubes to each bag so that each student has 25 cubes. Note: Base 10 rods are referred to as ten-sticks throughout the lesson.

• Pennies (50 per student pair)

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

Fluency

10 10

Choral Response: Subtract 0 or Subtract All Students subtract 030or subtract all to build subtraction fluency within 10. Display 5 – 5 = .

Differentiation: Support

What is 5 – 5? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

5-5= 0

Encourage students to use their fingers when needed to take away all at once or to take away 0.

Display the answer. Repeat the process with the following sequence:

4-4

3-3

5-0

4-0

3-0

8-8

8-0

9-9

7-0

Whiteboard Exchange: 6 as an Addend Students find a total and use the commutative property to write a related addition sentence to build addition fluency within 20. After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display 1 + 6 = . Write the equation and then find the total.

1+6= 7

Display the completed addition sentence: 1 + 6 = 7. Change the order of the addends to write a related addition sentence. (Point to the addends.) 58

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 4

Display a related addition sentence: 6 + 1 = 7. Repeat the process with the following sequence:

3+6

2+6

9+6

5+6

0+6

7+6

4+6

6+6

8+6

Counting on the Rekenrek by Tens and Ones Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for work with tens and ones. Show students the rekenrek. Start with all the beads to the right side. Let’s count to 71 the Say Ten way. Say how many beads there are as I slide them over. Slide over 10 beads in each row all at once as students count to 7 ten. 1 ten, 2 ten, 3 ten, 4 ten, 5 ten, 6 ten, 7 ten

Student View

Slide over 1 more bead as students count to 7 ten 1. 7 ten 1 Slide all the beads back to the right side. Let’s count to 71 the regular way. Say how many beads there are as I slide them over. Repeat the process as students count by tens and ones to 71. 10, 20, 30, 40, 50, 60, 70, 71

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

7 ten 6 76

9 ten 3 93

9 ten 8 98

Launch

10 30

Materials—T: Centimeter cube, base 10 rod (ten-stick); S: Centimeter cubes, base 10 rods (ten-sticks) 10

Students compose groups of 10 ones and trade them for 1 ten. Make sure students have ten-sticks and cubes sorted into piles. Hold up a ten and a one. We call these tools a cube and a stick when we measure. Today, we are not going to measure. For our work today, we will call them ones and tens. Tell partners to place 23 ones between them. What is the total? 23 Have we composed any tens yet? No. Write the total as 0 tens 23 ones. Let’s compose a ten. Group 10 ones and trade them for 1 ten. (Hold up a ten-stick.)

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 4

Guide students to group their ones and have them trade 10 ones for 1 ten, returning the 10 ones to the pile of cubes. How many tens and ones are there now? 1 ten 13 ones Write the total in unit form as 1 ten 13 ones. Do we still have a total of 23? Why? Yes, we did not change the number of cubes. We just traded 10 cubes for a ten-stick. Can we compose another ten from the ones that are left? How can we do that? Yes. There are more than 10 ones. We can trade another 10 ones for 1 ten. Have students compose another ten and trade 10 ones for 1 ten-stick. How many tens and ones are there now? 2 tens 3 ones Write the total in unit form as 2 tens 3 ones.

UDL: Representation To develop students’ understanding of and flexibility with place value concepts, consider making an anchor chart to show some different ways one number, such as 23, can be represented.

Do we still have a total of 23? Why? Yes, we did not change the number of cubes. We just traded 10 more cubes for another ten-stick. We can make 23 using groups of tens and ones in many ways. (Gesture to the different ways of recording the total.) 23 ones, 1 ten 13 ones, and 2 tens 3 ones all represent the same number, 23. When we have composed as many tens as we can, we write digits in the tens place and in the ones place to represent the total as a number.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

Write 23. What are the values of the digits 2 and 3 in the number 23? 20 and 3 Draw arms from 23 to make a number bond and write 20 and 3 as the parts. Have students clean up. Or if students need more practice, have them repeat the process with 18, 27, or 35. Transition to the next segment by framing the work. Today, we will continue to compose groups and trade 10 ones for 1 ten. 10 10

Learn Trade Coins

30 10

Materials—T/S: Dimes, pennies

Students group 10 pennies and trade them for 1 dime. Display the picture of a penny. What is the name of this coin? It’s a penny! The value of a penny is 1 cent. Display the picture of a dime. This is a dime. The value of a dime is 10 cents. Display the picture of the two children. Invite students to think–pair–share about the following situation. Senji has 10 pennies. Kioko has 1 dime. Senji wants to trade his 10 pennies for Kioko’s 1 dime. Is that fair? Why? 62

Teacher Note To fully grasp place value concepts, students need experience with pregrouped models (ten-sticks and cubes) and nonproportional models (coins). When students compose a ten using cubes and ten-sticks by trading these objects rather than physically grouping them because the sticks have already been grouped by tens, such pregrouped models are still proportional. Coins are not groupable in the sense that 1 dime is not literally made of 10 pennies. Students trade 10 pennies for the dime. Coins are nonproportional because the new unit (dime) is not visually 10 times larger than the base unit (penny). These types of models help students internalize the fact that 10 ones are equivalent to 1 ten, regardless of the representation. Working with nonproportional models such as coins will prepare students for work with place value disks in grade 2.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 4

Yes, it is fair because 10 pennies is 10 cents and 1 dime is 10 cents. Yes, it is like trading 10 cubes for a ten-stick. We can trade 10 pennies for 1 dime. It is the same as composing a group of 10 ones and trading them for 1 ten. Distribute dimes and pennies to pairs of students. Model how to group and trade 10 pennies for 1 dime as students follow along with their coins.

Coin Combinations Materials—T/S: Dimes, pennies

Students find all the possible combinations of tens and ones for a given total. Pretend you have 30 cents in your pocket. You may have just dimes, just pennies, or dimes and pennies. Use your coins to figure out which coins you could have. Have pairs of students find and then share at least one possible coin combination. If they mention other coins, validate their ideas and refocus students on pennies and dimes. Circulate and ask questions to advance students’ thinking. For example: • A penny is 1 cent. A dime is 10 cents. How many cents do you have? • Is there a way to make 30 cents with different coins? Then show 30 pennies. Have partners also set out 30 pennies. Ask them to sort their remaining dimes and pennies into two piles, one pile for the dimes and one pile for the pennies. Let’s find all the different ways we could make 30 cents. One way is 30 pennies. Count the 30 pennies and arrange them in 5-groups as pairs do the same. Write the number of pennies as 0 tens 30 ones. Can we compose a ten? How?

Promoting Mathematical Practice As students move to using dimes and pennies to represent numbers, they reason abstractly and quantitatively. Dimes and pennies are nonproportional representations of tens and ones because students cannot see 10 pennies inside a dime. This requires students to think more abstractly. Consider asking the following questions: • Which coin represents a ten? Which coin represents a one? Why? • How do you know a dime represents a 10 even though it is not made out of 10 pennies?

1 ▸ M5 ▸ TA ▸ Lesson 4

EUREKA MATH2

Trade 10 pennies for 1 dime as pairs do the same. Chorally count the total starting with the dime. 10, 11, … , 29, 30 How many tens and ones do you see? 1 ten 20 ones Write the total in unit form as 1 ten 20 ones. 1 ten and 20 ones is the same as how many ones? 30 Have we composed all the tens we can? No, we can still trade more groups of 10 pennies. Repeat the process of grouping, trading, and chorally counting. How many tens and ones are there? 2 tens 10 ones Write the total in unit form as 2 tens 10 ones. 2 tens 10 ones is the same as 1 ten 20 ones. It is also the same as how many ones? 30 Repeat the process of grouping, trading, and chorally counting. Write the total in unit form as 3 tens 0 ones. Have students look at the recordings of equivalent unit forms for 30. What do you notice about these representations? These are all the ways we made 30. The number of tens goes up by 1 ten each time. The number of ones goes down each time. Which way helps us write 30 as a two-digit number? 3 tens and 0 ones Circle 3 tens and 0 ones. 30 is 3 tens and 0 ones. (Write 3 and 0 as you say each digit.) 64

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 4

What is the value of the digit 3? What is the value of the digit 0? 3 is 3 tens. 0 is 0 ones. Draw arms from 30 to make a number bond and write 30 and 0 as the parts. As needed, provide more practice with trading ones for tens using 25, 32, or 44 pennies.

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

5 min

Materials—T: Dimes, pennies

Objective: Represent a number in multiple ways by trading 10 ones for a ten. Display the picture of Senji and Kioko. Invite students to discuss the similarities and differences between the two sets of coins the children are thinking about. What is different about Senji’s money and Kioko’s money? Senji has 16 coins. Kioko has 7 coins. Kioko has a dime and pennies. Senji has only pennies. What is the same about the two sets of coins they have? They both have 16 cents. Copyright © Great Minds PBC

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

Kioko has a ten and some ones. Senji only has ones. How do you know they both have 16 cents?

Teacher Note

They both have 1 ten and 6 ones, only in different coins. Senji could trade 10 pennies for 1 dime, and then they would have the same coins. Set out 16 pennies. Here are 16 ones. We can trade 10 ones for 1 ten. Then we have 1 ten and 6 ones. How do we write 1 ten and 6 ones as a two-digit number? Write 1 in the tens place and 6 in the ones place.

Consider having students play Take and Trade to provide additional practice with trading ones for tens. Students use a handful of cubes and 5 ten-sticks. They group and trade as many ones for tens as they can. There are likely to be extra ones. Use pennies and dimes as a variation.

Record 16 and write tens and ones over the numbers as shown. How can we represent the same number in different ways using tens and ones? We can use all ones. We can trade some ones for tens.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

As students work, ask questions like these: • How do you know you have traded for or composed all of the tens? • What is the new total? How do you know?

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 4

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

Name

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

2. Use your pennies and dimes. Trade pennies for a dime.

1. Use your cubes and sticks. Trade cubes for a stick.

ten

Total

8 18

Draw the tens and ones.

ones

tens

Total

ones

ten

Total 27

PROBLEM SET

3 13

Draw the tens and ones.

ones

tens

Total

ones

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 4

4. Show ways to make 38. Use only ones, or tens and ones.

3. Show ways to make 20. Use only tens, only ones, or tens and ones.

Use dimes and pennies to help you.

10 10

tens

ones

tens

ones

10 10 10

tens

ones

tens

ones

2 18

10 10

tens

1 28

10 tens

ones

0 20

tens

ones

0 38 20 ones is the same as

tens.

PROBLEM SET

38 ones is the same as

PROBLEM SET

tens

ones.

LESSON 5

Reason about equivalent representations of a number.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

Name

Write the total in two ways. 10

Lesson at a Glance Students work with different representations of the same total. Some representations show all tens composed, others show no tens composed, and still others show a mix of tens and ones. Students compare the representations and find totals to confirm the equivalence of the sets.

Key Question • Why can different representations show the same total? 10

Achievement Descriptors 1.Mod5.AD1 Represent a set of up to 99 objects with a two-digit

number by composing tens. 1.Mod5.AD2 Represent two-digit numbers within 99 as tens and ones. 1.Mod5.AD3 Determine the values represented by the digits of a

two-digit number.

Sample:

tens

ones is the same as

tens

ones. 55

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 5

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Copy or print the Match: Place Value cards and Match: Place Value Mat to use for demonstration.

Launch Learn

10 min 10 min

30 min

• Equivalent Representations • Match: Place Value • Problem Set

Land

10 min

• 100-bead rekenrek • Match: Place Value cards (digital download) • Match: Place Value Mat (digital download)

Students • Match: Place Value cards (1 set per student pair, in the student book)

• To prepare for the Match game, remove the Match: Place Value cards and Match: Place Value Mat from the student books. Each pair of students will need to place a mat in a personal whiteboard. Cut out a set of Match: Place Value cards for each student pair.

• Match: Place Value Mat (1 per student pair, in the student book)

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

Fluency

10 10

Choral Response: Subtract 0 or Subtract All Students subtract 030or subtract all to build subtraction fluency within 10. Display 2 – 2 = .

What is 2 – 2? Raise your hand when you know.

Differentiation: Challenge

Wait until most students raise their hands, and then signal for students to respond.

2-2= 0

0 Display the answer.

To increase the challenge and engagement, consider presenting problems with larger numbers. For example, present 27 – 27, 68 – 0, 105 – 105, 113 – 0, or 1,000 – 1,000.

Repeat the process with the following sequence:

1-1

2-0

1-0

6-6

6-0

7-7

9-0

0-0

10 - 10

Whiteboard Exchange: 4, 5, or 6 as an Addend Students find a total and use the commutative property to write a related addition sentence to build addition fluency within 20. After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display 4 + 3 = .

4+3= 7 3+4= 7

Write the equation and then find the total. Display the completed addition sentence: 4 + 3 = 7.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 5

Change the order of the addends to write a related addition sentence. (Point to the addends.) Display a related addition sentence: 3 + 4 = 7. Repeat the process with the following sequence:

7+4

9+4

5+3

7+5

9+5

6+3

7+6

9+6

Counting on the Rekenrek by Tens and Ones Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for work with tens and ones. Show students the rekenrek. Start with all the beads to the right side. Let’s count to 82 the Say Ten way. Say how many beads there are as I slide them over. Slide over 10 beads in each row all at once as students count to 8 ten. 1 ten, 2 ten, 3 ten, 4 ten, 5 ten, 6 ten, 7 ten, 8 ten

Student View

Slide over 2 more beads, one at a time, as students count to 8 ten 2. 8 ten 1, 8 ten 2 Slide all the beads back to the right side. Let’s count to 82 the regular way. Say how many beads there are as I slide them over.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

Repeat the process as students count by tens and ones to 82. 10, 20, 30, 40, 50, 60, 70, 80, 81, 82 Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

8 ten 7 87

9 ten 4 94

9 ten 9 99

Launch

10 30

Students discuss the equivalence of different representations. Display the pictures of10crayons.

30 crayons

3 boxes of crayons

What do you notice? Some crayons are in a pile. Some are in boxes. How many crayons are in a box? 10

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 5

Would you rather have 3 boxes of 10 crayons or a pile of 30 crayons? Why? I would rather have boxes to keep them neat. I would rather have a pile. Then I can see all the colors. Invite students to think–pair–share about whether the pile of 30 and the 3 boxes of 10 have the same total number of crayons. Encourage partners to explain how they know. Yes. 3 tens is 30. I counted by ten to be sure. Each crayon in the pile is 1. We can think about the pile of 30 crayons as 30 ones. Record 30 ones under the pile. Ask students what number to write to represent 30 ones. Record 30 below the unit form. Each box has 10 crayons. We can think about the 3 boxes of 10 crayons as 3 tens. Record 3 tens below the boxes. Ask students what number to write to represent 3 tens. Record 30 below the unit form.

Promoting Mathematical Practice As students play Would You Rather, they construct viable arguments and critique the reasoning of others. In this instance, students have the interesting task of constructing an argument that is both mathematical and nonmathematical. They may prefer one choice over the other for personal reasons while still recognizing that both representations have the same total.

30 ones and 3 tens are both ways to write 30. 3 tens has all the tens composed, and 30 ones has no tens composed.

30 crayons

3 boxes of crayons

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

Display the pennies and dimes.

50 pennies

5 dimes

Invite students to think–pair–share about which set of coins they would rather have. Would you rather have 50 pennies or 5 dimes? Why? I would rather have 50 pennies because that’s a lot more coins. 5 dimes is better because 50 pennies is too many to put in my pocket. Each penny is 1 cent. We can think about the 50 pennies as 50 ones. Record 50 ones under the pennies. Ask students what number to write to represent 50 ones. Record 50 below the unit form. Each dime is 10 cents. We can think about the 5 dimes as 5 tens. Record 5 tens under the dimes. Ask students what number to write to represent 5 tens. Record 50 below the unit form. 50 ones and 5 tens are both ways to make 50. 50 ones is the same as 5 tens. Transition to the next segment by framing the work. Today, we will compare totals when all of the tens are composed, some of the tens are composed, and none of the tens are composed.

10 EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 5 10

Learn

30 10

Equivalent Representations Students determine the equivalence of sets using place value concepts. Display the pair of Match: Place Value cards

3 tens 2 ones

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

Pair students and ask them to work together, using their whiteboards as needed, to determine whether the cards represent the same amount. Use the following questions to facilitate a class discussion. Record students’ thinking. How many is 3 tens 2 ones? How do you know? 32. I wrote 3 in the tens place and 2 in the ones place. I drew 3 tens and 2 ones, then I counted: 10, 20, 30, 31, 32. How many is 2 dimes and 12 pennies? How do you know? 32. I counted: 10, 20, 21, … , 32. 2 dimes is 2 tens. 10 pennies is a ten too. 3 tens is 30. 2 more is 32. Confirm that both cards show 32. Then point to the card showing unit form. This card shows all the tens composed. We can easily see how many tens and ones there are. That helps us find the total. Consider repeating the process with other pairs of cards if needed.

Match: Place Value Materials—T/S: Match: Place Value cards, Match: Place Value Mat

Students match different representations of the same total. Demonstrate and explain how to play Match: Place Value by using the following directions: • Each pair of students places six cards from the set faceup. The rest of the cards go into one pile to the side. • Partners find two cards that match because they have the same total. They place the matching cards on the colored squares on the mat.

3 tens 2 ones

10 10 10

UDL: Representation Consider having students use cubes or coins to represent the cards before comparing them. Students may also make drawings to find the totals.

• Partners show that the totals are the same, recording their thinking on the mat.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 5

• After confirming that the cards match, partners set them aside. Then partners draw two new cards from the pile to make the set of six cards complete again. They look for another match. Pair students. Distribute the cards and make sure students have the mat inserted in their whiteboards.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Match: Place Value Mat

Circulate as students play. Ask questions such as these to assess their thinking: • What is the total of this card? • How do you know these totals are the same? • What are the digits in this total? • What is the value of each digit in the total? Have students play until they find matches for all the cards or until time is up. Save the cards for additional practice at another time.

3 tens 2 ones 32

Consider starting with matching cards that show the same items and building understanding by going to different items and then to unit form. Use the following sequence: • Use cards with the same pictures on them: strawberries and strawberries, cubes and cubes.

is the same as

• Compare two different kinds of pictures, such as strawberries and cubes.

30 + 2 = 32

• Compare a card that shows unit form with a card that shows pictures, such as strawberries or cubes. 1

EM2_0105TE_A_L05_removable_is_the_same_as_student_work_CE.indd 1

07/04/21 3:56 PM

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be read aloud.

Differentiation: Support

Teacher Note Expect to see a range of strategies. Some students may count all or count on to find totals. Others will compose tens or use place value. Students may also reason about the relationship between the cards. For example: I see 3 tens on one card and 3 dimes on the other. That’s the same. I also see 2 ones and 2 pennies. Those are the same, too. The cards match.

10 EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5 30

Land Debrief

5 min

Objective: Reason about equivalent representations of a number. Display the picture of two students with a pair of Match: Place Value cards.

2 tens 6 ones

Adrien and Zoey play Match.

26 ones

Invite students to think–pair–share about whether the cards match. Did they find a match? Yes, 2 tens and 6 ones is 26. 26 ones is also 26. Display Adrien’s drawing. Adrien showed his card like this. What is the total? How do you know? 26. 10, 20, 21, … , 26 Write 26 to label the drawing. Display Zoey’s drawing. Zoey showed her card like this. What is the total? How do you know? 26. She drew dots to make 2 groups of 10, then drew 6 more. That’s the same total as Adrien’s picture.

10 10

Write 26 to label the drawing. Adrien’s card shows all the tens composed. Zoey’s card shows no tens composed. Invite students to think–pair–share about how to make a ten with some of the tens composed.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 5

What is a way to make 26 with only some tens composed? 1 ten 16 ones Why can different representations show the same total? They may have all the tens composed, some of the tens composed, or none of the tens composed. The total is still the same.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

Name

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

2. Write how many in two ways.

1. Write the totals. Draw lines to match.

ones is the same as

ten

ones is the same as

tens

ones.

one.

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 5

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 5

4. Do the cards match?

3. Draw or write each total a new way. Sample:

Show how you know. Sample:

They are a match because they both show 40. 10

5 tens 2 ones 10

10 10 10 10

PROBLEM SET

They are not a match. One shows 28 and the other one shows 30.

7 tens 1 one

PROBLEM SET

LESSON 6

Add 10 or take 10 from a two-digit number.

EUREKA MATH2

1 ▸ M5 ▸ TA

Name

1. What is 10 more than 25?

4. Circle more tens. Fill in the number bond.

2. What is 10 less than 25?

35 Show how you know.

EUREKA MATH2

1 ▸ M5 ▸ TA

15 Show how you know.

20 Write how many tens and ones.

3. Circle tens.

tens

3 3

ones

5. Circle the time. Fill in the number bond.

6 56

Write how many tens and ones.

tens

1:00

ones

TO P I C T I C K E T

1:30

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 6

Lesson at a Glance Students count forward and backward by tens. They look at recordings of the counts and notice a pattern in the digits in the tens place. They study the pattern further by using concrete materials to add 10 to a number or take 10 from the number. In one activity, students watch a video and model the actions of adding and taking 10. There is no Problem Set in this lesson. This allows students to spend more time working with concrete manipulatives.

Key Questions • What do you notice about the digit in the tens place when you add 10 to a number? • What do you notice about the digit in the tens place when you take 10 from a number?

Achievement Descriptor 1.Mod5.AD9 Mentally find 10 more or 10 less than a two-digit number.

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The 4, 5, or 6 as an Addend Sprints and the Tens and Ones removables must be torn out of student books. The Tens and Ones removables must also be placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

25 min

• 100-bead rekenrek • Tens and Ones removable (digital download)

• Ten More Patterns

Students

• Ten Less Patterns

• 4, 5, or 6 as an Addend Sprint (in the student book)

• Ko’s Coins

Land

15 min

• Base 10 rods (ten-sticks) (5) • Centimeter cubes (3) • Tens and Ones removable (in the student book) • Bag of 50 pennies and 6 dimes (1 per student pair)

• Copy or print the Tens and Ones removable to use for demonstration. • Ready the bags of coins that were assembled in lesson 4. Save for use in a later lesson.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 6

Fluency

10 10

Sprint: 4, 5, or 6 as an Addend Materials—S: 4, 5, or 625as an Addend Sprint EUREKA MATH 1 ▸ M5 ▸ TA ▸ Lesson 6 ▸ Sprint ▸ 4, 5, or 6 as an Addend Students find a part or total to build addition fluency within 20. 2

Have students read the instructions Sprintand complete the sample problems. Write the part or the total. 1.

2+4=■

5+8=■

Teacher Note

Read the answers to Sprint A quickly and energetically. Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B. Celebrate students’ effort and success. Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A. Lead students in one fast-paced and one slow-paced counting activity, each with a stretch 57 or physical movement. Copyright © Great Minds PBC

Consider asking the following questions to discuss the patterns in Sprint A: • What do you notice about problems 1–5? 6–10? 11–15? • What strategy did you use to solve problem 4? For which other problems could you use the same strategy?

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 6

Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B. Direct students to Sprint B. Take your mark. Get set. Improve! Time students for 1 minute on Sprint B. Stop! Underline the last problem you did.

Teacher Note Count on by tens from 0 to 100 for the fastpaced counting activity. Count back by tens from 100 to 0 for the slow-paced counting activity.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint B quickly and energetically. Count the number you got correct and write the number at the top of the page. Stand if you got more correct on Sprint B. Celebrate students’ improvement.

Launch

10 25

Materials—T: 100-bead rekenrek

Students count up15and back by tens on a rekenrek. Show students the rekenrek. Start with all the beads to the right side. Say how many beads there are as I slide them over. Slide over 6 beads in the first row all at once. 6 Slide over 10 beads in the second row all at once. 16 Copyright © Great Minds PBC

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 6

How do you know there are 16? 6 and 10 is 16. Continue to slide over 10 beads all at once in each row until 86 beads have been moved. Have students count by tens to 86 as you move each row of beads. Display the ascending tens and ones chart. These are the numbers we counted. The chart shows each number’s digits in the tens place and in the ones place. What do you notice? The digit in the ones place is always 6. The digit in the tens place changes. It goes up 1 each time. Highlight the digits in the tens place. There is a pattern. We added 1 ten each time. What is the value of 1 ten? 10

tens ones

6 16 26 36 46 56 66 76 86

tens ones

96 86 76 66 56 46 36 26 16

Write + 10 next to the chart.

Promoting Mathematical Practice Throughout this lesson, as students add and subtract 10 all at once to a number and they recognize that the tens digit changes while the ones digit stays the same, they are looking for and expressing regularity in repeated reasoning. Recognizing these patterns gives students the conceptual understanding they need to understand the standard algorithms for addition and subtraction in grade 2.

Suppose we add another ten. What is the new total? How do you know? 96 You can use the chart to see the next number. 9 comes after 8. 6 stays the same. Repeat the process, this time starting with 96 on the rekenrek and counting back by tens. Stop at 16. Display the descending tens and ones chart. Ask students to identify the pattern. Label the chart – 10. Have students use the pattern to figure out the final number, 6. Transition to the next segment by framing the work. Let’s add 10 to or take 10 from different numbers. Today, we will think about how that changes the digit in the tens place. 88

10 EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 6 10

Learn

25 15

Ten More Patterns Materials—T: Tens and Ones removable; S: Centimeter cubes, base 10 rods (ten-sticks), Tens and Ones removable

Students use ten-sticks to count forward by tens. Distribute cubes and ten-sticks and have students put them in piles at the top of their work area. Make sure students have the Tens and Ones removable inserted into a personal whiteboard.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Tens and Ones

Tens

Students may want to put a 0 in the tens column to complete the pattern. Explain how that is fine as 0 means none when writing the number of tens in a chart or next to the word ten but that we do not write 0 to write the numbers 1–9.

Ask students to place one cube next to their chart. How many tens? 0

UDL: Representation

How many ones? 1 Demonstrate writing 1 in the ones place on the chart as students do the same.

EM2_0105TE_A_L06_removable_place_value_chart_studentwork_CE.indd 59

Teacher Note

Ones

08/02/21 8:16 PM

Add 10 by placing a ten-stick next to your cube. Again, ask students how many tens and ones there are. Write 1 in the ones place and in the tens place on the chart as students do the same.

Consider supporting students by having them use a different format. Instead of using ten-sticks and cubes, have students draw lines (also called quick tens) and dots to represent the amounts and find 10 more and 10 less.

What is 1 and 10 more? 11

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 6

What do you think 10 more than 11 will be? Why? 21 We will have 2 tens and 1 one. Repeat the process through 51. For each new total ask, 10 more than (the previous total) is …? Invite students to think–pair–share about the patterns they see on the chart. What patterns do you see on the chart? The ones digit stays the same. It is always 1. The tens digit goes up by 1. 1, 2, 3, 4, 5. We added 10 every time: 11, 21, 31, …. Why does the digit in the tens place change while the digit in the ones place stays the same? When we add 10 all at once, we change the number of tens but the number of ones stays the same.

Differentiation: Challenge Invite students to count by tens starting at any two-digit number as far as they can, even past 100.

What is the value of this 1 in 11? (Point to the tens place.) 10 What is the value of the 2 in 21? 20 10 and 10 more is 20. 11 and 10 more is 21. When we add 10 to a number, the digit in the tens place is 1 more, but the digit in the ones place stays the same.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 6

Ten Less Patterns Materials—T: Tens and Ones removable; S: Centimeter cubes, base 10 rods (ten-sticks), Tens and Ones removable

Students use ten-sticks to count backward by tens. Tell students to erase their chart. Have students show 43 by using ten-sticks and cubes. Have students place them next to their chart. How many tens? 4 How many ones? 3 Record the digits on the tens and ones chart as students do the same. What is the total?

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Tens and Ones

43 Tell students to take ten by removing a ten-stick. Ask students how many tens and ones there are now. Record the answers as students do the same. 10 less than 43 is …? 33

Tens

Ones

What do you think 10 less than 33 is? Why? 3

23 We will have 2 tens and 3 ones. 60

EM2_0105TE_A_L06_removable_place_value_chart_studentwork_CE.indd 60

08/02/21 8:16 PM

1 ▸ M5 ▸ TA ▸ Lesson 6

EUREKA MATH2

Repeat the process through to 3. For each new total ask, 10 less than (the previous total) is …? Invite students to think–pair–share about the patterns they see on the chart. What patterns do you see on the chart? The digit in the ones stays the same. It is always 3. The tens digit goes down by 1. 4, 3, 2, 1. We took 10 each time: 43, 33, 23, 13, 3. Why does the digit in the tens place change while the digit in the ones place stays the same? When we take 10 all at once, we change the number of tens, but the number of ones stays the same. What is the value of the 2 in 23? 20 What is the value of the 1 in 13? 10 20 minus 10 equals 10, and 23 minus 10 equals 13. When we take 10 from a number, the digit in the tens place is 1 less, but the digit in the ones place stays the same. Have students set aside their ten-sticks and cubes until it is time for the Topic Ticket.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 6

Ko’s Coins Materials—S: Bag of pennies and dimes

Students use coins to add 10 and take 10 from a two-digit amount. Distribute one bag of pennies and dimes to each pair of students. Then play part 1 of the video, which shows Ko putting coins in her pocket and then finding another dime. Ask partners to use their pennies and dimes to find how much money Ko has in her pocket now. Remind them, if needed, that she has 2 dimes and 7 pennies. How much money does Ko have? How do you know?

UDL: Representation Consider supporting students by having them use a different format. Rather than using dimes and pennies, have students draw circles labeled with 10 and 1 to represent the amounts.

2 dimes and 7 pennies. 20, 21, … , 27 cents. 1 dime and 7 pennies is 17 cents. If we add 1 dime, we have 27 cents. Play part 2 of the video, which shows Ko throwing a dime into a fountain at the park. Ask partners to use their pennies and dimes to find how much money Ko has in her pocket now.

UDL: Action & Expression

She just took a dime away. Now she has 1 dime and 7 pennies.

As students use dimes and pennies to practice 10 more and 10 less, consider supporting them in monitoring their own progress. Provide questions that guide self-monitoring and reflection, such as these:

10 cents less than 27 cents is 17 cents.

• How is this problem like other problems?

Dimes are the same as ten cents. We can use dimes to show adding 10 or taking 10. Let’s do that some more.

• What is still confusing to me about this problem? What can I do to help myself?

How many cents does Ko have now? How do you know? 17 cents. She threw the dime she found into the fountain.

Have partners show 54 cents with dimes and pennies.

• What patterns do I notice?

What is 10 more than 54? How do you know? 64 You just add a dime, or 10, to 54.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 6

Display the two place value charts. Confirm that 10 more than 54 is 64. 54 is 5 tens and 4 ones. 64 is 6 tens and 4 ones.

tens

ones

tens

ones

Record 54 and 64 in the charts as shown. Draw an arrow from 5 tens to 6 tens, and label it + 10. When we add a 10, the digit in the tens place is 1 more. Leave the place value charts displayed but erase the recording. Have students show 42 cents with dimes and pennies. What is 10 less than 42? How do you know? 32

tens

ones

tens

ones

It is 1 ten less than 42. You just take away a dime. Confirm that 10 less than 42 is 32. Record 32 and 42 in the charts as shown. Draw an arrow from 4 tens to 3 tens and label it – 10. When we take a 10, the digit in the tens place is 1 less. As time allows, use the following suggestions to repeat the process: • 74 cents (show 10 less) • 85 cents (show 10 more)

10 EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 6 25

Land Debrief

10 min

Objective: Add 10 or take 10 from a two-digit number.

Teacher Note

Display 24 shown two ways. How many does each drawing show? How do you know? I think the lines are ten and the dots are one: 20, 21, 22, 23, 24. The circles are labeled with 10 and 1. 2 tens and 4 ones is 24. Ask students to choose one of these ways to show 24 and copy it on their whiteboard. Then partner students.

10 10

Partner A, draw to show 10 more than 24. Partner B, draw to show 10 less than 24. Display the three place value charts. Write 24 in the place value chart in the middle.

tens

ones

tens

ones

tens

ones

Eureka Math2 refers to drawings like this that use lines for tens and dots for ones as quick tens. When students draw quick tens, they do not need to label the units because the representation is proportional. A line represents a ten-stick of cubes and the dot represents a single cube. However, when students use nonproportional models such as circles that represent both tens and ones, they label each circle with 10 or 1 to clarify what unit the drawing represents.

Partner A: What is 10 more than 24? How do you know? It’s 34. We just drew 1 more ten.

Teacher Note

Write 34 in the place value chart on the right. Partner B: What is 10 less than 24? How do you know? It’s 14. I erased 1 ten. Write 14 in the place value chart on the left. What do you notice about the digit in the tens place when the number is 10 more?

Consider providing distributed practice with 10 more and 10 less using a quick draw activity. In this activity, someone generates a two-digit number (teacher or student). Then students represent 10 more or 10 less than that number by drawing on a whiteboard. Students hold up their whiteboards for feedback.

It is 1 more ten.

1 ▸ M5 ▸ TA ▸ Lesson 6

EUREKA MATH2

What do you notice about the digit in the tens place when the number is 10 less? It is 1 less ten. Draw an arrow from 2 tens to 3 tens, and label it + 10. Draw another arrow from 2 tens to 1 tens, and label it – 10.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

EUREKA MATH2 1 ▸ M5 ▸ TA ▸ Lesson 6

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 6 ▸ Sprint ▸ 4, 5, or 6 as an Addend

EUREKA MATH2

1 ▸ M5 ▸ TA ▸ Lesson 6 ▸ Sprint ▸ 4, 5, or 6 as an Addend

Number Correct:

Write the part or the total.

Number Correct:

Write the part or the total.

3+4=■

11.

3+6=■

1+4=■

11.

1+6=■

4+4=■

12.

4+6=■

2+4=■

12.

2+6=■

5+4=■

13.

5+6=■

3+4=■

13.

3+6=■

8+4=■

14.

8+6=■

6+4=■

14.

6+6=■

9+4=■

15.

9+6=■

7+4=■

15.

7+6=■

3+5=■

16.

3+■=7

1+5=■

16.

1+■=5

4+5=■

17.

4+■=9

2+5=■

17.

2+■=7

5+5=■

18.

5 + ■ = 11

3+5=■

18.

3+■=9

8+5=■

19.

■

+ 5 = 11

6+5=■

19.

■

+3=9

10.

9+5=■

20.

13 = 7 + ■

10.

7+5=■

20.

11 = 5 + ■

Topic B Use Place Value to Compare In topic B, students compare two-digit numbers by using the skills they have acquired over the course of the year. These include reading and writing comparison symbols, grouping ones to compose tens, and understanding that each digit’s value is based on its place in a number. Previously, students compared numbers by simply knowing that one comes before the other in the count sequence or by considering the size (or length) of the totals. For example, students may have reasoned that 26 cm is greater than 17 cm because they used more cubes to make 26 cm than they did to make 17 cm, or one object is visually longer than the other object. In module 5, students look for and make use of place value structure to compare two-digit numbers. They are presented with increasingly complex comparisons to highlight the meaning of the digits in the tens and ones places. They both have 2 tens, but 4 ones is greater than 2 ones.

24 > 22 Ones place different

3 tens is greater than 2 tens.

< 34

Tens place different

9 ones is greater than 1 one, but 3 tens is greater than 2 tens.

< 31

Both places different

The greater amount has the larger digit in the tens place.

42 > 24 Digits are reversed

EUREKA MATH2 1 ▸ M5 ▸ TB

At first, students compare the quantities of two groups of objects. They may need to compose tens first to write the total in a place value chart in a way that helps with the comparison. Students then use the chart to reason about the numbers of tens and ones to compare the totals. They represent the comparison by writing a number sentence by using the symbols >, =, or < and explain why it is true. Students are given two digits and asked to write two different numbers, the largest number and the smallest number they can write with the digits, such as 45 and 54 with the numbers 4 and 5. Comparing these numbers helps solidify the idea that the greater number has the larger digit in the tens place.

tens

ones

tens

ones

Students compare sets of coins in a problem-solving context: How can the value of a smaller set of coins be greater than the value of a larger set of coins? After determining the coin types and total amounts, students are challenged to add coins to one set to make the sets have the same value. This prepares students to make the next ten in topic C.

K 10 Kai

1 1

Lucia

1 1

17 + 3 = 20

L 10 10

EUREKA MATH2

1 ▸ M5 ▸ TB

Progression of Lessons Lesson 7

Lesson 8

Lesson 9

Use place value reasoning to compare two quantities.

Use place value reasoning to write and compare 2 two-digit numbers.

Compare two quantities and make them equal.

4 tens 19 ones

5 tens 6 ones

tens

ones

10 10 10

tens

ones

tens

ones

tens

ones

4 tens 19 ones is 59 when we compose tens. 59 and 56 both have 5 tens. 9 ones is greater than 6 ones.

100

10 10 10 10 10 10 10 10 10

If we add 4 pennies to 26 cents, we can trade 10 pennies for a dime. That makes 30 cents.

I can make 39 and 93 with the digits 3 and 9. 3 tens is less than 9 tens, so 39 < 93.

LESSON 7

Use place value reasoning to compare two quantities.

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

Name

Compare. Write <, =, or >.

Lesson at a Glance Students compare two quantities, either presented as pictures or written in unit form. They reason about the number of tens and ones in the totals and use that information to compare the quantities. Students represent their comparisons by writing comparison number sentences.

Key Question • How can we compare two totals?

Achievement Descriptor 1.Mod5.AD4 Compare two-digit numbers by using the symbols >,

=, and <.

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 7

Agenda

Materials

Lesson Preparation

Fluency

Teacher

None

Launch Learn

10 min 10 min

25 min

• Compose and Compare

• None

Students • None

• Problem Set

Land

15 min

103

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

Fluency

10 10

Choral Response: Subtract 1 or Subtract 1 Less Students subtract 125 or subtract 1 less to build subtraction fluency within 10. Display 5 – 1 = .

What is 5 – 1? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 4

5-1= 4

Display the answer. Repeat the process with the following sequence:

4-1

2-1

1-1

5-4

4-3

2-1

3-1

3-2

Choral Response: 5-Groups to 10 with Pennies Students recognize the value of a group of pennies and tell how many more are needed to make 10 cents to prepare for comparing coin combinations in lesson 9. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display 9 pennies. How many cents? 9 cents

104

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 7

How many more cents are needed to make 10 cents? 1 cent When I give the signal, say the addition sentence starting with 9 cents. 9 cents + 1 cent = 10 cents Display the addition sentence and the additional penny. What can we exchange 10 pennies for? 1 dime

9¢ + 1¢ = 10¢

Display the 10 pennies exchanged for a dime.

Teacher Note

Repeat the process with the following sequence:

1¢ + 9¢ = 10¢

8¢ + 2¢ = 10¢

4¢ + 6¢ = 10¢

3¢ + 7¢ = 10¢

2¢ + 8¢ = 10¢

5¢ + 5¢ = 10¢

7¢ + 3¢ = 10¢

0¢ + 10¢ = 10¢

6¢ + 4¢ = 10¢

Whiteboard Exchange: Compare Numbers Students compare numbers within 30 by using symbols to prepare for comparing quantities and numerals. Display the numbers 9 and 2. Write a number sentence by using the greater than, equal to, or less than symbol to compare the two numbers. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Copyright © Great Minds PBC

To increase energy and engagement, consider using various voices or response styles for the last question. For example, have students whisper, shout, or tell a partner that they can exchange 10 pennies for 1 dime.

Language Support Consider displaying sentence frames to support students with using comparison symbols and language.

> < than is less = to is equal

is greater than

. . .

105

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

Display the number sentence: 9 > 2. When I give the signal, say the number sentence starting with 9. Ready?

9 > 2

9 is greater than 2. Repeat the process with the following sequence:

8=8

6<7

10 < 15

19 > 14

13 > 12 17 < 20 21 > 20 28 < 29

Launch

10 25

Students count and compare the totals of two sets. 15

Malik

Kioko

Display the children and the crayons. Use the Math Chat routine to engage students in mathematical discourse. Who has more crayons, Malik or Kioko? How do you know? Give students quiet think time. Have students give a silent signal when they are ready. Invite them to discuss their thinking with a partner. Display the crayons and place value charts. Facilitate a class discussion about the question. Record students’ ideas by using the pictures and the place value charts.

Malik

tens

Kioko

ones

tens

ones

Kioko has more crayons. She has 32 crayons. I see 3 tens and 2 ones. Malik only has 28 crayons. I see 2 groups of 10 and 8 ones. 106

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 7

The boxes of crayons are tens. How does having composed groups of 10 help you compare the two sets of crayons? It is easier to count them. We can see she has 3 boxes of 10. But he only has 2 groups of 10. So, she must have more. Point to the corresponding digits in the place value charts as you ask these questions. What is the value of the 2 in 28? 20 What is the value of the 3 in 32? 30 Which is greater, 20 or 30? 30 Write the total of each child’s crayons below the place value charts.

Differentiation: Support If needed, students may represent the quantities shown with ten-sticks and cubes. Encourage them to trade 10 ones for 1 ten.

Which is greater, 28 or 32? Why? 32 is greater. It has more tens. 32 has more tens than 28, so it is greater, even though 28 has more ones. Let’s write a number sentence to compare 28 and 32. Let’s start with 28. Is 28 less than, greater than, or equal to 32? Less than Draw a less than symbol between the totals and read the number sentence: 28 is less than 32. When deciding who has more, which should you think about first—the boxes of crayons or the loose crayons? Why? The boxes. They have 10 crayons in them. The loose crayons are just ones. Transition to the next segment by framing the work. Today, we will compose tens and use them to help us compare other totals.

107

10 EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7 10

Learn

25 15

Compose and Compare Students use pictures to compose tens, compare totals, and explain their reasoning.

Differentiation: Support

Tell students to turn to the page that shows marbles in their student book. Have students point to the picture of the jars. How many tens? 4 tens How many extra ones?

tens

ones

tens

ones

1 one Ask students to write the digits in the place value chart. Then have them write the total on the blank on the left at the bottom of the page.

Some students may try to write the total before they compose all the tens. Remind students that when they write a number, the digit in the tens place represents how many tens there are when all the tens are composed. To attend to precision, students should compose as many tens as possible and then write the total. Prompt students by asking the following question: • Look at your picture again. Did you compose all the tens before you found the total?

Have students point to the scattered marbles. How could we make it easier to count the total marbles? We could make tens. Ask students to compose tens by circling groups of 10 marbles. Have them complete the place value chart and write the total on the blank on the right at the bottom of the page. They should not write a comparison symbol yet. Which picture shows more marbles? The picture with jars of marbles shows more. Invite students to think–pair–share about the picture of jars of marbles. How do you know that the picture with jars of marbles shows more marbles?

108

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 7

Support student-to-student dialogue during discussion by inviting the class to agree or disagree, ask a question, share a new idea, or restate an idea in their own words.

Promoting Mathematical Practice

There are 4 jars with 10. We can only make 3 groups of 10 in the other picture. 4 tens is more than 3 tens, so 41 is greater than 39. 41 comes after 39 when we count. 4 tens is 40. 3 tens is 30. So, 41 marbles is more than 39. 41 marbles is more than 39 marbles because 4 tens is more than 3 tens. Does it matter that 39 has 9 ones and 41 only has 1 one? Why? No, because 41 has more tens. Tens are bigger than ones. Have students write the greater than symbol in the number sentence.

Students look for and make use of structure when they compare two-digit numbers by using place value. Previously, students may have compared numbers by simply knowing one was greater than the other or knowing that one comes before the other in the count sequence. Now, students can use the structure of a number to compare the digits in the tens place and then the digits in the ones place, if necessary.

Direct students to the problem presented in unit form. Have them draw the tens and ones, compose more tens if possible, and complete the place value charts. Students may draw tens and ones in a variety of ways, such as by making quick tens or labeled circles. They should not write the comparison number sentence yet.

4 tens 19 ones

5 tens 6 ones

tens

ones

tens

ones

We started with 4 tens and 19 ones. When we compose another ten, how many tens and ones are there? 5 tens 9 ones

109

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

What number is 4 tens and 19 ones? 59 Teacher Note

What number is 5 tens and 6 ones? 56

Some students may think 5 tens 6 ones is greater than 4 tens 19 ones because it shows more tens than 4 tens 19 ones. Point out that they need to compose all the tens before they use place value and compare them.

Tell students to write a symbol between the totals at the bottom of the page to make a true number sentence. Confirm that 59 is greater than 56. Guide students to read the number sentence aloud from left to right. When we compare numbers, we look at the tens place first because tens are bigger than ones.

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

59 and 56 both have 5 tens. How do you know that 59 is greater than 56? I looked at the ones place. 59 has more ones than 56. If the tens are the same, we can compare two numbers by looking at the ones. Invite students to work with a partner on the next two problems in the student book. Circulate, and assess and advance understanding by using the following questions and prompts:

tens

ones

tens

ones

• Which total is greater? Which total is less? How do you know? • Read your number sentence. Is it true? Why? When students finish, begin a class discussion by inviting a few students to share their work. Use questions to guide the discussion, such as these: • How did you find the total? Did you compose any tens? • Read your number sentence. Is it true? How do you know? • What place did you look at first to compare the totals? Why?

tens

ones

tens

ones

42 2

LESSON

EM2_0105TE_B_L07_classwork_studentwork.indd 2

10/04/21 5:53 AM

Differentiation: Support Help students recall that the open part of the comparison symbol faces the larger number and the pointy part of the symbol faces the smaller number. Consider having students draw and label all the symbols on their whiteboard as a reference.

> = < greater than equal to less than 110

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 7

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

10 min

Objective: Use place value reasoning to compare two quantities. Display Logan’s stickers.

UDL: Action & Expression In this lesson, students use these skills acquired over the course of the year: comparing, composing, and place value understanding. To support students in monitoring their own progress with these skills, consider providing questions such as these that guide selfmonitoring and reflection: • How is this problem like other problems? • How are my math skills growing? • What is still confusing? What can I do to help myself?

Logan has 3 sheets of stickers. Each sheet has 10 stickers. He also has 2 rocket ship stickers. How many stickers does Logan have? How do you know? 32 3 tens and 2 ones 3 tens is 30. 30, 31, 32. Display Violet’s stickers. Invite students to think–pair–share about the number of stickers Violet has. How many stickers does Violet have? How do you know? 23 We can compose 2 tens and there are 3 extra ones. The 2 groups of 10 are 20. 20, 21, 22, 23.

111

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

Display both sets of stickers.

32 23 Who has more stickers? Who has less? Logan has more. Violet has less. What symbol should we write to compare their stickers? Greater than Write >. Let’s read the number sentence together. 32 is greater than 23. Why is the number sentence true? 3 tens is more than 2 tens. How do we know 3 tens is greater than 2 tens? Because 3 tens is 30 and 2 tens is 20. Can we compose any more tens in 23? Why? No, we need 10 ones, and we only have 3 ones. Does it matter that 23 has more ones than 32? Why? No, because tens are bigger than ones. How can we compare two totals? We see which total has more tens. If the tens are the same, we can see which total has more ones.

112

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 7

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

113

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

Name

1. Write how many tens and ones.

Write <, =, or > to compare.

tens

ones

tens

ones

114

tens

ones

tens

ones

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 7

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 7

2. Write <, =, or > to compare.

tens

ones

tens

ones

tens

ones

tens

ones

tens

ones

tens

ones

3. Draw and then compare.

53 17 ones

17 tens

ones

tens

ones

7 tens

4. Write any number to make the number sentence true.

59 < 68

23 PROBLEM SET

6 tens 3 ones 4 tens 7 ones

PROBLEM SET

59 >

> Sample:

115

LESSON 8

Use place value reasoning to write and compare 2 two-digit numbers.

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

Name

Write <, =, or >.

Lesson at a Glance Students write numerals in different orders to make and compare two-digit numbers. Repeated practice helps solidify the idea that the greater number has the larger digit in the tens place. When presented with the digits 0–9, students reason about the smallest and largest two-digit numbers they can make.

Key Question • How do you know which are the smallest and which are the biggest two-digit numbers we can make?

Achievement Descriptors 1.Mod5.AD3 Determine the values represented by the digits of a

two-digit number.

1.Mod5.AD4 Compare two-digit numbers by using the symbols >,

=, and <.

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 8

Agenda

Materials

Lesson Preparation

Fluency

Teacher

The Double Place Value Chart removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 15 min

20 min

• Roll and Compare • Problem Set

Land

15 min

• None

Students • Double Place Value Chart removable (in the student book) • 10-sided dice (2 per student pair)

117

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

Fluency

10 15

Choral Response: Subtract 1 or Subtract 1 Less Students subtract 120 or subtract 1 less to build subtraction fluency within 10. Display 10 – 1 = .

What is 10 – 1? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 9

Differentiation: Challenge

10 - 1 = 9

Display the answer. Repeat the process with the following sequence:

9-1

9-8

8-7

8-1

7- 1

7- 6

6-1

To increase the challenge and engagement and to build subtraction fluency within 20 or beyond, consider presenting problems with larger numbers. For example, 17 – 1, 20 – 1, 46 – 1, 60 – 1, 11 – 10, 14 – 13, 20 – 19, or 37 – 36.

10 - 9

Choral Response: 5-Groups to 20 with Pennies and Dimes Students recognize the value of a group of coins and tell how many more are needed to make the next ten to prepare for comparing coin combinations in lesson 9. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display 9 pennies. How many cents? 9 cents

118

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 8

How many more cents to make the next ten? 1 cent When I give the signal, say the addition sentence starting with 9 cents. 9 cents + 1 cent = 10 cents Display the addition sentence and the additional penny. What can we exchange 10 pennies for? 1 dime Display the 10 pennies being exchanged for a dime. Repeat the process with the following sequence:

9¢ + 1¢ = 10¢

19¢ + 1¢ = 20¢

8¢ + 2¢ = 10¢

18¢ + 2¢ = 20¢

15¢ + 5¢ = 20¢

16¢ + 4¢ = 20¢

6¢ + 4¢ = 10¢

4¢ + 6¢ = 10¢

14¢ + 6¢ = 20¢

17¢ + 3¢ = 20¢

Whiteboard Exchange: Compare Numbers Students compare numbers within 20 in different forms by using symbols to prepare for comparing quantities and numerals. Display the number 10 and the expression 10 + 2. Write a number sentence by using the greater than, equal to, or less than symbol to compare. Write the total before comparing.

119

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the number sentences. When I give the signal, say the number sentence starting with 10. Ready? 10 is less than 12.

10 < 10 + 2 10 < 12

Repeat the process with the following sequence: 10 = 1 ten

19 > 1 ten 6 ones

10 + 4 > 13

1 ten 7 ones = 10 + 7

17 < 2 tens

10 = 10

19 > 16

14 > 13

17 = 17

17 < 20

Launch

15 20

Materials—S: Double Place Value Chart removable

Students compare15two numbers that use the same digits but in a different order. Make sure students have the Double Place Value Chart removable in their whiteboards. Display the two dice. What digits do you see? 9 and 3 Invite students to think–pair–share about the numbers they could write by using the numbers displayed on the dice. What two numbers can we write by using 9 and 3? 39 and 93

120

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 8

Tell students to write each number in a place value chart and draw them by using tens and ones. Invite a few students to share their drawings.

tens

ones

Teacher Note

10 10 10

tens

ones

Some students may be inclined to add the numbers on the dice. Make sure students understand that for this activity, the dice show the digits they are using to write twodigit numbers.

10 10 10 10 10

10 10 10 10

39 and 93 are not the same number even though they have the same digits. Why aren’t they the same? The 3 comes first in 39 and the 9 comes first in 93. 39 has 3 tens. 93 has 9 tens. The numbers have different tens, so 93 is bigger than 39. Write 93. What is the value of the 9 in 93? 90 What is the value of the 3 in 93? 3

121

1 ▸ M5 ▸ TB ▸ Lesson 8

EUREKA MATH2

Draw a number bond for 93 with the parts 90 and 3. Write 39. What is the value of the 3 in 39? 30 What is the value of the 9 in 39? 9 Draw a number bond for 39 with the parts 30 and 9. Circle the 90 and the 30 in the number bonds. Which is greater, 90 or 30? 90 Which is less, 90 or 30? 30 Does it matter that 39 has 9 ones and 93 only has 3 ones? Why? No, it does not matter because tens are bigger than ones. Ask students to write a number sentence comparing 39 and 93. They may write 39 < 93 or 93 > 39. Have students show thumbs-up to indicate which of the two number sentences they wrote. Repeat the process by displaying dice that show 4 and 6. Transition to the next segment by framing the work. Today, we will write numbers and compare them by thinking about the value of their digits.

122

10 EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 8 15

Learn

20 15

Roll and Compare

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Place Value Chart

Materials—S: 10-sided dice, Double Place Value Chart removable

Students write and compare two different numbers made with the same two digits.

tens

ones

64 60

Partner students. Distribute two dice to each pair and make sure they have their Double Place Value Charts ready in their whiteboards. Give the following directions for the activity:

tens

ones

• Partner A rolls one die and partner B rolls the other die.

46 40

• Both partners use both digits to write the two possible numbers that can be made in the place value charts (for example, 46 and 64).

10 + 10 + 10 + 10 + 6 = 46

46 1

• Both partners draw tens and ones to represent each number they wrote. EM2_0105TE_B_L08_place_value_chart_studentwork3.indd 1

• Each partner writes a comparison number sentence (for example, 46 < 64 or 64 > 46). • Partners share and validate each other’s work. Allow 8–10 minutes for the activity. As students work, circulate and ask the following assessing and advancing questions: • Which place did you look at to compare the numbers? Why? • Read your number sentence. Is it true? How do you know? • What is the value of the digit in both numbers? After about 6–7 minutes of play, gather students to summarize the learning by asking these questions. If we have two digits, how could we organize the digits to make the biggest number possible? We could put the bigger digit in the tens place to make the biggest number. The more tens you have, the bigger the number is.

07/04/21 8:09 PM

UDL: Engagement Consider allowing students to choose whether to show the numbers by drawing them or by using Hide Zero cards. Students can explain why one number is more or less than the other number based on the value of each digit, as seen when the cards are split apart.

4 02 4 02

2 04 2 04 123

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

If we have two digits, how could we organize the digits to make the smallest number possible?

Differentiation: Challenge

We could put the smaller digit in the tens place to make the smallest number we could.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 15

Students may not need to draw the number as tens and ones. Some may be able to use only the place value chart or a number bond to explain their reasoning. Provide an additional challenge by having students find the difference between the two numbers being compared. Consider offering the 1–120 number path to support them.

Land Debrief

Promoting Mathematical Practice

10 min

Objective: Use place value reasoning to write and compare 2 two-digit numbers. Display the digits 0–9.

These are all the digits. Let’s read them together. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

As students roll and compare, they construct viable arguments and critique the reasoning of others. Students have the chance to explain to each other why their comparison statement is true. If partners disagree about how to write a true comparison number sentence, encourage them to explain their work to each other by using the place value charts and drawings. They should also be encouraged to ask each other questions.

When we write a digit in the tens place and a digit in the ones place, we make a two-digit number. In a two-digit number, the tens place can have any digit from 1 to 9.

124

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 8

Ask students to share different two-digit numbers they can make. Have them use their whiteboards if needed. Invite students to think–pair–share about the smallest number they can make. What is the smallest two-digit number you can make? How did you figure it out? 10 is the smallest two-digit number. 1 is the smallest digit that can go into the tens place and 0 is the smallest digit that can go into the ones place. Write 10.

Teacher Note Students may try making a two-digit number by using 0 in the tens place. For example, they may suggest 01. Tell them that when there are 0 tens and some ones, we do not write 0 in the tens place. 01 is read as “one.” One is a one-digit number.

What is the biggest two-digit number you can make? How did you figure it out? It’s 99. Nine is the biggest digit. It makes the most tens and the most ones, so we can put it in both places. Write 99 to the right of 10. Then draw a < symbol. Let’s read this comparison number sentence together. 10 is less than 99. If time allows, extend student thinking with the following discussion. 99 is the largest two-digit number because it has a 9 in the tens place and a 9 in the ones place. Write 99 < 100 and read it aloud. Even though 99 has 9 in both places, it is not greater than all numbers. 100 has the smallest digits, 1 and 0, but it is greater than 99. That’s because the 1 is in a place we will learn about another time: the hundreds place!

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

125

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

Name

1. Write a number sentence to compare.

21 2. Draw and write a number sentence to compare.

tens ones 3 10

tens ones

tens ones 8

tens ones

10 10

29 10

30 36

126

> 5 18 < 81 49 = 49 68 < 86

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 8

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

14 ones 4 tens

4. Write any number to make the number sentence true.

80 ones 7 tens

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 8

Sample:

99 = 99

3. Circle the true number sentence.

99 > 10

Draw an X on the false number sentence. Show how you know.

37 > 73

37 < 73 99 < 100

PROBLEM SET

127

LESSON 9

Compare two quantities and make them equal.

EUREKA MATH2

1 ▸ M5 ▸ TB

Name

1. Count how many cents. Write a number sentence with <, =, or >.

Lesson at a Glance Students reason about how the value of a smaller set of coins can be greater than the value of a larger set of coins. Students make the value of each set equal by adding pennies to compose ten and by trading for a dime. This lesson prepares students for making the next ten in topic C.

Key Question • How can we make a smaller total equal to a greater total?

Achievement Descriptor

1.Mod5.AD4 Compare two-digit numbers by using the symbols >,

=, and <.

2. Write <, =, or >.

2 tens

20 ones

121

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 9

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Subtraction Expression cards must be torn out of student books and cut apart. Consider whether to prepare these materials in advance, to have students prepare them during the lesson, or to use the cards from module 2. If students show proficiency within 10, consider using the cards within 20 from module 3. Consider saving these for use in lesson 17.

Launch Learn

10 min 15 min

25 min

• Make it Equal • Problem Set

Land

10 min

• None

Students • Subtraction Expression cards (1 set per student pair, in the student book) • Bag of 50 pennies and 6 dimes (1 per student pair)

• Ready the bags of coins that were last used in lesson 6.

129

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 9

Fluency

10 15

Choral Response: 5-Groups to 30 with Pennies and Dimes Students recognize25 the value of a group of coins and tell how many more to make the next ten to prepare for comparing coin combinations. 10

After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display 8 pennies.

Language Support Later in this lesson, students see circles as representations of coins without the visual cue of the actual coin. Consider supporting students by posting a coin anchor chart to reference as they work.

How many cents? 8 cents How many more cents to make the next ten? 2 cents When I give the signal, say the addition sentence starting with 8 cents. 8 cents + 2 cents = 10 cents Display the addition sentence and the additional pennies. What can we exchange 10 pennies for? 1 dime

8¢ + 2¢ = 10¢

Display the 10 pennies exchanged for a dime. Repeat the process with the following sequence:

18¢ + 2¢ = 20¢

130

28¢ + 2¢ = 30¢

17¢ + 3¢ = 20¢

27¢ + 3¢ = 30¢

16¢ + 4¢ = 20¢

21¢ + 9¢ = 30¢

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 9

Match: Subtraction Expressions Materials—S: Subtraction Expression cards

Students identify equivalent expressions to build subtraction fluency within 10.

2-1

2-2

5 -3

8-4

10 - 10

9 -0

7-3

8-6

10 - 9

Provide sets of Subtraction Expression cards within 20 from module 3 to students who demonstrate proficiency with subtraction within 10.

4-3

Pair students. Distribute a set of cards to each student pair and have them play Match by using the following procedure. Consider doing a practice round with students.

2-1

• Match two expressions that have equal differences. If there are no matches, replace a few cards with different cards from the pile. • Place the matched cards to the side and replace them with two new cards from the pile.

10 - 9 Front

• Lay out nine cards expression side up.

• Turn over the cards to see if the differences are the same.

Differentiation: Challenge

1 Back

• Continue until no more matches can be made. Circulate as students work and provide support as needed.

131

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 9 10

Launch

15 25

Materials—S: Dimes, pennies

Students find ways 10that fewer coins can have a higher value than a greater number of coins. Pair students and display the bags of coins. Share the following scenario. Kai and Lucia have coins in their purses. Kai has 8 coins. Lucia has 2 coins. Kai has more coins, but less money than Lucia. Which coins could each of them have?

Kai

Lucia

Distribute the bags of dimes and pennies to partners and have students work for 2 to 3 minutes to find a solution. Circulate and look for pairs who find more than one accurate solution. Invite a few pairs to share their solutions. If no one finds a valid solution, model the solution with coins as students follow along. Record students’ ideas. Encourage students to ask each other questions and make observations about one another’s work. Have students refer to the Talking Tool as needed.

Promoting Mathematical Practice In Launch, students construct viable arguments and critique the reasoning of others as they work together to determine how Kai can have more coins, but less money. Because there are multiple solutions to this problem, it serves as a great opportunity for students to critique each other’s reasoning, since students need to explain why they can both be correct even though they found different solutions.

Kai’s 8 coins are pennies. That is 8 cents. Lucia’s 2 coins are dimes. That is 20 cents. 8 is less than 20. Kai’s 8 coins are 1 dime and 7 pennies. That is 17 cents. Lucia’s 2 coins are 2 dimes. That is 20 cents. 17 is less than 20. Kai’s 8 coins are 8 pennies. That is 8 cents. Lucia’s 2 coins are 1 dime and 1 penny. That is 11 cents. 8 is less than 11. Have students set their coins aside. Transition to the next segment by framing the work. We found some ways to show how Lucia can have more money even though Kai has more coins. Now let’s find a way for them to have the same amount of money. 132

10 EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 9 15

Learn

25 10

Make it Equal

Materials—S: Dimes, pennies

Students compare two quantities and add to the lesser amount to make the totals equal. Have students turn to the word problem in their student book. Read it aloud as students follow along. Have them retell the story to a partner. Reread the first two sentences, one at a time. After each sentence, have students draw the coins that are mentioned as tens and ones. Then help students examine their drawing.

EUREKA MATH2

How much money does Lucia have? 20 cents Who has more coins but less money? How do you know?

1 ▸ M5 ▸ TB ▸ Lesson 9

Name

Read Kai has 1 dime and 7 pennies. Lucia has 2 dimes. How many cents does Kai need to have the same total cents as Lucia? Draw

K 10

1 1

Some students may suggest trading a dime for 10 pennies and subtracting cents to make the two amounts equal. Validate this thinking and ask them to also find a way to make the money equal by adding coins.

1 1

L 10 10

How much money does Kai have? 17 cents

Differentiation: Challenge

Write

17 + 3 = 20 Kai needs

cents

. 1

EM2_0105TE_B_L09_classwork_studentwork.indd 1

UDL: Representation

08/04/21 6:03 PM

Kai; she has 8 coins that make 17 cents. Lucia’s 2 coins make 20 cents. Reread the question. Ask students to work with a partner to add to their drawing and then answer the question. Then invite students to share their work. We counted on from 17 to 20. Kai needs 3 cents. Kai and Lucia both have a dime. Kai has 7 pennies, but she needs 10 cents to have the same cents as Lucia. 7 + 3 = 10, so Kai needs 3 cents.

If coins still prove difficult for some students to work with, consider providing the information in another format. Provide students with manipulatives they can use to represent the values of the dimes and pennies. Consider having students use Unifix cubes to represent dimes by stacking 10 cubes.

Kai’s 17 cents plus 3 cents equals 20 cents. That’s the same amount of money Lucia has. Let’s write 17 + 3 = 20 to show that thinking.

133

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 9

Guide students to complete the statement by using pennies or cents as the unit. Direct students to take out their whiteboards. Display the image of coins. How much money does Rob have? How do you know? 28 cents 2 dimes are 20 cents and 8 pennies are 8 cents. 20 + 8 = 28. How much money does Liv have? How do you know? 30 cents 3 dimes are 30 cents. Who has less money? How do you know? Rob has less money. 28 is less than 30. Have students work with their partner to make Rob’s money the same as or equal to Liv’s money. Students may show the problem by drawing the coins as tens and ones. Others may use coins to show the problem.

Rob

R 10 10 1 1 1 1 1 1

Liv

1 1

L 10 10 10

28 + 2 = 30

Write a number sentence to show your thinking. Invite a pair to share their work. Bring the class to a consensus on the solution. When one total is less, we can add more to it to make it equal to the greater total.

Rob

Liv

35 + 5 = 40

As time allows, repeat the process by using one or two more sets of coins: • Rob has 3 dimes and 5 pennies, and Liv has 4 dimes. • Rob has 5 dimes and Liv has 4 dimes and 1 penny. Rob

Liv

50 = 41 + 9 134

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 9

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 15

Land Debrief

5 min

Materials—S: Dimes, pennies

Objective: Compare two quantities and make them equal. Partner students and make sure their coins are ready. Ask partner A to put out 3 dimes and partner B to put out 2 dimes and 6 pennies. Partner A: How much money do you have? 30 cents Partner B: How much money do you have? 26 cents Who has less money? How do you know? Partner B 26 cents is less than 30 cents.

135

1 ▸ M5 ▸ TB ▸ Lesson 9

EUREKA MATH2

Invite partners to think–pair–share about the following prompt. Add some coins to make your money equal. Be ready to explain how you did it. Partner B added 4 pennies to make 10 cents. Then we traded 10 pennies for a dime. Now we both have 3 dimes. Revoice and record student thinking. 30 cents is 26 cents plus 4 cents. How did we make a smaller total equal to a greater total? We added more cents to the smaller amount.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

136

EUREKA MATH2 1 ▸ M5 ▸ TB ▸ Lesson 9

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 9

Name

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 9

Read Val has 1 dime and 2 pennies.

Read Val has 5 coins.

Kit has 2 dimes.

Kit has 2 coins.

How many does Val need to have the same cents as Kit?

Kit has more cents.

Draw

Sample:

Draw

Val

Kit

1 1 1 1

10 1

1 1

10 1

10 Write

12 + 8 = 20

Write

cents

Kit needs

cents

117

118

PROBLEM SET

pennies.

137

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 9

EUREKA MATH2

1 ▸ M5 ▸ TB ▸ Lesson 9

3. Compare.

Draw. Add to make them equal.

10 10

10 10 10

Write a number sentence to show how you made them equal.

28 + 2 = 30 4. Compare.

Draw. Add to make them equal.

10 10 10 10

10 10 10

Write a number sentence to show how you made them equal.

138

PROBLEM SET

119

Topic C Addition of One-Digit and Two-Digit Numbers In topic C, students add a two-digit number to a one-digit number. Students apply their place value understanding of tens and ones to make easier problems. They use a variety of models such as cubes, drawings, number bonds, and number paths to represent, solve, and explain their strategies. When solving problems where the ones do not compose a new ten (e.g., 41 + 7 = 48), students use the familiar strategy of decomposing the two-digit addend into tens and ones. For example, to find 41 + 7, students think of 41 as 4 tens 1 one. 41 + 7 = 40 + 1 + 7 They use the associative property to group the 1 and 7 first and then they add the tens: 40 + 1 + 7 = 40 + 8 = 48 Students prepare for solving problems where the ones compose ten (e.g., 28 + 2 = 30) by finding an unknown addend in strings of related problems. For example, 2 is the unknown addend in the string of problems shown. The patterns that emerge help students see that they can make the next ten by looking at the digit in the ones place and finding its partner to 10. Students use the same strategy as in earlier problems: They decompose the two-digit addend into tens and ones. They combine the ones to make ten and then add the tens.

8 + 2 = 10 18 + 2 = 20 28 + 2 = 30

Students apply their learning to problems where the ones compose a new ten and some ones (e.g., 75 + 7 = 82). For these problems they make “the next” ten. Making the next ten requires students to use a strategy that is parallel to the make ten strategy. • The next ten after 75 is 80. • I need 5 more to make the next ten. • I can get 5 by breaking up 7 into 5 and 2. • I can add 5 from the 7 to 75 to get the next ten, 80. • Now I have 80 and 2 more from the 7. That’s 82.

140

EUREKA MATH2 1 ▸ M5 ▸ TC

The discussions embedded in the lessons of this topic help students move toward choosing their tools and strategies thoughtfully. They study sets of problems and talk about how they can know before they add whether addends do not make ten, exactly make another ten, or make the next ten and some ones. Although students are expected to show mastery of one- and two-digit addition at the end of this topic, they may use a variety of tools, including cubes and drawings, to help them solve problems. Expect variety in students’ recordings that show and explain their addition strategy.

141

EUREKA MATH2

1 ▸ M5 ▸ TC

Progression of Lessons Lesson 10

Lesson 11

Lesson 12

Add the ones first.

Add the ones to make the next ten.

Decompose an addend to make the next ten.

71 72 73 74 75 76 77 78 79 80 I can add the ones first: 3 + 6 = 9. Then I can add the tens back in: 40 + 9 = 49.

73 +

I know 7 and 3 make ten. So 73 and 7 make the next ten, 80.

I can choose a tool. I will break up the addend 7 to make the next ten with 28.

142

EUREKA MATH2 1 ▸ M5 ▸ TC

Lesson 13

Lesson 14

Reason about related problems that make the next ten.

Determine which equations make the next ten.

8 needs 2 to make ten. So any addend that ends in 8 needs 2 more to make the next ten.

Does Not Make 10

Makes Next 10

Makes Next 10 and Extra Ones

37 + 2

16 + 4

12 + 9

I can look at the ones and see what strategy will work best to find the total.

143

LESSON 10

Add the ones first.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10

Name

Add.

24 + 3 =

Lesson at a Glance Students add a two-digit number to a one-digit number. They decompose the two-digit addend into tens and ones. They combine the ones with the one-digit addend. Then they add the total to the tens. Students draw models and write number sentences to show how they decompose to make an easier problem.

Key Question • Why can it be helpful to break up a number into tens and ones to add it to another number?

Achievement Descriptor

33 + 6 =

1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 50, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

129

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 10

Agenda

Materials

Lesson Preparation

Fluency

Teacher

The Raceway Addition Game removables must be torn out of student books. Consider whether to tear out one per student pair in advance or to have students tear them out during the lesson.

Launch Learn

10 min 10 min

30 min

• Decompose to Add • Raceway Addition Game • Problem Set

Land

10 min

• None

Students • Raceway Addition Game removable (1 per student pair, in the student book) • Counter • 6-sided dot die (1 per student pair)

145

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10

Fluency

10 10

Whiteboard Exchange: Relate Subtraction and Addition 30 Students relate subtraction and addition to build an understanding of subtraction as an unknown-addend problem. 10

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display 10 – 9 = ____. Write the subtraction equation. Write a related addition sentence starting with 9 that would complete the equation. Display the related addition sentence.

10 - 9 = 1

9 + 1 = 10

Write the answer to the subtraction equation. Display the difference. Repeat the process with the following sequence:

146

9-8= 1

7-6= 1

10 - 8 = 2

8-6= 2

8+ 1 =9

6+1 =7

8 + 2 = 10

6+2= 8

10 - 7 = 3

8-5= 3

9-5= 4

7-3= 4

7 + 3 = 10

5+3= 8

5+4=9

3+4=7

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 10

Whiteboard Exchange: Model Numbers with Quick Tens and Ones Students model and say a two-digit number using tens and ones to prepare for adding two-digit numbers to one-digit numbers.

Teacher Note

Display the number 11. Encourage students to draw dots in 5-group rows or columns when drawing the ones.

Draw tens and ones to show the number 11. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

1 ten 1 one

Display the answer. On my signal, say how many tens and how many ones. Ready? 1 ten 1 one

Teacher Note

Display the number in unit form. Repeat the process with the following sequence:

Although drawing 1 ten and 10 ones to represent the number 20 is mathematically correct, invite students to group the extra ones into another ten whenever possible.

147

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10 10

Launch

10 30

Students represent and add a two-digit number to a one-digit number. Display the picture of1041 rocks in containers. Zoey collects rocks. Invite students to think–pair–share about Zoey’s collection of rocks. What do you notice about her collection? 4 boxes have 10 rocks. One box has only 1 rock. Why are there empty spots? She has 41 rocks. Confirm that Zoey has 41 rocks so far. Display the picture of the collection with 7 more loose rocks. She gets 7 more rocks. How many rocks does she have now? Ask students to draw a picture and write a number sentence on their whiteboard to find the total. Look for a student who draws tens and ones and invite them to share. Imani, how many rocks does she have now? How do you know?

Differentiation: Support

10 1

41 + 7 = 48

1 1

Instead of drawing, students can use cubes to add a two-digit number to a onedigit number.

Zoey has 48 rocks. I drew 41 as tens and a one. Then I drew 7 more ones. That made 4 tens and 8 ones. 41 + 7 = 48 Ask students to show thumbs-up if they used the same strategy.

148

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 10

Record 41 + 7 = ____. Imani thought of 41 as 4 tens 1 one. Write 40 + 1 + 7 = ____. She added the ones first. 1 + 7 = 8. Write a number bond by drawing arms from 1 and 7 and write the total of 8.

Teacher Note

What is 40 + 8? 48 Write 48 as the total of 40 + 1 + 7. So what is 41 + 7? 48 Write the total to complete the equation 41 + 7 = ____. Why does adding the ones first make this problem easier? We know 1 + 7 and we know 40 + 8. Sometimes doing two simple problems is more efficient than doing a problem like 41 + 7. Transition to the next segment by framing the work. Today, we will practice adding the ones first to make other addition problems easier.

When working on their own, students may show their thinking by using number bonds in different ways. See these examples:

41 + 7 40

41 + 7

40 + 8 = 48

1 + 7 = 8 40 + 8 = 48

41 + 7 40 1 + 7 8 40 + 8 = 48

149

10 EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10 10

Learn

30 10

Decompose to Add Students decompose a two-digit addend into tens and ones and add the ones first. Display the picture of 25 rocks in containers. How many rocks are in this collection? How do you know?

Differentiation: Challenge

There are 25 rocks. There are 2 tens and 5 ones. Suppose we add 4 more rocks to this collection. How many rocks would there be then? Pair students. Have partners find the total by drawing the problem and writing a number sentence. Then have students turn and talk to their partner to compare their work. Look for a student who draws 25 as 2 tens 5 ones and combines the ones first. Invite them to share.

Use 26 + 6. Students are likely to decompose 26 as 20 and 6 and add the ones first. They may mentally add 20 and 12 or add 10 and then 2. 26 + 6 = 20 + 6 + 6 = 20 + 12 = 32

5+4=9 20 + 9 = 29 You made an easier problem to find the total of 25 + 4. How? First, I added the ones and got 9. Then I added 9 to 20. Write 25 + 4 = ____ and invite students to follow along on their whiteboard. We drew 25 as 2 tens, or 20, and 5 ones. We also drew 4 more ones. Write 20 + 5 + 4 = ____. Let’s add the ones first. What is 5 + 4? 9

150

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 10

Write a number bond by drawing arms from 5 and 4 and write the total of 9.

Promoting Mathematical Practice

What is 20 + 9? 29

As students add by decomposing the first addend into tens and ones, they look for and make use of structure. For example, in the expression 25 + 4, students use the structure of 25 as 2 tens 5 ones:

Write 29 as the total of 20 + 5 + 4. So what is 25 + 4? 29

25 + 4 = 20 + 5 + 4

Write the total to complete the equation 25 + 4 = ____. Invite students to think–pair– share about how decomposing made the problem easier.

Then they use their intuitive understanding of the associative property to group the 5 and the 4 before adding in the tens, making use of the structure of a three-addend expression:

How did we make an easier problem? We broke 25 into 20 and 5 so we could add the ones and then the tens. As time allows, repeat the process with 33 + 6 and 52 + 3. Release responsibility to the students as appropriate.

20 + 5 + 4 = 20 + 9 = 29 Consider asking the following questions:

Raceway Addition Game

• How did you represent the two-digit addend? Why was that helpful?

Materials—S: Raceway Addition Game removable, counter, 6-sided dot die

• What did you add together first? Why does that work? What did you do next?

Students practice adding a two-digit number to a one-digit number. Gather students and give them the directions for the Raceway Addition game.

32 + 7

3 + 43 2 + 26

52 + 5

End

75 + 3

34 + 4

63 + 5

2 + 35

END

Raceway

31 + 7

37 + 2 21 + 8

Addition

66 + 3

46 + 3 53 + 5 64 + 5 75 + 2 4 + 25

23 + 3

54 + 3

43 + 4 61 + 7

54 + 2

1 ▸ M5 ▸ TC ▸ Lesson 10 ▸ Raceway Addition Game

28 + 1

123

END

End

24 + 3

• Students take turns rolling a die and solving the problem on the space where they land. Students may select tools to help them add, such as drawing the tens and ones or using number bonds. • Each student must land on the last problem on their track before crossing the finish line. If they roll a number that is too high, they wait until their next turn to roll again.

EUREKA MATH2

• Each partner places a counter on a car at the starting line. Students move around separate tracks, but each track has the same number of spaces.

151

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10

Distribute the materials and have students play for 6 to 7 minutes. As they work, assist as necessary. Notice which tools students choose to help them add. For example, students could choose mental math, drawing, or number bonds.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

5 min

Objective: Add the ones first. Write 3 + 6 = ____. What is 3 + 6? 9 Write 9 to complete the equation. Write 43 + 6 = ____. What easier problem do you see in 43 + 6? 3+6 Circle 3 + 6. How can knowing 3 + 6 help us with 43 + 6? If I know 3 + 6, 43 + 6 will just be 40 more. We can think of 43 as 40 and 3. Write 40 + 3 + 6 = ____.

152

UDL: Representation After drawing the number bond and finding the total, consider pausing and asking students to stop and think about how breaking up an addend makes a problem easier. Emphasize that it can be easier to add parts such as 3, 6, and 40 rather than 43 and 6.

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 10

Let’s add the ones first. What is 3 + 6? 9 Write a number bond by drawing arms from 3 and 6 and write the total of 9. What is 40 + 9? 49 Write 49 as the total of 40 + 3 + 6. So what is 43 + 6? 49 Write the total to complete the equation 43 + 6 = _____. Why can it be helpful to break up a number into tens and ones to add it to another number? We can add the ones first and then add the ten. Breaking up the number makes two easy problems instead of one harder problem.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

153

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10

Name

3. Add.

1. Add the ones first. 10

50 + 7 + 2 =

20 + 5 + 2 =

Show how you know. 10

50 + 6 + 3 =

20 + 5 + 3 =

154

25 + 3 =

35 + 3 =

33 + 5 =

54 + 3 =

54 + 4 =

81 + 7 =

83 + 7 =

2. Add the ones first.

25 + 2 =

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10

125

126

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 10

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 10

4. Write the unknown part.

50 + 7 +

= 59

54 +

= 58

70 + 4 +

= 78

94 +

= 99

5. Write a number sentence. Sample:

25 +

49 +

75 +

81 +

PROBLEM SET

127

155

LESSON 11

Add the ones to make the next ten.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

Name

Add.

15 +

= 20

Lesson at a Glance Students look at two-digit numbers on the rekenrek and think about how many more ones they need to make the next ten. They study sequences of related equations and notice the usefulness of identifying partners to 10 in the ones place. They make easier problems by adding partners to 10 first.

Key Question • How is knowing partners to 10 helpful when adding a two-digit number to a one-digit number?

25 + 5 =

Achievement Descriptor

1.Mod5.AD7 Add a two-digit number and a one-digit number that

have a sum within 50, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

35 + 5 =

139

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 11

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Make sure each student pair has a Number Path to 120 from module 3 lesson 14. If more are needed, they will need to be torn out of the student books and each section cut out. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. Consider saving these for use throughout the topic.

Launch Learn

5 min 5 min

40 min

• 100-bead rekenrek • Math Past resource

• Use a Basic Fact

Students

• How Many to Make Ten?

• Number Path to 120 (1 per student pair, in the student book)

• Make an Easier Problem • Problem Set

Land

10 min

157

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

Fluency

5 5

Whiteboard Exchange: Relate Subtraction and Addition 40 Students relate subtraction and addition to build an understanding of subtraction as an unknown-addend problem. 10

7-5= 2

5+2= 7

Display 7 – 5 = ____. Write the subtraction equation. Write a related addition sentence starting with 5 that would complete the equation. Display the related addition sentence. Write the answer to the subtraction equation. Display the difference. Repeat the process with the following sequence:

158

5-3= 2

5-2= 3

6-3= 3

6-2= 4

3+ 2= 5

2+3=5

3+3=6

2+4=6

7-2= 5

8-3= 5

9-3= 6

8-2= 6

2+5=7

3+5=8

3 +6= 9

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 11 5

Launch

5 40

Materials—T: 100-bead rekenrek, Math Past resource

Students discuss how 10 many more they need to make the next ten by exploring the Math Past resource.

Math Past The Yoruba people of West Africa have deep mathematical traditions dating back centuries. They are also famous for their drumming!

Show 14 on the rekenrek. Say how many the Say Ten way. 1 ten 4 The Yoruba people from West Africa call this 4 past 10. Invite students to think–pair–share about why the Yoruba people call 14 4 past 10. Why do you think they call it 4 past 10? 14 is 10 and 4 more. When we count, 14 is 4 more than 10. Show 15 on the rekenrek. Say how many the Say Ten way. 1 ten 5 The Yoruba people call this 5 before 20. Invite students to think–pair–share about why the Yoruba people call 15 5 before 20.

Our numbers are based on ten, but Yoruba numbers, like Maya numbers, are based on 20. One distinguishing aspect of the Yoruba system is that it uses subtraction to name numbers. For example: 15

5 before 20 4 before 20 3 before 20 2 before 20 1 before 20

Review the Math Past in the Module Resources for more information and teaching resources.

Why do you think they call it 5 before 20? 15 is 5 less than 20. 15 and 5 make 20.

159

1 ▸ M5 ▸ TC ▸ Lesson 11

EUREKA MATH2

The Yoruba people are thinking about how many more they need to make the next ten, which is 20. 15 and 5 more make 20. Show 16 on the rekenrek. What is the next ten? 20 How many more are needed to make 20? 4 16 and 4 more make 20. The Yoruba people say 4 before 20 for 16. If time allows, repeat the process with 17, 18, and 19. Transition to the next segment by framing the work. Today, we will look at some other two-digit numbers and see how many ones we need to make the next ten. 5 5

Learn

40 10

Use a Basic Fact Materials—T: 100-bead rekenrek

Students use the basic fact 8 + 2 to make the next ten. Consider using choral response for the following questions. Show 8 on the rekenrek. How many? 8

160

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 11

How many more ones do we need to make ten? 2 Slide over 2 beads to make ten. Say the number sentence that shows how we made the next ten. 8 + 2 = 10 Show 18 as a new starting number. How many? 18 What is the next ten? 20 How many more ones do we need to make the next ten? 2 Slide over 2 beads to make 20. Say the number sentence that shows how we made the next ten. 18 + 2 = 20 Repeat the process by using 28, 38, 48, 58, 68, 78, and 88 as new starting numbers. Display the list of number sentences you recorded. These are the number sentences we showed on the rekenrek. What do you notice? The totals count by tens. We added 2 every time. The first addend always has 8 in the ones place. 8 and 2 are partners to 10. When a two-digit number has 8 ones, we can add 2 to make the next ten.

8 18 28 38 48 58 68 78 88

+ + + + + + + + +

2 2 2 2 2 2 2 2 2

= = = = = = = = =

10 20 30 40 50 60 70 80 90 161

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

How Many to Make Ten? Materials—S: Number Path to 120

Students find the unknown partner that makes the next ten. Pair students. Give each set of partners the six sections of the Number Path to 120 to assemble or distribute the number paths that they already assembled in module 3. Ask pairs to take their student books and move to workspaces where they have enough room to put together or lay out the number path sections (1-20, 21-40, 41-60, 61-80, 81-100).

Differentiation: Support Students may also benefit from making the next ten concretely by using Unifix Cubes.

Once the number paths are ready, ask students to turn to the string of related problems in their student book. Direct their attention to the first problem. Consider guiding students with the digital interactive number path. What is 7’s partner to 10? 3 Have students write the unknown addend in their books. Guide them to show 7 + 3 = 10 by using their fingers to hop on the number path. Direct them to the next problem. Find 17 on the number path. What is the next ten? 20 Hop to 20. How many times did you hop? 3

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

Name

Have students write the unknown addend in their books.

= 10

Use the same procedure for 27 + 3 = 30 and 37 + 3 = 40. Have students complete both the total (the next ten) and the unknown addend.

17 +

= 20

27 +

37 +

47 +

57 +

Invite students to complete the last two problems on their own (47 + 3 = 50 and 57 + 3 = 60). Some students may continue to use the number path while others make use of the pattern. Copyright © Great Minds PBC

EM2_0105TE_C_L11_classwork_studentwork.indd 99

162

Promoting Mathematical Practice Students look for and express regularity in repeated reasoning when they find the unknown addend in a sequence of problems where the first addends all have the same digit in the ones place. Students come to understand that they can use partners to 10 to figure out which addend is needed to get to the next ten. This is the first step toward extending the make ten strategy to larger numbers.

08/04/21 6:22 PM

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 11

Display the list of equations with the 7s highlighted. What do you notice? I can count the totals by tens. We added 3 every time. The first addend always has 7 in the ones place. Why did we add 3 to make the next ten every time?

7 17 27 37 47 57

+ + + + + +

3 3 3 3 3 3

= = = = = =

10 20 30 40 50 60

Differentiation: Support Consider having students draw the problems to understand why the tens digit grows by 1 each time. For example:

7 and 3 are partners to 10. They make ten. Invite students to think–pair–share about what the next number sentence on the list would be. What would be the next number sentence on our list? 67 + 3 = 70 Display the list of three equations with the tens place highlighted. What happens to the number of tens when we make the next ten? There is 1 more ten.

17 + 3 = 20 27 + 3 = 30 37 + 3 = 40

Why does the number of tens grow by 1? It happens because we made another ten with the ones. We used the ones from both addends to compose a new ten. Have students clean up the number paths.

Make an Easier Problem Students add the ones first to make the next ten and to make an easier problem. Write 25 + 5 = ____. Which partners to 10 do you see in 25 + 5? 5+5

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We can think of 25 as 20 and 5. Circle 5 + 5. (Gesture to 25 + 5.) How can knowing partners to 10 help us make an easier problem? If we make ten with 5 + 5, then we can just add 10 to 20. That is 30. Write 20 + 5 + 5. We can add the ones that make ten first. Write a number bond by drawing arms from 5 and 5 to a total of 10. What is 20 and 10? 30 So what is 25 + 5?

Differentiation: Challenge Write three equations: 25 + 5 = ___ 21 + 9 = ___ 27 + 3 = ___ Ask students to explain why they all have the same total, 30. Consider having students write their own equations that result in a total that is the next ten. Have partners trade equations and find the totals.

30 Write 21 + 9 = ____. Have students follow along on their whiteboard. Invite partners to find the total by using mental math or by drawing. Invite a student to share the partners to 10 that helped them to make an easier problem.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be read aloud. Students may use cubes, number paths, drawings, or number bonds to complete the problems.

164

5 EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 11 40

Land Debrief

5 min

Objective: Add the ones to make the next ten. Display the segment of the number path with the equation. What is the part we know? 73 Circle 73. What is the next ten? 80 Invite students to think–pair–share about the number of hops there will be from 73 to 80.

71 72 73 74 75 76 77 78 79 80

73 +

How many hops are there from 73 to 80? How do you know? There are 7 hops. I know because I counted the spaces on the number path. There are 7 hops. I know because 3 and 7 are partners to 10. So 73 and 7 make 80. Draw an arrow from 73 to 80 and label it + 7. Complete the equation. Which partners to 10 do you see? 3 + 7 = 10 How can finding 3 + 7 = 10 help us make it easier to figure out 73 + 7? If we do 3 + 7 first, we get 10. Then we add 10 and 70. That’s 80.

Language Support Support students to verbalize their ideas by providing a sentence frame that can help them describe how one number sentence can help them solve another number sentence. ___ + ___ helps me figure out ___ + ___ because ___.

165

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EUREKA MATH2

How is knowing partners to 10 helpful when you add a two-digit number to a one-digit number? We can look for the number of ones to make the next ten. When the ones are partners to 10, you make the next ten. Then you just add tens to tens to get the answer.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

166

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 11

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

Name

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

2. Make 10 or the next 10.

1. Make 10.

= 10

+ 5 = 10

= 10

16 +

= 20

12 +

= 20

+ 3 = 10

= 10 26 + 4 =

22 + 8 =

36 + 4 =

32 + 8 =

Sample:

= 10

135

136

PROBLEM SET

167

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 11

3. Make the next 10.

21 + 9 =

43 + 7 =

22 + 8 =

44 + 6 =

25 +

46 +

= 50

= 35 + 5

= 54 + 6

= 38 + 2

= 59 + 1

168

= 30

60 = 55 +

PROBLEM SET

137

LESSON 12

Decompose an addend to make the next ten.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 12

Name

Add. Show how you know.

24 + 8 =

37 + 6 =

Lesson at a Glance Students share a variety of ways to add 28 and 6 during a Math Chat, including making the next ten. Students make ten when combining sets and adding a two-digit number to a one-digit number. They are encouraged to show their thinking by using drawings or number bonds, but students may also self-select cubes or number paths.

Key Question

• How can we make an easier problem when adding a two-digit number to a one-digit number?

Achievement Descriptor 1.Mod5.AD7 Add a two-digit number and a one-digit number that

have a sum within 50, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

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EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 12

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Copy or print the student work with the sets of marbles, crayons, and pencils to use for demonstration.

Launch Learn

10 min 10 min

30 min

• Make the Next Ten

• None

Students • None

• Break Apart an Addend • Problem Set

Land

10 min

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Fluency

10 10

Choral Response: Tell Time 30the nearest half hour to build fluency with telling time Students tell time to from topic A. 10

Display the clock that shows 3:00. What time does the clock show? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

3:00

3:00 Display the answer. Repeat the process with the following sequence:

172

5:00

6:00

9:00

9:30

2:30

8:30

1:00

11:30

12:00

6:30

4:30

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 12

Choral Response: Subtract 4, 5, or 6 Students subtract 4, 5, or 6 to build subtraction fluency within 10.

6-4= 2

Display 6 – 4 = ______ . What is 6 – 4? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 2 Display the answer. Repeat the process with the following sequence:

7-4

7-5

8-5

8-6

9-6

9-4

10 - 6

9-5

Whiteboard Exchange: Model Numbers with Quick Tens and Ones Students find how many more to make the next ten and write a number sentence to develop fluency adding one-digit numbers to two-digit numbers. After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the number 18. Draw tens and ones to show the number 18.

Display the answer. How many more do we need to make the next ten? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

18 + 2 = 20

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Display two additional ones. Write an addition sentence starting with 18. Display the addition sentence. Repeat the process with the following sequence:

Launch

10 30

Students discuss how to find a total by decomposing an addend to make the next ten. 10

Display the picture of the roller coaster. What do you notice? 10 children can fit in a car. The last roller coaster car has two empty seats. 28 children are on the roller coaster—10, 20, 28. 6 children are in line. Use the Math Chat routine to engage students in mathematical discourse. Give students a few minutes of silent think time to find the total number of children shown in the picture. Have students give a silent signal to indicate when they are ready. Ask students to discuss their thinking with a partner. Circulate and listen as they talk. Identify a few students to share their ideas with the class. If possible, choose a student who finds the total by thinking of 28 and then making the next ten by adding 2 more to make 30. (See Traun’s sample work.) If no one shares making the next ten, then demonstrate how. 174

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 12

Invite the selected students to share their thinking with the whole group. As students share, record their ideas. Have students use the Talking Tool to engage with one another. How many total children are there? How did you figure it out? Felipe: 34 children. 28 children are on the roller coaster. I counted on 6 more. Ming: I see 10 and 10. I added 8 and 2 to make another ten. That is 30. 30 + 4 = 34. Traun: 28 children are on the roller coaster. 28 and 2 more make 30. 30 + 4 = 34. There are 28 students on the rollercoaster. What is the next ten? 30 Traun, how did you know that 28 and 2 make the next ten? 8 and 2 are partners to 10, so 28 and 2 make 30. Where did the 2 come from? You can break apart the number of children standing in line, 6, into 2 and 4. How does breaking apart the 6 children in line make finding the total easier? We can get 2 to make a ten. 28 and 2 make 30. We can easily add 30 and 4. Transition to the next segment by framing the work. Today, we will make addition problems easier by breaking apart an addend to make the next ten.

175

10 EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 12 10

Learn

30 10

Make the Next Ten Students combine two sets of objects by composing a ten to make the next ten. Tell students to turn to the page that shows the sets of objects. Direct their attention to the marbles. How many marbles are in the first group? 28 What is the next ten?

UDL: Action & Expression Consider providing access to a Number Path to 120 to support students in identifying the next ten. In this example, they would point to 28 and identify 30 as the next ten. They can use their finger to count hops from 28 to 30.

30 How many more marbles do we need to make 30? Where can we get them? 2 We can break up the other group of 8 into 2 and 6. Invite students to circle 30 marbles. What is the total number of marbles? How do you know? 36 There are 3 tens and 6 ones. Show the student page and model making the next ten using a number bond. Prompt students to follow along. Write 28 + 8 = ____. Point to 28. What is the next ten? 30 How many does 28 need to make 30? 2

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EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 12

Where can we get 2? We can break up 8 into 2 and 6. Draw a number bond to decompose 8 into 2 and 6.

Promoting Mathematical Practice EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 12

Name

(Circle the numbers 28 and 2.) What is 28 and 2?

28 + 8 = 36

30 + 6 = 36

30 (Write 30 + 6 = ____.) What is 30 and 6?

73 + 9 = 82

Students are encouraged to think about how many ones are needed to make the next ten, rather than counting on. This helps students see how they can use this strategy without a countable representation.

80 + 2 = 82

Write 36. 65 + 6 = 71

So, what is 28 + 8? 36 Write the total in the original equation.

When students use a drawing, a number bond, or a three-addend number sentence to show how to add by making the next ten, they model with mathematics.

70 + 1 = 71

107

Repeat the process with the next two sets, releasing responsibility to the students as appropriate.

Break Apart an Addend Students find a total by decomposing an addend to make the next ten. Have students ready their personal whiteboards. Write 35 + 6 = ____ and ask students to do the same. Ask them to draw 35 and 6 with quick tens. (Point to 35.) How can we make the next ten? How do you know?

35 + 6 = 41

Differentiation: Support Allow students to use cubes or a number path to complete the problems rather than drawings or number bonds.

We can make 40 with 5 ones from the 6 ones. 5 and 5 are partners to 10, so 35 and 5 make the next ten, 40. Prompt students to circle 40 and write the total, 41.

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Then guide students to make the next ten with a number bond using the process used in the previous segment:

35 + 6 = 41

• Write the equation and point to the first addend. • Determine the next ten and how many ones are needed to make it. (Encourage students to consider partners to 10.)

40 + 1 = 41

• Break apart the second addend with a number bond. • Write the new, easier number sentence. • Write the total in the original equation. Have students erase their whiteboads and write 39 + 8 = ____. Ask them to find the total by making the next ten. Invite them to select the tool of their choice, such as drawings, number bonds, cubes, or a number path, to complete the problem. As students work, circulate to support and assess their thinking.

178

Teacher Note A numerical representation can be shown in more than one way. For example, you may just circle the 28 and 2 to show the composition as in the sample. Or, it may be helpful to label the circled numbers as the next ten.

28 + 8 = 36 6

30 2

Some students may benefit from seeing the composition represented by a three-addend number sentence.

28 + 8 = 36 2

28 + 2 + 6 = 36 30 Take care to avoid making a procedure of any particular recording. The recording is a tool to help students show and explain their thinking.

10 EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 12 30

Land Debrief

5 min

Objective: Decompose an addend to make the next ten. Display Felipe’s tool, a drawing. How did Felipe use a drawing to add 75 and 7? He drew tens and ones to show 75 and 7. Then he circled 5 ones from 75 and 5 ones from 7 to make the next ten, 80.

10 10 10 10 10 10 10

Teacher Note

Felipe

75 + 7 = 82

Display Ming’s tool, a number bond. How did Ming use a number bond to add 75 and 7? She broke up 7 into 5 and 2, just like Felipe. She made the next ten, 80, by circling 75 and 5.

75 + 7 = 82 80

Display Traun’s tool, the number path. How did Traun use the number path to add 75 and 7? He looked at 75 and thought about how many more he needed to make 80. Then he saw it was 5, so he drew an arrow with + 5. Then he had to add 2 more because 7 is 5 and 2.

Ming

+5 +2 75 80 82 Traun

Level 3 strategies such as make the next ten require time and practice to learn. At first students directly model with a drawing or cubes. They progress to independently using number bonds and number sentences. Expect variety in their representations. If students use cubes, encourage them to show what they did with a drawing. When working independently, it is not necessary for students to draw a picture and use number bonds; they may choose one or the other. Some students may choose to use the number path and record their hops with arrows:

+5 +1 35 40 41

We can add by breaking up one addend to make the next ten with the other addend. We can use many tools to help us make ten, like cubes, drawings, number bonds, and the number path. Turn and talk. Which tool is most helpful to you when you make the next ten?

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

179

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 12

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 12

Name

2. Make the next 10 to add. Show how you know.

1. Add. Show how you know.

35 + 5 =

28 + 2 =

75 + 5 =

180

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 12

35 + 9 =

28 + 5 =

75 + 7 =

19 + 4 =

17 + 4 =

29 + 6 =

38 + 6 =

89 + 7 =

87 + 8 =

143

144

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 12

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 12

3. Write the unknown part.

18 + 2 +

= 23

18 +

= 23

25 + 5 +

= 34

45 +

= 54

4. Write a number sentence. Sample:

19 +

24 +

36 +

48 +

PROBLEM SET

145

181

LESSON 13

Reason about related problems that make the next ten.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 13

Name

Add.

4+8=

Lesson at a Glance Students use a number path to find totals using the make the next ten strategy. They find the totals in a string of related problems by decomposing the one-digit addend to make the next ten with the two-digit addend. Students find the totals of related problems and discuss the patterns they find.

Key Question • How does the make the next ten strategy help us add?

Achievement Descriptor

14 + 8 =

24 + 8 =

1.Mod5.AD7 Add a two-digit number and a one-digit number that

have a sum within 50, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

157

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 13

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Number Path to 40 must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 15 min

25 min

• None

Students

• Number String

• Number Path to 40 (in the student book)

• Problem Set

• Number Path to 120 (1 per student pair, in the student book)

Land

10 min

• The Number Path to 120 is composed of 6 pieces. It must be torn out of student books and cut into pieces. Decide whether to prepare one set of 6 pieces per student pair in advance or to have students prepare them during the lesson.

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EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 13

Fluency

10 15

Choral Response: Tell Time 25the nearest half hour to build fluency with telling time Students tell time to from topic A. 10

Display the clock that shows 2:00. What time does the clock show? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

2:00

2:00 Display the answer. Repeat the process with the following sequence:

184

4:00

6:00

8:00

8:30

1:30

7:30

11:00

6:30

12:00

7:30

3:30

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 13

Choral Response: Subtract 4, 5, or 6 Students subtract 4, 5, or 6 to build subtraction fluency within 10.

8-4= 4

Display 8 – 4 = ____. What is 8 – 4? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 4 Display the answer. Repeat the process with the following sequence:

10 - 5 10 - 4

5-4

8-5

7-6

9-6

5-5

10 - 6

Number Path Hop: Hop to the Next Ten Materials—S: Number Path to 40

Students represent addition within 40 on the number path by writing a number sentence to develop fluency with making the next ten when adding to a two-digit number. Make sure students have a personal whiteboard with a Number Path to 40 removable inside. After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

185

EUREKA MATH2

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Display the expression 18 + 3. Write the expression 18 + 3. Circle 18 on your number path. Display the number 18 circled. Hop to the next ten on your number path. Label your hop. Display the labeled hop.

18 + 3 +2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

How many more do we need to hop to add 3 altogether? 1 Hop 1 more on your number path. Label your hop. Display the labeled hop. Write the complete number sentence. Display the total. Repeat the process with the following sequence:

18 + 4

18 + 6 28 + 5 26 + 5 26 + 7

18 + 3 = 21 +2 +1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

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EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 13 10

Launch

15 25

Materials—S: Number Path to 120

Students represent10addition scenarios by showing hops on a number path. Pair students. Give partners the six sections of the Number Path to 120 to assemble, or distribute the number paths they assembled in lesson 11. Have pairs move to workspaces where they have enough room to put together or lay out the number path. Share the following scenario. There are 100 science projects at the school science fair. Each project is on a table with a number. The tables are in order from 1 to 100. Teachers ask a few students at a time to choose a science project and then to give the student who created it a compliment. Display the image of the students talking.

Science Fair

The first group of students notice that all of their table numbers end in 5. They each decide to compliment the student who is 7 tables up from them. They wonder if there will be a pattern in the table numbers they will go to. Invite students to turn and talk about the story.

Tell students to use their number paths to find the table numbers that the students go to. Consider showing their thinking on the digital interactive number path. Nate starts at table 5. He goes to the table that is 7 up from 5 to deliver his compliment. What table number does he go to? How do you know? We hopped 1 space at a time and landed on 12. We hopped 5 to 10 and then we hopped 2 more to 12. We just hopped to 12. We know 5 + 7 = 12.

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Violet starts at table 15. She goes to the table that is 7 up from 15 to deliver her compliment. What table number does she go to? How do you know? If possible, invite a pair who makes the next ten to share their thinking. We hopped 5 to the next ten, which is 20. Then we hopped 2 more to 22. Sam starts at table 25. He goes to the table that is 7 more than 25 to deliver his compliment. What table number does he go to? How do you know? It’s 32. We hopped 5 to the next ten, which is 30. Then we hopped 2 more to 32. Liv starts at table 35. She goes to the table that is 7 more than 35 to deliver her compliment. What table number does she go to? How do you know? It’s 42. We hopped 5 to the next ten, which is 40. Then we hopped 2 more to 42. Display the list of number sentences for each situation. What do you notice? All of the students’ first table numbers have 5 ones. We added 7 each time.

5 + 7 = 12

In the new table numbers, the ones place always has a 2.

15 + 7 = 22

The tens place goes up 1 ten.

25 + 7 = 32

What did we do the same every time on the number path?

35 + 7 = 42

Differentiation: Challenge Invite students to consider what the table number would be if they walked up 7 from table 65.

We always hopped 5 to make the next ten. We always hopped 2 more. We always hopped 5 to make the next ten. 5 ones needs 5 more to make a ten. We broke up the 7 into 5 and 2 to make ten. Then we always had 2 ones left. So, do the table numbers the students went to have a pattern too? Yes, they all end in 2 ones. Have pairs set aside their number paths. 188

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 13

Transition to the next segment by framing the work. Today, we will make ten to add and look for patterns between the problems. 10 15

Learn

25 10

Number String Students find the totals of related problems and explain the patterns they see. Have students ready their personal whiteboards. Display each problem in the following sequence. For each problem, ask students to find the total, and provide work time. Students can signal when they are ready. The sample work shows solutions that were found by using number bonds, but students may self-select from several tools (see Teacher Note). Display the first problem. What is 8 + 6? How do you know?

8+6=?

8 + 6 = 14 2

Teacher Note Students may choose to show how they made the next ten in a variety of ways.

I made ten. 8 and 2 is 10. 10 and 4 is 14. Display the total and the second problem. What is 18 + 6? How do you know? It’s 24. I broke up 6 into 2 and 4. 18 and 2 make the next ten, 20.

8 + 6 = 14 18 + 6 = ?

18 + 6 = 24 2

10 10

18 + 6 = 24. 18 is 10 more than 8, and 8 + 6 = 14, so I just added 10 more. Display the total and the third problem. What is 28 + 6? How do you know? 34. I broke up 6 into 2 and 4. 28 and 2 make the next ten, 30. Copyright © Great Minds PBC

8 + 6 = 14 18 + 6 = 24 28 + 6 = ?

28 + 6 = 34 2

+4 30

34 189

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 13

It’s 34. 28 is 10 more than 18, and 18 + 6 = 24, so I just added 10 more. Invite students to think–pair–share about what the next problem will be.

Differentiation: Support

What will the next problem be? Why? It will be 38 + 6 because the first part gets bigger by 10 each time. And we add 6 each time.

Consider using color to highlight the patterns in the number string.

Display the total and the final problem. Before students find the total, ask the following question. Do you see a pattern that can help us figure out 38 + 6? The totals all have 4 ones. The tens place in the totals are going up 1 ten every time. The totals are counting by tens: 14, 24, 34, 44.

8 + 6 = 14 18 + 6 = 24 28 + 6 = 34

38 + 6 = 44 2

6 6 6 6

= = = =

14 24 34 44

38 + 6 = ? Differentiation: Challenge

Display the total.

8 + 6 = 14

Invite students to think–pair–share about why there is always 4 in the ones place.

18 + 6 = 24

We always broke up 6 into 2 and 4 to make ten with 8.

+ + + +

Have students make the next ten to confirm the total.

Why is there always 4 in the ones place?

8 18 28 38

28 + 6 = 34 38 + 6 = 44

Show several addition expressions with one-digit addends. See the examples below. Invite partners to choose one expression and to use it as a starting problem to write their own number string. Partners may solve their own string or trade their string with another pair’s string.

Choose one

As time allows, continue the string with 48 + 6, and so on. Have students do the following: • Predict the next problem, • use the pattern to find the total, and

5+8

6+7

3+8

7+9

6+9

9+4

9 + 4 = 13 19 + 4 = 23 29 + 4 = 33

• confirm the total by making the next ten. Alternatively, present a related problem from further down in the sequence, such as 68 + 6. Have students compare it to other problems in the set.

190

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 13

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be read aloud. 10 cubes, number paths, drawings, or number bonds to complete the Students may use problems. Encourage students to show their thinking. 15

Land Debrief

5 min

Objective: Reason about related problems that make the next ten. Gather students with their Problem Sets. Select a problem that most students finished, such as 28 + 7 = 35. Invite students to think–pair–share about how they found the total. Consider charting the various tools students used to make the next ten.

Promoting Mathematical Practice As students consider how others represented the problem, they construct viable arguments and critique the reasoning of others.

I used the pattern 15, 25, 35.

Consider asking the following questions:

I drew quick tens and ones. I circled a ten.

• How did you find the total? Why did you do it that way?

I drew a number bond. I broke up 7 into 2 and 5 to make the next ten, 30. I used the number path. I hopped 2 to 30 and then 5 to 35.

• How did your partner find the total? How is that way the same or different from the way you found the total? • What questions can you ask your partner about how they found the total?

191

1 ▸ M5 ▸ TC ▸ Lesson 13

EUREKA MATH2

How does the make the next ten strategy help us add? With big numbers, it means you don’t have to count on. It’s quicker because you can look for a smaller fact you know. It helps you because you can do a problem with big numbers just in your head.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

192

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 13

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 13

Name

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 13

2. Make 10 or the next 10 to add.

1. How many pencils?

5+6=

8+7=

15 + 6 =

18 + 7 =

25 + 6 =

28 + 7 =

Circle to make 10 or the next 10.

pencils

Write the number sentence that comes next.

pencils

35 + 6 = 41 153

154

PROBLEM SET

Write the number sentence that comes next.

193

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 13

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 13

3. Add.

7+6=

17 + 6 =

27 + 6 =

37 + 6 =

= 24 + 9

= 34 + 9

53 = 44 +

194

63 = 54 +

PROBLEM SET

155

LESSON 14

Determine which equations make the next ten.

EUREKA MATH2

1 ▸ M5 ▸ TC

Name

Add.

22 + 7 =

Lesson at a Glance Students analyze and find the totals for related addition problems. They use repeated reasoning to help them recognize when they can make ten or make the next ten. They test the patterns they find on additional sets of problems to confirm their thinking.

Key Question • Why can it be useful to look at the numbers in the ones place before you solve a problem?

Achievement Descriptor

26 + 4 =

13 + 8 =

1.Mod5.AD7 Add a two-digit number and a one-digit number that

have a sum within 50, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

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EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 14

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Subtract within 20 Sprints and the Sort and Solve cards must be torn out of student books. Each of the Sort and Solve cards must also be cut out. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Will it Make the Next Ten? • Sort and Solve • Problem Set

Land

10 min

• Sort and Solve cards (digital download)

Students • Subtract within 20 Sprint (in the student book) • Sort and Solve cards (1 set per student pair, in the student book) • Crayons (1 red crayon, 1 green crayon, 1 yellow crayon per student)

• Copy or print the Sort and Solve cards to use for demonstration.

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1 ▸ M5 ▸ TC ▸ Lesson 14

Fluency

10 10

Sprint: Subtract Within 20 Materials—S: Subtract30 Within 20 Sprint EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Sprint ▸ Subtract within 20

Students write the difference to build subtraction fluency within 20. 10

Sprint Have students read the instructions and complete the sample problems. Subtract. 1.

6–1=■

8–5=■

Teacher Note The Sprint focuses mainly on subtraction problems students have practiced in Fluency in topics A–C. The types of problems include subtract 1, subtract 1 less, and subtract 4, 5, or 6.

Direct students to Sprint A. Frame the task. I do not expect you to finish. Do as many problems as you can, your personal best. Take your mark. Get set. Think! Time students for 1 minute on Sprint A. Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint A quickly and energetically. Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B. Celebrate students’ effort and success. Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A. Lead students in one fast-paced and one slow-paced counting activity, each with a stretch 159 or physical movement.

Teacher Note Consider asking the following questions to discuss the patterns in Sprint A: • What do you notice about problems 1–5? About 6–10? About 11–15? • What strategy did you use to solve problem 16?

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EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 14

Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B. Direct students to Sprint B.

Teacher Note Have students count on by tens from 4 to 94 for the fast-paced counting activity.

Take your mark. Get set. Improve! Time students for 1 minute on Sprint B.

Have students count back by tens from 94 to 4 for the slow-paced counting activity.

Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint B quickly and energetically. Count the number you got correct and write the number at the top of the page. Stand if you got more correct on Sprint B. Celebrate students’ improvement.

Launch

10 30

Materials—S: Crayons

Students find the totals of related problems and discuss their 10 strategies for solving them. Tell students to turn to the three-column chart of equations in their student book. Guide their attention to the blue column. Ask them to add 17 and 2 and to signal when they are ready. What is 17 + 2? Did you make the next ten? Why? 19

17 + 2 = 19 10

I didn’t make the next ten because 7 and 2 only make 9.

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1 ▸ M5 ▸ TC ▸ Lesson 14

Ask students to find the total of 17 + 3 and to signal when they are ready.

17 + 3 = 20

What is 17 + 3? Did you make the next ten? Why? 20 I did make the next ten. 7 and 3 are partners to 10. Ask students to find the total of 17 + 4 and to signal when they are ready. What is 17 + 4? Did you make ten to find the total? How did you do that? 21

17 + 4 = 21 20 3

17 needs 3 more to make 20. I broke up 4 into 3 and 1. 20 and 1 is 21. For 17 + 4 we can make the next ten and have extra ones. Display the completed problems. Ask students to look at them carefully. Invite students to think–pair–share about when they need to make the next ten to add. Do we always make the next ten to add? Why? No, there aren’t always enough ones to make ten. Tell students to take out their red, yellow, and green crayons. Have them look at their work on the problems in the blue column and guide them to do the following:

red 17 + 2 =

Differentiation: Support

• Use a red crayon to circle the problem where the numbers do not make the next ten. • Use a green crayon to circle the problem where the numbers do make the next ten. • Use a yellow crayon to circle the problem where the numbers make the next ten and there are extra ones. Transition to the next segment by framing the work. Today, we will figure out how to tell if we can make the next ten in a problem before we find the total.

200

green 17 + 3 =

Encourage students to use tools to find the totals. For example, they may draw, use a number path, or use cubes.

yellow 17 + 4 =

10 EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 14 10

Learn

28 + 1 =

28 + 2 =

green 17 + 3 =

Turn students’ attention to the first problem, 28 + 1, in the green column of the threecolumn chart.

red

35 + 4 =

35 + 5 =

35 + 6 =

green

yellow

green

yellow

28 + 3 =

yellow

129

1 ▸ M5 ▸ TC ▸ Lesson 14

17 + 4 = 06/02/21 6:53 AM

Let’s take time to make sense of this problem before we solve it. Look at the numbers in the ones place. Can we make the next ten? Why?

red

EUREKA MATH2

Students look at the numbers in the ones place to see whether they will make the next ten.

red 17 + 2 =

Name

Materials—S: Crayons

EM2_0105TE_C_L14_classwork_studentwork.indd 129

Will It Make the Next Ten?

No, we can’t. 8 and 1 make 9. They are not partners to 10. Have students add to confirm their idea and ask a student to share their total. Our idea was correct. We did not make the next ten. When we put together the ones in each addend, they do not make ten. Let’s use our red crayon to circle 28 + 1. Ask students to look at 28 + 2. Let’s take time to make sense of this problem before we solve it. Look at the numbers in the ones place. Can we make the next ten? Why? Yes, I think we can. 8 and 2 are partners to 10. Have students add to confirm their idea and ask a student to share their total. Our idea was correct. We made the next ten. When we put together the ones in each addend, they make ten. Let’s use our green crayon to circle 28 + 2. Ask students to look at 28 + 3. Let’s take time to make sense of this problem before we solve it. Look at the numbers in the ones place. Can we make the next ten? Why? Yes, we can. 8 and 2 are partners to 10. And 8 and 3 make more than that. We’ll make ten and have more left.

201

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Look at the first addend, 28. How many does it need to make the next ten? 2 Where can we get 2 to add to 28? From the 3 How many extra ones will we have? 1 Have students add to confirm their idea and ask a student to share their total. Our idea was correct. We made the next ten. When we put together the ones in each addend, they make more than ten. We even have extra. Let’s use our yellow crayon to circle 28 + 3. Display the three categories and read them out loud.

Does Not Make 10

Makes Next 10

Makes Next 10 and Extra Ones

Pair students and have partners find the total of the problems in the pink column. Ask students to use their crayons to circle the problems according to the categories shown. When they finish, ask students to share their work for each problem. Display the problems students circled in red.

17 + 2 = 19

Look at your work. Why do all of these problems go together?

28 + 1 = 29

We circled them with the red crayon. They do not make the next ten.

35 + 4 = 39

Why can’t we make the next ten in these problems?

17 + 3 = 20

The ones add to less than ten. Display the problems students circled in green. Look at your work. Why do all of these problems go together?

28 + 2 = 30 35 + 5 = 40

We circled them in green. They make the next ten.

17 + 4 = 21

Why can we make the next ten in these problems?

28 + 3 = 31

The ones are partners to 10.

35 + 6 = 41

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EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 14

Display the problems students circled in yellow.

Promoting Mathematical Practice

Look at your work. Why do all of these problems go together? We circled them in yellow. They make the next ten and have extra ones. Why can we make the next ten and have extra ones in these problems? When you put together the ones, they make more than 10. Is there a way to see if we can make the next ten before we solve the problem? How? Yes. We can look at the ones and think about if they make partners to 10. Yes. If the ones make less than 10, then we can’t make the next ten.

Sort and Solve Materials—T/S: Sort and Solve cards

Students play a sorting game to determine, without finding the total first, if given problems will make a new ten. Make sure pairs have the Sort and Solve cards. Ask them to lay out the three category cards. Demonstrate the activity. Put the problem cards in a pile. Partner A chooses a card.

Does Not Make 10

Makes Next 10

Makes Next 10 and Extra Ones

37 + 2

16 + 4

12 + 9

Partners A and B, you will find the total and check your thinking. Use your personal whiteboards. If you need to, change the group where you placed the card.

Going forward, students can use their understanding of the structure of addition expressions to select an appropriate strategy and to reason about whether their answer makes sense.

UDL: Engagement

Together, take time to make sense of the problem by looking at the numbers in the ones place. Sort the card by placing it into a group: Does Not Make 10, Makes Next 10, or Makes Next 10 and Extra Ones.

Partner B chooses the next card.

Students look for and express regularity in repeated reasoning when they use a sequence of problems to explain whether they can make the next ten in an addition problem. Later, they will look for and make use of structure when they predict which problems will or will not make the next ten before finding the total.

Foster collaboration during the game by assigning clear partner roles. Review the activity goal, directions, and group norms before pairs begin. Consider explicitly adding into group norms the social-emotional skills that students will be practicing. These include sharing, taking turns, and respectfully disagreeing.

203

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14

As students work, ask the following questions to assess and advance student thinking: • How do you know if you can make a new ten? • What is the next ten?

Differentiation: Challenge Invite students to make their own cards that would fit into the three categories.

• How many more do you need to get to the next ten? • How many extra ones will there be? • What is the total? How do you know?

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

5 min

Objective: Determine which equations make the next ten. Display the three expressions. Invite students to think–pair–share about which problem will make the next ten with no extra ones. Which problem will make the next ten with no extra ones? How do you know?

21 + 4 25 + 5 29 + 6

It’s 25 + 5. 5 and 5 are partners to 10. Look at 21 + 4. Will the total make the next ten? Why? No, 1 + 4 is only 5.

204

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 14

Look at 29 + 6. What do you notice? The ones make more than 10. How would you show 29 + 6 and find the total? We could make ten with a number bond. You’d have to break up the 6 into 1 and 5. We could draw quick tens and circle another ten, then count the tens and ones. We could hop on the number path. We would start at 29 and go 6 more. Why can it be useful to look at the numbers in the ones place before you solve a problem? You can tell if you can just add the ones or if you have to think about a way to break apart a number to make the next ten. You might choose a different tool. If you see you can just add the ones, you might use your fingers. If you have to break apart a number, you might draw.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

205

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Sprint ▸ Subtract within 20

Number Correct:

Subtract.

Number Correct:

Subtract.

10 – 4 = ■

11.

7–4=■

10 – 4 = ■

11.

6–4=■

10 – 5 = ■

12.

7–5=■

10 – 5 = ■

12.

6–5=■

10 – 6 = ■

13.

7–6=■

10 – 6 = ■

13.

6–6=■

10 – 9 = ■

14.

7–1=■

10 – 9 = ■

14.

6–0=■

10 – 1 = ■

15.

7–0=■

10 – 1 = ■

15.

6–1=■

9–4=■

16.

17 – 4 = ■

8–4=■

16.

16 – 4 = ■

9–5=■

17.

17 – 5 = ■

8–5=■

17.

16 – 5 = ■

9–6=■

18.

19 – 4 = ■

8–6=■

18.

18 – 4 = ■

9–8=■

19.

19 – 6 = ■

8–7=■

19.

18 – 6 = ■

10.

9–1=■

20.

20 – 4 = ■

10.

8–1=■

20.

20 – 5 = ■

160

206

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Sprint ▸ Subtract within 20

162

EUREKA MATH2 1 ▸ M5 ▸ TC ▸ Lesson 14

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14

Name

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14

2. Add. green

1. Add. red

red

15 + 4 =

22 + 7 =

18 + 2 =

red

29 yellow

green

15 + 5 =

green

12 + 8 =

29 + 6 =

green

25 + 6 =

yellow

22 + 9 =

51 + 4 =

yellow

25 + 7 =

31 Circle the number sentence.

Circle the number sentence.

33 + 7 =

red yellow

14 + 3 =

Red: Does not make 10.

Green: Makes the next 10.

Yellow: Makes the next 10 and extra ones.

169

170

PROBLEM SET

207

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14

EUREKA MATH2

1 ▸ M5 ▸ TC ▸ Lesson 14

3. Write number sentences that match the set. Does Not Make 10

Makes Next 10

3+4=7

3 + 7 = 10

3 + 9 = 12

26 + 2 = 28

28 + 2 = 30

26 + 5 = 31

5+3=8

5 + 5 = 10

5 + 7 = 12

34 + 2 = 36

34 + 6 = 40

34 + 7 = 41

Makes Next 10 and Extra Ones

Sample:

208

PROBLEM SET

171

Topic D Addition and Subtraction of Tens Now that students have added 10 to a two-digit number, subtracted 10 from a two-digit number, and added a one-digit number to a two-digit number, they are ready to work with 2 two-digit numbers. This topic completes grade 1 work with subtraction. It also advances students toward the goal of adding any 2 two-digit numbers, which they will do in topic E, by increasing their proficiency with three skills: • Add tens to a multiple of ten. • Subtract tens from a multiple of ten. • Add tens to any two-digit number. To add and subtract tens, students extend their Level 2 strategies of counting on and back. They represent units of ten by using rows of beads on a rekenrek, quick ten drawings, or their fingers. To add, they count on tens. To subtract, they count back tens or think about addition and count on tens from the known part to get to the total.

20, 30, 40, 50, 60, 70

80, 70, 60, 50, 40

Students also solve addition and subtraction problems involving multiples of ten by using a Level 3 strategy. They represent the equation in unit form and notice an easier one-digit fact. They use the same strategy to find an unknown part in an addition or subtraction equation involving multiples of ten.

20 + 20 = 40

40 – 20 = 20

2 tens + 2 tens = 4 tens

4 tens – 2 tens = 2 tens

To practice adding and subtracting tens, students are presented with number sentences that include two addition or subtraction expressions. For example, 20 + 30 = 60 – 10 (true) or 50 + 10 = 60 – 10 (false). They determine whether the number sentences are true or false by calculating the value of each expression. 210

EUREKA MATH2 1 ▸ M5 ▸ TD

Students use a rekenrek, drawings, and place value charts to add tens to any two-digit number. They model and solve problems such as 25 + 20. At first, they may count on by tens from the first addend (e.g., 25, 35, 45). Through practice and studying patterns, they advance to using place value strategies. For example, to add 25 + 20, students think of 25 as 2 tens 5 ones and 20 as 2 tens. Students add the 2 tens in 20 to the 2 tens in 25.

Students notice that adding tens to a two-digit number causes the digit in the tens place to change, but the digit in the ones place remains the same. Students subtract from two-digit numbers in grade 2. To culminate topics C and D and to prepare for adding 2 two-digit numbers, students add one-digit numbers and multiples of ten to two-digit numbers. At first, they do this in a choral count. They count in unison while the teacher records the count. The teacher strategically pauses students and asks them to determine missing numbers in the sequence using addition or patterns they notice in the recording. Then they add a string of numbers — one-digit numbers, two-digit numbers, and multiples of ten — to try to get to 100.

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EUREKA MATH2

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Progression of Lessons Lesson 15

Lesson 16

Lesson 17

Count on and back by tens to add and subtract.

Use related single-digit facts to add and subtract multiples of ten.

Use tens to find an unknown part.

EUREKA MATH2

Name

Add or subtract.

70 + 20 =

70 – 20 =

4–

= 70

40 –

= 10

+ 20 = 90

60 –

= 10

90 –

= 10

90 =

+ 80

7 tens – 2 tens = 5 tens

I can count on by tens to add.

192

187

I can use 7 + 2 = 9 to help me figure out 70 + 20. I can use 7 – 2 = 5 to help me figure out 70 – 20.

212

4+ 40 +

7 tens + 2 tens = 9 tens

I can count back by tens to subtract (take away).

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

1 ▸ M5 ▸ TD ▸ Lesson 16

PROBLEM SET

I can use 4 + 3 = 7 to help me figure out 40 + ? = 70. I can use 4 – 3 = 1 to help me figure out 40 – ? = 10.

EUREKA MATH2 1 ▸ M5 ▸ TD

Lesson 18

Lesson 19

Lesson 20

Determine if number sentences involving addition and subtraction are true or false.

Add tens to a two-digit number.

Add ones and multiples of ten to any number.

tens

ones

tens

ones

I can add ones or tens to a number by using a strategy I know. I can show my thinking.

I can find the total of the expressions on both sides of the equation. If the totals are the same, the number sentence is true.

+ Adding 30 is adding 3 tens. When we add tens, only the tens digit in the total is more.

213

LESSON 15

Count on and back by tens to add and subtract.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 15

Name

Add or subtract. Show how you know.

80 – 40 =

Lesson at a Glance Students self-select strategies to use to solve a word problem involving subtracting more than 1 ten from a multiple of ten. They practice and discuss counting back to subtract tens and counting on to add tens by using drawings, the rekenrek, and their fingers (as units of ten).

Key Question

• What are some ways to add tens or take away tens?

Achievement Descriptor 1.Mod5.AD5 Add or subtract multiples of 10.

70 + 20 =

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EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 15

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Gather a variety of math tools for students to choose from and have them available for use. Examples of math tools could be number paths, cubes or base 10 rods, and personal whiteboards.

Launch Learn

10 min 10 min

30 min

• Share, Compare, and Connect

• 100-bead rekenrek

Students • Assorted math tools

• Count Back by Tens to Subtract • Count On by Tens to Add • Problem Set

Land

10 min

215

EUREKA MATH2

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Fluency

10 10

Whiteboard Exchange: Bar Graphs 30 Students answer questions about a horizontal bar graph to build fluency with interpreting data with three categories from module 2. 10

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the bar graph. The graph shows the animals on a farm.

Farm Animals

How many chickens are on the farm?

Totals

Display the total: 12. How many cows are on the farm? Display the total: 11. How many pigs are on the farm?

11 8

Display the total: 8. Continue with the following questions. How many more cows are on the farm than pigs? 3 How many more chickens are on the farm than pigs? 4 How many fewer cows are on the farm than chickens? 1 216

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 15

What is the total number of animals on the farm? 31

Choral Response: Subtract within 10 Students say the difference to build subtraction fluency within 10. Display 10 – 2 = _____ . What is 10 – 2? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 8

10 - 2 = 8

Display the answer. Repeat the process with the following sequence:

10 - 8

10 - 7

10 - 3

9-2

9-7

9-6

9-3

8-3

8-5

Beep Counting by Tens Students complete a number sequence to build fluency with counting by tens. Invite students to participate in Beep Counting. Listen carefully as I count by tens. I will replace one of the numbers with the word beep. I will count up, and I will count down. Raise your hand when you know the beep number. Ready? Display the sequence 10, 20, _____. 10, 20, beep. Wait until most students raise their hands, and then signal for students to respond.

10, 20, 30

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Repeat the process with the following sequence:

50, 60,

80, 90,

30,

, 50 30, 20,

70, 60,

100, 90,

20,

Launch

10 30

Materials—S: Assorted math tools

Students self-select 10 strategies and tools to use to solve a word problem. Display the picture of the partially unrolled stickers to build context for students. Promoting Mathematical Practice

How many stickers are unrolled so far? How do you know? There are 30 stickers unrolled. You can count the groups by ten: 10, 20, 30. Display the word problem and read it aloud. Miss Lin had a roll of 90 stickers. She gave 30 stickers to students. How many stickers are left on the roll? Have students retell the story to a partner. Ask them to engage with the problem by using the Read–Draw–Write process. Invite students to self-select strategies and tools such as base 10 rods, fingers, personal whiteboards, or number paths. Encourage all students, even those who can solve by using mental math, to justify their solutions with a representation.

218

As students decide which strategy to use to solve the sticker problem, they use appropriate tools strategically. Throughout the year, students have built up their mathematical “toolbox” of strategies, which they can now apply to this new problem type. Encourage students to think strategically by asking the following questions: • Why did you choose to solve the problem that way? Did it work well? • What other way could you use to solve the problem? Why might that way be helpful?

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 15

Circulate and notice the variety of student work. Select two students to share their work in the next segment. Take Away Tens

Count Back by Tens

Count On by Tens

- 10- 10- 10

90 - 30 = 60

60 70 80 90

30 40 50 60 70 80 90

90 - 30 = 60

30 + 60 = 90

Let’s talk about the different ways you solved this problem. 10 10

Learn

30 10

Share, Compare, and Connect Materials—T: Student work

Teacher Note If students count on by tens (think addition) to subtract, invite them to share their thinking. Students may say they started at 30 and counted up 6 tens to 90.

Students discuss different ways to solve a word problem. Invite the students whose work was selected in the previous segment to share their work. Share the most accessible strategy first. Encourage the class to use the Talking Tool to engage with one another and with the mathematics. Consider the following sample discussion. How many stickers are left on the roll? 60 stickers

30 40 50 60 70 80 90 30 + 60 = 90 Help the class compare strategies by asking, “How is counting on by tens to subtract different than counting back by tens to subtract?”

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EUREKA MATH2

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Take Tens Away (Sakon’s Way) Sakon, how did you figure out how many stickers are left? I drew 9 tens for the 90 stickers. I crossed off 3 tens for the 30 stickers she gave away. There are 6 tens left. That means 90 – 30 = 60.

Count Back by Tens (Lucia’s Way) Lucia, how did you figure out how many stickers are left? I started at 90 and counted back 3 tens. I landed on 60. That’s how I knew that 90 – 30 = 60. Invite students to think–pair–share about how the two different ways are similar. Sakon crossed off tens. Lucia counted back by tens. What is the same about their ways of solving this problem?

90 - 30 = 60 - 10- 10- 10 60 70 80 90 90 - 30 = 60

They both started with 90. Then they both subtracted 30. They both got 60. It’s like when we counted back by ones to subtract, but now we’re counting 10 at a time. Transition to the next segment by framing the work. Today, we will practice counting back to subtract tens and counting on to add tens.

Count Back by Tens to Subtract

Teacher Note If most students typically count on to subtract, rather than count back, show their strategy on the rekenrek (or by using fingers). For example, to find 80 – 40, start by showing the rekenrek with 40 beads on the left side. Consider this sample discussion: • To think addition, or to count on to subtract, we start with the part we know, 40. • Count on by tens with me until we get to the total, 80.

Students count back by tens on a rekenrek and with their fingers to subtract.

Slide a row of beads to the left all at once. Do this four times as students count. Ask this question:

Show the rekenrek with 50 beads on the left side.

• How many tens did we count?

Materials—T: 100-bead rekenrek

How many beads?

Write 40 + 40 = 80. Ask this question:

• So, what is 80 – 40?

Let’s count back by tens to figure out 50 – 30. How many tens are in 30? 3 tens

220

Help students recall as needed that when they count on to subtract, the answer is not the last number they say. Rather, it is how many tens they counted.

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 15

We will start at 50 and take away 30, or 3 tens. Count back by tens with me. Slide a row of beads to the right all at once. Do this three times as students count. 50, … , 20 What is 50 – 30? 20 Repeat the process with the rekenrek for 70 – 20 and 80 – 40. Then ask students to show 8 fingers the math way. Tell them that each finger is a ten. Guide them to count on their fingers by tens to 80. How many tens are in 80? 8 tens Together, let’s count back by tens to figure out 80 – 40. How many tens are in 40? 4 tens Demonstrate lowering 1 finger at a time as the class counts back from 80 to 40. What is 80 – 40? How do you know? It’s 40. We said 40 last. It’s 40. I know because we have 4 fingers up. That’s 4 tens.

Differentiation: Support When counting back, students may say 80 and put a finger down. Help students to remember not to put a finger down until they take 10.

Count On by Tens to Add Materials—T: 100-bead rekenrek

Students count on by tens on a rekenrek and with fingers to add. Transition to adding tens. Show the rekenrek with 50 beads on the left side. Ask students to confirm the number.

221

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Let’s count on by tens to figure out 50 + 40. How many tens are in 40? 4 tens We will start at 50 and add 40, or 4 tens. Count on by tens with me. Slide a row of beads to the left all at once. Do this four times as students count.

Teacher Note If needed, consider using the rekenrek to provide distributed practice with counting on and counting back to add and subtract tens from multiples of 10. Encourage students to follow along by using their fingers.

50, … , 90 What is 50 + 40? 90 Repeat the process with the rekenrek for 30 + 60. Then guide students to use their fingers to count on by tens to figure out 20 + 50.

Differentiation: Challenge Invite students to count on by tens starting at any multiple of 10 as far as they can, even past 100. Also ask them to count back by tens starting at 100 or 120.

How many tens are in 20? 2 tens Tell students to put up 2 fingers the math way. How many tens are in 50? 5 tens Demonstrate raising 1 finger at a time as the class counts on from 20 to 70. What is 20 + 50? 70

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions and word problems may be read aloud.

222

UDL: Action & Expression Consider having students use the interactive Digital Number Path to 120 to support them in demonstrating and explaining their ideas for 20 + 20 = 40 and 40 – 30 = 10.

10 EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 15 30

Land Debrief

5 min

Objective: Count on and back by tens to add and subtract. Display the picture of 20 stickers. Let’s pretend you have these 2 sheets of 10 stickers. How many stickers do you have in all? 20 Suppose you got 20 more stickers. How many stickers would you have then? How do you know? 40 stickers I know because I counted on by tens. I started with 20 and then I counted 30, 40. I know that 2 tens and 2 tens is 4 tens, and 4 tens is 40. Display the picture of 40 stickers. Suppose you give away 30 stickers. How many stickers would you have then? How do you know? If you take away 3 sheets, that leaves 1. One sheet is 10 stickers. 10 stickers; I counted back by tens: 40, 30, 20, 10. I counted on: 30, 40. That’s 1 sheet so 10 stickers. What are some ways to add tens or take away tens? We can count on to add tens. And we can count on to take away too. We can count back to take away tens.

Exit Ticket

5 min

223

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 15

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 15

Name

3. Count up by tens.

30, 40

1. Ms. Mack picks 20 berries. Then she picks 30 more.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 15

4. Count down by tens.

90, 80

How many berries does she have now?

5. Add or subtract.

20 + 30 = 50

She has

berries.

30 + 20 =

40 – 20 =

60 + 30 =

70 – 30 =

90 – 40 =

2. There are 50 pillows in the store. 40 of them are sold. How many pillows are in the store now?

50 – 40 = 10 There are

224

= 40 + 50

pillows in the store. 175

176

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 15

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 15

Read Ms. Mack has 90 pencils. She gives away 60. How many pencils does she have now? Draw

Write

She has

pencils.

PROBLEM SET

177

225

LESSON 16

Use related single-digit facts to add and subtract multiples of ten.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 16

Name

Add or subtract.

70 + 20 =

Students solve addition and subtraction equations involving multiples of ten by representing them in unit form (number of tens and ones) and noticing the easier, related one-digit facts they know. They play a game to practice mentally adding and subtracting multiples of ten.

Key Question

• How can facts we know help us add and subtract multiples of ten?

Achievement Descriptor

7 tens + 2 tens = 9 tens

70 – 20 =

Lesson at a Glance

1.Mod5.AD5 Add or subtract multiples of 10.

7 tens – 2 tens = 5 tens

187

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 16

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Add or Subtract Tens removables must be torn out of student books and placed in personal whiteboards. The Numbers Up! cards must be torn out of student books and cut apart. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. Consider saving the Add or Subtract Tens removables for use in lesson 17.

Launch Learn

10 min 5 min

35 min

• Add Multiples of Ten • Subtract Multiples of Ten • Numbers Up! • Problem Set

Land

10 min

• Add or Subtract Tens removable (digital download)

Students • Base 10 rods (10 per student pair) • Add or Subtract Tens removable (in the student book) • Numbers Up! cards (1 set per group of 3 students, in the student book)

• Copy or print the Add or Subtract Tens removable to use for demonstration. Consider saving this for use in lesson 17. Note: Base 10 rods are referred to as ten-sticks throughout the lesson.

227

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Fluency

10 5

Whiteboard Exchange: Bar Graphs 35 Students answer questions about a vertical bar graph to build fluency with interpreting data with three categories from module 2. 10

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the bar graph. The graph shows students’ lunch choices.

Lunch Choices Totals

How many students chose a taco? Display the total: 7. How many students chose a cheeseburger? Display the total: 12. How many students chose a sandwich? Display the total: 2. Continue with the following questions. How many more students chose a cheeseburger than chose a sandwich? 10 How many more students chose a cheeseburger than chose a taco? 5 How many fewer students chose a sandwich than chose a taco? 5 228

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 16

How many total students chose a lunch? 21

Choral Response: Subtract Within 10 Students say the difference to build subtraction fluency within 10. Display 5 – 2 = _____. What is 5 – 2? Raise your hand when you know.

5-2= 3

Wait until most students raise their hands, and then signal for students to respond. 3 Display the answer. Repeat the process with the following sequence:

5-3

6-2

6-4

7- 2

7- 5

7- 3

6-3

8-2

8-6

Beep Counting by Tens Students complete a number sequence to build fluency with counting by tens. Invite students to participate in Beep Counting. Listen carefully as I count by tens. I will replace one of the numbers with the word beep. Raise your hand when you know the beep number. Ready? Display the sequence 40, 50, _____. 40, 50, beep. Wait until most students raise their hands, and then signal for students to respond.

40, 50, 60

229

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Display the answer. Repeat the process with the following sequence:

60,

, 80 80, 90,

100,

, 120 60, 50,

80,

, 60 100, 90,

120, 110,

Launch

5 35

Students use their hands to represent units of ten and to add. Tell students to show10 10 with their fingers the math way. Wiggle your fingers. How many fingers? 10 Today, our fingers are ones. Make a group of ten with your fingers by clasping your hands together. (Demonstrate clasping hands.) We can think of all of our fingers as 10 ones or 1 ten. Have students unclasp their hands. Invite two volunteers to come forward. Tell them to show ten by clasping their hands together. Gesture to both volunteers and ask this question. How many fingers? How do you know? 20 fingers. I counted by tens: 10, 20. 2 tens is 20. Invite two more volunteers to come forward. Tell them to also show ten with their hands clasped together. Gesture to all four volunteers and ask this question.

230

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 16

How many fingers? How do you know? 40 fingers. I counted by tens: 10, … , 40. I counted on by tens from 20: 20, 30, 40. 4 tens is 40. Have the volunteers return to their seats. We can write a number sentence to show our friends’ hands by writing the number of fingers, or ones, like this. Write 20 + 20 = 40. Or we can make the problem easier by thinking about the number of clasped hands, or tens, and write it like this. Write 2 tens + 2 tens = 4 tens. Turn and talk: What is the same about these number sentences? What is different about them? Highlight the 2s and 4s in the number sentences, as shown. What addition fact do you see in both number sentences? 2+2=4 2 + 2 = 4 is an easier problem than 20 + 20 = 40. We can use that to make the problem easier by thinking, 2 tens plus 2 tens equals 4 tens. 4 tens is 40. Transition to the next segment by framing the work.

UDL: Action & Expression As students add and subtract by thinking about facts they know as numbers in unit form (e.g., 3 tens), help them monitor their own progress by providing these questions that guide self-monitoring and reflection: • How is this problem like other problems I have solved? • How is thinking of this part as groups of ten helping me?

Today, we will find and use facts we know to help us add and subtract efficiently.

231

10 1 ▸ M5 ▸ TD ▸ Lesson 16 5

Learn

EUREKA MATH2

35 10

Add Multiples of Ten Materials—T: Add or Subtract Tens removable; S: Base 10 rods, Add or Subtract Tens removable

Students add multiples of ten by relating problems to basic facts within 10. Pair students and assign each partner as either partner A or partner B. Distribute ten-sticks to each student pair. Write 30 + 30 = _____. Let’s find the total by making an easier problem. Ask partner A to show the first addend and partner B to show the second addend with ten-sticks. Partner A, how many tens do you have? 3 tens Partner B, how many tens do you have? 3 tens Partners, how many total tens do you have? 6 tens How many is 6 tens? 60 So, what is 30 + 30? 60 Write 60 to complete the equation. Repeat the process with 30 + 20 or 40 + 50.

232

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 16

Make sure that each student has the Add or Subtract Tens removable inside their whiteboard. Write 50 + 40 at the top of the addition section. Have students follow along.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Add or Subtract Tens

How many tens are in 50? 5 tens

tens +

tens =

tens –

tens =

tens

Write 5 in the equation. How many tens are in 40? 4 tens Write 4 in the equation.

tens

What is 5 tens + 4 tens? How do you know? It’s 9 tens. 5 + 4 = 9. Write 9 to complete the equation.

145

Differentiation: Challenge

EM2_0105TE_D_L16_removable_ add_or_subtract_tens_studentwork1_CE.indd 145

17/02/21 4:34 PM

So, what is 50 + 40? 90 Write = 90 to complete the original problem. What addition fact do you see that helped us figure out 50 + 40 = 90? 5+4=9 Repeat the process with 20 + 70. Release responsibility to the students as appropriate. Then have students put aside their removable.

Subtract Multiples of Ten Materials—T: Add or Subtract Tens removable; S: Base 10 rods, Add or Subtract Tens removable

Students subtract multiples of ten by relating problems to basic facts within 10.

Change the addends so that the total crosses 100. For example, use 80 + 40 = 120 (8 tens + 4 tens = 12 tens). Students may write 120 as 12 tens, 120, or 1 hundred 2 tens.

Differentiation: Support If students do not know facts within 10 from memory, they may use their fingers to count on or count back by ones or tens. They may also continue to use ten-sticks.

Write 60 – 20 = _____. Let’s find the total by making an easier problem.

233

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Ask partners to show the total, 60, with ten-sticks. How many tens do we have? 6 tens We need to subtract 20. How many tens are in 20? 2 tens Have partners subtract 2 tens. Partners, how many tens are left? 4 tens How many is 4 tens? 40 So, what is 60 – 20? 40 Write 40 to complete the equation. Repeat the process with 90 – 40 or 80 – 20. Ask students to pick up their whiteboards and look at the Add or Subtract Tens removable. Write 50 – 40 at the top of the subtraction portion. Have students follow along. How many tens are in 50?

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Add or Subtract Tens

5 tens Write 5 in the equation at the bottom of the page. How many tens are in 40?

tens +

tens =

tens

tens –

tens =

tens

4 tens Write 4 tens in the equation. What is 5 tens – 4 tens? How do you know? It’s 1 ten. 5 – 4 = 1.

234

EM2_0105TE_D_L16_removable_ add_or_subtract_tens_studentwork2_CE.indd 145

145

16/02/21 2:59 PM

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 16

Write 1 to complete the equation. So, what is 50 – 40? 10 Write = 10 to complete the original problem. What subtraction fact do you see that helped us figure out 50 – 40 = 10? 5–4=1

UDL: Engagement

Repeat the process with 70 – 40 or 80 – 50. Release responsibility to the students as appropriate.

Numbers Up! Materials—S: Numbers Up! cards

Students find the unknown total or part when given two multiples of ten. Form groups of three students and assign each player as player A, player B, or player C. Display the picture of three players. Give students these directions for the Numbers Up! game: • Place the pile of cards number side down. Players B and C each take a card. They hold their cards against their foreheads so they can’t see their own number, but the other players can.

Depending on students’ needs, consider a variation or an alternative to Numbers Up! As a variation, partners may use the cards to add or subtract two multiples of ten. They may use the Add or Subtract Tens removable to write the equations in two ways. As an alternative to Numbers Up!, have partners use the Add or Subtract removable to play Roll and Add by doing the following: • Roll two 10-sided dice. • Record their roll as an addition expression by using numbers of tens (e.g., 4 tens + 5 tens).

• Player A looks at both cards and says the total of the two numbers. 30 30

20 20

• Add and write the total number of tens. • Write a corresponding number sentence in standard form (e.g., 40 + 50 = 90). To play Roll and Subtract, partners write the larger number shown on the dice first and the smaller number second.

235

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EUREKA MATH2

• Players B and C figure out the number on their own cards by using the total and the other player’s part. • Players B and C look at their cards to confirm their answers. • Players may switch roles for the next round. Distribute sets of cards to each group and have them play for 5 to 6 minutes. Provide support as needed.

Problem Set Differentiate the set by selecting problems for students to finish independently within the shorter timeframe. 10 Problems are organized from simple to complex. Directions and word problems may be read aloud. 5

Land Debrief

Promoting Mathematical Practice 5 min

Objective: Use related single-digit facts to add and subtract multiples of ten. Display the 3 buses. Each bus carries 10 students. How many students are in all 3 buses? How do you know? 30 students 3 tens is 30. Display the 6 buses. Three more buses pull up. Each of these buses carries 10 students, too. How many students are there now? How do you know?

Students reason abstractly and quantitatively when they solve the bus problem by thinking in terms of tens. This problem requires students to decontextualize on two levels to solve. First, they need to understand that, even though they cannot see the students inside the buses, they can count the buses to determine how many students there are. Next, they need to decontextualize each bus as a ten and reason about units to solve. They then recontextualize by converting tens to buses and buses to students.

60 students. 3 tens and 3 tens is 6 tens. 6 tens is 60. 236

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 16

Write 30 + 30 = 60. How can facts we know help us add and subtract multiples of ten? For example, how did using 3 + 3 = 6 make this problem easier? You don’t have to worry about counting all those big numbers. You can just use the easier fact. I know 3 + 3, so it’s faster than counting on by tens. Leave the 6 buses displayed and pose a second problem. Suppose 4 buses drive away. How many students are in the buses that are left? 20 students I know because 6 – 4 = 2. 2 buses is 2 tens, and that’s 20. Cross off 4 buses and write 60 – 40 = 20. What fact that we know helped us figure out 60 – 40 = 20? How did it help us? 6–4=2 I know 6 – 4, so it is easier than counting back by tens.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

237

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 16

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 16

Name

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 16

Read

4 packs of 10 crayons are on the desk.

1. Add or subtract.

20 + 30 =

4 packs of 10 crayons are in the desk.

How many crayons are there in all?

2 tens + 3 tens = 5 tens 30 – 20 =

8 tens +

238

How many nuts does he have left? Draw

Draw

ten

9 tens Write

8 tens –

He gives away 5 bags.

ten =

80 – 10 =

Max has 9 bags of 10 nuts.

3 tens – 2 tens = 80 + 10 =

Read

ten =

Write

40 + 40 = 80 7 tens

There are 185

186

PROBLEM SET

crayons.

90 – 50 = 40 Max has

nuts.

LESSON 17

Use tens to find an unknown part.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

Name

Find the unknown part.

20 +

= 40

70 -

Lesson at a Glance Students engage in a Math Chat routine and share ways to find an unknown addend. Then they practice finding unknown addends and subtrahends by using two strategies: by counting on or back by tens and by thinking of an easier, known fact.

Key Question

= 30

• What strategies can we use to find an unknown part?

Achievement Descriptor 1.Mod5.AD5 Add or subtract multiples of 10.

195

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 17

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Prepare sets of Subtraction Expression cards from lesson 9 for each student pair.

Launch Learn

10 min 10 min

30 min

• Find an Unknown Addend • Find an Unknown Subtrahend • Problem Set

Land

10 min

• Add or Subtract Tens removable (digital download)

Students • Subtraction Expression cards (1 set per student pair) • Add or Subtract Tens removable (in the student book) • Assorted math tools

• The Add or Subtract Tens removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance, to have students assemble them during the lesson, or to use the ones prepared in lesson 16. • Copy or print the Add or Subtract Tens removable to use for demonstration, or use the one prepared in lesson 16. • Make assorted math tools available for students to choose from and use in the lesson. Consider providing students with base 10 rods and a number path.

241

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

Fluency

10 10

Match: Subtraction Expressions 30 Expression cards Materials—S: Subtraction

Students identify equivalent expressions to build subtraction fluency within 10. 10

Have students form pairs. Distribute a set of cards to each student pair and have them play according to the following procedure. Consider doing a practice round with students.

2-1

2-2

5-3

8-4

10 - 10

9-0

7-3

8-6

10 - 9

Differentiation: Challenge Provide sets of Subtraction Expression cards within 20 from module 3 to students who demonstrate proficiency with subtraction within 10.

4-3

• Lay out nine cards, expression-side up. • Match two equal expressions. If there are no matches, replace a few cards with different cards from the pile.

2-1

10 - 9

• Turn over the cards to check that the expressions are equal. Front

• Place the matched cards to the side and replace them with two new cards from the pile. • Continue until no more matches can be made. Circulate as students work and provide support as needed.

1 Back

242

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 17

Beep Counting: 10 More, 10 Less Students complete a number sequence to build fluency with mentally finding 10 more or 10 less than a number. Invite students to participate in Beep Counting. Listen carefully as I count on or count back by tens. I will replace one number with the word beep. Raise your hand when you know the beep number. Ready? Display the sequence 21, 31, _____ . 21, 31, beep. Wait until most students raise their hands, and then signal for students to respond. 41

21, 31, 41

Display the answer. Repeat the process with the following sequence:

42,

, 62

74, 84,

, 23

46, 36,

68,

,48

95, 85,

27, 17,

Launch

10 30

Materials—T: Add or Subtract Tens removable; S: Add or Subtract Tens removable, assorted math tools 10

Students share and discuss different ways to find the unknown part in an equation. Make sure students have the Add or Subtract Tens removable inside a personal whiteboard.

243

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1 ▸ M5 ▸ TD ▸ Lesson 17

Write 20 + _____ = 70 at the top of the addition portion. Have students do the same. Use the Math Chat routine to engage students in mathematical discourse. What is the unknown part? How do you know? Give students 1 to 2 minutes of silent think time. Students may choose to use mental math, a basic fact, a drawing, base 10 rods, or a number path to solve the problem.

tens +

tens =

tens

Then invite students to discuss their ideas with a partner. Listen for students who find the unknown part by • thinking of the easier related fact, 2 + 5 = 7, or • counting on by tens from 20, 5 times (20, … , 70). Facilitate a class discussion by inviting one or two students to show their work and share their thinking. If needed, demonstrate the strategies mentioned above. Support student-to-student dialogue by having students refer to the Talking Tool. Encourage students to agree or disagree, ask a question, give a compliment, or restate an idea in their own words. How did you find the unknown part? I drew 2 tens and I counted on to 7 tens. I added 5 more tens. That is 50.

20 + 50 = 70

What is another way to find the unknown part? I know 2 + 5 = 7, so 2 tens + 5 tens = 7 tens. 5 tens is 50. So, 20 plus what number equals 70? 50

244

tens +

tens =

tens

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 17

Complete the equation by writing the unknown part. If we think of a fact we know, we can use it to find an unknown part. If we do not think of a fact, we can count on by tens. Transition to the next segment by framing the work. Today, we will find unknown parts in equations.

tens +

tens =

tens

10 10

Learn

Differentiation: Challenge 30 Present the equations as word problems with coins, as in this example:

Find an Unknown Addend

Corey has 40 cents. He needs 80 cents to buy a ball. How much more money does he need?

Materials—T/S: Add or Subtract Tens removable

Students connect counting on by tens to the Level 3 strategy of using a related fact to solve. On the Add or Subtract Tens removable, write 40 + _____ = 80 at the top of the addition portion. Have students follow along.

Teacher Note

Tell students to draw quick tens to represent 40. Let’s draw more tens to count on to 80. Draw tens one at a time as students follow along. Have them chorally count by tens from 40 to 80. Circle the tens that we added.

Encourage students to use dimes or to draw labeled circles to help them solve the problem.

tens +

tens =

tens

Some students may be able to use their fingers to count on and count back, rather than drawing the tens. Help them recall that they can think of each finger as a unit of 10. Other students may benefit from the concrete support of using base 10 rods.

245

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

How many tens did we count on? 4 tens How many is 4 tens? 40 Guide students to record each known number of tens (4 and 8) in the correct spaces, leaving the unknown number of tens space blank. Point to the blank space.

UDL: Representation Consider creating a chart and highlighting the easier, related fact in each problem throughout the lesson as the class shares their thinking.

What is the unknown number of tens? How do you know? 4 We counted on 4 tens. Have students write 4 in the blank. Point to the blank space for the unknown in the original equation. What is this unknown part? How do you know? 40 4 tens is the same as 40. Ask students to write 40 in the blank in the original equation. Turn and talk. Which way is more helpful to you: finding an unknown part by counting on by tens, or thinking about the number of tens as an easier, related fact? Have students erase their whiteboard. Provide more practice by engaging them in a Whiteboard Exchange routine to solve 30 + _____ = 80 and 70 + _____ = 90. They may solve these problems by thinking of the number of tens or by counting on. • Tell students to turn their boards over so the red side is up when they are ready. Say, “Red when ready!” • When most students are ready, tell students to hold up their whiteboard to show you their work. • Give quick individual feedback, such as “Yes!” or “Check your count.” For each correction, return to validate the corrected work. How did you use tens to find an unknown part? I counted on by tens.

Promoting Mathematical Practice Students look for and make use of structure when they think of a problem in unit form (e.g., 3 tens + _____ = 8 tens) and use a basic fact (e.g., 3 + _____ = 8) to find the unknown part, because they notice the similarity in structure between the two number sentences. As students move toward using the standard algorithms to add and subtract in grade 2, this understanding will allow them to make sense of their work, rather than simply memorizing the steps.

I thought about the number of tens as a fact I know. 246

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 17

Find an Unknown Subtrahend

Differentiation: Challenge

Materials—T/S: Add or Subtract Tens removable

Students connect counting back by tens to the Level 3 strategy of using a related fact to solve a problem.

Present the equations as word problems with coins. For example:

On the Add or Subtract Tens removable, write 70 – _____ = 50 at the top of the subtraction portion. Have students follow along.

Corey has 70 cents. He buys a ball. He has 50 cents left. How much money does he spend?

Tell students to draw quick tens to represent 70.

Encourage students to use dimes or draw labeled circles to help them solve the problem.

Let’s cross off tens and count back to 50. Cross off tens one at a time as students follow along. Have them chorally count back by tens from 70 to 50.

Teacher Note

Point to the tens that were crossed off. How many tens did we cross off? 2 tens

tens -

tens =

tens

How many is 2 tens? 20 Guide students to record each known number of tens (7 and 5) in the correct spaces, leaving the unknown number of tens space blank. Point to the blank space. What is the unknown number of tens? How do you know? 2 We counted back 2 tens. Have students write 2 in the blank. Point to the blank space for the unknown value in the original equation. What is this unknown part? How do you know? 20 2 tens is the same as 20. Ask students to write 20 in the blank in the original equation. Copyright © Great Minds PBC

If students use counting on to subtract, demonstrate their strategy as well. The following sample shows a way to find the unknown part in 70 – _____ = 50. Tell students that to count on to subtract, we start with the part we know, 50. Draw quick tens. Tell students that we start at 50 and count on by tens until we get to the total, 70. Ask students how many tens they counted. Write 50 + 20 = 70. Ask students what the unknown part is in 70 – _____ = 50. Students may also solve by thinking about addition by using the number of tens. They may say that they know 5 tens + 2 tens = 7 tens, so, 7 tens – 2 tens = 5 tens, and 2 tens is 20.

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1 ▸ M5 ▸ TD ▸ Lesson 17

EUREKA MATH2

Turn and talk. Which way is more helpful to you, finding an unknown part by counting back by tens, or thinking about the number of tens as a fact you know? Have students erase their whiteboards. Provide more practice by engaging them in a Whiteboard Exchange routine to solve 90 – _____ = 60, and 80 – _____ = 40. They may solve these problems by thinking of the number of tens or by counting back. • Tell students to turn their boards over so the red side is up when they are ready. Say, “Red when ready!” • When most are ready, tell students to hold up their whiteboard to show you their work. • Give quick individual feedback, such as “Yes!” or “Check your total.” For each correction, return to validate the corrected work. How did you use tens to find an unknown part? I counted back by tens. I thought about the number of tens as a fact I know.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions and word problems may be read aloud. 10

Land Debrief

5 min

Objective: Use tens to find an unknown part. Gather students and display the hand and 2 dimes. Baz has these dimes, and he also has some dimes hidden under his hand. He has 60 cents altogether. 248

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 17

Invite students to think–pair–share about how much money is under Baz’s hand. How much money is under his hand? How do you know? 40 cents I know because 20 cents is showing, and I counted back from 60 to 20. I put up 4 fingers. (Shows 4 fingers.) 40 cents; I know because I started at 20 and counted on 4 tens to 60. 40 cents; I know that 2 + 4 = 6, so 20 + 40 = 60. 40 cents; 2 dimes + 4 dimes = 6 dimes. Display 6 dimes to confirm students’ thinking. Display the two number bonds. Discuss the part–whole relationship.

Some of you thought about 20 and 40 as the parts and 60 as the total. Others thought about 2 tens and 4 tens as the parts and 6 tens as the total. What strategies can we use to find an unknown part? We can count on or back by tens. I can use the number of tens to think of an easier fact I know.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

249

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

Name

1. Find the unknown part.

3 tens +

5 tens –

7 tens – 70 –

250

4–

40 +

= 70

40 –

= 10

+ 20 = 90

60 –

= 10

90 –

= 10

= 60

= 20 tens = 9 tens

60 +

tens = 2 tens

50 – 6 tens +

tens = 6 tens

30 +

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

= 90 90 =

tens = 4 tens

+ 80

= 40 191

192

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 17

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

Read

Max has 30 flies in a jar.

There are 60 books in a box.

He gets more flies.

40 are old books.

Now he has 80 flies.

The rest are new books.

How many more flies did Max get?

How many books are new?

Draw

Write

30 + 50 = 80 Max got

more flies.

193

194

Read

Zan has these dimes:

Dan has these dimes:

Zan finds some dimes.

Dan loses some dimes.

Now he has 9 dimes.

Now he has 3 dimes.

How much money did Zan find?

How much money did Dan lose?

Draw

Write

Zan found

new books.

PROBLEM SET

Read

60 + 30 = 90

60 – 40 = 20 There are

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 17

PROBLEM SET

cents.

60 – 30 = 30 Dan lost

cents.

251

LESSON 18

Determine if number sentences involving addition and subtraction are true or false.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18

Name

Circle the number sentence if it is true. Draw an X on the number sentence if it is false.

Lesson at a Glance Students determine whether number sentences are true or false and discuss their reasoning. They calculate the addition or subtraction expression on either side of the equal sign to find whether both sides represent the same amount.

Key Question • How can we tell if a number sentence is true or false?

60 - 40

Achievement Descriptors

30 – 10

1.Mod1.AD6 Determine whether addition and/or subtraction number

sentences are true or false. 1.Mod5.AD5 Add or subtract multiples of 10.

209

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 18

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Count by Tens Sprint must be torn out of student books. Consider whether to prepare these materials in advance or to have students tear them out during the lesson.

Launch Learn

10 min 15 min

25 min

• True or False? • Match: Addition and Subtraction Expressions • Problem Set

Land

10 min

• None

Students • Count by Tens Sprint (in the student book) • Match: Addition and Subtraction Expressions cards (1 set per student pair, in the student book)

• Some students may choose to use cubes or the number path to confirm their thinking about why number sentences are true or false. Consider making these tools available as needed. • The Match cards must be torn out of student books and cut apart. Consider whether to prepare the cards in advance or to have students prepare them during the lesson.

253

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18

Fluency

10 15

Sprint: Count by Tens Materials—S: Count by25Tens Sprint MATH 1 ▸ M5 ▸ TD ▸ Lesson 18 ▸ Sprint ▸ Count by Tens Students complete a numberEUREKA sequence to build fluency with counting by tens. 2

Sprint Have students read the instructions and complete the sample problems. Write the unknown number. 1. 2.

40, 30, 20, ■ 10 90, 100, ■, 120 110

Direct students to Sprint A. Frame the task. Teacher Note

I do not expect you to finish. Do as many problems as you can, your personal best. Take your mark. Get set. Think!

Consider asking the following questions to discuss the patterns in Sprint A:

Time students for 1 minute on Sprint A.

• What do you notice about problems 1–6? About problems 7–12?

Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

• What strategy did you use to solve problem 13? What strategy did you use to solve problem 19?

Read the answers to Sprint A quickly and energetically. Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B.

Teacher Note

Celebrate students’ effort and success. Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A. Lead students in one fast-paced and one slow-paced counting activity, each with a stretch or physical movement. Copyright © Great Minds PBC

197

Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B. 254

Count on by tens from 0 to 120 for the fast-paced counting activity. Count back by tens from 120 to 0 for the slow-paced counting activity.

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 18

Direct students to Sprint B. Take your mark. Get set. Improve! Time students for 1 minute on Sprint B. Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint B quickly and energetically. Count the number you got correct and write the number at the top of the page. Stand if you got more correct on Sprint B. Celebrate students’ improvement.

Launch

15 25

Students discuss whether number sentences are true or false. Display the story and10 read it aloud. Turn and talk. What number bond could we draw to represent this story?

There are 50 grapes in a bowl. 30 grapes are green. 20 grapes are red.

Use the following questions to generate and record a number bond. What is the total in this story? How do you know? 50; it says there are 50 grapes in the bowl. What are the parts in this story? How do you know? 30 and 20; they are the two colors or groups of grapes.

255

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18

Pair students. Ask partners to write addition and subtraction number sentences to represent the story and the number bond. They do not need to write all of the possibilities. Share a few different number sentences and ask students to explain their reasoning. Display the list of number sentences. Point to the first one.

20 + 30 = 50

Here are some number sentences I wrote. Show thumbs-up if you agree that this number sentence matches the story. Show thumbs-up if you think this number sentence is true. Call on a student to share their reasoning. They may use the story or the total to justify why it is true. Emphasize that it is true because both sides of the equal sign show the same amount: 50. Repeat the process with the next three number sentences. Emphasize that true number sentences can have addition or subtraction on either side of the equal sign as long as the amounts on either side of the equal sign are the same. Read the last number sentence. Have students turn and talk about whether this number sentence matches the story. Is this number sentence true or false? Why?

50 = 30 + 20

50 – 20 = 30

20 = 50 – 30

Teacher Note 30 – 50 = 20 is students’ first time seeing a number sentence that is false, but it cannot be shown to be false by calculating because finding 30 – 50 requires working with negative numbers. Help students make sense of why this number sentence is false by focusing on the part-total relationships, rather than the amount each side represents. 50 is the total, and 30 is a part. To subtract, we take a part from the total. If we start with a part, there are not enough to take away the total. Number sentences such as these help students see that while they can write the addends of an addition expression in any order without changing the total, the same is not true of subtraction expressions, where the order matters.

It’s false. 30 take away 50 doesn’t make 20. Differentiation: Challenge

If we start with 30 grapes there aren’t enough to take away 50. Yes, this number sentence is false. We have 20 on one side of the equal sign. For this number sentence to be true, the other side has to make 20, too.

30 – 50 = 20

On the other side we have 30 – 50. If there are only 30 grapes, then there are not enough grapes to take away 50 because 50 is more than 30.

Provide a number bond with different numbers of tens and have students write a math story and as many matching number sentences as they can with them.

Draw an X on the number sentence. Transition to the next segment by framing the work. Today, we will talk about more number sentences to see if they are true or false.

256

10 EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 18 15

Learn

25 10

True or False?

Students calculate to determine whether number sentences are true or false. Display the false number sentence.

UDL: Representation

Let’s figure out if this number sentence is true or false.

Activate prior knowledge by helping students recall how to determine if a number sentence containing two expressions is true or false. Ask the following questions:

What is 20 + 30?

• What is a true number sentence?

• What is a false number sentence?

20 + 30

50 + 10

Write 50 below 20 + 30. What is 50 + 10?

• What can we do with the expressions on either side of the equal sign to figure out if the number sentence is true or false?

60 Write 60 below 50 + 10. The total for each expression on either side of the equal sign is not the same. This number sentence is false. Draw an X on the number sentence. A number sentence is true when the expressions on both sides of the equal sign represent the same amount.

Teacher Note If time allows, encourage students to revise false number sentences to make them true. For example: • False: 20 + 30 = 50 + 10 • True: 30 + 30 = 50 + 10

257

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18

Display the following number sentences one at a time. Engage students in a Whiteboard Exchange routine to determine whether each of the following number sentences is true or false. Have students complete the work. Have students show their thinking, including drawing an X on false number sentences. Consider having students stand. Encourage them to notice the symbols for addition and subtraction. • Tell students to turn their whiteboards over so the red side is up when they are ready. Say, “Red when ready!” • When most are ready, tell students to hold up their whiteboard to show you their work. • Give quick individual feedback, such as “Yes!” or “Check your total.” For each correction, return to validate the corrected work.

Teacher Note Students may use varied reasoning to determine if the number sentences are true or false. They may simply calculate the total on either side of the equation, use relational thinking about parts on either side of the equal sign, or a combination of both.

50 - 40 = 30 - 20 10

After each number sentence, ask the following question. How do you know this number sentence is true or false?

30 + 30 = 80 - 20 60

30 + 20 + 10 = 50 + 10 10 + 10 = 20 - 10 50

50 – 40

30 – 20

30 + 30

80 – 20

10 + 10

20 – 10

30 + 20 + 10

50 + 10

Match: Addition and Subtraction Expressions Materials—S: Match: Addition and Subtraction Expressions cards

Students match expressions that are equal. Demonstrate the following variation on the Match card game: • Partners work together. They get out six cards from their set. The rest of the cards go in a pile to the side. 258

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 18

• Partners find two expression cards that are equal because they represent the same amount. They use their whiteboards to show how the cards match. Students may use tools such as cubes or the number path as needed. • Partners set aside the cards that match, draw two new cards from the pile to replace them, and repeat the process.

45 + 5

20 + 10

30 + 50

90 - 40 60 - 30 50 - 20

Students can find cards that do not match and use them to write comparison number sentences with the greater than and less than symbols. Individual students may also write their own true and false number sentences and then trade them with their partner’s sentences.

• Partners play until they have found all the matches. Distribute the Match cards to partners. As students play, circulate and ask them to explain why two cards are a match.

Differentiation: Challenge

20 + 10 = 60 - 30

Problem Set Differentiate the set by selecting problems for students to finish independently within the shorter timeframe. Problems are organized from simple to complex. 10

Directions may be read aloud. 15

Promoting Mathematical Practice

Land Debrief

5 min

Objective: Determine if number sentences involving addition and subtraction are true or false. Let’s play Convince Me. I’ll go first to try and convince you. Display the false number sentence, which invites discussion about a common misconception.

50 + 10

Students construct viable arguments and critique the reasoning of others when they play Convince Me. This requires students to consider the teacher’s position critically and construct a precise argument to explain why the teacher is wrong. If students have trouble critiquing the teacher’s position, or they have difficulty understanding one another’s arguments, encourage them to ask questions or express what they don’t understand about someone else’s reasoning.

259

1 ▸ M5 ▸ TD ▸ Lesson 18

EUREKA MATH2

I think this number sentence is true because both expressions have 50 and 10. Ask students to show thumbs-up if they agree the number sentence is true. I can tell that some of you are not convinced. You did not show thumbs-up. Why do you disagree? This number sentence is false, not true. One expression is minus and the other is plus. 50 – 10 = 40 and 50 + 10 = 60. The sides show different amounts. You convinced me! The number sentence is false because 40 is not equal to 60. Draw an X on the false number sentence. How can we tell if a number sentence is true or false? We can see if the expressions on both sides of the equal sign make the same amount.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

260

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 18

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18 ▸ Sprint ▸ Count by Tens

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18 ▸ Sprint ▸ Count by Tens

Number Correct:

Write the unknown number.

Number Correct:

Write the unknown number.

0, 10, 20, ■

13.

0, ■, 20, 30

10, 20, 30, ■

13.

10, ■, 30, 40

40, 50, 60, ■ 70

14.

40, ■, 60, 70 50

50, 60, 70, ■ 80

14.

50, ■, 70, 80 60

80, 90, 100, ■ 110

15.

80, ■, 100, 110 90

90, 100, 110, ■ 120

15.

90, ■, 110, 120 100

100, 90, 80, ■ 70

16.

100, ■, 80, 70 90

110, 100, 90, ■ 80

16.

110, ■, 90, 80 100

70, 60, 50, ■ 40

17.

70, ■, 50, 40 60

80, 70, 60, ■ 50

17.

80, ■, 60, 50 70

30, 20, 10, ■

18.

30, ■, 10, 0

40, 30, 20, ■

18.

40, ■, 20, 10

10, 20, ■, 40

19.

■,

10, 20, 30

0, 10, ■, 30

19.

■,

10, 20, 30

50, 60, ■, 80 70

20.

■,

100, 110, 120 90

40, 50, ■, 70 60

20.

■,

100, 110, 120 90

90, 100, ■, 120 110

21.

■,

90, 80, 70 100

80, 90, ■, 110 100

21.

■,

20, 10, 0

10.

110, 100, ■, 80 90

22.

■,

20, 10, 0

10.

100, 90, ■, 70 80

22.

■,

90, 80, 70 100

11.

80, 70, ■, 50 60

23.

■,

110, 100, 90 120

11.

70, 60, ■, 40 50

23.

■,

110, 120, 130 100

12.

40, 30, ■, 10

24.

■,

110, 120, 130 100

12.

30, 20, ■, 0

24.

■,

110, 100, 90 120

198

200

30 0 30

261

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18

Name

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 18

2. Make a true number sentence.

1. Circle the number sentence if it is true.

Draw an X on the number sentence if it is false.

30 + 40 = 50 + 20

= 30 + 40

50 - 40 = 30 – 20 90 – 60 =

70 + 20 = 80 + 10

20 + 20 + 20 =

60 - 30 = 30 – 20

= 80 – 50

3. Write your own true number sentence. Circle. Sample:

70 + 10 = 80 20 + 20 = 40 - 20

50 - 30 = 20 + 20 4. Write your own false number sentence. Draw an X. Sample:

60 - 30 =

262

30 + 20 + 10 = 50 + 10

207

70 – 50 = 30 208

PROBLEM SET

LESSON 19

Add tens to a two-digit number.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

Name

Add.

Lesson at a Glance Students use the rekenrek and drawings to show adding tens to two-digit numbers. They represent the addends and the total by using place value charts, and they discuss how the digits in the tens place change but the digits in the ones place stay the same.

Key Question

48 + 10 =

54 + 20 =

• What happens to the digits when you add tens to a number?

Achievement Descriptor 1.Mod5.AD6 Add a two-digit number and a multiple of 10 that have

a sum within 100.

217

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 19

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Double Place Value Chart removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Add Tens to Two-Digit Numbers • More Coins for Ko • Problem Set

Land

10 min

• 100-bead rekenrek • Double Place Value Chart removable (digital download)

Students • Double Place Value Chart removable (in the student book)

• Copy or print the Double Place Value Chart removable to use for demonstration.

265

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

Fluency

10 10

Beep Counting: 10 More, 10 Less Students complete30 a number sequence to build fluency with mentally finding 10 more or 10 less than a number. 10

Invite students to participate in Beep Counting. Listen carefully as I count on or count back by tens. I will replace one of the numbers with the word beep. Raise your hand when you know the beep number. Ready? Display the sequence 59, 69, _____ . 59, 69, beep. Wait until most students raise their hands, and then signal for students to respond.

59, 69, 79

79 Display the answer. Repeat the process with the following sequence:

82,

, 102 84, 94,

, 25

56, 46,

88,

, 68 103, 93,

21, 11,

Choral Response: True or False Number Sentences Students determine if a number sentence containing two expressions is true or false to prepare for comparing expressions in lesson 25. Display the number sentence 8 + 3 = 3 + 8. Is this number sentence true or false? Raise your hand when you know. 266

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 19

Wait until most students raise their hands, and then signal for students to respond. True Display the answer.

Teacher Note Consider asking students to determine the value of each expression in the number sentence to confirm whether it is true or false.

Repeat the process with the following sequence:

8+3=8+2+1

5+9=9+5

5+9=5+5+5

5+4+5=9+5

True

False

True

6 + 7 = 10 + 3

7+6=3+4+3

1+9+8=8+1+9

5 + 7 = 12 - 5

True

False

True

False

Choral Response: Add or Subtract in Unit and Standard Form Students add or subtract units of ones or tens to develop place value understanding. Display 2 ones + 1 one = _____ . What is 2 ones + 1 one? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 3 ones Display the answer: 3 ones.

2 ones + 1 one = 3 ones 2+1=3 2 tens + 1 ten = 3 tens 20 + 10 = 30

267

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

Display the equation with the numbers in standard form. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.) 2+1=3 Continue with 2 tens + 1 ten = _____. Repeat the process with the following sequence:

3 ones + 2 ones

5 ones + 2 ones

3 ones + 4 ones

4 ones + 5 ones

2 ones – 1 one

3 tens + 2 tens

5 tens + 2 tens

3 tens + 4 tens

4 tens + 5 tens

2 tens – 1 ten

3 ones – 1 one

3 ones – 2 ones

5 ones – 2 ones

5 ones – 3 ones

3 tens – 1 ten

3 tens – 2 tens

5 tens – 2 tens

5 tens – 3 tens

Launch

10 30

Materials—T: 100-bead rekenrek

Students add tens 10 on the rekenrek and use the place value chart to represent them. Show the rekenrek with 17 beads on the left side. How many beads? 17

268

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 19

Starting on the third row, slide 3 rows of beads to the left. Slide each row all at once. How many beads? How do you know? 47 beads; I counted on by tens: 17, 27, 37, 47. There was 1 ten and you added 3 more. That makes 4 tens 7 ones, or 47. Display the double place value chart. We started at 17. (Write 17.) And we ended up at 47. (Write 47.) What do you notice about the digits in 17 and 47?

tens

ones

tens

ones

The digit in the ones place is the same. The digit in the tens place changed. It is 3 more. The digit in the tens place is 3 more than in 17 because we added 3 tens. (Point to 47.) What is the value of 3 tens? 30

Write + 30. Present a new problem. Show the rekenrek with 25 beads on the left side. How many beads? 25 Starting on the fourth row, slide over 5 rows of beads to the left. Slide each row all at once.

269

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

How many beads? How do you know? 75 beads; I counted on by tens: 25, 35, 45, 55, 65, 75. There were 2 tens and you added 5 more. That makes 7 tens 5 ones, 75. Display the place value chart. We started at 25. (Write 25.) And we ended up at 75. (Write 75.)

tens

ones

tens

ones

What do you notice about the digits in 25 and 75? The digit in the ones place is the same. The digit in the tens place changed. It is 5 more. The digit in the tens place is 5 more than in 25 because we added 5 tens. (Point to 75.) What is the value of 5 tens?

50 Write + 50. Transition to the next segment by framing the work. Today, we will notice how the digit in the tens place changes when we add tens to two-digit numbers.

270

10 EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 19 10

Learn

30 10

Add Tens to Two-Digit Numbers Materials—T/S: Double Place Value Chart removable

Students add and represent their work by using place value charts. Make sure that students have the Double Place Value Chart removable inserted into a whiteboard. Show the removable and have students follow along as you write the following into the chart:

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19 ▸ Double Place Value Chart

41 + 30 = 71

• 41 + 30 = _____ , in the rectangle at the top • 41, in the place value chart on the left • 30, below the arrow, next to the plus sign Tell students to draw quick tens to represent 41. Demonstrate drawing 4 tens and 1 one. Point to the equation and ask students whether it is addition or subtraction.

tens

ones

tens

ones

211

Ask students to draw 3 more tens to represent 30. EM2_0105SE_D_L19_removable_place_value_chart.indd 211

12/03/21 7:46 PM

Let’s count on by tens from 41. 41, 51, 61, 71 Write 71 in the place value chart on the right. How many tens are in the first addend? 4 tens How many more tens did we add? 3 tens How many tens are in the total? 7 tens

271

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

Point to the corresponding digits on the place value charts as you revoice the numbers of tens as an addition problem. 4 tens + 3 tens = 7 tens Why did the digit in the ones place stay the same in both places? The ones stayed the same because we only added tens. We only added tens, so the digit in the ones place stayed the same. The digit in the tens place changes because we added tens. Write 71 to complete the original equation. Ask students to erase. Write 54 + 40 = _____ in the rectangle at the top of the removable. Ask students to write 54 in the place value chart on the left and 40 below the arrow next to the plus sign. Have students think–pair–share to find the total. They may draw tens and ones, count on by tens, or just add tens by using the place value charts. Ask students to write the total in the place value chart on the right and in the equation. Ask one or two students to share their work and bring the class to a consensus on the answer. If time allows, repeat the process with 36 + 60.

More Coins for Ko Students add tens to two-digit numbers and discuss what they notice about the digits. Play part 1 of the video, which shows Ko putting coins that total 17 cents in her pocket and then finding 3 dimes. Display the equation 17 + 30 = _____ . Have students think–pair–share to answer the following questions. They may choose to use their Double Place Value Chart removable to record their thinking.

272

17 + 30 =

Promoting Mathematical Practice Students look for and express regularity in repeated reasoning when they notice that adding tens to a two-digit number causes the digit in the tens place to change, but the digit in the ones place remains the same. Recognizing this pattern can help students make sense of strategies such as combining like units or making the next ten.

UDL: Representation Consider recoding and highlighting the digit in the ones place in the first addend and in the total of the equation. Record each equation to help students recognize the pattern of the digit in the ones place staying the same in the addend and the total.

41 + 30 = 54 + 40 = 36 + 60 = 17 + 30 = 47 + 20 =

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 19

How much money does Ko have? How do you know? 47 cents; she started with 17 cents, and then she found 3 dimes. We can count on by tens. 17, 27, 37, 47. 47 cents; 3 dimes is 3 tens. 1 ten + 3 tens = 4 tens. The 7 ones stay the same.

17 + 30 =

Write 47 to answer the equation. Play part 2 of the video, which shows Ko finding more dimes and throwing all her coins into the fountain. Display the equation 47 + 20 = _____ . Have students think–pair–share to answer the following question. They may use their Double Place Value Chart removable to record their thinking.

47 + 20 =

How much money did Ko throw into the fountain? How do you know? 67 cents; she found 2 dimes. We can count on by tens. 47, 57, 67. 67 cents. 2 dimes is 2 tens. She had 4 tens and 7 ones. 4 tens + 2 tens = 6 tens. The ones stay the same, 7.

47 + 20 =

Write 67 to answer the equation. What happens to the digits when we add tens to a number? The digit in the tens place gets bigger but the ones place stays the same.

273

10 EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19 30

Land Debrief

5 min

Objective: Add tens to a two-digit number. Display the three equations. Direct students’ attention to the first equation, 30 + 20 = _____ . Ask students to solve it mentally or with fingers and give a silent signal when they are ready. Have the class chorally share the total. Write the total.

30 + 20 =

Direct students’ attention to 35 + 20 = _____ . Have students think–pair–share to find the total by using mental math or fingers. How did you find the total?

35 + 20 =

I saw 3 tens and 2 tens. That is 5 tens. There are 5 ones. 5 tens 5 is 55. I counted on. 35, 45, 55. I know 30 + 20 = 50 and 5 more is 55. Write the total. Direct students’ attention to 20 + 35 = _____ . Have students think–pair–share to find the total.

20 + 35 =

How did you find the total? This problem is the same as 35 + 20. The parts are just in a different order. I saw 2 tens and 3 tens. That is 5 tens. There are 5 ones. 5 tens 5 is 55. I counted on from the second addend because it’s bigger. 35, 45, 55. Write the total.

274

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 19

These last two problems show us that we can add in any order. Look at all three number sentences. What happens to the digits when we add tens to a number? The digit in the tens place changes. It gets bigger. But the digit in the ones place stays the same.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

275

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

Name

Read Baz has 35 berries.

Read

He picks 20 more berries.

Kit has 3 boxes of crayons and 4 more.

How many berries does he have now?

She gets 2 more boxes.

Draw

How many crayons does she have now? Draw

10 10

Write

35 + 20 = 55

34 + 20 = 54 Kit has

276

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

Baz has

crayons. 213

214

PROBLEM SET

berries.

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 19

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 19

3. Add.

32 + 30 =

= 28 + 60

70 + 18 =

49 + 20 =

66 + 30 =

= 50 + 43

PROBLEM SET

215

277

LESSON 20

Add ones and multiples of ten to any number.

EUREKA MATH2

1 ▸ M5 ▸ TD

Name

EUREKA MATH2

1 ▸ M5 ▸ TD

2. Circle the number sentence if it is true. Draw an X on the number sentence if it is false.

1. Add or subtract.

30 + 40

20 + 30

2 tens + 2 tens = 4 tens

60 - 20 =

35 + 40 =

225

226

TO P I C T I C K E T

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 20

Lesson at a Glance Students engage in choral counting and notice patterns in the tens and ones places. Then they add a string of numbers, two at a time, to get to 100 (or more). Students self-select strategies to use in a variety of problems, including adding ones to a multiple of ten and adding ones or a multiple of ten to a two-digit number.

Key Question • How does looking at the digits in the tens and ones places help you to add?

Achievement Descriptors 1.Mod5.AD6 Add a two-digit number and a multiple of 10 that have a sum within 100. 1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 50,

relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Add to 100 cards must be torn out of student books, cut apart, and shuffled. Each pair of students needs one set of cards. Consider whether to prepare these materials in advance or to have students tear out, cut, and shuffle them during the lesson.

Launch Learn

10 min 10 min

30 min

• Get to 100

• Chart paper (3 pieces) • Marker • Add to 100 cards (digital download)

• Add to 100

Students

• Problem Set

• Add to 100 cards (1 set per student pair, in the student book)

Land

10 min

• Chart paper (1 piece per student pair)

• Copy or print the Add to 100 cards to use for demonstration.

• Marker

279

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

Fluency

10 10

Beep Counting: 10 More, 10 Less Students complete30 a number sequence to build fluency with mentally finding 10 more or 10 less than a number. 10

Invite students to participate in Beep Counting. Listen carefully as I count on or count back by tens. I will replace one of the numbers with the word beep. Raise your hand when you know the beep number. Ready? Display the sequence 39, 49, _____ . 39, 49, beep. Wait until most students raise their hands, and then signal for students to respond.

39, 49, 59

59 Display the answer. Repeat the process with the following sequence:

62,

, 82

, 95, 105

, 14, 24

66, 56,

87,

, 67

, 13, 3

, 91, 81

Choral Response: True or False Number Sentences Students determine if a number sentence is true or false to prepare for reasoning about the equality of equivalent expressions in lesson 25. Display the number sentence 4 + 8 = 8 + 4. Is this number sentence true or false? Raise your hand when you know. 280

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 20

Wait until most students raise their hands, and then signal for students to respond. True Display the answer. Repeat the process with the following sequence:

4+4+4=8+4

6+9=9+6

1+9+5=6+9

3+7+3=6+7

True

5 + 8 = 10 + 4

9+7=6+5+4

2+4+8=8+2+4

14 – 8 = 6 + 8

False

True

False

Choral Response: Add or Subtract in Unit and Standard Form Students add or subtract units of ones or tens to develop place value understanding. Display 2 ones + 2 ones = _____ . What is 2 ones + 2 ones? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 4 ones

2 ones + 2 ones = 4 ones 2+2=4 2 tens + 2 tens = 4 tens 20 + 20 = 40

Display the answer. On my signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.) 2 ones + 2 ones = 4 ones Copyright © Great Minds PBC

281

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

Display the equation with the numbers in standard form. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.) 2+2=4 Continue with 2 tens + 2 tens = _____ . Repeat the process with the following sequence:

4 ones + 2 ones

6 ones + 3 ones

3 ones + 4 ones

2 ones + 7 ones

3 ones – 1 one

4 tens + 2 tens

6 tens + 3 tens

3 tens + 4 tens

2 tens + 7 tens

3 tens – 1 ten

5 ones – 2 ones

6 ones – 3 ones

6 ones – 2 ones

7 ones – 4 ones

5 tens – 2 tens

6 tens – 3 tens

6 tens – 2 tens

7 tens – 4 tens

Launch

10 30

Materials—T: Chart paper, marker

Students choral count by tens and notice patterns. 10 Gather the class and show them the chart paper in landscape orientation. Begin a first column by writing 50 in the top left corner of the paper. Take a moment to think about what the next few numbers would be if we count by ones. Show thumbs-up when you are ready. Invite students to chorally count by ones starting at 50. Record the count in rows. Start a new row with the next ten. Ask students to watch the marker carefully so the recording 282

Teacher Note Recording choral counts on chart paper allows students to notice patterns. They may also revisit previous counts to look for additional patterns, confirm how to write certain numbers, or simply enjoy recounting.

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 20

guides their pace and lets the class sound like one unified voice. Leave ample space around each number to record patterns that students may notice later. Count and record up to 69. Under 60, draw a line to start the third row. Do not write 70 yet. What number comes next? How do you know? 70; it comes after 69. 50, 60, 70. It is counting by tens as you go down. Write 70 on the line. Continue to count and record up to 85. Draw three lines and circle the third line (where 88 belongs). What number goes here? How do you know? 88. I counted on 3. 88. I see a pattern counting by tens: 58, 68, 78, 88. Write 86, 87, and 88 on the three lines. Continue to count and record up to 99. Draw a line where 100 belongs. What number goes here? How do you know? 99, 100. I counted on. I see a pattern with tens: 50, 60, 70, 80, 90. The next ten is 100.

283

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

Write 100 on the line. Circle the first column and label it tens. Guide students to count by tens the math way from 10 to 100 to help students see that 10 tens make 100. 100 is 10 tens.

Teacher Note Students do not need to master the concept that 10 tens make 100 in grade 1.

As time allows, invite students to share other patterns they see. The following are possible observations: • As you move down the columns, the numbers increase by 10. • As you move up the columns, the numbers decrease by 10. • In the columns, the tens digits change but the ones digits stay the same. • In the rows, the ones digits change but the tens digits stay the same. Label or highlight observations directly on the chart. Consider using a different color for each pattern students notice. Encourage place value language by reminding students to use the words tens and ones as they share their ideas. Consider asking students to revoice other students’ patterns in their own words, e.g., “She saw a pattern of adding 10.” Transition to the next segment by framing the work. Today, we will add ones and tens and try to get to 100.

284

10 EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 20 10

Learn Get to 100

30 10

Materials—T: Chart paper, marker

Students add a string of ones and tens to get to 100 as a class. Show students chart paper in landscape orientation. Begin a row by writing 6 and then 30 in the top left corner of the paper. Draw a box around each number. Ask students to find the total of 6 and 30 by using mental math or on their personal whiteboard. Students may use a number path or cubes if needed. Have them give a silent signal when they are ready.

UDL: Action & Expression Help students recall that mathematicians take time to plan and make sense of the addends before deciding on a strategy. Consider guiding students’ thinking aloud decision making by providing sentence frames such as this one: If I had a problem that was tens plus ones, such as ___, then I would choose ___ strategy because I know ___ .

36; there are 3 tens and 6 ones.

Provide sentence frames to help with think-aloud strategies for other combinations, such as:

30 and 6 is 36.

• Tens + tens

What is the total? How do you know?

Draw to represent each number and record the addition the arrow way below your drawing. Next to 30, write the number 40 and draw a box around it. Ask students to add 36 and 40. Have them give a silent signal when they are ready. After they share the total, draw to represent 40 and record the addition the arrow way. Next to 40, write the number 4 and draw a box around it. Repeat the process of having students add the numbers and share the total. Draw and record the process on the chart. We are at 80. Have we gotten to 100 yet? How do you know? No, 80 comes before 100. We are not yet at 100. 8 tens make 80, and 10 tens make 100. Let’s add another number. Turn and talk: Which number should we add to make 100?

• Two-digit numbers + ones • Two-digit numbers + tens After they work, ask students how they solved the problem and how well their strategy worked for them. Ask them if they would use the same strategy next time or try another one.

Teacher Note The picture book Let’s Count to 100! by Masayuki Sebe may complement this lesson. It features 100 unique objects that invite children to search and count. Masayuki Sebe has authored many books featuring 100. Students may also enjoy 100 People, 100 Things, 100 Animals on Parade, and 100 Hungry Monkeys.

285

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

Next to 4, write the number 20 and draw a box around it. Repeat the process of having students add the numbers and share the total. Draw and record the process on the chart. Differentiation: Challenge

Add to 100 Materials—T: Add to 100 cards, chart paper; S: Add to 100 cards, chart paper, marker

Vary the activity by having students lay out all the cards faceup. Ask them to strategically choose cards to get as close to 100 as they can without going over 100.

Students practice adding tens and ones to get to 100.

• Place the cards in a pile, facedown. • Each partner chooses a card. Partners place their cards side by side at the top of the chart paper.

2 3 4 7 8 9 30 40 50

10 20 30

• After the first round, partners take turns choosing one card and placing it in the row of numbers at the top of the chart paper. • With each new card, partners work together to add the amount on the new card to the previous total. • Partners play until they reach or pass 100, or until time is up. Partner students and distribute a piece of chart paper and a set of cards to each pair.

How can you show your thinking?

6 6

30 + 30

36 286

10 + 10

Consider saving the Add to 100 cards for students to practice with at other times of the day. Partners could do the same activity again or they could do the challenge variation. Alternatively, they could each choose two cards and find the total. Then partners can compare their totals to see which is greater (or less).

Differentiation: Support Draw quick tens to represent the addends in each expression.

As partners play, advance and assess their thinking by asking the following questions. What is the total now? How did you find it?

Teacher Note

1 ▸ M5 ▸ TD ▸ Lesson 20 ▸ Add to 100

219

• Partners find the total and record their thinking directly below the cards. They can show their work in any way they choose. They do not need to use the arrow way or drawings from the previous segment.

0 1 5 6 10 20 60 70

EUREKA MATH2

Ask a volunteer to be your partner to demonstrate the activity. Use the following procedure:

2 56

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 20

Land Debrief

5 min

Objective: Add ones and multiples of ten to any number. Display the expressions. Engage students in the Take a Stand routine.

50 + 37

57 + 30

Look at these two problems. Turn and talk: Do they have the same total? How do you know?

Promoting Mathematical Practice

Ask students to stand if they think the problems have the same total, and then have them sit down. Ask students to stand if they think the problems do not have the same total, and then have them sit down. Invite students from each group to share their reasoning. Record their thinking. They have the same total. In both problems there are 5 tens and 3 tens. They’re just in a different order. But we can add in any order, so there are 8 tens in both problems. In both problems there are only 7 ones.

50 + 37

57 + 30

Students look for and make use of structure when they use place value reasoning to show that 50 + 37 and 57 + 30 have the same total. This Land allows students to expand their intuitive understanding of the commutative property of addition. Students already know that they can add in any order, and here they reason that they can decompose the numbers into tens and ones and add those parts in any order without changing the total.

Write an equal sign between the expressions.

287

1 ▸ M5 ▸ TD ▸ Lesson 20

EUREKA MATH2

Even though the addends aren’t the same, the totals are the same. In both problems there are 5 tens, 3 tens, 7 ones, and 0 ones. How does looking at the digits in the tens and ones places help you to add? We can just add the tens or ones. We do not need to count on. We can use easy facts to help us add the tens and then the ones. Then we can put it all together.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

288

EUREKA MATH2 1 ▸ M5 ▸ TD ▸ Lesson 20

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

Name

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

Read Kit has these marbles.

Read

She gets 12 more.

Liv has these nuts.

How many marbles does she have?

She gets 20 more.

Draw

How many nuts does she have?

Draw

10 10

Write

23 + 20 = 43 Liv has

40 + 12 = 52

nuts.

Kit has 221

222

PROBLEM SET

marbles.

289

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

EUREKA MATH2

1 ▸ M5 ▸ TD ▸ Lesson 20

3. Add. Show how you know.

45 + 4 =

60 + 30 + 3 =

= 63 + 2

30 + 20 + 10 =

45 + 40 =

15 + 50 =

66 + 30 =

290

= 72 + 10

PROBLEM SET

223

Topic E Addition of Two-Digit Numbers Now that students have experienced adding two-digit numbers to one-digit numbers and adding a multiple of 10 to a two-digit number, they are ready to add 2 two-digit numbers. Students leverage place value understanding to make problems easier. They use a variety of concrete, pictorial, and abstract tools to model addends as tens and ones. Students record their reasoning by using a written method and then explain their strategy. The goal of topic E is to build number sense that allows students to flexibly manipulate two-digit addends. At first, students self-select ways to combine groups of cubes that represent 2 two-digit numbers. They share how they decomposed each group and combined the resulting parts. Subsequent lessons present the three following ways to add 2 two-digit numbers: • Add like units: Decompose both addends into tens and ones, combine tens with tens and ones with ones, and then put tens and ones together. • Add tens first: Decompose one addend into tens and ones, combine the tens with the other addend, and then add the ones. • Make the next ten: Decompose one addend into tens and ones, combine some (or all) of the ones with the other addend (in many cases to make the next ten), and then add the remaining parts. Add Like Units

292

Add Tens First

Make the Next Ten (Add Ones First)

EUREKA MATH2 1 ▸ M5 ▸ TE

These three strategies present different ways to add 2 two-digit numbers, primarily to promote flexible thinking; mastering each of the strategies is less important than attaining flexible thinking. When students compare their various recordings, it helps them to identify equivalent expressions that make a problem easier. For example, 35 + 15 is equivalent to 30 + 5 + 10 + 5, but the second expression makes it easy to add 3 tens + 1 ten and 5 + 5. This type of discussion leads students to the general understanding that different ways of thinking about a problem result in the same total. Using Level 3 strategies, such as those presented in this topic, takes time and practice. Students may self-select the strategies and tools they use to solve the problems, as long as they are able to record and explain their solution pathways.

293

EUREKA MATH2

1 ▸ M5 ▸ TE

Progression of Lessons Lesson 21

Lesson 22

Lesson 23

Use varied strategies to add 2 twodigit addends.

Decompose both addends and add like units.

Decompose an addend and add tens first.

I can break up the addends into tens and ones. Then I can combine the tens with tens and ones with ones.

I can break up an addend into tens and ones. Then I can add the tens first to the first addend.

I can break up the tens and ones and combine them in different ways.

294

EUREKA MATH2 1 ▸ M5 ▸ TE

Lesson 24

Lesson 25

Decompose an addend to make the next ten.

Compare equivalent expressions used to solve two-digit addition equations.

40 is the next ten. 35 needs 5 more. I can break up 25 into 5 and 20 to make 40.

The number sentence is true because both sides equal 40. We can make easier problems by combining the parts in different ways.

295

LESSON 21

Use varied strategies to add 2 two-digit addends.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 21

Name

Draw as tens and ones. Add.

15 + 14 =

Lesson at a Glance Students use place value strategies to combine pairs of two-digit numbers. They represent the addends with cubes, and then they selfselect ways to combine the parts using tens and ones. Students share and discuss their strategies.

Key Question

• What are some ways to combine groups of cubes to find the total?

Achievement Descriptor 1.Mod5.AD8 Add 2 two-digit numbers that have a sum within 50,

relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

233

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 21

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Make 50 cards must be torn out of student books and cut apart. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. Consider saving the cards for use in lesson 22.

Launch Learn

10 min 10 min

30 min

• Combine Tens and Ones

• 100-bead rekenrek • Make 50 cards (digital download) • Chart paper (2 sheets)

• Make 50

Students

• Problem Set

• Unifix® Cubes (40)

Land

• Make 50 cards (1 set per student pair, in the student book)

10 min

• Copy or print the Make 50 cards to use for demonstration. Consider saving this set for demonstration in lesson 22.

297

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 21

Fluency

10 10

Choral Response: Add a Multiple of 10 on the Rekenrek 30 rekenrek Materials—T: 100-bead

Students add 10 and 20 to a two-digit number 10 to prepare for adding pairs of two-digit numbers. Show students the rekenrek. Start with 14 beads to the left side. How many beads? (Gesture to the 14 beads.) 14 How many beads will there be if I slide over 10 more? 24

Student View

Let’s check! (Slide over 10 beads in the third row all at once.) 10 (Point to the third row.) 20 (Point to the top row.) 4 (Point to the beads in the second row.) Yes! 14 + 10 = 24. Slide the third row of beads back to the right side, again showing 14 on the rekenrek. How many beads? (Gesture to the 14 beads.) 14 How many beads will there be if I slide over 20 more? 34 Let’s check! (Slide over 20 beads in the third and fourth rows all at once.) 20 (Point to the third and fourth rows.) 30 (Point to the top row.) 4 (Point to the 4 beads in the second row.) Yes! 14 + 20 = 34.

298

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 21

Repeat the process of adding 10 and 20 to the following sequence of starting numbers:

Choral Response: Add Multiples of 10 Students add multiples of 10 to develop fluency with strategies for adding pairs of two-digit numbers. Display the equation 10 + 10 = . What is 10 + 10? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 20

10 + 10 = 20

Display the answer.

Teacher Note

Repeat the process with the following sequence:

20 + 10 = 30

40 + 10 = 50

20 + 20 = 40

30 + 20 = 50

20 + 40 = 60

20 + 60 = 80

60 = 10 + 50

80 = 10 + 70

50 + 20 = 70

Use the rekenrek or restate the problem in unit form to support students with the task. Consider using one or both supports for the first few problems, as the addends increase, or if students hesitate.

299

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 21

Whiteboard Exchange: Make Ten to Add

Teacher Note

Students make ten to prepare for adding pairs of two-digit numbers. Display the equation 9 + 2 = _____ . Write the equation. Break apart one addend to make ten and find the total. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

9 + 2 = 11 1 1 9 + 1 = 10 10 + 1 = 11

Display the number bond, the equations, and the total. Repeat the process with the following sequence:

3 + 9 = 12

8 + 3 = 11

4 + 8 = 12

11 = 7 + 4

11 = 6 + 5

14 = 5 + 9

12 = 5 + 7

Launch

30cards, chart paper Materials—T: Make 50

Students self-select ways to combine two groups of cubes that show 10 tens and ones.

Students may choose to decompose either addend to make ten. The following sample solution demonstrates another way to add 9 and 2.

9 + 2 = 11 1

8 8 + 2 = 10 10 + 1 = 11

Differentiation: Support If students need support with the strategy, consider using the following questions and prompt: • Which addend is closer to 10? • How many more do we need to make ten? • Use a number bond to decompose the other addend to make ten.

Gather students and present the two Make 50 cards that show 25 and 23, cubes side up. Use the Math Chat routine to engage students in mathematical discourse. Today we are going to make 50. Turn and talk to make a good guess. If we add the cubes on these cards, will the total be 50 cubes? 300

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 21

Allow 1 or 2 minutes for students to find the total number of cubes on the cards. They may self-select tools such as cubes or personal whiteboards as needed. Have students show a silent signal when they are ready. Invite students to discuss their ideas with a partner. Listen for the following ways of thinking about tens and ones to add: • Add like units: For example, 2 tens + 2 tens = 4 tens. 5 ones + 3 ones = 8 ones. 4 tens 8 ones is 48. • Add tens first: For example, 25 + 20 = 45. 45 + 3 = 48. • Add ones first: For example, 25 + 3 = 28. 28 + 10 + 10 = 48. Facilitate a class discussion by inviting two or three students who used different ways of thinking to explain their ideas to the whole group. Record their ideas, which may differ from the samples shown. Have students refer to the Talking Tool as needed.

Teacher Note This lesson highlights three ways to decompose and combine addends. Students do not need to know or use the names of the three ways. The names are intended to help teachers understand each way of thinking. Students can show and explain how they decomposed the quantities and combined the resulting parts in any way that makes sense to them. Help students articulate their ideas by asking the following questions: • How did you break up the addends? • How did you combine the parts? Experience with decomposing and combining numbers builds number sense and supports working with more abstract numerical representations in upcoming lessons.

Differentiation: Challenge

Write 25 + 23 = 48.

Invite students to explain how they could change one of two Make 50 cards so that the total of the two cards would make exactly 50.

Did we make 50? Why? No. 48 is not 50. We need 2 more. Transition to the next segment by framing the work. To add the cubes on the cards, we thought about tens and ones in different ways. Today, we will combine other cards that show tens and ones to try to make 50.

301

10 EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 21 10

Learn

Teacher Note

30 10

Combine Tens and Ones

When using the cards, cubes, or quick ten drawings to add, students may arrange the addends next to one another or put one addend below the other.

Materials—T: Make 50 cards; S: Unifix Cubes

Students use Unifix Cubes to add two numbers with tens and ones. Pair students and assign each partner as partner A or partner B. Distribute cubes. Present the two Make 50 cards that show 35 and 15 cubes, cubes side up. Tell each partner to choose a card and use their cubes to make the number shown on it. Work together to find the total number of cubes. Let’s see if they make 50. Circulate and look for different ways to find the total. The following chart shows sample work based on the three ways of thinking that are described in Launch.

Add Like Units

35 + 15 30 + 10 + 5 + 5 40 + 10 = 50

302

Add Ones First (May Make the Next Ten)

Add Tens First

= 35 + 15 35 + 10 = 45 45 + 5 = 50

= 35 + 15 35 + 5 = 40 40 + 10 = 50

Differentiation: Challenge Consider having students combine the amounts by using number bonds and number sentences rather than by using cubes. 35 + 15 = 50 30 5

10 5

40 10 50

35 + 15 = 50 45

10 50

35 + 15 = 50 40

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 21

Invite two or three student pairs to share their work. Students may or may not share all of the ways shown in the chart. After the discussion, use cubes to demonstrate any way that was not discussed. What is the total? How do you know? 3 tens and 1 ten is 4 tens. 5 ones and 5 ones is 10. 5 tens is 50. 35 and 10 makes 45. 45 and 5 makes 50. 35 and 5 ones make 40. 40 and 10 is 50. Write 35 + 15 = 50. We made 50. Let’s try another one. Present the two Make 50 cards that show 19 and 32 cubes. Have partners choose a card and use their cubes to make the addend shown on it. Before you add, take time to make sense of the cubes. Think about how you can make this problem easier. What could you combine first? Invite students to talk with their partner and then combine the amounts. Ask one or two pairs who use different ways to solve the problem to share them with the class. If any of the following ways remain unshared, show 19 and 32 with cubes and demonstrate that thinking. Invite students to show thumbs-up if they did something similar. • Add like units: Combine 1 ten with 3 tens and 9 ones with 2 ones, and then add 40 and 11. • Add tens first: Break apart 32 into tens and ones. Add the tens and then the ones to 19. • Add ones first (may make the next ten): Break up 32 into 1 and 31. Make 20 with 19 and 1. Then find 20 + 30 + 1. We went over 50 this time! Turn and talk. Which way makes it easiest for you to add?

303

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 21

Make 50 Materials—S: Make 50 cards, cubes

Students use concrete models to combine two sets of tens and ones. Keep students paired. Demonstrate how to play Make 50. • Arrange the 18 Make 50 cards cubes side up. • Partners try to make as many pairs that equal 50 as they can. • Partner A goes first. Partner A chooses two cards and finds the total.

Differentiation: Support Adjust the level of difficulty by strategically removing pairs of cards from the set. For example, consider removing 23 and 27, 24 and 26, or 32 and 18.

• If the total is exactly 50, they get to keep the cards. If it is not 50, they put the cards back. • Then it is partner B’s turn to do the same thing. Distribute the Make 50 cards to partners. Students may find totals by using cubes, by drawing tens and ones, or by using mental math. No matter which tool they use, encourage students to explain how they decomposed the parts to find the total. Have students play for 6 or 7 minutes. Circulate and notice how students add. Which of the following ways do they use? • Add like units (tens/tens and ones/ones). • Add tens first. • Add ones first (may make the next ten).

Problem Set Differentiate the set by selecting problems for students to finish within the shorter timeframe. Problems are organized from simple to complex. Directions may be read aloud. Students may self-select tools and ways to solve the problems. 304

UDL: Engagement Students may not choose the most efficient way to add. Honor students’ choices by offering feedback that acknowledges their effort and use of prior knowledge. Here are a few examples. • You thought about a way to use tens and ones to help you add. I see you combined tens first, and then ones. • You used what you know about making ten to help you add. It looks like you decided to add ones to make ten first. • You remembered we can break up an addend to help us add. It looks like you added the tens from this card to the first set of cubes.

10 EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 21 30

Land Debrief

5 min

Materials—T: Make 50 cards, chart paper

Objective: Use varied strategies to add 2 two-digit addends. Present the two Make 50 cards that show 25 and 25. Show thumbs-up if you think these cubes make 50. Show thumbs-down if you think they do not make 50. Invite students to think–pair–share about the ways the cubes could be combined. What are some ways we could combine these cubes to add them? Listen for students who share one of the three ways highlighted in the lesson. Invite them to share and record their thinking. Share any of the three strategies that students do not mention.

Promoting Mathematical Practice As students work with addition expressions in which both addends are two-digit numbers, they make sense of problems and persevere in solving them. As the numbers that students are expected to work with get larger, the most efficient way to do so increasingly depends on what students are comfortable with and their own developing number sense. Encourage students to make sense of the problem as they see fit. The use of cubes can help students persevere if their number sense is not yet strong enough to lean on when working with large addends.

305

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EUREKA MATH2

Write 25 + 25 = 50. We made 50 again! Turn and talk. Which way is easiest for you to add two sets of cubes that have tens and ones? We can add tens and ones. We can also add the tens or the ones first. These are all ways to add 2 two-digit numbers.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

306

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 21

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 21

Name

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 21

2. Use cubes or draw as tens and ones. Sample: Add.

1. Write the total. Show how you know.

Total

11 + 18 =

19 + 15 =

34 10 + 10 + 10 + 4 = 34

3. Add.

Total

Show how you know.

26 + 14 =

30 + 10 = 40 231

232

PROBLEM SET

307

LESSON 22

Decompose both addends and add like units.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

Name

Add. Show how you know.

14 + 26 =

Lesson at a Glance Students add 2 two-digit numbers by decomposing both addends into tens and ones and then combining tens with tens and ones with ones. After guided practice using quick tens and number bonds to model problems, students practice doing this with a partner.

Key Question

18 + 16 =

• How does breaking up two-digit addends into tens and ones help us to add?

Achievement Descriptors 1.Mod1.AD6 Determine whether addition and/or subtraction number

sentences are true or false. 1.Mod5.AD8 Add 2 two-digit numbers that have a sum within 50,

relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

243

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 22

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Make 50 cards must be torn out of student books and cut apart. Consider whether to prepare these materials in advance, to have students assemble them during the lesson, or to use the ones prepared in lesson 21.

Launch Learn

10 min 10 min

30 min

• 100-bead rekenrek • Make 50 cards (digital download)

• Add Like Units

Students

• Make 50

• Make 50 cards (1 set per student pair, in the student book)

• Problem Set

Land

10 min

• Unifix Cubes ®

• Copy or print the Make 50 cards for demonstration, or use the ones prepared in lesson 21.

309

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

Fluency

10 10

Choral Response: Add a Multiple of 10 on the Rekenrek 30 rekenrek Materials—T: 100-bead

Students add 10, 20, 30, or 40 to a two-digit 10 number to develop fluency with strategies for adding pairs of two-digit numbers. Show students the rekenrek. Start with 11 beads to the left side. How many beads? (Gesture to the 11 beads.) 11 Student View

How many beads will there be if I slide over 10 more? 21 Let’s check! (Slide over 10 beads in the third row all at once.)

10 (Point to the third row.) 20 (Point to the top row.) 1 (Point to the bead in the second row.) Yes! 11 + 10 = 21. Slide the third row of beads back to the right side, again showing 11 on the rekenrek. Repeat the process, this time adding 20 more beads. Repeat the process of adding multiples of 10 to the following sequence of starting numbers:

310

Add 20 Add 30

Add 30 Add 40

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 22

Choral Response: Add Multiples of 10 Students add multiples of 10 to develop fluency with strategies for adding pairs of two-digit numbers. Display the equation 30 + 10 = _____ . What is 30 + 10? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 40

30 + 10 = 40

Display the answer. Repeat the process with the following sequence:

40 + 10 = 50

60 + 10 = 70

30 + 20 = 50 50 + 20 = 70

60 = 30 + 30

80 = 50 + 30

70 = 30 + 40

20 + 40 = 60

90 = 30 + 60

Whiteboard Exchange: Make Ten to Add Students make ten to prepare for extending the strategy to adding pairs of two-digit numbers. Display the equation 9 + 4 = _____ . Write the equation. Break apart one addend to make ten and find the total.

9 + 4 = 13 1 3 9 + 1 = 10 10 + 3 = 13 311

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the number bond, the equations, and the total. Repeat the process with the following sequence:

6 + 9 = 15

8 + 5 = 13

7 + 8 = 15

13 = 7 + 6

16 = 7 + 9

12 = 6 + 6

17 = 8 + 9

Launch

10 30

Students share and discuss different ways to add two sets of dimes and pennies. Present the problem 10 and use the Math Chat routine to engage students in mathematical discourse. Display the hands holding coins. Two friends each have some coins. What coins do they each have? 2 dimes and 4 pennies They are wondering how much money they have together.

Teacher Note Students may draw the two addends horizontally or vertically to show how they combined the tens and ones in a variety of ways.

10 10

Give students 1 or 2 minutes of think time to find the total. Students may self-select tools such as coins, drawings, number sentences, number bonds, or mental math to find the total. Have them show a silent signal when they are ready. Invite students to discuss their ideas with a partner. Listen for students who find the total by combining tens with tens (dimes) and ones with ones (pennies).

312

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 22

Facilitate a discussion by inviting two or three students to share their thinking with the class. Have students refer to the Talking Tool as needed. Revoice or demonstrate combining tens with tens and ones with ones. Draw the coins as shown in the sample. Many of you combined the dimes and pennies to find the total.

10 10 10 10

(Circle the tens.) How many dimes, or tens, are there? 4 tens

Teacher Note In the discussion, keep the focus on how students decompose and combine the addends to find the total rather than on the tool or model they use. They may select to use any of the following tools or models:

How many is 4 tens?

• Decompose both addends and add like units (tens/tens, ones/ones).

• Decompose an addend and add tens first.

Label the tens 40.

• Decompose an addend and add ones first (may make the next ten).

(Circle the ones.) How many pennies, or ones, are there? 8 ones Label the ones 8. (Draw arms.) What is 40 and 8? 48 Write the total and then write the number sentence 24 + 24 = 48. Each hand holds 24 cents. Together, they have 48 cents. Point to the digits in the tens place: 2, 2, and 4. 2 tens and 2 tens make 4 tens. Did we make a new ten when we combined the ones? No. Transition to the next segment by framing the work. Today, we will add two-digit numbers together by adding tens to tens and ones to ones. We will see if we make a new ten!

313

10 EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22 10

Learn

30 10

Add Like Units Materials—T: Make 50 cards

Students decompose numbers into tens and ones and add like units. Present the Make 50 cards that show 11 and 39, number side up. Let’s try and make 50 again. Turn and talk: If we add the numbers on these cards, do you think they will make 50?

Make sure students have personal whiteboards. Demonstrate interactively as students follow along. Instead of using cubes, we will draw these numbers as tens and ones to find the total. Write 11 + 39 = _____ . Then draw 11 as 1 ten 1 one. This shows 11. Let’s draw the other addend, 39, under 11. That makes it easier to see the tens and ones in both numbers. Draw 39 as 3 tens 9 ones. Let’s combine the tens. (Circle the tens.) How many is 4 tens? 40 Label the tens 40. Let’s combine the ones. (Circle the ones.) How many is 10 ones? 10 Label the ones 10. What is 40 and 10? 50

314

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 22

Write 40 + 10 = 50. So what is 11 + 39? 50 Write 50 to complete the original equation. We broke up the addends 11 and 39. Invite students to think–pair–share about how they combined the tens and ones. What parts did we combine? We combined the tens with tens and the ones with ones. Confirm students’ thinking by revoicing their ideas. Tell students to erase their whiteboard. Demonstrate the same problem by using number bonds as students follow along. Write 11 + 39 = . Draw arms from 11 and from 39 to make number bonds. How can we write each addend by using tens and ones? We can write 11 as 1 ten and 1 one. 39 is 3 tens and 9 ones.

Promoting Mathematical Practice Students look for and make use of structure when they find the total of an addition expression by breaking up the addends into tens and ones. Adding by making use of the place value structure of two-digit numbers allows students to rely on their established number sense with single digit numbers.

Write in the parts for each number bond. We have four parts. Let’s add tens to tens and ones to ones. Write 10 + 30 + 1 + 9. Draw arms from 10 and 30 and from 1 and 9 to make number bonds. Write in the total for each number bond as you state the equation. 10 + 30 = 40, and 1 + 9 = 10. 40 + 10 = 50, so 11 + 39 = 50. Write 50 to complete the original equation. Then, in the original equation, point to the digit in the tens place of each number (1, 3, and 5) and ask this question. 1 ten and 3 tens make 4 tens. The total has 5 tens. How did we make a new ten? When we put together 1 and 9, we made a ten. It was when we added the ones together. 1 and 9 make 10.

UDL: Action & Expression Before beginning with 45 + 18, prompt students to think about how many tens are in each addend, and how many total tens there are. Encourage them to use this thinking as a strategy they can use as they play Make 50 in the next segment. Prompt them to ask themselves these questions as they play: • How many tens are there? • Is that more than or less than 50?

315

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

Tell students to erase their whiteboard. Present the Make 50 cards that show 15 and 19, number side up. Repeat the process of modeling the problem by adding like units. Depending on the needs of your class, use either quick tens or number bonds to model the problem. Guide students to notice that by combining the ones, they composed a new ten and there were extra ones.

Make 50 Materials—S: Make 50 cards, Unifix Cubes

Students combine 2 two-digit numbers by decomposing them into tens and ones. Pair students and help them recall how to play Make 50. Tell students that this time they will play with the number side up on the cards rather than the cube side up as they did in lesson 21. • Arrange the 18 Make 50 cards with the number side up. • Partners try to make as many pairs that equal 50 as they can. • Partner A goes first. Partner A chooses two cards and finds their total. • If the total is exactly 50, partner A keeps the cards. If it is not 50, they put the cards back. • Then it is partner B’s turn to do the same thing. Distribute the Make 50 cards to partners. Tell students to show and explain how they decompose the parts to find the total. Encourage students to try combining tens and then ones, but allow them to self-select models (e.g., Unifix cubes, quick tens, number bonds) and ways of thinking about the problem. Have students play for 6 or 7 minutes. Ask assessing and advancing questions, such as the following.

Differentiation: Support Adjust the level of difficulty by strategically removing pairs of cards from the set. For example, consider removing 23 and 27, 24 and 26, or 32 and 18.

Teacher Note Students may add the addends in any order. For example, they may start with the larger addend first. Depending on the addends and their order, students may notice ways to solve the problem other than by adding like units. For example, the following recording shows adding ones first to make the next ten. Validate their thinking and the fact that there is more than one way to find the total.

Which pairs of cards make a total of 50? How do you know? How did you find the total? Which parts did you put together first? How can you show your thinking by using drawings, number bonds, or number sentences?

316

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 22

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. Directions may be 10 read aloud. Students may self-select tools and ways to solve the problems. 10

Land Debrief

5 min

Objective: Decompose both addends and add like units. Display the totem pole. Invite students to notice and wonder about it. This is a totem pole. Totem poles are logs that have been carved and painted. Each pole is unique to the culture that it represents. This is an eagle totem pole from an Inuit village.

Teacher Note Inuit clans take their names from nature, and often they include animals in their names such as the eagle, bear, beaver, and raven. This is an example of an Eagle Clan totem pole.

Ask students to count the number of feathers on each wing or tell them that there are 12. Write 12 + 12 = . How could we find the total number of feathers on the wings? We can break up each of the addends into 1 ten and 2 ones. Then we can add the tens and add the ones. Invite students to explain how number bonds can be used to show breaking apart 12. Record their thinking. Then ask them to share how to add the tens and the ones and record this process.

317

1 ▸ M5 ▸ TE ▸ Lesson 22

EUREKA MATH2

How many feathers are there on the wings? 24 feathers Did we make a new ten? No. Why not? We only had 2 ones and 2 ones. That makes 4 ones, not 10. How does breaking up two-digit addends into tens and ones help us to add? When we break apart numbers into tens and ones, we add easy numbers. If we didn’t break them up, the numbers would be hard to add because they’re so big.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

318

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 22

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

Name

3. Add. Show how you know.

1. Add tens to tens and ones to ones. Write the total.

10 + 4 + 10 + 5 =

10 + 9 + 10 + 1 =

20 + 4 + 20 + 1 =

20 + 7 + 10 + 4 =

2. Add.

15 + 15 =

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

16 + 16 =

14 + 14 =

27 + 23 =

15 + 16 =

25 + 18 =

10 10

239

240

PROBLEM SET

319

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 22

4. Circle the true number sentences. Put an X on the false number sentences.

= 20 + 5 + 20 + 5

22 + 15

= 10 + 2 + 10 + 5

12 + 19

= 10 + 2 + 10 + 9

10 + 6 + 10 + 7 =

320

10 + 6 + 7

PROBLEM SET

241

LESSON 23

Decompose an addend and add tens first.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

Name

Add. Show how you know.

18 + 22 =

26 + 16 =

Lesson at a Glance Students watch a video that shows adding 2 two-digit numbers by decomposing the second addend into tens and ones, adding the tens to the first addend, and then adding the ones. Students practice this as a class by modeling problems with drawings and number bonds. Then they play a new game to practice adding two-digit numbers.

Key Question • How does breaking up one addend into tens and ones help us to add?

Achievement Descriptors 1.Mod1.AD6 Determine whether addition and/or subtraction number

sentences are true or false. 1.Mod5.AD8 Add 2 two-digit numbers that have a sum within 50,

relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

251

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 23

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Assemble 10 cubes to make ten-sticks. Each student pair needs 5 ten-sticks. Save these for use in lesson 24.

Launch Learn

10 min 10 min

30 min

• Add Tens First • Total Capture • Problem Set

Land

10 min

• Unifix® Cubes (49)

Students • Eureka Math2 Numeral Cards (1 set per student group) • Unifix® Cubes (50 per student pair) • Total Capture gameboard (1 per student pair, in the student book) • Crayon

323

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

Fluency Numbers Up!

10 10

Materials—S: Numeral30 Cards

Students find an unknown total or part to prepare for unknown 10 addend problems. Have students form groups of three. Assign roles: Player A is one part, player B is one part, and player C is the total. Distribute sets of cards to each group and have them play according to the following rules. Consider doing a practice round with students. • Players A and B each take a card and hold it to their own foreheads so they can’t see the number. • Player C looks at both cards and says the total. • Players A and B find the number on their own card, based on the total and the other part. • Player C confirms the two parts. If the total is 8, and my partner has 5, I must have 3.

If the total is 8, and my partner has 3, I must have 5.

The total is 8.

Player C

Player A

Player B

Circulate as students play the game and provide support as needed. Have students switch roles after a few rounds.

324

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 23

Choral Response: Add a Multiple of 10 Students add 10 and 20 to a two-digit number to develop fluency with strategies for adding pairs of two-digit numbers. Display the equation 14 + 10 = _____ .

14 + 10 = 24

What is 14 + 10? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 24

14 + 20 = 34

Continue with 14 + 20 = _____ . Repeat the process with the following sequence:

16 + 10 = 26

19 + 10 = 29

21 + 10 = 31

24 + 10 = 34

32 + 10 = 42

16 + 20 = 36

19 + 20 = 39

21 + 20 = 41

24 + 20 = 44

32 + 20 = 52

Launch

UDL: Representation

Materials—T/S: Unifix30Cubes

Students represent the action in a video to add by combining tens first. 10

Play the video called the Play Day 1, which shows two classes going to a theater. Invite students to notice and wonder about what they see.

Consider providing students with additional representations of the problem by using more abstract models, such as number bonds and number sentences.

Let’s figure out how many students are in the two classes at the play. There are 23 students in one class and 26 students in the other class.

325

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

Pair students and distribute Unifix Cubes. Guide students to use the cubes to represent the 23 students and 26 students in each class. Have students find the total. Invite two or three students to share their thinking. Help students ask one another questions and make observations about one another’s work. Have them refer to the Talking Tool as needed. How many students are there? How do you know? There are 49 students. I see 4 tens and 9 ones.

Teacher Note

49; I moved the ones together. 49; there are 23 students in one class. 23 and 20 is 43. 43 and 6 is 49. Affirm students’ thinking. Ask students to show 23 and 26 with their cubes again. Show 23 and 26 cubes. Guide students to add the tens in 26 to 23 first. How many students are in the first class? (Point to the cubes that show 23.) 23 students Let’s add the tens first. Break up the second class to show 26 as 2 tens and 6 ones. Slide the 6 cubes in 26 away from the tens. Have students do the same.

The goal of this topic is for students to break up one or both addends and combine the resulting parts to find the total. This lesson focuses on decomposing one addend and adding the tens first. However, there are other valid ways to find the total, such as those shown below. Encourage students to try adding tens first, but also allow them to selfselect how they solve the problems when they work independently.

Add the tens from 26 first. What is 23 and 20? 43 (Slide the 6 ones back.) What is 43 and 6?

9 Add Like Units

Add Ones First

49 We didn’t make a new ten. Why not? Because 3 and 6 make 9, not 10. The ones have to make 10 to get another ten. Have students set their cubes aside. Transition to the next segment by framing the work. Today, we will add 2 two-digit numbers by breaking up one addend to add the tens first. We will see if we make a new ten!

326

10 EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 23 10

Learn

30 10

Add Tens First Students consider how adding the tens first makes an easier problem. Have students ready their personal whiteboard. Write 28 + 12 = and ask students to do the same. Tell students to draw 28 and 12 as tens and ones. Demonstrate interactively as students follow along. We drew 28 as tens and ones. Now we can combine 28 with the 1 ten from 12. (Circle 28 and the 1 ten from 12.) How many is 28 + 10? 38 Circle 38 in the drawing. Write 38 below the drawing. Now let’s add the ones from 12. (Write + 2 next to 38.) What is 38 + 2? How do you know? It’s 40. I counted on: 38, 39, 40. I know it’s 40 because 8 and 2 make 10. 30 and 10 make 40. Write = 40 to complete 38 + 2. So what is 28 + 12? 40

Teacher Note Emphasize how this way of solving is different from adding like units in lesson 22. In lesson 22, students decomposed both addends. In this lesson, students choose one addend to decompose so that they can add the tens first. Show that one addend remains the same.

Break Up Both Addends

Break Up One Addend

Write = 40 to complete the original equation. Invite students to think–pair–share about how they broke up the addend. How did we break up the addend 12? We broke up 12 into 1 ten and 2 ones. Which parts did we combine first? We combined 28 and the 1 ten, or 10.

327

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

Confirm students’ thinking by revoicing their ideas and summarizing the steps to add. Tell students to erase their whiteboard. Demonstrate the same problem using number bonds as students follow along. Write 28 + 12 = _____ . Draw arms from 12 to make a number bond. How many tens and ones are in 12? 1 ten 2 ones Write 10 and 2 as the parts of the number bond. Let’s add 10 to the first addend, 28. Write 28 + 10. What is 28 + 10? 38 Write 38 under 28 + 10 as shown.

Differentiation: Support Allow students to use cubes to show their thinking rather than a drawing or number bonds.

Now let’s add the ones from 12. Write + 2. What is 38 + 2?

Differentiation: Challenge

40 Write = 40 to complete 28 + 10 + 2. So what is 28 + 12? 40

Have students consider a second and third strategy to solve 28 + 12. Instruct students to use their whiteboard to show the strategy they chose and share the strategy with a partner.

Write = 40 to complete the original equation. Then, in the original equation, point to the digit in the tens place of each number (2, 1, and 4) and ask students this question. 2 tens and 1 ten make 3 tens. The total has 4 tens. How did we make a new ten?

Teacher Note

When we put together 38 and 2, we made the next ten. It was when we added the ones together. 8 and 2 make 10.

328

Helping students see how 4 tens was made is key in this lesson. Consider using cubes to show how 8 and 2 make the next ten.

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 23

Tell students to erase their whiteboard. Write 29 + 14 and repeat the process of modeling and solving the problem. Depending on the needs of your class, use either quick tens or number bonds to model it. Guide students to notice that by combining the ones, they composed a new ten and there were extra ones. Differentiation: Support

Total Capture Materials—S: Total Capture gameboard, crayon

Adjust the level of difficulty by cutting the gameboard. Have students use only the top two rows. Problems in the first two rows use simpler addends.

Students play a game to practice adding two-digit numbers. Partner students and have one student of each pair turn to the Total Capture gameboard. Give directions for the game.

11 + 16 =

18 + 12 =

19 + 21 =

15 + 24 =

23 + 17 =

17 + 24 =

28 + 14 =

29 + 15 =

38 + 15 =

49 + 16 =

57 + 19 =

215

• Whoever has captured or colored the most problems when time is up wins.

Make sure each pair of students has one gameboard and that each partner in a pair has a different color crayon. Circulate and encourage students to do the following: • Strategically choose problems to solve. • Try adding tens first with self-selected tools (e.g., cubes, quick tens, number bonds). • Show and explain how they decomposed the parts to find the total.

1 ▸ M5 ▸ TE ▸ Lesson 23

EUREKA MATH2

14 + 14 =

• When they finish, partners compare their totals. The partner with the largest total colors in both problems by using their crayon. (In lieu of coloring, students may choose to use Xs and Os or write their first initial in the boxes.)

Total Capture

Name

• Each partner chooses a problem and finds the total.

• Partners share one gameboard. Each partner chooses a different color crayon.

No matter which version of the gameboard students use, encourage them to rise to their personal best. For example, if students are successful with their current strategy, encourage them to add written notation that matches their thinking, or to try a different way to break apart and solve the next problem.

Promoting Mathematical Practice As students play Total Capture, they choose appropriate tools strategically. Encourage students to use the tool that is most helpful to them. This can be a physical tool such as cubes, a pictorial tool such as drawing tens and ones, or a purely mathematical tool such as a number bond. The suggested advancing questions in this segment promote this mathematical practice.

329

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

Have students play for 6 or 7 minutes. Ask the following assessing and advancing questions. How did you break up an addend (or addends)? Which parts did you add first? What tool did you use—cubes, drawings, number bonds, or number sentences? Why did you choose that tool? How do you know who has the larger total?

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be 10 read aloud. Students may self-select tools and ways to solve the problems. 10

Land Debrief

5 min

Objective: Decompose an addend and add tens first. Display 25 + 16 with both addends decomposed into tens and ones. Point to the four parts: 20, 5, 10, and 6. How did this student break up the addends? They broke up each one into tens and ones. (Point to 30 + 11 = 41.) How did they combine the parts to get 30 + 11?

25 + 16 = 41 20 5 10 6 30 + 11 = 41

If you put together the tens, they make 30. The ones, 5 and 6, make 11. 330

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 23

Draw arms to connect the parts to their total in the equation. For example, draw arms from 20 and 10 to the 30 in the equation. Point out that both number sentences have the same total. Display 25 + 16 = 41 with one addend decomposed into tens and ones. Point to the two parts: 10 and 6.

25 + 16 = 41

How did this student break up the addends?

10 6

They only broke up one addend into tens and ones. (Point to 35 + 6 = 41.) How did they combine the parts to get 35 + 6? They put together the 25 with the 10 from 16. 25 and 10 makes 35.

35 + 6 = 41

6 is how many ones are left from 16. Circle 25 and 10. Point out that both number sentences have the same total. We can break up both addends or we can break up one addend. How does breaking up one addend into tens and ones help us to add? It helps because then we can add the tens first. Then we just add the ones. It makes the problem a little easier.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

331

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

Name

2. Add tens first.

13 + 10 + 5 =

1. Add.

15 + 16 =

27 + 16 =

332

18 + 20 + 4 =

13 + 15 =

Write a new number sentence.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

18 + 24 =

Write a new number sentence.

27 + 10 + 6 = 43 247

248

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 23

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 23

4. Circle the true number sentences.

3. Add.

Put an X on the false number sentences.

Show how you know.

12 + 17 =

18 + 12 =

30 17 + 18

= 14 + 17

= 29 + 12

26 + 24

= 17 + 10 + 8

= 26 + 10 + 4

12 + 20 + 5 =

PROBLEM SET

249

250

PROBLEM SET

28 + 12

12 + 25

333

LESSON 24

Decompose an addend to make the next ten.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

Name

Add. Show how you know.

18 + 12 =

Lesson at a Glance Students watch a video that is similar to the one they viewed during lesson 23. The video shows adding 2 two-digit numbers by decomposing the second addend to make the next ten with the first addend. Students practice this as a class by modeling problems with drawings and number bonds. Then they play a game to practice adding two-digit numbers.

Key Question • How is breaking up an addend helpful?

Achievement Descriptors 1.Mod1.AD6 Determine whether addition and/or subtraction number

sentences are true or false. 1.Mod5.AD8 Add 2 two-digit numbers that have a sum within 50,

19 + 23 =

relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

257

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 24

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Have the sets of 5 ten-sticks from lesson 23 ready.

Launch Learn

10 min 10 min

30 min

• Make the Next Ten • Total Capture • Problem Set

Land

10 min

• Unifix® Cubes (44)

Students • Eureka Math2 Numeral Cards (1 set per student group) • Unifix® Cubes (50 per student pair) • Total Capture gameboard (1 per student pair, in the student book) • Crayon

335

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

Fluency Numbers Up!

10 10

Materials—S: Numeral30 cards

Students find an unknown total or part to build addition and subtraction fluency 10 within 10. Have students form groups of three. Assign roles: Player A is one part, player B is one part, and player C is the total. Distribute sets of cards to each group and have them play according to the following rules. Consider doing a practice round with students. • Players A and B each take a card and hold it on their own foreheads so they can’t see the number. • Player C looks at both cards and says the total. • Players A and B find the number on their own card, based on the total and the other part. • Player C confirms the two parts. Circulate as students play the game and provide support as needed. Have students switch roles after a few rounds. If the total is 8, and my partner has 5, I must have 3.

If the total is 8, and my partner has 3, I must have 5.

The total is 8.

Player C

336

Player A

Player B

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 24

Choral Response: Add a Multiple of 10 Students add 10, 20, 30, or 40 to a two-digit number to develop fluency with strategies for adding pairs of two-digit numbers. Display the equation 11 + 10 = . What is 11 + 10? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 21

11 + 10 = 21 11 + 20 = 31

Continue with 11 + 20 = . Repeat the process with the following sequence:

13 + 20 = 33

22 + 20 = 42

17 + 30 = 47

28 + 30 = 58

13 + 30 = 43

22 + 30 = 52

17 + 40 = 57

28 + 40 = 68

Teacher Note Use the rekenrek or restate the problem in unit form to support students with the task as needed. Consider using one or both supports for the first few problems, as the addends increase, or if students hesitate.

Launch

Materials—T/S: Unifix30Cubes

Students represent the action in a video to add 2 two-digit numbers by making 10 the next ten. Play the video called Play Day 2, which shows two classes going to a theater. Invite students to notice and wonder about what they see and to compare this video to the one they watched during lesson 23. Let’s figure out how many students are in the two classes at the play.

337

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

Pair students and distribute Unifix Cubes. Guide students to use the cubes to represent the 19 students and 25 students in each class. Encourage students to think about what the classes do in the theater and to use that information to help them find the total. Invite two or three students to share their thinking. Help students ask one another questions and make observations about one another’s work. Have them refer to the Talking Tool as needed. How many students are there? How do you know? There are 44 students. There are 19 students in one class. 19 and 20 is 39. 39 and 5 is 44. 44; I moved a one to make ten. Now I have 4 tens and 4 ones. Affirm students’ thinking. Then, if needed, ask students to show 19 and 25 with their cubes again. Show students 19 and 25 cubes. Guide students to model making the next ten to add. How many students are in the first class? (Point to the cubes that show 19.) 19 students What is the next ten after 19?

Teacher Note The goal of this topic is for students to break up one or both addends and combine the resulting parts to find the total. This lesson focuses on decomposing one addend to make the next ten with the other addend. However, there are other valid ways to find the total, such as adding like units, or adding tens first. Encourage students to try making ten, but also allow them to self-select how to solve the problems when they work independently.

Teacher Note Instead of cubes, consider demonstrating by using a more abstract model such as number bonds and number sentences as shown.

20 How many does 19 need to make 20? 1 Where can we get 1? From 25 25 is 2 tens 5 ones. We can break up the 5 ones into 1 and 4. We can add 1 to 19 to make the next ten. Take one cube from 5 and make ten by moving it near the 9 cubes in 19. Have students follow along. What is the total? How do you know? 44; we have 4 tens and 4 ones.

338

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 24

Have students set their cubes aside. Transition to the next segment by framing the work. Today, we are going to add 2 two-digit numbers by breaking up an addend to make the next ten. 10 10

Learn

30 10

Make the Next Ten Students consider how making the next ten results in an easier problem. Make sure students have their personal whiteboard ready. Write 35 + 25 = and ask students to do the same. Tell students to draw 35 and 25 as tens and ones. Demonstrate interactively as students follow along. Let’s start with the first addend. What is the next ten after 35? 40 How can we make 40? We can add 5 ones from 25. Circle 35 and 5 ones from 25. Label them 40. Now let’s add the tens from 25. Next to 40, write + 20. What is 40 + 20? 60 Write = 60 to complete 40 + 20. So what is 35 + 25? 60

339

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

Write = 60 to complete the original equation. Invite students to think–pair–share about how they broke up the addend. How did we break up the addend 25? We broke up 25 into 5 and 20. Which parts did we combine to make the next ten? We combined 35 and 5 to make the next ten. Confirm students’ thinking by revoicing their ideas and summarizing the steps to add. Tell students to erase their whiteboard. Demonstrate the same problem using number bonds as students follow along. Write 35 + 25 = . How many does 35 need to make the next ten?

Teacher Note When writing the number bond that shows the second addend decomposed, it may be helpful to write the parts so that the part needed to make the next ten comes first, as shown.

5 Draw arms from 25 to make a number bond. Write 20 and 5 as the parts. We have three parts now. Write 35 + 5 + 20. Then draw arms from 35 and 5 to a total of 40. What is 40 + 20? 60 Write = 60 to complete 35 + 5 + 20. So what is 35 + 25? 60 Write = 60 to complete the original equation. Write 18 + 16 and repeat the process of modeling and solving the problem. Depending on the needs of your class, use either quick tens or number bonds to model it. Guide students to notice that they made the next ten, and there were extra ones and a ten.

340

Differentiation: Challenge When adding, students may choose to decompose either addend. Pose a problem such as 12 + 28 and challenge students to think about the problem strategically by asking these questions: • Does it make more sense to decompose the first addend or the second one? Why? • Which addend would you rather make ten with? Why?

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 24

Total Capture Materials—S: Total Capture gameboard, crayon

Students play a game to practice adding two-digit numbers.

Differentiation: Support

Partner students and have one student of each pair turn to the Total Capture gameboard. Remind students how to play. Notice that the directions differ from those in lesson 23. In this version of the game, the student with the smallest total colors the sections of both problems.

37 + 13 =

19 + 12 =

18 + 14 =

17 + 16 =

26 + 15 =

29 + 13 =

25 + 18 =

29 + 22 =

38 + 23 =

35 + 36 =

• Whoever has captured or colored the most problems when time is up wins.

Make sure each pair of students has one gameboard and that each partner in a pair has a different color crayon. Circulate and encourage students to do the following: • Strategically choose problems to solve. • Try adding by making the next ten with self-selected tools (e.g., cubes, quick tens, number bonds). • Show and explain how they decomposed the parts to find the total. Have students play for 6 or 7 minutes. Ask the following assessing and advancing questions.

As they try making ten to solve, some students may know how many the first addend needs to make the next ten, but they may need support to decompose the second addend to “get” the ones. Students may count back on their fingers to decompose the second addend, or they may draw the problem.

1 ▸ M5 ▸ TE ▸ Lesson 24

18 + 12 =

EUREKA MATH2

15 + 15 =

223

• When they finish, partners compare their totals. The partner with the smallest total colors in both problems by using their crayon. (In lieu of coloring, students may choose to use Xs and Os or write their first initial in the boxes.)

Total Capture

Name

• Each partner chooses a problem and finds the total.

• Partners share one gameboard. Each partner chooses a different color crayon.

Adjust the level of difficulty by cutting the gameboard. Have students use only the top two rows, which have simpler addends.

Promoting Mathematical Practice As students play Total Capture with a partner, they have the opportunity to construct viable arguments and critique the reasoning of others. If students add in different ways, ask them to explain how they would use their way to find the total for their partner’s equation. If students disagree about a total, or about whose total is smaller, encourage them to ask questions about their partner’s reasoning.

How did you break up an addend (or addends)? Which parts did you add first?

341

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

What tool did you use—cubes, drawings, number bonds, or number sentences? Why did you choose that tool? How do you know who has the smaller total?

UDL: Engagement Consider modeling questions that students should ask themselves to encourage planning for and monitoring their work.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud.

• What are the two addends? • Should I break apart both addends or just one? • Is this model working? Should I try something else?

Land Debrief

Teacher Note

Expect students to use a variety of ways to show how they decomposed the addend and combined the tens with the first addend.

5 min

Objective: Decompose an addend to make the next ten. Display 18 + 12 = solved three different ways. Show one way at a time. The first way is by adding like units. The second way is by adding tens first. The third way is to make the next ten. In all three ways, one or both addends were decomposed. Invite students to analyze each work sample by using a variation of the Five Framing Questions routine. The reponses provided for the following questions show a possible answer for each work sample.

18 + 12 = 10 8 10 2 10 + 10 + 8 + 2 = 30 20

18 + 12 =

10 2

2 10

18 + 10 + 2 = 30

18 + 2 + 10 = 30

28 + 2

Have students notice and organize.

35 + 25 = 60

20 5

40 + 20 = 60 Some students may simply decompose an addend and then use mental math to find the total.

How did this student find the total? They broke up both addends into tens and ones. They added tens, then ones, then they put those totals together. They broke up the 12 into 10 and 2. They added 18 and 10 first. Then they added 2 more. 342

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 24

They broke up 12 into 2 and 10 so they could make the next ten with 18. 18 and 2 makes 20, plus 10 more makes 30. Display all three samples at the same time. Help students reveal the strategies. Let’s focus on breaking apart addends. Where do you see addends broken apart in the work? In the first one they broke up 18 and 12. In the others they broke up only 12. All of the addends that are broken up get put into tens and ones. Help students to distill the information and know how these strategies help them to add. How do you think breaking apart addends helped these students? You can make easier problems by breaking apart numbers. Breaking apart numbers lets you make the problems smaller. Guide students to further know how these strategies help them. What are some ways to make an easier problem? You can break numbers into tens and ones to add in different ways. You can add tens with tens, ones with ones, and then put them together. You can add the tens from the second number to the first number, then add the ones. You can think about what the next ten is and make it.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

343

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

Name

3. Add. Show how you know.

1. Circle to make the next ten. Add.

19 + 12 =

28 + 16 =

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 24

19 + 11 =

18 + 14 =

29 + 16 =

= 25 + 16

2. Add.

19 + 1 + 12 =

25 + 5 + 11 =

4. Circle the true number sentence. Put an X on the false number sentence.

19 + 13 =

344

25 + 16 =

15 + 15

255

256

PROBLEM SET

= 10 + 10

15 + 17

= 20 + 12

LESSON 25

Compare equivalent expressions used to solve two-digit addition equations.

EUREKA MATH2

1 ▸ M5 ▸ TE

Name

Add. Show how you know.

13 + 16 =

Lesson at a Glance Students use self-selected strategies and tools to solve a two-digit addition problem. Then they share and discuss their work and find that different strategies result in the same total. Students analyze a number sentence with expressions that represent two ways to decompose two-digit addends. They determine that the expressions are equal and that the number sentence is true.

Key Question • What are some ways to make an easier problem?

Achievement Descriptors

16 + 14 =

1.Mod1.AD6 Determine whether addition and/or subtraction number

sentences are true or false. 1.Mod5.AD8 Add 2 two-digit numbers that have a sum within 50,

relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

29 + 13 =

263

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 25

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Have assorted math tools, such as Unifix Cubes and number paths, available for students to self-select as they solve problems.

Launch Learn

10 min 15 min

20 min

• Equivalent Yet Easier Expressions

• 100-bead rekenrek

Students • Assorted math tools

• Problem Set

Land

15 min

347

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25

Fluency

10 15

Whiteboard Exchange: Subtract Within 20 20 Students select a strategy and find the difference to build subtraction fluency within 20.

Teacher Note

Display 11 – 9 = .

Write the equation and find the answer. Show how you know. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

11 - 9 = 2

Display the answer. Repeat the process with the following sequence:

12 - 9 = 3

11 - 8 = 3

12 - 8 = 4

11 - 7 = 4

You may see a variety of strategies in students’ work, including but not limited to take from ten, count on to ten, or count back to ten. Consider asking students to use a specific strategy for certain problems, or consider using this fluency activity as a formative assessment to see which strategies students use. Take from Ten

Count On to Ten

11 - 9 = 2

11 - 9 = 2 + 1+ 1

10 1 10 - 9 = 1 1 + 1 = 2

11 - 6 = 5

14 - 9 = 5

10 11

Count Back to Ten 11 - 9 = 2 - 8 - 1 2

10 11

12 - 7 = 5

Choral Response: Make the Next Ten on the Rekenrek Materials—T: 100-bead rekenrek

Students identify a number shown on the rekenrek and say the number sentence to make 10 or 20 to develop fluency with strategies for adding pairs of two-digit numbers. Show students the rekenrek. Start with 9 beads to the left side.

348

Student View

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 25

How many beads? (Gesture to the 9 beads.) 9 On my signal, say the number sentence to make 10, starting with 9. Ready? 9 + 1 = 10 Slide over 1 more bead to make 10. Show 19 beads to the left side.

Student View

How many beads? (Gesture to the 19 beads.) 19 On my signal, say the number sentence to make 20, starting with 19. Ready? 19 + 1 = 20 Slide over 1 more bead to make 20. Repeat the process with the following sequence:

Choral Response: True and False Number Sentences Students determine if a number sentence is true or false to prepare for noticing the equality of equivalent expressions. Display the number sentence 10 + 5 = 15. Is the number sentence true or false? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. True

10 + 5 = 15 True 349

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25

Display the answer. Teacher Note

Repeat the process with the following sequence:

10 + 4 > 15

8 + 10 > 15

20 > 10 + 9

10 + 3 = 12 + 1

False

True

10 + 6 < 14 + 2

11 + 3 < 10 + 7

13 + 6 < 8 + 10

False

True

False

After students determine that a number sentence is false, consider asking them the following questions about how they could make the number sentence true: • How could you change one number or symbol to make the number sentence true? • What comparison symbol would make the number sentence true? (Gesture to the comparison symbol.)

Teacher Note 10

Launch

20math tools Materials—S: Assorted

Students add 2 two-digit numbers by using a self-selected strategy. 15

Write 15 + 25 = and ask students to write the equation on their whiteboards. If your class would benefit from a more complex problem, use 25 + 45 instead. Tell students to self-select strategies and math tools that are available to find the total. Make sure they record their thinking. Circulate and look for student work to share in the next segment. If possible, select samples that invite discussion of at least two of the following strategies and that include expressions showing ways of breaking apart addends.

350

Depending on the needs of your class, consider having pairs or small groups of students solve the problem in two or three ways and record those ways on chart paper. Post the charts around the room and invite students to walk around and look at their peers’ work. Share the following norms: • Look but don’t touch, just like in a museum or gallery. • Be quiet as you notice or wonder about the work. Once students have had time to see all the work that is posted, gather the class to debrief. Invite students to share their observations and use them to facilitate a discussion about the different strategies.

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 25

We can get the same total even when we break up the addends and combine the parts in different ways. Add Like Units

15 + 25

Add Tens First

15 + 25

10 5 20 5 20 5 10 + 20 + 5 + 5 = 40 15 + 20 + 5 = 40 30

Add Ones First (May Make the Next Ten)

15 + 5 + 20 = 40

As students finish, have them turn and talk to a partner to share their work and confirm the solution. Then invite one of the students you identified to share their work. Use the work to facilitate a class discussion with the following questions. Refer students to the Talking Tool as needed. Which addend or addends did they break apart? Why? What parts did they add together first? Why?

Teacher Note The student work samples here are examples of what students might do. Students’ work may vary, including the expression they write after decomposing the addends.

Where do you see their new, easier expression? Listen for and revoice student responses that mention the following ideas: • They broke apart both numbers and added the tens and then the ones. • They broke apart the 25 so they could add the tens first. • They broke apart the 25 so they could make the next ten with 15. Transition to the next segment by framing the work. Today, we will compare the ways we made an easier problem and found the total.

351

10 1 ▸ M5 ▸ TE ▸ Lesson 25 15

Learn

EUREKA MATH2

20 15

Equivalent Yet Easier Expressions Students share and compare equivalent expressions to see that the same problem can be solved in different ways. Write a number sentence. On one side of the equal sign use the expression 15 + 25, and on the other side write an expression that shows breaking apart one or both addends based on a student’s work from Launch. The chart shows samples. The following sample dialogue uses 15 + 25 = 15 + 5 + 20. This number sentence shows 15 + 25. (Point to 15 + 25.) It also shows one way to break up those addends. (Point to 15 + 5 + 20.) Is the number sentence true or false? How do you know? It’s true because both sides of the equal sign make 40. It’s true. There is a 15 on both sides of the equal sign. 25 is on both sides too because 20 + 5 = 25. Record student thinking. Write another number sentence. Write the previously used expression based on the first student’s work on one side of the equal sign and an expression based on a second student’s work from Launch on the other side. The chart shows samples. The following sample dialogue uses 15 + 5 + 20 = 10 + 20 + 5 + 5.

352

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 25

This number sentence shows some ways used to find 15 + 25. Is the number sentence true or false? How do you know? It’s true because both sides of the equal sign make 40. It’s true. I see 15 and 25 on both sides of the equal sign. On this side 10 and 5 make 15, and 20 and 5 make 25. On the other side, 20 and 5 make 25, and there’s already 15. How are the expressions on either side of the equal sign different? One of them breaks apart both addends into tens and ones. The other expression only breaks apart the 25. We can get the same total even when we break up the addends and combine the parts in different ways.

Problem Set

Promoting Mathematical Practice As students consider whether complex equations such as 15 + 5 + 20 = 10 + 20 + 5 + 5 are true or false, they construct viable arguments and critique the reasoning of others. Some students may make use of the structure of the expressions, combining some of the addends until both sides look the same, while others will rely on finding the total for both sides and seeing if the totals are the same. Students may need to be convinced that all of these paths are viable. Encourage them to ask questions about strategies they don’t understand and to explain their thinking to one another.

Differentiate the set by selecting problems for students to finish independently within the timeframe, but make sure that everyone is assigned to complete 28 + 22. Problems are organized from simple to complex. Directions may be read aloud.

353

15 EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25 20

Land Debrief

UDL: Representation

10 min

Objective: Compare equivalent expressions used to solve two-digit addition equations. Invite students to discuss three different ways to solve the same equation. Display the three ways one at a time. For each way, ask the following questions and provide think time.

As the class analyzes the three ways, consider making an anchor chart for students to refer to as they practice adding two-digit numbers in the future. The sample chart models each way with number bonds and drawings. Depending on the needs of your class, select just one or two models to use on the chart.

How did this student break up the addends to make an easier problem? How did the student combine the parts? For the first way, which shows adding like units, listen for responses such as these. The addends are broken up into tens and ones. They added the tens to tens and the ones to ones. Then they put it all together to get the total. For the second way, which shows adding tens first, listen for responses such as these. The 22 is broken apart into tens and ones.

28 + 22 = 50 20 8 20 2 20 + 20 + 8 + 2 = 50 40

The tens from 22 got added to 28 first, and then the ones. For the third way, which shows making the next ten, listen for responses such as these. The 22 is broken apart into tens and ones. They wrote the ones first and made the next ten with 28. After making the next ten, then the tens got added.

28 + 22 = 50 20 2 28 + 20 + 2 = 50 48 28 + 22 = 50

Why did all three students get the same total? They just thought about the problem differently. They broke it apart in different ways and put the parts together in different ways.

354

2 20 28 + 2 + 20 = 50 30

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 25

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

355

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25

Name

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25

2. Circle true or false. Show how you know.

1. Circle true or false.

True

16 + 24 = 16 + 4 + 2 False

True

False

True

14 + 10 + 7 = 10 + 10 + 4 + 7

False

True

False

356

259

260

PROBLEM SET

EUREKA MATH2 1 ▸ M5 ▸ TE ▸ Lesson 25

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25

EUREKA MATH2

1 ▸ M5 ▸ TE ▸ Lesson 25

4. Show 2 ways to add.

3. Add.

26 + 18 =

Show how you know.

28 + 22 =

= 23 + 16

14 + 26 =

= 13 + 29

PROBLEM SET

261

262

PROBLEM SET

26 + 18 =

357

This page may be reproduced for classroom use only.

358

Name

tens

Fill in the number bond.

Write how many tens and ones.

1. Circle tens.

Module Assessment

ones is

EUREKA MATH2 1 ▸ M5 ▸ Module Assessment

This page may be reproduced for classroom use only.

359

82 + 10 =

What is 10 more than 43?

ones

82 – 10 =

What is 10 less than 76?

tens

EUREKA MATH2 1 ▸ M5 ▸ Module Assessment

This page may be reproduced for classroom use only.

360

Show how you know.

4. Write >, =, or <.

90 – 40 =

36 + 30 =

= 70 + 20

3. Add or subtract.

EUREKA MATH2 1 ▸ M5 ▸ Module Assessment

This page may be reproduced for classroom use only.

361

6. Circle the time.

13 + 15 =

Show how you know.

5. Add.

6:30

11:00

3:30

= 23 + 7

27 + 15 =

EUREKA MATH2 1 ▸ M5 ▸ Module Assessment

Achievement Descriptors: Proficiency Indicators 1.Mod1.AD6 Determine whether addition and/or subtraction number sentences are true or false. Partially Proficient Determine whether addition and/or subtraction number sentences with one operation symbol (e.g., 3 + 4 = 7) are true or false. Circle the number sentence if it is true. Draw an X on the number sentence if it is false.

3+4=8

Proficient Determine whether number sentences involving two addition expressions or two subtraction expressions (e.g., 5 + 2 = 6 + 1 or 6 – 4 = 3 – 1) are true or false.

Determine whether number sentences involving both addition and subtraction expressions (e.g., 4 + 1 = 7 – 2) or three addends (e.g., 2 + 2 + 1 = 3 + 2 + 0) are true or false.

Circle the number sentence if it is true.

Draw an X on the number sentence if it is false.

5+3=2+6

362

Highly Proficient

9-3=2+4

EUREKA MATH2 1 ▸ M5

1.Mod5.AD1 Represent a set of up to 99 objects with a two-digit number by composing tens. Partially Proficient

Proficient

Represent a set of up to 50 objects with a two-digit number by composing tens.

Represent a set of up to 99 objects with a two-digit number by composing tens.

Represent a set of 100–120 objects with a written numeral by composing tens.

Circle all the groups of 10.

tens

Highly Proficient

ones

Total

tens

ones

Total

tens

ones

Total

363

EUREKA MATH2

1 ▸ M5

1.Mod5.AD2 Represent two-digit numbers within 99 as tens and ones. Partially Proficient

Proficient

Highly Proficient

Represent two-digit numbers within 50 as tens and ones.

Represent two-digit numbers within 99 as tens and ones.

Represent numbers through 100–120 as tens and ones.

Draw the number with tens and ones.

Show the total with a number bond or number sentence.

Draw the number with tens and ones.

114

1.Mod5.AD3 Determine the values represented by the digits of a two-digit number. Partially Proficient

Proficient

Highly Proficient

Determine the number represented by given amounts of tens and ones.

Determine the values represented by the digits of a two-digit number.

Write the total.

Fill in the number bond.

6 tens and 3 ones is

63 60

364

EUREKA MATH2 1 ▸ M5

1.Mod5.AD4 Compare two-digit numbers by using the symbols >, =, and <. Partially Proficient

Proficient

Compare two-digit numbers by using the symbols >, =, and < when the numbers have the same digit in the tens place.

Compare two-digit numbers by using the symbols >, =, and < when the numbers have the same digit in the ones place or none of the digits in either place are the same.

Write >, =, or <.

Highly Proficient Compare numbers to 120 by using the symbols >, =, and <. Write >, =, or <.

110

102

1.Mod5.AD5 Add or subtract multiples of 10. Partially Proficient

Proficient

Highly Proficient

Add or subtract 10 from a multiple of ten.

Add or subtract multiples of 10 within 100.

Add or subtract.

Add or subtract multiples of 10 within 100 by using a related single-digit fact (e.g., find 30 + 60 by thinking 3 tens + 6 tens = 9 tens).

50 + 10 =

60 + 20 =

Add. Show how you know.

70 – 10 =

50 – 30 =

30 + 60 = 3 + 6 = 9

30 + 60 = 90

365

EUREKA MATH2

1 ▸ M5

1.Mod5.AD6 Add a two-digit number and a multiple of 10 that have a sum within 100. Partially Proficient

Proficient

Add a one-digit number and a multiple of 10 that have a sum within 100.

Add a two-digit number and a multiple of 10 that have a sum within 100.

Add.

6 + 70 =

56 + 40 =

366

Highly Proficient

EUREKA MATH2 1 ▸ M5

1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 50, relate the strategy used to a

written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations. Partially Proficient

Proficient

Add a two-digit number and a one-digit number that have a sum within 50 when composing a ten is not required and relate the strategy used to a written method.

Add a two-digit number and a one-digit number that have a sum within 50 when composing a ten is required, relate the strategy used to a written method, and explain the reasoning used.

Add.

Add. Show how you know.

24 + 5 = 29 20

20 + 4 + 5 = 29

Explain multiple strategies for adding a two-digit number and a one-digit number. Add. Show how you know.

27 + 5 = 32

27 + 5 = 32 30 3

Highly Proficient

I broke up 5 to make the next ten with 27 27.. 30 and 2 is 32 32..

30 3

I broke up 5 to make the next ten with 27 27.. 30 and 2 is 32 32.. Show another way to add.

27 + 5 = 32

9 20

7 + 5 = 12 20 + 12 = 32

I added the ones first. 7 and 5 is 12 12.. 20 and 12 is 32 32..

367

EUREKA MATH2

1 ▸ M5

1.Mod5.AD8 Add 2 two-digit numbers that have a sum within 50, relate the strategy used to a written method,

and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations. Partially Proficient Add 2 two-digit numbers that have a sum within 50 when composing a ten is not required and relate the strategy used to a written method. Add.

22 + 14 = 36 4 26 + 10 = 36

Proficient

Highly Proficient

Add 2 two-digit numbers that have a sum within 50 when composing a ten is required, relate the strategy used to a written method, and explain the reasoning used.

Add 2 two-digit numbers that have a sum within 100, including when composing a ten is required, relate the strategy used to a written method, and explain the reasoning used.

Add.

26 + 14 = 40

4 30 + 10 = 40

58 + 24 = 82

I broke apart 14 to make the next 10 with 26 26.. 30 and 10 is 40 40..

50 8 20 4 50 + 20 = 70 8 + 4 = 12

70 + 12 = 82

I broke apart both numbers into tens and ones. I added the tens, then the ones, then added the totals.

368

EUREKA MATH2 1 ▸ M5

1.Mod5.AD9 Mentally find 10 more or 10 less than a two-digit number. Partially Proficient

Proficient

Find 10 more and 10 less than a two-digit number by using drawings, manipulatives, or other tools.

Mentally find 10 more or 10 less than a two-digit number.

Use cubes or draw to show 35.

What is 10 more than 67?

What is 10 more than 35?

Highly Proficient

What is 10 less than 45?

1.Mod5.AD10 Tell time to the hour and half hour on analog and digital clocks. Partially Proficient

Proficient

Tell time to the hour on analog and digital clocks.

Tell time to the half hour on analog and digital clocks.

Circle the time.

12:00 2:00 4:00

11:00 11:30 12:30

Highly Proficient

369

Observational Assessment Recording Sheet Grade 1 Module 5

Student Name

Place Value Concepts to Compare, Add, and Subtract Achievement Descriptors 1.Mod1.AD6

Determine whether addition and/or subtraction number sentences are true or false.

1.Mod5.AD1

Represent a set of up to 99 objects with a two-digit number by composing tens.

1.Mod5.AD2

Represent two-digit numbers within 99 as tens and ones.

1.Mod5.AD3

Determine the values represented by the digits of a two-digit number.

1.Mod5.AD4

Compare two-digit numbers by using the symbols >, =, and <.

1.Mod5.AD5

Add or subtract multiples of 10.

1.Mod5.AD6

Add a two-digit number and a multiple of 10 that have a sum within 100.

1.Mod5.AD7

1.Mod5.AD8

1.Mod5.AD9

Mentally find 10 more or 10 less than a two-digit number.

1.Mod5.AD10

Tell time to the hour and half hour on analog and digital clocks. PP Partially Proficient

Notes

370

Dates and Details of Observations

This page may be reproduced for classroom use only.

P Proficient

HP Highly Proficient

EUREKA MATH2 1 ▸ M5 ▸ Observational Assessment Recording Sheet

Module Achievement Descriptors by Lesson ● Focus content ○ Supplemental content Lesson Achievement Descriptor

Topic A 1

Topic B 5

Topic C 10

Topic D 14

1.Mod1.AD6

Topic E 19 20 21

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1.Mod5.AD1

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1.Mod5.AD2

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1.Mod5.AD3

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●

1.Mod5.AD4

● ● ●

1.Mod5.AD5

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1.Mod5.AD6

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1.Mod5.AD7

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●

1.Mod5.AD8

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1.Mod5.AD9 1.Mod5.AD10

22 23 24 25

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This page may be reproduced for classroom use only.

371

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Module Assessment

EUREKA MATH2

1 ▸ M5 ▸ Module Assessment

Name

1. Circle tens.

Write how many tens and ones. Fill in the number bond.

50 5

tens

3 3

ones is

372

This page may be reproduced for classroom use only.

358

tens

ones

What is 10 more than 43?

What is 10 less than 76?

82 + 10 =

82 – 10 =

359

EUREKA MATH2 1 ▸ M5

EUREKA MATH2

1 ▸ M5 ▸ Module Assessment

5. Add. 3. Add or subtract.

Show how you know.

90 = 70 + 20 36 + 30 =

90 – 40 =

13 + 15 = 28

Show how you know.

35 < 53

78 > 69

This page may be reproduced for classroom use only.

4. Write >, =, or <.

360

361

30 = 23 + 7

27 + 15 = 42

6. Circle the time. 3:30 11:00 6:30

373

Terminology The following terms are critical to the work of grade 1 module 5. This resource groups terms into categories called New, Familiar, and Academic Verbs. The lessons in this module incorporate terminology with the expectation that students work toward applying it during discussions and in writing. Items in the New category are discipline-specific words that are introduced to students in this module. These items include the definition, description, or illustration as it is presented to students. At times, this resource also includes italicized language for teachers that expands on the wording used with students. Items in the Familiar category are discipline-specific words introduced in prior modules or in previous grade levels. Items in the Academic Verbs category are high-utility terms that are used across disciplines. These terms come from a list of academic verbs that the curriculum strategically introduces at this grade level.

New digit Numbers like 7 and 5 are called digits. When we write digits next to each other, we make another number. For example, we write the digits 7 and 5 next to each other to make 75. (Lesson 2) compose To compose means to be put together, or group. (Lesson 3)

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place A digit’s place is its position in a number. Numbers with two digits have two places: the tens place and the ones place. (Lesson 3) value Value is how much something is worth. For example, in the number 53, the 5 is in the tens place, so it has a value of 50. (Lesson 3)

Familiar addend compare efficient equal equation expression false fewer greater less minus number sentence

EUREKA MATH2 1 ▸ M5

one(s) part partners represent subtract take away ten(s) total true unit unknown

Academic Verbs Module 5 does not introduce any academic verbs from the grade 1 list.

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Math Past Yoruba Counting Words Where do number words come from? Do other people use different words to represent numbers? What do other people’s number words mean? Write the word nineteen and ask students why they think we use that word to mean 1 ten and 9 ones. It may help to add space between nine and teen, or to underline the two parts of the word as you read it. Students should point out that the word nine is in nineteen. Some may notice that teen kind of looks and sounds like ten. In the first four modules, students learned how different people have represented and written numbers throughout history. The ways we write numbers can affect our number sense and the kinds of calculations we can perform. For example, adding and subtracting with Roman numerals is notoriously difficult! The words we use for numbers are also connected to our number sense. The connection between words and number sense is deep. We learn the words for numbers before we learn to write them, and words for numbers developed earlier in human history than written numerals, since spoken language developed first. Tell the class you met someone who says that where they grew up, they say “5 before 20” to describe a number. Ask students what number they think this person is describing. A number path can be used to help students answer this question.

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Tell the class that this is how the Yoruba people of western Africa describe the number 15. The Yoruba people form a large ethnic group, and the Yoruba language is the native language of between 30 and 40 million people! In addition to having deep mathematical traditions dating back centuries, they are also famous for their music, which features advanced drumming techniques. Unlike our decimal or base-10 system, the Yoruba number system is a vigesimal, or base-20 system. Many people in different regions of western Africa use base-20 systems, and they are used in the Americas too. For example, the Maya system, which we saw in modules 3 and 4, is also a base-20 system. The different and interesting aspect of the Yoruba system is its reliance on subtraction. Remind students how we use tens to make our numbers, making as many groups of 10 as we can, and then saying how many ones are left. Ask students why they think we use 10 this way. Hint: What do most people have 10 of that you can use to count? Fingers! When counting from 10 to 20 in Yoruba, the number words start out with a similar meaning to ours. They also describe 10 and some ones, which can be roughly translated as follows. 11

1 past 10

2 past 10

3 past 10

4 past 10

EUREKA MATH2 1 ▸ M5

Then, at 15, the numbers start to be described differently. 15

5 before 20 4 before 20 3 before 20 2 before 20 1 before 20 Ask students if they can think of a reason the Yoruba people use 20 this way. Hint: Just like most people have 10 fingers, most people also have 10 toes. Put them together and that’s 20. Things get more complex as you move past 20. For example, the word for 35 translates roughly to five before two twenties, and the word for 45 is described as five from ten from three twenties or three twenties minus ten minus five. This goes beyond first grade learning but could be a good challenge for advanced students with the aid of the 1–120 number path. Remember, between 30 and 40 million people describe their numbers this way! Children who grow up learning to count this way can use these numbers fluidly. They learn the numbers through hands-on activities that use objects like pebbles or beans, and through traditional games like Ayo, or Oware, a version of Mancala seen here.

For example, knowing that you’re counting from 20 to 30, you can put up fingers one at a time to count 21, 22, 23, and 24. When you put the fifth finger up, the understanding is that now you mean 5 before 30, or 25. To get from 25 to 30, you put fingers down one at a time, counting 4 before 30 (26), 3 before 30 (27), 2 before 30 (28), 1 before 30 (29), and finally when all fingers are down, you have reached 30. Use one hand to count from 20 to 30 the Yoruba way as a class. Ways of describing numbers that differ from our own can seem counterintuitive at first. In a sense, to understand the Yoruba number words, you need to understand the basics of addition and subtraction. However, each of the words tells you what it means. Consider the English number words twelve and fifty. Neither of these words is descriptive of the number it represents. Fifty derives from the Old English words for five (fif) and group of ten (tig). Similarly, twelve comes from the Old English word twelf, which means two left, as in two left after 10. Since we no longer speak Old English, these descriptions are lost on us and on our students! In fact, research shows that this lack of descriptiveness hinders young learners’ number sense. In many other languages, number words are more descriptive. For example, in Mandarin Chinese, thirteen is said “ten-three.” Understanding the limits of our point of view and incorporating other cultures’ perspectives into our thinking can only make us stronger as we work with math!

How did the Yoruba people come to count this way? One theory is that this number pattern was developed so that if the multiple of 10 is understood, you can count on one hand.

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Materials The following materials are needed to implement this module. The suggested quantities are based on a class of 24 students and one teacher. 1

10-sided dice, set of 24

100-bead demonstration rekenrek

Base 10 rods, plastic, set of 50

Centimeter cubes, set of 500

Chart paper sheets

Computer with internet access

Counters

Counting collections

24 Crayons (1 red crayon, 1 green crayon, 1 yellow crayon per student)

1 Eureka Math2™ Hide Zero® cards, student extension set of 12 1

Eureka Math2™ Numeral Cards, set of 12 decks

Learn books

Markers

Pencils

650

Pennies

Personal whiteboards

Personal whiteboard erasers

Projection device

Dimes

Scissors

Dot dice, set of 12

Teach book

Dry-erase markers

Unifix® Cubes, set of 1,000

Eureka Math2™ Hide Zero® cards, basic student set of 12

Work mats

Eureka Math2™ Hide Zero® cards, demonstration set

Visit http://eurmath.link/materials to learn more. Please see lesson 2 for a list of organizational tools (cups, plates, number paths, etc.) suggested for the counting collection.

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Works Cited Carpenter, Thomas P., Megan L. Franke, and Linda Levi. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann, 2003.

Franke, Megan L., Elham Kazemi, and Angela Chan Turrou. Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom. Portsmouth, NH: Stenhouse, 2018.

Carpenter, Thomas P., Megan L. Franke, Nicholas C. Johnson, Angela C. Turrou, and Anita A. Wager. Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education. Portsmouth, NH: Heinemann, 2017.

Hattie, John, Douglas Fisher, and Nancy Frey. Visible Learning for Mathematics: What Works Best to Optimize Student Learning. Thousand Oaks, CA: Corwin Mathematics, 2017.

CAST. Universal Design for Learning Guidelines version 2.2. Retrieved from http://udlguidelines.cast.org, 2018. Clements, Douglas H. and Julie Sarama. Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge, 2014. Danielson, Christopher. How Many?: A Counting Book: Teacher’s Guide. Portland, ME: Stenhouse, 2018. Danielson, Christopher. Which One Doesn’t Belong?: A Teacher’s Guide. Portland, ME: Stenhouse, 2016. Empson, Susan B. and Linda Levi. Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH: Heinemann, 2011. Flynn, Mike. Beyond Answers: Exploring Mathematical Practices with Young Children. Portsmouth, NH: Stenhouse, 2017. Fosnot, Catherine Twomey, and Maarten Dolk. Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann, 2001.

Huinker, DeAnn and Victoria Bill. Taking Action: Implementing Effective Mathematics Teaching Practices. Kindergarten– Grade 5, edited by Margaret Smith. Reston, VA: National Council of Teachers of Mathematics, 2017. Kelemanik, Grace, Amy Lucenta, Susan Janssen Creighton, and Magdalene Lampert. Routines for Reasoning: Fostering the Mathematical Practices in All Students. Portsmouth, NH: Heinemann, 2016. Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. New York: Routledge, 2010. National Research Council. Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001. Online Etymology Dictionary, s.v. “fifteen,” accessed July 1, 2020, https://www.etymonline.com/search?q=fifteen. Online Etymology Dictionary, s.v. “fifty,” accessed July 1, 2020, https://www.etymonline.com/search?q=fifty. Online Etymology Dictionary, s.v. “twelve,” accessed July 1, 2020, https://www.etymonline.com/search?q=twelve.

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EUREKA MATH2

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Parker, Thomas and Scott Baldridge. Elementary Mathematics for Teachers. Okemos, MI: Sefton-Ash, 2004.

Van de Walle, John A. Elementary and Middle School Mathematics: Teaching Developmentally. New York: Pearson, 2004.

Shumway, Jessica F. Number Sense Routines: Building Mathematical Understanding Every Day in Grades 3–5. Portland, ME: Stenhouse Publishing, 2018.

Van de Walle, John A., Karen S. Karp, LouAnn H. Lovin, and Jennifer M. Bay-Williams. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3–5, 3rd ed. New York: Pearson, 2018.

Smith, Margaret S. and Mary K. Stein. 5 Practices for Orchestrating Productive Mathematics Discussions, 2nd ed. Reston, VA: National Council of Teachers of Mathematics, 2018. Smith, Margaret S., Victoria Bill, and Miriam Gamoran Sherin. The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom, 2nd ed. Thousand Oaks, CA: Corwin Mathematics; Reston, VA: National Council of Teachers of Mathematics, 2020.

Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Cultures. Chicago: Chicago Review Press, 1999. Zwiers, Jeff, Jack Dieckmann, Sara Rutherford-Quach, Vinci Daro, Renae Skarin, Steven Weiss, and James Malamut. Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Retrieved from Stanford University, UL/ SCALE website: http://ell.stanford.edu/content/mathematicsresources-additional-resources, 2017.

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Credits Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module. All United States currency images Courtesy the United States Mint and the National Numismatic Collection, National Museum of American History. For a complete list of credits, visit http://eurmath.link/ media-credits. Cover, Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48-1/4, W. 60-1/4 in. (122.6 x 153 cm.). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists

Rights Society (ARS), NY. Photo Credit: Image copyright © The Metropolitan Museum of Art. Image source: page 14 (left): elbud/ Shutterstock.com; Art Resource, NY; page 51, Leonid Iastremskyi/ Pixel-shot/Alamy Stock Photo; pages 52, 53, tarmofoto/ Shutterstock.com; page 70, Pornsngar Potibut/Shutterstock.com; page 76, (left) elbud/Shutterstock.com; page 82, (top) Nynke van Holten/Shutterstock.com, (bottom, composite image), cynoclub/ Shutterstock.com, Kuznetsov Alexey/Shutterstock.com; pages 111, 112, mejorana/Shutterstock.com; pages 159, 376 (right), Robert Burch/Alamy Stock Photo; page 218, lattesmile/Shutterstock. com; page 223, Direnko Kateryna/Shutterstock.com; page 224, Nataliya Nazarova/Shutterstock.com; page 317, Lissandra Melo/Shutterstock.com; page 376, (left) GagliardiPhotography/ Shutterstock.com; page 377, (center) i_am_zews/Shutterstock. com, (bottom), photka/Shutterstock.com; All other images are the property of Great Minds.

381

Acknowledgments Kelly Alsup, Dawn Burns, Jasmine Calin, Mary Christensen-Cooper, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Brittany duPont, Melissa Elias, Lacy Endo-Peery, Scott Farrar, Krysta Gibbs, Melanie Gutierrez, Eddie Hampton, Tiffany Hill, Robert Hollister, Christine Hopkinson, Rachel Hylton, Travis Jones, Kelly Kagamas Tomkies, Liz Krisher, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Ashley Meyer, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Andrea Neophytou Hart, Kelley Padilla, Kim L. Pettig, Marlene Pineda, Elizabeth Re, John Reynolds, Meri Robie-Craven, Robyn Sorenson, Marianne Strayton, James Tanton, Julia Tessler, Philippa Walker, Lisa Watts Lawton, MaryJo Wieland

Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

Trevor Barnes, Brianna Bemel, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper,

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EM2 Teach Grade 1 Module 5 UTE

Articles inside

Topic E

Math Past

Works Cited

Credits

Terminology

Acknowledgments