STEMscopes Georgia Math Student Notebook Grade 2 by acceleratelearning

Grade 2 Student Notebook

GEORGIA

Student Notebook – Grade 2 ISBN: 978-1-64861-269-5 Published by Accelerate Learning Inc. 5177 Richmond Ave, Suite 800, Houston, TX 77056. Copyright © 2023 by Accelerate Learning Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written consent of Accelerate Learning Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

To learn more, visit us at www.stemscopes.com.

GEORGIA

Student Notebook - Grade 2

Scope Name

Table of Contents

Page Number

Represent Numbers to 1,000

Compare and Order Numbers

Addition and Subtraction Strategies

Addition and Subtraction Problem Solving

Arrays

Two-Dimensional Shapes

Three-Dimensional Solids

Fractions

Length

103

Time

117

Money

135

Data Analysis

141

Patterns

151

iii

GEORGIA

Student Notebook - Grade 2

Table of Contents (Cont.) Scope Name Page Number Skills Quizzes

161

Glossary of Terms

191

Workspace

225

Represent Numbers to 1,000

Explore 1

Represent Numbers to 1,000

Name: _______________________ Date: __________

Grouping Hundreds and Tens to Count Collections

Draw a pictorial model for the total number of straws at each station. Write how many hundreds and tens there are in this number. Write how many groups of ten there are in the total number. Station 1

Pictorial Model

Number of Straws _____ Hundreds _____ Tens _____ groups of ten in _____

Station 2 Pictorial Model

Number of Straws _____ Hundreds _____ Tens _____ groups of ten in _____

Represent Numbers to 1,000 | 3

Explore 1

Represent Numbers to 1,000

Station 3 Pictorial Model

Number of Straws _____ Hundreds _____ Tens _____ groups of ten in _____

Station 4 Pictorial Model

Number of Straws _____ Hundreds _____ Tens _____ groups of ten in _____

4 | Represent Numbers to 1,000

Represent Numbers to 1,000

Explore 1 Station 5 Pictorial Model

Number of Straws _____ Hundreds _____ Tens _____ groups of ten in _____

Station 6 Pictorial Model

Number of Straws _____ Hundreds _____ Tens _____ groups of ten in _____

Reﬂect What was the most efficient way to count the straws?

Represent Numbers to 1,000 | 5

Represent Numbers to 1,000

Explore 2

Station 1

Name: _______________________ Date: __________

Grouping Hundreds, Tens, and Ones to Count Collections Pictorial Model

Number of Seeds ____ Hundreds

____ Tens ____ Ones _____ groups of ten in _____ Decompose this number in another way. Pictorial Model

Number of Seeds

____ Hundreds ____ Tens ____ Ones

Represent Numbers to 1,000 | 7

Represent Numbers to 1,000

Explore 2 Station 2 Pictorial Model H

Number of Seeds ____ Hundreds

____ Tens ____ Ones _____ groups of ten in _____ Decompose this number in another way. Pictorial Model

Number of Seeds

____ Hundreds ____ Tens ____ Ones

8 | Represent Numbers to 1,000

Represent Numbers to 1,000

Explore 2 Station 3 Pictorial Model H

Number of Seeds ____ Hundreds

____ Tens ____ Ones _____ groups of ten in _____ Decompose this number in another way. Pictorial Model

Number of Seeds

____ Hundreds ____ Tens ____ Ones

Represent Numbers to 1,000 | 9

Represent Numbers to 1,000

Explore 2 Station 4 Pictorial Model H

Number of Seeds ____ Hundreds

____ Tens ____ Ones _____ groups of ten in _____ Decompose this number in another way. Pictorial Model

Number of Seeds

____ Hundreds ____ Tens ____ Ones

10 | Represent Numbers to 1,000

Represent Numbers to 1,000

Explore 2 Station 5 Pictorial Model H

Number of Seeds ____ Hundreds

____ Tens ____ Ones _____ groups of ten in _____ Decompose this number in another way. Pictorial Model

Number of Seeds

____ Hundreds ____ Tens ____ Ones

Represent Numbers to 1,000 | 11

Represent Numbers to 1,000

Explore 2 Station 6 Pictorial Model H

Number of Seeds ____ Hundreds

____ Tens ____ Ones _____ groups of ten in _____ Decompose this number in another way. Pictorial Model

Number of Seeds

____ Hundreds ____ Tens ____ Ones

Reﬂect Explain how you decomposed one of the numbers in another way. ______________________________________________________ ______________________________________________________ 12 | Represent Numbers to 1,000

Explore 3

Represent Numbers to 1,000

Name: _______________________ Date: __________

Representing Numbers in Different Ways

Represent each given number in standard form, picture form, expanded form, and word form. Group 1 Standard form:

Pictorial model:

Expanded form:

Word form:

___ + ___ + ___

Group 2 Standard form:

Pictorial model:

Expanded form:

Word form:

Represent Numbers to 1,000 | 13

Represent Numbers to 1,000

Explore 3 Group 3 Standard form:

Pictorial model:

Expanded form:

Word form:

___ + ___ + ___

Group 4 Standard form:

Pictorial model:

Expanded form:

Word form:

___ + ___ + ___

14 | Represent Numbers to 1,000

Represent Numbers to 1,000

Explore 3 Group 5 Standard form:

Pictorial model:

Expanded form:

Word form:

___ + ___ + ___

Reﬂect Explain expanded form in your own words. ______________________________________________________ ______________________________________________________ ______________________________________________________

Represent Numbers to 1,000 | 15

Represent Numbers to 1,000

Explore 4

Name: _______________________ Date: __________

Counting and Place Value Patterns Start at the given seat number. Skip count by fives, tens, twenty-fives, or hundreds. Fill in the missing seat numbers, and answer the questions. Skip count by FIVES.

65 What do you notice about the place value pattern between these numbers? ____________________________________________________ ____________________________________________________ If the pattern continues, what could be the missing digit in this seat number?

22_

Represent Numbers to 1,000 | 17

Represent Numbers to 1,000

Explore 4 Skip count by HUNDREDS.

103 What do you notice about the place value pattern between these numbers? ____________________________________________________ ____________________________________________________ If the pattern continues, what could be the missing digit in this seat number? _03

Skip count by TENS.

119 What do you notice about the place value pattern between these numbers? ____________________________________________________ ____________________________________________________ If the pattern continues, what could be the missing digit in this seat number?

4_9

18 | Represent Numbers to 1,000

Represent Numbers to 1,000

Explore 4 Skip count by FIVES.

50 What do you notice about the place value pattern between these numbers? ____________________________________________________ ____________________________________________________ If the pattern continues, what could be the missing digit in this seat number?

74_

Skip count by HUNDREDS.

32 What do you notice about the place value pattern between these numbers? ____________________________________________________ ____________________________________________________ If the pattern continues, what could be the missing digit in this seat number?

_32

Represent Numbers to 1,000 | 19

Represent Numbers to 1,000

Explore 4 Skip count by TWENTY-FIVES.

25 What do you notice about the place value pattern between these numbers? ____________________________________________________ ____________________________________________________ If the pattern continues, what could be the missing digit in this seat number?

6_0

Reﬂect How can you apply the patterns you noticed to count backward? Give an example.

______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________

20 | Represent Numbers to 1,000

Even and Odd

Name: _______________________ Date: __________

will eat. will eat.

Draw how many pieces of food the Draw how many pieces of food the

Leftover pieces of food:

Represent Numbers to 1,000 | 21

Number sentence: __________________________________________________________

How do you know? _________________________________________________________

Is the starting total even or odd odd? ______________________________________________

Total number of pieces of food:

Station 1

Count the pieces of food at each station. Share the pieces equally between the two animals. Complete each table, and answer the questions. Write a number sentence to show the pieces of food each animal ate plus any leftover pieces of food.

Explore 5

Represent Numbers to 1,000

will eat. will eat.

Draw how many pieces of food the Draw how many pieces of food the

Station 2 Leftover pieces of food:

will eat. will eat.

Draw how many pieces of food the Draw how many pieces of food the

Leftover pieces of food:

22 | Represent Numbers to 1,000

Number sentence: __________________________________________________________

How do you know? _________________________________________________________

Is the starting total even or odd odd? ______________________________________________

Total number of pieces of food:

Station 3

Number sentence: __________________________________________________________

How do you know? _________________________________________________________

Is the starting total even or odd odd? ______________________________________________

Total number of pieces of food:

Explore 5

Represent Numbers to 1,000

will eat. will eat.

Draw how many pieces of food the Draw how many pieces of food the

Station 4 Leftover pieces of food:

will eat. will eat.

Draw how many pieces of food the Draw how many pieces of food the

Leftover pieces of food:

Represent Numbers to 1,000 | 23

Number sentence: __________________________________________________________

How do you know? _________________________________________________________

Is the starting total even or odd odd? ______________________________________________

Total number of pieces of food:

Station 5

Number sentence: __________________________________________________________

How do you know? _________________________________________________________

Is the starting total even or odd odd? ______________________________________________

Total number of pieces of food:

Explore 5

Represent Numbers to 1,000

will eat. will eat.

Draw how many pieces of food the Draw how many pieces of food the

Station 6 Leftover pieces of food:

24 | Represent Numbers to 1,000

_______________________________________________________________________

What do odd numbers have in common?

_______________________________________________________________________

Reﬂect What do even numbers have in common?

Number sentence: __________________________________________________________

How do you know? _________________________________________________________

Is the starting total even or odd odd? ______________________________________________

Total number of pieces of food:

Explore 5

Represent Numbers to 1,000

Compare and Order Numbers

Explore 1

Name: _______________________ Date: __________

Identifying Numbers Greater Than or Less Than

Look at each Store Ad. Build the original price with the base ten blocks. Use the blocks to determine the discounted price and competitor’s price. Complete the table by writing the numbers and drawing a pictorial model for each number.

Store Ad 1

Discounted Price

Store Ad 2

Discounted Price

Original Price

$23 Original Price

$245

Competitor’s Price

$ Competitor’s Price

Compare and Order Numbers | 27

Compare and Order Numbers

Explore 1

Store Ad 3

Discounted Price

Store Ad 4

Discounted Price

Store Ad 5

Discounted Price

28 | Compare and Order Numbers

Original Price

$767

Original Price

$135

Competitor’s Price

Original Price

$495

Competitor’s Price

Compare and Order Numbers

Explore 1 Store Ad 6

Discounted Price

Original Price

Competitor’s Price

$519

Reﬂect Which numbers were greater than the original prices?

______________________________________________________ ______________________________________________________ Which numbers were less than the original prices?

______________________________________________________ ______________________________________________________ What place value changes when you add or take away 10?

______________________________________________________ ______________________________________________________ What place value changes when you add or take away 100?

______________________________________________________ ______________________________________________________

Compare and Order Numbers | 29

Explore 2

Compare and Order Numbers

Name: _______________________ Date: __________

Comparing and Ordering Numbers Part I Plot the number of words each student spelled correctly on a number line. Compare the numbers in more than one way by using symbols <, >, or = and comparative language: greater than, less than, or equal to. Circle the name of the student who won each round. Tony vs. AJ

500

700

600 Comparison 1

Comparison 2

Write a comparison statement.

_________________________

________________________.

Compare and Order Numbers | 31

Compare and Order Numbers

Explore 2 Shreya vs. Gia

500

1,000

Comparison 1

Comparison 2

Write a comparison statement.

_________________________

________________________.

Rodney vs. Imari

800

900

1,000

Comparison 1

Comparison 2

Write a comparison statement.

_________________________

________________________. 32 | Compare and Order Numbers

________________________.

Compare and Order Numbers

Explore 2 Ellyn vs. Max

500

1,000

Comparison 1

Comparison 2

Write a comparison statement.

_________________________

________________________.

Adhira vs. Camille

300

600

Comparison 1

Comparison 2

Write a comparison statement.

_________________________

________________________.

Compare and Order Numbers | 33

Compare and Order Numbers

Explore 2

Part II List and order the contestants from the greatest number of correct words to the least number of correct words. Plot these numbers on the number line to determine who won the spelling bee. Student’s Name

0 Reﬂect Who won the spelling bee?

Words Spelled Correctly

500

1,000

______________________________________________________ 34 | Compare and Order Numbers

Addition and Subtraction Strategies

Explore 1

Name: _______________________ Date: __________

Addition and Subtraction with Two 2-Digit Numbers

Estimate a solution, and then solve each problem using your mental math strategies. Show your work in each box. Write your solution, and explain your strategies in words.

Grocery Shopping Task 1

Estimation: $____

Total Spent: $____

Explain your strategy in words. ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________

Addition and Subtraction Strategies | 37

Addition and Subtraction Strategies

Explore 1 Grocery Shopping Task 2

Estimation: $____

Total Spent: $____

Estimation: $____

Total Spent: $____

Addition and Subtraction Strategies

Explore 1 Grocery Shopping Task 4

Estimation: $____

Total Spent: $____

Estimation: $____

Total Spent: $____

Addition and Subtraction Strategies | 39

Addition and Subtraction Strategies

Explore 1 Grocery Shopping Task 6

Estimation: $____

Total Spent: $____

Explain your strategy in words. ______________________________________________________ ______________________________________________________ ______________________________________________________ Reﬂect What strategy was easier to use with addition? ______________________________________________________

______________________________________________________

______________________________________________________ What strategy was easier to use with subtraction? ______________________________________________________

______________________________________________________ How did estimating before solving the problem help you? ______________________________________________________

______________________________________________________ 40 | Addition and Subtraction Strategies

Name: _______________________ Date: __________

Estimation:

Mental math strategy:

Number sentence:

Solution:

Mental math strategy:

Number sentence:

Solution:

Addition and Subtraction Strategies | 41

Pictorial model:

Estimate the sum of the values of the gems in each bag using compatible numbers. Use mental math strategies to solve. Check your strategy using base ten blocks, and draw a pictorial model.

Addition with More Than Two 2-Digit Numbers

Explore 2

Addition and Subtraction Strategies

42 | Addition and Subtraction Strategies

Estimation:

Explore 2

Mental math strategy:

Number sentence:

Solution:

Mental math strategy:

Number sentence:

Solution:

Pictorial model:

Addition and Subtraction Strategies

Mental math strategy:

Number sentence:

Solution:

Mental math strategy:

Number sentence:

Solution:

Pictorial model:

Addition and Subtraction Strategies | 43

_______________________________________________________________________

Reﬂect How is estimating using compatible numbers a helpful strategy?

Estimation:

Explore 2

Addition and Subtraction Strategies

Explore 3

Addition and Subtraction Strategies

Name: _______________________ Date: __________

Explaining Addition and Subtraction Strategies

Estimate and solve each Party Purchase Task Card. Study the two possible strategies. Decide which strategy would not correctly solve the problem, and explain why the strategy is incorrect. Card 1 Estimate:

Solve:

Strategy _____ does not work to find the correct answer because _____________________________________________________ _____________________________________________________

Card 2 Estimate:

Solve:

Strategy _____ does not work to find the correct answer because _____________________________________________________ _____________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Addition and Subtraction Strategies | 45

Addition and Subtraction Strategies

Explore 3 Card 3 Estimate:

Solve:

Strategy _____ does not work to find the correct answer because _____________________________________________________ _____________________________________________________

Card 4 Estimate:

Solve:

Strategy _____ does not work to find the correct answer because _____________________________________________________ _____________________________________________________

Reﬂect Explain a strategy you like to use when solving an addition or subtraction word problem. ______________________________________________________ ______________________________________________________ 46 | Addition and Subtraction Strategies

Addition and Subtraction Problem Solving

Name: _______________________ Date: __________

Pictorial Model

Exhibit Number

Number Sentence with Solution

Addition and Subtraction Problem Solving | 49

Number Sentence Using a Symbol for the Unknown

Part I Use your manipulatives to solve each problem. Draw a pictorial model of your base ten blocks to show your solution. Write a number sentence for your model using a symbol for the unknown, and then write a second number sentence with your solution.

Represent and Solve One-Step Problems

Explore 1

Addition and Subtraction Problem Solving

Pictorial Model

50 | Addition and Subtraction Problem Solving

Exhibit Number

Explore 1 Number Sentence with Solution

Number Sentence Using a Symbol for the Unknown

Addition and Subtraction Problem Solving

Models

Addition and Subtraction Problem Solving | 51

_______________________________________________________________________

Reﬂect Explain how to create a bar model in your own words.

Exhibit Number

Part II Record the letters of the two models that could be used to solve each problem.

Explore 1

Addition and Subtraction Problem Solving

Explore 2

Name: _______________________ Date: __________

Represent and Solve Multistep Problems Complete each table with a pictorial model or a number sentence with a symbol for the unknown. Solve each problem. Wave Pool Pictorial model:

Number sentence with unknown: ? + 54 + 22 = 95 Solution:

Lazy River Pictorial model:

Number sentence with unknown: 92

Solution:

Addition and Subtraction Problem Solving | 53

Addition and Subtraction Problem Solving

Explore 2 Funnel Slide Pictorial model:

Number sentence with unknown:

100 52

Solution:

Dump-and-Pour Playground Pictorial model:

Number sentence with unknown:

Solution:

Reﬂect Compare how you solved these two problems. What is the same and what is different? ______________________________________________________ ______________________________________________________ ______________________________________________________ 54 | Addition and Subtraction Problem Solving

Addition and Subtraction Problem Solving

Explore 2 Tube Slide Pictorial model:

Number sentence with unknown: ? – 12 – 5 = 83 Solution:

Tidal-Wave Slide Pictorial model:

Number sentence with unknown: 28 + 33 + 34 = ? Solution:

Reﬂect What do you need to remember when solving multistep problems? ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Addition and Subtraction Problem Solving | 55

Arrays

Explore 1

Arrays

Name: _______________________ Date: __________

Arrays with Concrete Objects Part 1 Count the number of objects in the array. Circle the strategy you used to count the objects. Write an equation to represent the total number of objects, and then label the package for the toy factory.

Package 1

Counting one by one Skip counting

Repeated addition Equation:

Package 2

Counting one by one Skip counting

Repeated addition Equation:

Arrays | 59

Arrays

Explore 1 Package 3

Counting one by one Skip counting

Repeated addition Equation:

Package 4

Counting one by one Skip counting

Repeated addition Equation:

Package 5

Counting one by one Skip counting

Repeated addition Equation:

60 | Arrays

Arrays

Explore 1

Part II Using the objects in the basket and the Direction Card, build an array on the Story Mat. Draw a model of your array. Write an equation to represent the total number of objects, and then label the package for the toy factory. Package 1

Model of array:

Equation:

Package 2

Model of array:

Equation:

Arrays | 61

Arrays

Explore 1 Package 3

Model of array:

Equation:

Package 4

Model of array:

Equation:

Package 5

Model of array:

Equation:

62 | Arrays

Explore 2

Arrays

Name: _______________________ Date: __________

Arrays with Pictorial Models Use the grid paper to draw a pictorial model of the array for each Task Card. Write the equation to represent the total number of magic beans Jane planted. Task Card 1 Equation:

Task Card 2 Equation:

Arrays | 63

Arrays

Explore 2 Task Card 3 Equation:

Task Card 4 Equation:

64 | Arrays

Arrays

Explore 2 Task Card 5 Equation:

Task Card 6 Equation:

Arrays | 65

Arrays

Explore 2 Task Card 7 Equation:

Task Card 8 Equation:

66 | Arrays

Two-Dimensional Shapes

Explore 1

Name: _______________________ Date: __________

Sorting 2-D Shapes Draw how your group sorted the two-dimensional shapes.

What attributes did you use to sort the shapes? ______________________________________________________ Is there another way to sort the shapes? ______________________________________________________ Choose two shapes, write the letters, and explain how the shapes are the same and how they are different. ______________________________________________________ ______________________________________________________ ______________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Two-Dimensional Shapes | 69

Two-Dimensional Shapes

Explore 2

Name: _______________________ Date: __________

Classifying 2-D Shapes Write the names of the mystery shapes in bag 1. Label the shapes with their attributes.

Two-Dimensional Shapes | 71

Explore 2

Two-Dimensional Shapes

Write the names of the mystery shapes in bag 2. Label the shapes with their attributes.

72 | Two-Dimensional Shapes

Explore 2

Two-Dimensional Shapes

Write the names of the mystery shapes in bag 3. Label the shapes with their attributes.

What do these shapes have in common? ____________________________________________________ ____________________________________________________ Word Bank: triangle, square, rhombus, trapezoid, hexagon, circle, rectangle, quadrilateral, pentagon, crescent, cloud, heart Reﬂect What is the relationship between the numbers of sides, vertices, and angles for regular 2-D shapes? ______________________________________________________ ______________________________________________________ ______________________________________________________

Two-Dimensional Shapes | 73

Two-Dimensional Shapes

Explore 3

Name: _______________________ Date: __________

Drawing 2-D Shapes

Draw each shape you created, and list the attributes.

_____ vertices _____ angles _____ sides My shape is a ________________.

Two-Dimensional Shapes | 75

Explore 3

Two-Dimensional Shapes

_____ vertices _____ angles _____ sides My shape is a ________________.

Reﬂect Why is there more than one answer to some Task Cards? ______________________________________________________ ______________________________________________________ ______________________________________________________

76 | Two-Dimensional Shapes

Explore 4

Two-Dimensional Shapes

Name: _______________________ Date: __________

Identifying Lines of Symmetry Part I Draw a line to show how you folded each shape to create a line of symmetry. Answer the question.

How can you tell if a shape has a line of symmetry? ______________________________________________________ ______________________________________________________

Two-Dimensional Shapes | 77

Two-Dimensional Shapes

Explore 4

Part II Draw a line to show how each shape was folded. Write “yes” if it shows a line of symmetry or “no” if it does not show a line of symmetry. Answer the question.

_________

Which shapes were folded in a way that did not show a line of symmetry? Explain how you could tell these were not lines of symmetry. ______________________________________________________ ______________________________________________________ 78 | Two-Dimensional Shapes

Three-Dimensional Solids

Explore 1

Name: _______________________ Date: __________

Sorting 3-D Solids Draw a circle for each category, write the names of the real-world solids inside, and fill in the blank to explain how you sorted the 3-D solids.

I sorted by ___________________________________________. What is another way to sort the 3-D solids?

I sorted by ___________________________________________. Reﬂect What attributes do not help identify an object as a three-dimensional solid?

Three-Dimensional Solids | 81

Three-Dimensional Solids

Explore 2

Name: _______________________ Date: __________

Classifying 3-D Solids

List the attributes of the solids in each group, name the exhibit, and then draw a model of each solid. _________ Exhibit (Name of solid)

List the attributes and draw a model of the solids in this group.

_________ Exhibit (Name of solid)

List the attributes and draw a model of the solids in this group.

C_________ Exhibit (Name of solid)

List the attributes and draw a model of the solids in this group.

Three-Dimensional Solids | 83

Three-Dimensional Solids

Explore 2 _________ Exhibit (Name of solid)

List the attributes and draw a model of the solids in this group.

_________ Exhibit (Name of solid)

List the attributes and draw a model of the solids in this group.

Reﬂect How are a cone and a cylinder similar and different?

84 | Three-Dimensional Solids

Explore 3

Three-Dimensional Solids

Name: _______________________ Date: __________

Relationships between Cubes and Rectangular Prisms

Fill in the Venn diagram with the similarities and differences of the two solids.

Reﬂect Which block do you think will work the best as a die for the board game? Explain your answer. ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Three-Dimensional Solids | 85

Three-Dimensional Solids

Explore 4

Name: _______________________ Date: __________

Drawing 3-D Solids Use dots and lines to draw a model of each block. List the name of the three-dimensional solid with the same attributes. Block 1: Model:

Attributes:

Block 2: Model:

Attributes:

Three-Dimensional Solids | 87

Three-Dimensional Solids

Explore 4

Block 3: Model:

Attributes:

Block 4: Model:

88 | Three-Dimensional Solids

Attributes:

Three-Dimensional Solids

Explore 4

Block 5: Model:

Attributes:

Reﬂect What attribute is difficult to draw on some of the three-dimensional solids?

______________________________________________________ ______________________________________________________

Three-Dimensional Solids | 89

Fractions

Explore 1

Name: _______________________ Date: __________

Partitioning Objects

Fold and cut each colored piece of fabric into equal parts. Draw lines on the rectangle to show your equal parts. Label each equal part as either one-half, one-third, or one-fourth. Red Fabric Cut into 2 equal parts.

How many parts make one whole? What is this whole partitioned into?

Fractions | 93

Fractions

Explore 1 Green Fabric Cut into 3 equal parts.

How many parts make one whole? What is this whole partitioned into?

Blue Fabric Cut into 4 equal parts.

How many parts make one whole? What is this whole partitioned into?

94 | Fractions

Fractions

Explore 1 Yellow Fabric Cut into 2 equal parts that are different from your red fabric.

How many parts make one whole? What is this whole partitioned into?

Orange Fabric Cut into 3 equal parts that are different from your green fabric.

How many parts make one whole? What is this whole partitioned into?

Fractions | 95

Explore 1

Fractions

Black Fabric Cut into 4 equal parts that are different from your blue fabric.

How many parts make one whole? What is this whole partitioned into?

Reﬂect Compare and contrast your pieces of red and yellow fabric. ______________________________________________________ ______________________________________________________ ______________________________________________________ What do you notice about the size of the pieces as you partition your fabric into more and more pieces? ______________________________________________________ ______________________________________________________ ______________________________________________________ 96 | Fractions

Explore 2

Fractions

Name: _______________________ Date: __________

Examples and Nonexamples

Draw a model of each candy bar or chocolate cup. Write how many parts it is partitioned into, and decide if the parts are equally sized. Explain whether the model is an example or nonexample of halves, thirds, or fourths. Chocolate Cup 1

How many parts make one whole chocolate cup? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________. Candy Bar 2

How many parts make one whole candy bar? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

Fractions | 97

Fractions

Explore 2 Candy Bar 3

How many parts make one whole candy bar? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________.

Chocolate Cup 4

How many parts make one whole chocolate cup? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________.

98 | Fractions

Fractions

Explore 2 Candy Bar 5

How many parts make one whole candy bar? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________.

Chocolate Cup 6

How many parts make one whole chocolate cup? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________.

Fractions | 99

Fractions

Explore 2 Candy Bar 7

How many parts make one whole candy bar? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________.

Candy Bar 8

How many parts make one whole candy bar? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________.

100 | Fractions

Fractions

Explore 2 Candy Bar 9

How many parts make one whole candy bar? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________. Candy Bar 10

How many parts make one whole candy bar? Are the parts equal in size?

This is a(n) _____________ of _____________ because (example/nonexample)

(halves/thirds/fourths)

___________________________________________. Reﬂect Does a shape have to be partitioned in the exact same way to make the parts equal? Explain. ______________________________________________________

Fractions | 101

Length

103

Length

Explore 1

Name: _______________________ Date: __________

Construct Measuring Instruments

Measure the items using the measuring instruments. Record the measurements in the tables below. Station 1 Length with Inch Tiles

Length with Ruler

Book 1: ______ inch tiles

Book 1: ______ inches

Book 2: ______ inch tiles

Book 2: ______ inches Station 2

Length with Paper Clips

Length with Ruler

Book 1: ______ paper clips

Book 1: ______ inches

Book 2: ______ paper clips

Book 2: ______ inches

Station 3 Length with Centimeter Cubes

Length with Ruler

Book 1: ______ cm cubes

Book 1: ______ inches

Book 2: ______ cm cubes

Book 2: ______ inches

Length | 105

Length

Explore 1 Station 4 Length with Linking Cubes

Length with Ruler

Book 1: ______ linking cubes

Book 1: ______ inches

Book 2: ______ linking cubes

Book 2: ______ inches

Station 5 Length with Pennies

Length with Ruler

Book 1: ______ pennies

Book 1: ______ inches

Book 2: ______ pennies

Book 2: ______ inches

Reﬂect Which measuring instrument is more accurate in measuring the books? Explain why.

______________________________________________________ ______________________________________________________ How does measuring with a ruler compare to measuring with the instrument you constructed?

______________________________________________________ ______________________________________________________ ______________________________________________________ 106 | Length

Explore 2

Length

Name: _______________________ Date: __________

Length Using Formal Measuring Tools Part I Complete the table for each item being measured around the classroom.

Item Being Measured

Measurement Tool

Estimation

Actual Length

Will this item ﬁt in a box or in the cabinet? Yes No Yes No Yes No Yes No Yes No Yes No

Length | 107

Length

Explore 2

Part II Use a ruler to measure each object using the given units. Record each object’s length in the table. Object

Stapler

Pen

Notebook

Sticky note pad

Scissors

Actual Length

____ cm

____ in.

____ cm

____ in.

Read the questions. Compare the length of the two objects. Write a number sentence to solve, and label your answer with units. 1. How much longer is the stapler than the sticky note pad? ____________________________________________________ 2. How much longer is the notebook than the pen? ____________________________________________________ 3. How much longer are the scissors than the pen? ____________________________________________________ Reﬂect If you want to measure the length of the classroom, which measurement tool would you use? Why?

______________________________________________________ ______________________________________________________ 108 | Length

Length

Explore 3

Name: _______________________ Date: __________

Inverse Relationships

Use a ruler to measure the length of your foot in both centimeters and inches. Draw a number line representing centimeters and a number line representing inches to model your findings. Answer the question to reflect.

Write your measurements for your foot in the table below. Centimeters

Inches

Reﬂect What is the relationship between the size of the unit and the number of units?

Length | 109

Explore 4

Length

Name: _______________________ Date: __________

Solving Problems with Length

Write the answer to each Task Card next to the correct letter. A

Reﬂect How do rulers help solve addition and subtraction word problems involving length? Explain. ______________________________________________________

Length | 111

Explore 5

Length

Name: _______________________ Date: __________

Representing Addition and Subtraction on a Number Line

Use the number line and counter to act out addition and subtraction for each Frog Problem-Solving Card. Draw the solution for each card, and write the number sentence that describes it. Card 1

Number sentence: ______________________________________ Card 2

Number sentence: ______________________________________ Card 3

Length | 113

Length

Explore 5 Card 4

Number sentence: ______________________________________ Card 5

Number sentence: ______________________________________ Card 6

Number sentence: ______________________________________ Card 7

Number sentence: ______________________________________ 114 | Length

Length

Explore 5 Card 8

Number sentence: ______________________________________

Reﬂect Explain a strategy you used as you solved an addition or subtraction problem using an open number line. ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________

Length | 115

Time

117

Explore 1

Time

Name: _______________________ Date: __________

A.M. and P.M. Use the time line you created to complete the following table. A.M. Activities

P.M. Activities

Reﬂect Is noon in the a.m. or p.m.? Explain.

______________________________________________________ ______________________________________________________ Is midnight in the a.m. or p.m.? Explain.

Time | 119

Time

Explore 2

Name: _______________________ Date: __________

Hour-Hand Clocks

Use the clocks below to label the times on your time line. Write the hour each activity occurs. Be sure to include a.m. or p.m. A.M. Activities:

_____________

11 12 1 2 10 9 3 4 8 7 6 5

_____________

11 12 1 2 10 9 3 4 8 7 6 5

Time | 121

Time

Explore 2 P.M. Activities: _____________

_____________

11 12 1 2 10 9 3 4 8 7 6 5

_____________

11 12 1 2 10 9 3 4 8 7 6 5

Reﬂect How do you know where to place the hour hand on the clock?

______________________________________________________ ______________________________________________________ 122 | Time

Explore 3

Time

Name: _______________________ Date: __________

Hour- and Minute-Hand Clocks

Write the time for each arriving and departing flight. Answer the questions. Arrivals Terminal

Flight

FL303

NY121

CA432

WA599

CO287

Time

Departures Terminal

Flight

TX503

NV211

GA324

IL959

LA782

Time

Time | 123

Explore 3

Time

Reﬂect What does each number on the analog clock represent when writing the minutes? ______________________________________________________ What is an example of “half past” or “on the half hour”? ______________________________________________________ What is an example of “quarter past” or “on the quarter hour”? ______________________________________________________

124 | Time

Time

Explore 4

Name: _______________________ Date: __________

Digital and Analog Clocks

Record all the start and end times below by drawing in the clock hands and writing the digital times. Circle a.m. or p.m. Kindergarten Jump-Rope Contest Start

9 ____: ____

a.m.

End

p.m.

____: ____

a.m.

p.m.

1st-Grade Jump-Rope Contest Start

____: ____

a.m.

End

p.m.

____: ____

a.m.

p.m. Time | 125

Time

Explore 4 2nd-Grade Jump-Rope Contest Start

1 ____: ____

a.m.

End

p.m.

1 ____: ____

a.m.

p.m.

a.m.

p.m.

3rd-Grade Jump-Rope Contest Start

____: ____

126 | Time

a.m.

End

p.m.

12 ____: ____

Time

Explore 4 4th-Grade Jump-Rope Contest Start

____: ____

a.m.

End

p.m.

____: ____

a.m.

p.m.

5th-Grade Jump-Rope Contest Start

____: ____

a.m.

End

p.m.

____: ____

a.m.

p.m.

Reﬂect Look at the time on the clock to the right. How can you write the time 3 ways?

Time | 127

Explore 5

Time

Name: _______________________ Date: __________

Elapsed Time

Determine when each activity begins or ends by filling in the digital time, including a.m. or p.m. Measure the elapsed time to the hour or half hour using the time line. Go Fish Start time: ____:____ ___.___. End time: ____:____ ___.___.

How long will this activity last? __________________________ Bean Bag Toss Start time: ____:____ ___.___. End time: ____:____ ___.___.

Time | 129

Time

Explore 5 Bake Sale

Start time: ____:____ ___.___. End time: ____:____ ___.___.

How long will this activity last? __________________________ Magic Show Start time: ____:____ ___.___. End time: ____:____ ___.___.

How long will this activity last? __________________________

130 | Time

Time

Explore 5 Face Painting

Start time: ____:____ ___.___. End time: ____:____ ___.___.

How long will this activity last? __________________________ Sack Race Start time: ____:____ ___.___. End time: ____:____ ___.___.

How long will this activity last? __________________________

Time | 131

Time

Explore 5 Dunking Booth

Start time: ____:____ ___.___. End time: ____:____ ___.___.

How long will this activity last? __________________________ Talent Show Start time: ____:____ ___.___. End time: ____:____ ___.___.

How long will this activity last? __________________________

132 | Time

Time

Explore 5 Reﬂect Which activity will last the longest? Explain.

______________________________________________________ ______________________________________________________ Explain the steps you used to measure elapsed time on the time line.

Time | 133

Money

135

Value of a Collection of Bills and Coins

Name: _______________________ Date: __________

Bills and Coins

(Label your skip counts under the bills and coins.)

To-Go Order

(___ dollars or ___ cents)

Order Total

Money | 137

($ ___ or ___¢)

Order Total

Draw a pictorial model of the bills and coins each customer gave you. Skip count to find the total value of the group of bills and coins. Write the total cost of each to-go order in two ways.

Explore 1

Money

(Label your skip counts under the bills and coins.)

Bills and Coins (___ dollars or ___ cents)

Order Total

($ ___ or ___¢)

Order Total

138 | Money

________________________________________________________________________

Reﬂect How could you order your bills or coins to make skip counting easier?

To-Go Order

Explore 1

Money

Name: _______________________ Date: __________

Task Card

Show Your Work

Solution

Money | 139

Read each Task Card. Solve each problem by showing your work in the space provided using an equation or a pictorial model. Write your solution.

Solving Word Problems Involving Bills and Coins

Explore 2

Money

Show Your Work

Solution

140 | Money

_______________________________________________________________________

Reﬂect What strategy helped you the most when solving each word problem? _______________________________________________________________________

Task Card

Explore 2

Money

Data Analysis

141

Explore 1

Data Analysis

Name: _______________________ Date: __________

Organizing Data Using Pictographs Part I: Planning and Data Collection Create a question and 4 category options to survey the class. Question:

______________________________________________________ Categories: a. b. c. d.

Categories

Number of Votes

Data Analysis | 143

Data Analysis

Explore 1

Part II: Create a Pictograph Use the data you collected to create a pictograph. Don’t forget your title, labels, and a legend/key. ____________________________ Categories

Number of Votes

Each _______ = 1 vote Reﬂect What can you predict using the data from the pictograph?

______________________________________________________ ______________________________________________________

144 | Data Analysis

Explore 2

Data Analysis

Name: _______________________ Date: __________

Organizing Data Using Bar Graphs Use the data from your pictograph to create a bar graph.

________________________________

Reﬂect How is the bar graph the same as the pictograph? How is it different?

Data Analysis | 145

Explore 3

Data Analysis

Name: _______________________ Date: __________

Solving Problems by Interpreting Data Circle whether the data on each Data Card is displayed by tally marks, a table, a pictograph, or a bar graph. Write the Data Card’s title, list the categories, and write the number of student votes in each category. Draw a pictorial model, and write a number sentence to solve. Circle your answer. Mrs. Moon’s Class Data Tally marks Table Pictograph

Bar graph

Data title: Pictorial model: ______________________ Categories and number of students: 1. _______________ = ___

2. _______________ = ___

3. _______________ = ___

Number sentence:

4. _______________ = ___

Data Analysis | 147

Data Analysis

Explore 3 Ms. Hendrickson’s Class Data Tally marks Table Pictograph Bar graph Data title: Pictorial model: ______________________ Categories and number of students: 1. _______________ = ___

2. _______________ = ___

3. _______________ = ___

Number sentence:

4. _______________ = ___

Mr. Grisham’s Class Data Tally marks Table Pictograph Bar graph Data title: Pictorial model: ______________________ Categories and number of students: 1. _______________ = ___

2. _______________ = ___

3. _______________ = ___

Number sentence:

4. _______________ = ___

148 | Data Analysis

Data Analysis

Explore 3 Mrs. McMurray’s Class Data Tally marks Table Pictograph Bar graph Data title: Pictorial model: ______________________ Categories and number of students: 1. _______________ = ___

2. _______________ = ___

3. _______________ = ___

Number sentence:

4. _______________ = ___

Ms. Clancey’s Class Data Tally marks Table Pictograph Bar graph Data title: Pictorial model: ______________________ Categories and number of students: 1. _______________ = ___

2. _______________ = ___

3. _______________ = ___

Number sentence:

4. _______________ = ___

Data Analysis | 149

Data Analysis

Explore 3 Mr. Thompson’s Class Data Tally marks Table Pictograph Bar graph Data title: Pictorial model: ______________________ Categories and number of students: 1. _______________ = ___

2. _______________ = ___

3. _______________ = ___

Number sentence:

4. _______________ = ___ Question about the graph:

Reﬂect How could you use the data that was represented on each Data Card to determine how many students are in each class?

______________________________________________________ ______________________________________________________ ______________________________________________________ What other questions could be asked from the data collected for each class? ______________________________________________________

______________________________________________________

______________________________________________________ 150 | Data Analysis

Patterns

151

Patterns

Explore 1

Name: _______________________ Date: __________

Repeated Operations Identify and complete the pattern for each Task Card. Complete the description, and circle the operation that repeated in each pattern. Task Card 1 29, 27, 25, ____, ____ This pattern counts ____________ by ____ beginning with ___. (forward, backward) Addition

Subtraction

Task Card 2 125, ____, ____, ____, ____ This pattern counts ____________ by ____ beginning with ___. (forward, backward) Addition

Subtraction

Patterns | 153

Patterns

Explore 1 Task Card 3 25, 50, 75, 100, ____, ____

This pattern counts ____________ by ____ beginning with ___. (forward, backward) Addition

Subtraction Task Card 4

432, 422, 412, ____, ____ This pattern counts ____________ by ____ beginning with ___. (forward, backward) Addition

Subtraction Task Card 5

736, 737, 738, 739, ____, ____ This pattern counts ____________ by ____ beginning with ___. (forward, backward) Addition

154 | Patterns

Subtraction

Patterns

Explore 1 Task Card 6 ____, ____, ____, ____, ____

This pattern counts ____________ by ____ beginning with ___. (forward, backward) Addition

Subtraction

Reﬂect What do you notice about the pattern on Task Card 4?

______________________________________________________ ______________________________________________________ Describe the pattern you created for Task Card 6.

Patterns | 155

Patterns

Explore 2

Name: _______________________ Date: __________

Growing and Shrinking Patterns

Identify and complete the pattern for each Task Card by writing the number under each set and drawing what comes next. Circle whether the pattern is growing or shrinking. Task Card 1

Growing

Shrinking

Task Card 2

Growing

Shrinking

Task Card 3

Shrinking Patterns | 157

Patterns

Explore 2 Task Card 4

Growing

Shrinking

Task Card 5

Growing

Shrinking

Reﬂect What do you notice about the shape patterns?

______________________________________________________ ______________________________________________________ Describe the pattern you created for Task Card 5.

______________________________________________________ ______________________________________________________ ______________________________________________________ 158 | Patterns

Patterns

Explore 2

Complete the growing or shrinking pattern by writing the numbers on the lines. Circle whether the pattern is growing or shrinking. Task Card 6 $20, _____, _____, _____, _____, _____ Growing

Shrinking

Task Card 7 19, 17, 15, _____, _____, _____, _____, _____ Growing

Shrinking

Task Card 8 4 claps, 6 claps, 8 claps, _____, _____, _____, _____, _____ Growing

Shrinking

Patterns | 159

Patterns

Explore 2 Task Card 9 $2, $4, $6, _____, _____, _____, _____, _____ Growing

Shrinking

Task Card 10 20, _____, _____, _____, _____, _____ Growing

Shrinking

Reﬂect What do you notice about Mr. Green’s pattern?

______________________________________________________ ______________________________________________________ Describe the pattern you created for Task Card 10.

______________________________________________________ ______________________________________________________ ______________________________________________________ 160 | Patterns

Skills Quizzes

161

Skills Quiz

Represent Numbers to 1,000

Name: _______________________ Date: __________

Represent Numbers to 1,000

1. Look at the base ten blocks below.

What is the base-ten numeral represented here? ___________ 2. Draw the number 214 using base ten blocks.

Represent Numbers to 1,000 | 163

Represent Numbers to 1,000

Skills Quiz

4. Count on from the given numbers in the table. Use the pattern. Count By

Fill in the blanks.

115, 120, 125, ______ ______, ______ ______, ______

10s

431, 441, ______ ______, ______ ______, ______

25s

0, 25, 50, 75, 100, 125, 150, ______ ______, ______

100s

306, 406, ______ ______, ______ ______, ______

5. How many hundreds, tens, and ones make the number 408? __________________________________________________ 6. Ann and Fred have 16 cookies. Ann says this is an even number of cookies; Fred says it is an odd number. Who is correct? ____________________ Draw a picture to show that person is correct.

Write an equation that proves that person is correct. ____________________

164 | Represent Numbers to 1,000

Compare and Order Numbers

Skills Quiz

Name: _______________________ Date: __________

Compare and Order Numbers

Place each number on the number line. Put a <, >, or = in each circle below to make the statement true. 1.

598

500

543

550

254

200

600

300

100

389

400

109

800

142

150

875

200

875

850

900

Compare and Order Numbers | 165

Compare and Order Numbers

Skills Quiz

5. Place each number on the number line. List the numbers in order from least to greatest. 457, 507, 491

400

450

500

550

_________________________________________ 6. Place each number on the number line. List the numbers in order from greatest to least. 776, 682, 804

600

700

800

_________________________________________ 7. What number is 10 more than 562?

__________________

8. What number is 100 more than 830?

__________________

9. What number is 100 less than 678?

__________________

10. Write a number that is less than 137.

__________________

166 | Compare and Order Numbers

Skills Quiz

Addition and Subtraction Strategies

Name: _______________________ Date: __________

Addition and Subtraction Strategies

Solve each problem by using the strategy of your choice. 1. 55 + 13 + 15 + 17

2. 93 – 64

3. 67 – 40

4. 24 + 36 + 18

5. 42 + 35 + 13

6. 72 – 29

7. Solve this problem by using two different strategies. Be sure to show your work. 86 – 47

Addition and Subtraction Strategies | 167

Skills Quiz

Addition and Subtraction Strategies

Andrew and Bobby both had some base ten blocks. The pictures below show how many blocks they each had. Write how many blocks each boy had. Then, answer the questions that follow. Andrew

Bobby

________________

8. How many blocks did the boys have combined? Show your work below.

168 | Addition and Subtraction Strategies

9. What is the difference in the number of blocks the two boys had? Show your work below.

Skills Quiz

Addition and Subtraction Problem Solving

Name: _______________________ Date: __________

Addition and Subtraction Problem Solving

1. William had 35 baseball cards. His grandpa gave him 25 more for his birthday. How many baseball cards does William have now? Draw base ten blocks to help you show your work. Write an equation to represent your answer.

2. Madison lives on a farm and has a lot of chickens. On Monday, she collected 24 eggs. On Tuesday, she collected some more. In all, she collected 78 eggs. How many eggs did she collect on Tuesday? Fill in the bar model to help you solve the problem.

Addition and Subtraction Problem Solving | 169

Addition and Subtraction Problem Solving

Skills Quiz

3. Eric has 21 model airplanes. He bought 46 more. Then, Eric gave 38 away. How many does he have left? Use a number line to help you solve.

4. Smith Elementary second graders collected canned goods for three days. They collected 12 cans on Monday, 36 cans on Tuesday, and some more on Wednesday. In total, they collected 72 cans. How many cans did they collect on Wednesday? Fill in the bar model below to help you solve the problem.

5. Use base ten blocks to solve the following number sentence. 28 + 71 = ? 170 | Addition and Subtraction Problem Solving

Skills Quiz

Arrays

Name: _______________________ Date: __________

Arrays

Use repeated addition to find the total number of objects in each set. Write a repeated addition equation to show the total. 1.

_________________________

Arrays | 171

Arrays

Skills Quiz 5.

_________________________

8. Carly had 8 dot stickers. She arranged them in an array. Draw two different ways she could have arranged them. Write a repeated addition equation to show the total.

_________________________

172 | Arrays

Two-Dimensional Shapes

Skills Quiz

Name: _______________________ Date: __________

Two-Dimensional Shapes

Use the word bank to help you answer the questions below. quadrilateral

hexagon

1. Draw a polygon with six sides and six angles.

pentagon

triangle

2. Draw a shape with 4 sides.

What is this shape called?

____________________

3. Draw a polygon with five sides and five angles.

4. Draw a two-dimensional shape with three sides.

What is this shape called?

____________________

Two-Dimensional Shapes | 173

Skills Quiz

Two-Dimensional Shapes

For each shape below, determine if the line drawn is or is not a line of symmetry. Write yes or no on the line next to each shape. 5. _______________

6. _______________

7. _______________

174 | Two-Dimensional Shapes

Three-Dimensional Solids

Skills Quiz

Name: _______________________ Date: __________

Three-Dimensional Solids

Write the name of the solid on the line below the solid. You may use the word bank to help with spelling. rectangular prism

cube

cylinder 1.

sphere

cone 2.

______________ 3.

______________ 4.

______________

Three-Dimensional Solids | 175

Three-Dimensional Solids

Skills Quiz

Write the name of the solid in the space beside the attributes that match. You may use the word bank to help with spelling. rectangular prism

cube

cylinder

cone

sphere

5. 1 circular face, 1 apex, no edges, and a curved surface 6. 6 square faces, 8 vertices, and 12 edges 7. 2 circular faces, no edges, no vertex, and 1 curved surface

8. 6 rectangular faces, 8 vertices, and 12 edges

9. Curved surface, 0 faces, 0 edges, and 0 vertices

10. Circle any solid that has more than 1 vertex.

176 | Three-Dimensional Solids

Fractions

Skills Quiz

Name: _______________________ Date: __________

Fractions

Read and answer the questions below. 1. Draw lines to partition the shape into halves.

2. Draw lines to partition the shape into fourths.

3. Draw lines to partition the shape into thirds.

One section of this object is called _____________.

Three sections of this object are called _____________.

Two sections of this object are called _____________.

4. Color in the shapes below that are examples of halves, thirds, or fourths.

Fractions | 177

Fractions

Skills Quiz 5. Split this shape into halves.

6. Split this shape into fourths.

7. Split this shape into thirds.

One section of this object is called _____________.

8. Look at the fractions represented in the shapes below.

Are all 3 rectangles divided into halves?

Yes or No

Explain your reasoning. ______________________________________________________ ______________________________________________________ ______________________________________________________ 178 | Fractions

Length

Skills Quiz

Name: _______________________ Date: __________

Length

1. Use the ruler to answer the question. 0

Inches

How long is the train? _________________ 2. Use the ruler to answer the question.

1 2 Centimeters

How long is the crayon? ______________ 3. Bob measured his foot with small paper clips and found it was about 8 paper clips long. Then, he measured his foot with a ruler and found it was about 10 inches long. Which measuring tool was more accurate?

Pennies

Ruler

Tiles Length | 179

Skills Quiz

Length

5. Johan ordered a jumbo hot dog for himself and a small hot dog for his little sister. Use the centimeter cubes to measure the length of each hot dog.

___________

6. Jarrod ordered 6 jumbo hot dogs that had a total length of 54 cm and 5 small hot dogs that had a total length of 35 cm. How much longer were the jumbo hot dogs than the small hot dogs?

180 | Length

Skills Quiz

Length

7. Carrie Ann went to the fabric store to buy some ribbon for herself and her friend. She needed 50 inches of ribbon for a project. Her best friend Jamie needed 16 inches less ribbon than Carrie Ann to make a wand. How many inches of ribbon did Jamie need from the fabric store?

Jamie needed _____ inches of ribbon.

8. Jeremy went to the beach with his family. They drew a line in the sand and practiced jumping as far as they could. Jeremy wanted to jump a total of 15 feet in three jumps. On his first try, he jumped 5 feet. His second jump length was 6 feet. How many more feet does Jeremy need on his third jump to make his goal of 15 total feet?

Jeremy needs to jump _____ feet on his third jump.

Length | 181

Time

Skills Quiz

Name: _______________________ Date: __________

Time

Write the time shown on the clock. Read under the clock to know whether to label the time a.m. or p.m. 1.

Afternoon

Morning

Nighttime

______________

Use the digital clock to draw the time on the analog clock.

3:45 4.

12:15 5.

7. Eric’s alarm clock goes off at six twenty-five every morning. Draw this time on the clock, and write it with the correct label on the line next to the clock. © Accelerate Learning Inc. – All Rights Reserved

8:55 6.

__________ Time | 183

Time

Skills Quiz Read the scenario. Use the time line to measure elapsed time.

8. Mario went to the park to play after dinner. He played from 6:30 p.m. to 7:00 p.m. How long did Mario play at the park?

Mario played at the park for _____________________.

9. Frankie rode his bike on Saturday for 1 hour and 30 minutes. He began riding at 10:00 a.m. What time did Frankie finish riding his bike?

Frankie finished riding his bike at _____________________.

184 | Time

Skills Quiz

Money

Name: _______________________ Date: __________

Money 1. Cindy has 4 dimes, 2 quarters, and 4 pennies. How much money does she have in all?

____________________________ 2. Kyle has 2 twenty-dollar bills, 4 ten-dollar bills, 1 five-dollar bill, and 1 one-dollar bill. How much money does he have in all?

____________________________ 3. Rachel has 2 quarters, 1 dime, and 1 nickel. How much money does she have in all?

____________________________ 4. James has two quarters, 3 dimes, and 2 pennies. How much money does he have in all?

Money | 185

Money

Skills Quiz 5. Allen had 75¢ until he spent 2 dimes and 3 nickels. How much money does Allen have now?

6. Liz spent 1 dime on a necklace. Quinton spent 1 quarter and 2 pennies on a shirt. How much money did they spend in all?

7. Gina spent 46¢ on a bag of chips at school. She handed the cafeteria clerk 2 quarters. How much change did Gina receive? What coins could the cafeteria clerk hand back?

8. Liz wants to buy some pencil toppers for 53 cents. She has one quarter, two dimes, and two nickels. Does she have enough money?

186 | Money

Data Analysis

Skills Quiz

Name: _______________________ Date: __________

Data Analysis

Use the graph below to answer the questions. Favorite Pets 10 9 8 7 6 5 4 3 2 1 0

Cat

Dog

Hamster

Pig

Fish

1. Which pet was the most favorite? _________________________ 2. How many more people liked cats than pigs? _________________ 3. How many people liked dogs and hamsters combined? __________ 4. What do the bars in this graph represent?

__________________________________________________

5. Write and solve an addition or subtraction problem by using the data from this graph.

__________________________________________________ __________________________________________________

Data Analysis | 187

Data Analysis

Skills Quiz

The students in second grade at Allen Elementary School took data on how many books they read in four months. The results are shown in the table below. Month

Number of Books

January

March

February April

6. Draw a bar graph to represent the data in the table.

2 6

7. Draw a pictograph to represent the data in the table. = 1 book

188 | Data Analysis

Patterns

Skills Quiz

Name: _______________________ Date: __________

Patterns

Identify and describe the pattern using repeated addition or subtraction. Write the next 2 numbers in the pattern. Pattern 1.

849, 749, 649, 549

This pattern _________ in intervals of ____. adds/subtracts

72, 74, 76, 78

This pattern _________ in intervals of ____. adds/subtracts

300, 325, 350, 375

This pattern _________ in intervals of ____. adds/subtracts

Next 2 Numbers

_____, _____ _____

4. Create and describe your own pattern using repeated subtraction of 5 or 10. 567, ______, ______, ______, ______, ______

Patterns | 189

Patterns

Skills Quiz

Identify and complete the growing or shrinking pattern. Describe the pattern by writing a g for growing or an s for shrinking. Growing or Shrinking

Pattern 5. _____

_____

6. 13, 14, 15, 16, _____, _____ 7. 13, 11, 9, 7, _____, _____ 8. Create and describe your own growing or shrinking pattern within 20. ______, ______, ______, ______, ______ My pattern is __________________ by ____ each time. (growing/shrinking)

190 | Patterns

GLOSSARY OF TERMS < <: less than sign; symbol used to show that the value on the left has a lower value than the value to the right of the symbol =: equal sign; symbol used to show that two sides of an equation have the same value >: greater than sign; symbol used to show that the value on the left has a higher value than the value to the right of the symbol 10 less/10 fewer: a decrease in the value of a number by 10 10 more: an increase in the value of a number by 10 100 less/100 fewer: a decrease in the value of a number by 100 100 more: an increase in the value of a number by 100 a.m.: half of the day beginning at midnight and ending at noon, also called morning acute angle: an angle that measures less than 90 degrees

adjacent add: to combine two or more numbers to get a sum, or total addend: a number that is added to another number addition: combining two or more numbers to get a sum, or total addition table: a table that uses the intersection as the sum of an addend on the top row and an addend on the far left column additive angle: states that the measures of the angle parts add up to the angle whole additive comparison: shows the difference between two amounts; tells how much more or less one is compared to the other additive property of area: states that the areas of two nonoverlapping spaces can be added together to find the total area additive volume: volumes of two nonoverlapping rectangular prisms can be combined to find the volume of a figure composed of them.

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GLOSSARY OF TERMS algorithm

assess

algorithm: a step-by-step process that can be apex: the highest point of a pyramid or cone used to solve problems apply: to use allocation: dividing up money and other approximately: close to correct; estimated resources altogether: how many in all

arc: a segment of the curve of a circle

amount: a quantity of something

area: a measurement of a space inside boundary lines; measured in square units

analog clock: a time-telling tool that has hours marked from 1 to 12 and minutes from 00–59; it uses moving hands that indicate both hour and minutes analysis: a detailed examination analyze: to explore and explain

area model: a rectangular model of multiplication or division that represents the total as the area; factors or quotient and divisor are represented by the side lengths area of a rectangle: a measurement of a surface or space inside a rectangle

angle: (1) a point where 2 sides meet on a polygon; (2) a geometric figure formed by two rays that are formed from intersecting lines, line segments, or planes

arithmetic pattern: a number pattern that adds, subtracts, multiplies, or divides at the same rate

answer: to respond or reply in reaction to a statement or question

assess: to evaluate the quality of something

array: objects or numbers arranged in equal angle measurement: the measure in degrees rows and columns of an angle formed by two rays where they ask: to inquire meet at a common point

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GLOSSARY OF TERMS associative property of addition

borrow

associative property of addition: states that base: the flat surface on which a threenumbers that are added can be grouped in dimensional solid rests any order and the sum will be the same base ten: a number system based on ten, associative property of multiplication: also known as the decimal system; used to states that numbers that are multiplied can assign place value to numbers, has 10 digits be grouped in any order and the product will from 0-9 be the same base ten blocks: blocks built from cubes to attribute: a characteristic used to describe model and represent ones, tens, hundreds, something, also known as property and thousands axes: the perpendicular lines on the coordinate base-ten numeral: any of the numbers 0–9 plane that both run through the point (0, 0) beaker: a container used to hold and axis: a line drawn on a graph to help the measure the volume of liquids reader understand the data belong: to be the property of balance: a tool used to measure the mass of benchmark fraction: a common fraction an object against which other fractions can be balanced budget: when your expenses equal compared your income billions: the place value that comes from one bar graph: a type of graph in which an thousand millions put together amount is shown using vertical or horizontal border: the outline of a shape rectangular bars borrow: to get money or other goods that will bar model: a pictorial representation of a problem where bars are used to represent the have to be returned from a bank or person known and unknown quantities © Accelerate Learning Inc. – All Rights Reserved

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GLOSSARY OF TERMS braces

clock

braces: curly marks used in pairs to group things together; { }

cent symbol: a symbol that represents cents, written after the number

brackets: square marks used in pairs to group things together; [ ]

center: the middle

budget: a plan for how money will be spent

centimeter: a metric unit of length that is 1/100 of a meter; abbreviated as “cm”

build: to construct by assembling or joining parts together

characteristic: one way to describe something

bundle: a group of something, usually ten

charity: an organization that helps others in need

calculate: to determine the value of something mathematically calculation: a mathematical determination capacity units: different-sized units used to measure how much a container can hold

check: a written document used to withdraw money and pay for goods from a bank account circle: a closed shape with 1 continuous curved side

cases: occurrences

circle graph: a type of graph in which an amount is shown using sections of a circle

categorize: to arrange as a collection of objects with shared attributes

classification: putting things with shared attributes together into groups

category: a group with specific characteristics classify: to put things with shared attributes into which data can be sorted together into groups cent: the smallest unit of money; the value of one penny 194

GLOSSARY OF TERMS closed figure closed figure: a figure where all the sides meet coin: a flat, round disk of metal that has a specific monetary value collect: to gather collection: a group of things (often related) column: objects that are lined up above and below each other; a vertical arrangement of objects combination: a joining or merging of different parts or qualities in which the component elements are individually distinct combined: put together common denominator: finding a shared multiple for the denominators of two fractions

composite figure (shape) comparative language: words and symbols such as greater than, less than, and equal to that demonstrate an understanding of numeric values compare: to determine similarities or differences between two or more objects or numbers compare and contrast: to examine the similarities and differences between two or more sets of objects or numbers comparison: the process or results of looking for similarities and/or differences among sets of objects or numbers compatible numbers: numbers that are close to the original value and make a problem easier to solve mentally complementary angles: two angles that can be combined to equal 90°

commutative property of addition: states that numbers can be added in any order and the sum will be the same

component: a part or element of a larger whole

commutative property of multiplication: states that numbers can be multiplied in any order and the product will be the same

composite figure (shape): a two-dimensional figure made up of two or more figures

compose: to put pieces together

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GLOSSARY OF TERMS composite number composite number: a whole number with more than two factors concept: an abstract idea conclusion: a judgment or inference concrete model: a model that uses physical objects to represent a number or an idea concrete object: a real object cone: a solid with exactly one base that is a circle and one apex; it has a curved surface and does not have an edge.

create (construct) coordinate plane: a two-dimensional surface created by two perpendicular vertical (y-axis) and horizontal (x-axis) lines that intersect coordinate system: a system that uses numbers to describe the location of points, lines, or figures coordinates: two numbers that represent an exact location of a point on a plane corresponding term: a term that appears in identical places in two separate situations cost: amount you must pay to get something

congruent: having exactly the same shape and size

count: to determine the total number of something

connect: to bring together

counting back: subtracting an equal amount each time

consider: to think carefully about consumer: someone who uses goods and services convert: to find an equal amount, using different units

counting on: adding an equal amount each time cover: to put or layer something on top of something else create (construct): to generate or produce something

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GLOSSARY OF TERMS credit credit: money that a bank or institution allows a person to use; must be paid back to the bank in the future, with interest

decimal point cylinder: a solid with 2 circular bases, no vertices or edges, and 1 curved surface data: numbers, words, observations, or measurements that are collected and recorded

credit card: a small plastic card used to purchase goods or services with money that must be paid back with interest to the bank or data point: a specific value in a data set institution in the future data set: numbers, words, observations, or measurements that are collected and cube: a solid with 4 square faces, 2 square recorded bases, 8 vertices, and 12 edges cubic centimeter: a unit of volume with each edge one centimeter long and the volume is one cubic centimeter

debit card: a small plastic card used to purchase goods or services, using money from a person’s bank account

cubic unit: the space taken up by a cube in which each side is 1 unit; used to measure volume

decagon: a polygon with exactly 10 sides and 10 vertices

curved side: a side that is rounded customary system: the system of measurement used most commonly in the United States customary units: the units commonly used in the United States to measure length (inches, feet, yards, and miles), capacity (cups, pints, quarts, and gallons), and weight (ounces, pounds, and tons) © Accelerate Learning Inc. – All Rights Reserved

decimal: a fraction with a denominator that is a power of 10 and is written with digits to the right of the decimal point decimal fraction: a fraction where the denominator is a power of 10—like 10 or 100 decimal notation: a form of a number that uses the decimal point in the correct place decimal point: the point between a whole number and part of a whole number 197

GLOSSARY OF TERMS decompose

distributive property of multiplication

decompose: to break apart

differ: to be unlike something else

decrease: to make smaller; to go down

difference: the distance between two numbers; the result of subtracting one number from another

degree: (1) a unit of measurement used to describe the size of an angle; (2) a unit of measurement to show how hot or cold something is demonstrate: to show clearly denominator: the bottom number of a fraction; represents the total number of equal parts in one whole denote: to indicate; to show a sign of something deposit: to add money to an account

digit: any of the numerals 0 through 9 digital clock: an electronic tool that shows the time in the form of numbers and symbols dime: a coin with a value of 10 cents dimension: something measurable (such as length, width, and height) discover: to find out about, recognize, or realize display: to make something that can be seen easily

describe: to tell about the characteristics of something using words

distance: the length between two locations

determine: to come to a decision or to decide something

distinguish: to perceive differences among things

develop: to change or grow

distributive property of multiplication: states that when you multiply two numbers, you can decompose one number into two parts, multiply each part by the other number, and then add them together

diagram: information shown in a graph or in picture form 198

GLOSSARY OF TERMS divide

environment

divide: to share or separate into equal groups draw conclusions: to gain understanding by or equal parts interpreting data dividend: the total amount that is being divided or shared equally divisible: able to be split apart into a certain number of equal groups division: the process of sharing or partitioning equally

drawing: illustration (pictorial model) earned: received for work that was done edge: where two faces meet on a threedimensional object edge length: how long it is along the line where two faces meet on a three-dimensional object

divisor: the number by which the dividend is being divided or shared; may represent the number of groups or how many in each group eighth: one part of a whole that is divided into eight equal pieces dodecagon: a polygon with exactly 12 sides elapsed time: the difference between when and 12 vertices something starts and when it ends dollar: one hundred cents; a paper bill that electronic payment: to buy goods or has a value of 100 cents services with a debit card, credit card, or dollar sign: a symbol that represents dollars, electronic transfer written before the number end: the farthest point of an object dot plot: a type of graph using dots to show endpoint: the point at the end of a line how many times each data point happens segment or a ray draw: to create a picture or diagram environment: the circumstances, objects, or conditions by which one is surrounded © Accelerate Learning Inc. – All Rights Reserved

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GLOSSARY OF TERMS equal equal: same or balanced

exhibit equiangular triangle: a triangle with all equal angles

equal addends: the numbers added together to form a sum; equal addends are the same equilateral triangle: a triangle with all equal addends sides equal area: same amount of surface space is covered in two or more objects or parts of a whole equal groups: sets of objects that have the same amount or number, or have the same value equal parts: pieces of an object or model that have the same size or value as the other parts of a whole equal shares: equal sizes, equal-size parts; parts of a shape that are the same size

equivalent: having the same amount or value equivalent fractions: fractions that represent the same amount; same whole partitioned a different way, written with different numerators and denominators estimate: (1) a reasonable guess that is close to the exact answer; (2) to make a reasonable guess that is close to the exact answer estimation strategies: methods used to gain an approximate calculation

evaluate: to solve for the value of an equal sign: a symbol (=) used to show that two expression sides of an equation are worth the same value even: whole numbers that end in 2, 4, 6, 8, or equal to: the same amount when compared 0; can be split equally between two groups to another amount example: a representation that follows a rule equation: a mathematical sentence that uses or has certain characteristics numbers, one or more operation symbols, exhibit: to display, show, and/or use and an equal sign something as an example 200

GLOSSARY OF TERMS expanded form

fixed expense

expanded form: a way to write a number as a factor pair: a set of two factors multiplied sum of each digit according to its place value together to find a product expanded notation: an expression showing the specific place value of each digit by multiplying each digit by its place value

false: not true or accurate

expense: money spent on a good or service

figure: (1) a form or outline; (2) an illustration, diagram, or representation

explain: to make plain or clear; to tell how or why something occurs or works a certain way explore: to investigate, study, or analyze exponent: a small number written to the right and above the base number that tells how many times to use the base number multiplied by itself express: to represent in words expression: a group of numbers and operation symbols with no equal sign extend: to increase in scope

fewer: less than

financial institution: a business that helps manage your money, such as a bank or credit union find: to recognize, discover, figure out, or solve first quadrant: the upper-right of the four areas on a plane divided by the x-axis and the y-axis, containing positive values for both the x- and y-coordinates five-dollar bill: a paper bill that has a value of five dollars

face: a flat surface of a solid object

fives: skip counting by adding 5 to get the next number

factor: a number that is multiplied by another number to find a product

fixed expense: an expense that is the same each month

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GLOSSARY OF TERMS fluency

graph title

fluency: the ability to understand and solve math problems efficiently and accurately

fractional value: two nonzero numbers written in the form of a/b

fold: to bend something over on itself

frequency: how many times something happens

follow: to conform foot: a unit of measure (length, width, height) that represents 12 inches; abbreviated as “ft.” form: (1) the visible shape or configuration of something; (2) to create formula: a rule written as an equation; uses symbols and describes a relationship between amounts fourth: one of four equal parts fourths: four equal parts fraction: a part of a group of objects, a number, or a whole

frequency table: a record of how many times a value in a data set occurs friendly (benchmark) numbers: numbers that are easy to work with for adding and subtracting gap: space, open distance between two measurements generate: to create or produce something goods and services: goods are items you buy. Services are actions provided, such as those received when getting a haircut or visiting a doctor.

graph: (1) a visual way to represent data; (2) fraction model: a representation of a fraction to put points on a coordinate plane based on in the real world their x- and y-values fractional parts: the number of equal parts of an object, a number, or a whole

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graph title: the name given to a graph that tells what the graph is about

GLOSSARY OF TERMS graphical display graphical display: pictorial representations of data produced in different forms of charts, plots, diagrams, and graphs greater than: more than; showing a relationship between numbers; > gross income: the total amount of money earned before taxes and expenses are subtracted group: a collection of objects or things kept together grouping symbols: symbols that help to organize mathematical expressions; braces { }, brackets [ ], and parentheses ( ) half: one part of a whole that is divided into two equal pieces half hour: 30 minutes; midpoint of one hour (60 minutes) half past: half past the hour, or a time that ends in 30; for example: half past 12 or 12:30 half-circle: one-half of a circle

hundred thousands height: how tall something is hendecagon: a polygon with exactly 11 sides and 11 vertices heptagon: a polygon with exactly 7 sides and 7 vertices hexagon: a polygon with exactly 6 sides and 6 vertices hierarchy: an order or arrangement of objects based on the relationships among their characteristics hour: at the exact hour (:00 minutes) of the day or of the night hour hand: the short hand on an analog clock human capital: the knowledge, skills, and abilities of a person or group of people hundred: a group of ten tens hundred thousands: the place value created when a group of 10 ten thousands are combined; ten times greater than the ten thousands place, one-tenth the millions place

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GLOSSARY OF TERMS hundreds (place) hundreds (place): the place value created when a group of 10 tens are combined; ten times greater than the tens place, one-tenth the thousands place

intersect inch: a unit of measure (length, width, height) smaller than 1 foot (1/12 of a foot); abbreviated as “in.” income: money earned

hundreds chart: a grid with the numbers one income tax: a tax paid to the government on to one hundred to help with counting and money earned number patterns hundredth: one part of a whole partitioned into 100 equal pieces hundredths: (1) parts of a whole partitioned into 100 equal pieces; (2) the place value that is two places to the right of the decimal identify: to recognize or name identity property of 0: the sum of zero and any number is equal to that number. identity property of multiplication: states that multiplying 1 by any number does not change the value illustrate: to make something clear with the use of examples improper fraction: a fraction in which the numerator is greater than the denominator; represents a value greater than one whole 204

incorrect result: an incorrect answer inequality: the state of being not equal in value, number, amount, or size informal language: a word or phrase that is not precise or specific information: factual data input-output table: a table showing numerical relationships between the input and output, often used to generate sets of ordered pairs for a rule interest: a charge that is paid to a lender in return for borrowing money interpret: to explain; to give or provide meaning intersect: to pass through each other © Accelerate Learning Inc. – All Rights Reserved

GLOSSARY OF TERMS intersecting lines intersecting lines: lines that cross at a point intersection: the point at which two lines cross interval: the distance between two values or points interval of time: a specific amount of time that has been measured

lend kilometer: a metric unit of length that represents 1,000 meters; abbreviated as “km” kite: a polygon with exactly 4 sides and 2 sets of adjacent sides that are equal in length. know: to understand how something works label: (1) a word or phrase indicating particular categories; (2) to describe or designate for the purpose of identification

inverse operations: opposite operations that are related labor: work investigate: to carry out an inquiry to discover information irregular shape: a shape where all the sides are not the same length

lay: to put down and set in position for use layer: one thickness or fold lying over another least amount: the smallest number

isosceles triangle: a triangle with at least two least to greatest: smallest to largest equal sides join: to put together

ledger: a record of all income and expenses

justify: to explain your thinking

legend (key): words or pictures on a graph, chart, or map that explain what the different parts mean

lend: to give money or goods and expect it to be returned 205

GLOSSARY OF TERMS length

mean

length: the distance from one location to another; how long something is

lines of symmetry: lines drawn to show congruent halves of a shape

length units: include customary units of inches, feet, yards, and miles; include metric units of millimeters, centimeters, and meters

liquid capacity: how much liquid can be held in a container; liquid volume

length units: centimeters (cm): unit for measuring the length of small items length units: inches (in.): unit for measuring the length of small items length units: millimeters (mm): unit for measuring the length of very small items; 10 mm = 1 cm less than: fewer than; shows a relationship between numbers < line: a one-dimensional figure that continues straight in both directions

liquid volume: the amount of liquid taking up space inside of a container loan: money borrowed based on certain conditions; usually paid back with interest locate: to find the place of something make: to create mass: the amount of matter in an object; measured in grams or kilograms mass and weight units: include customary units of pounds and ounces; include metric units of grams and kilograms

mathematical reasoning: a critical thinking skill that enables one to make use of mathematical skills to make sense of a line plot: a type of graph that shows how many concept or problem times each data point happens along a line mean: the average of a set of numbers; the line segment: a part of a line with two quotient when the sum of all numbers in a set endpoints is divided by the quantity of numbers in the set line graph: a type of graph in which amounts are shown using a line to connect data points

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GLOSSARY OF TERMS measure measure: to find the size of an attribute measurement: the amount of something established by measuring with tools measurement system: a collection of units with rules relating them; metric and customary are the most widely used measuring instrument: a ruler or any other tool that is used to measure measuring tape: a measuring tool made from linear tape, ribbon, cloth, or metal that helps us measure measuring tool: equipment that is used to find the amount or value of something; usually, the tool finds a number value that refers to a standard unit. median: the middle number in an ordered data set memory: recalling the answer to a numerical expression automatically without having to work through it mental computation: the process of working out math problems in your head without pencil and paper or calculators © Accelerate Learning Inc. – All Rights Reserved

mixed number mental math: to use strategies to solve problems without writing or modeling meter: a metric unit of length that represents 100 centimeters; abbreviated as “m” meterstick: a measuring tool that is a linear stick that measures 1 meter long metric system: the system of measurement based on international decimal understanding; uses meter, liter, and gram as the base units of length, capacity, and mass millions: the place value created when a group of 10 hundred thousands are combined; ten times greater than the hundred thousands place minute: a unit of time equal to 60 seconds; there are 60 minutes in 1 hour. minute hand: the long hand on an analog clock missing addend: the unknown addend, given an equation in which the total (sum) and one addend are known mixed number: a number containing a whole number and a proper fraction 207

GLOSSARY OF TERMS mode

nearest 10

mode: the most common number in a data set multiplication: a way to create a product by making equal groups, repeating addition, or model: (1) a representation; (2) to create a forming arrays representation or copy of something on a smaller scale multiplication table: a table that shows the product of two factors where a row and a money: coins and bills that have value and column intersect that can be exchanged for goods and services multiplicative comparison: comparing two more: bigger, larger, greater quantities and showing how many times larger one is than another more than: an amount that is larger than another amount multiplier: the number the multiplicand is multi-digit: a number made up of more than one 0–9 digit multiple: a product of two numbers; a number that can be divided evenly by another number multiple of 10: a product of 10 and another number; a number that can be divided evenly by 10 multiple of 100: a product of a number and 100; a number that can be divided evenly by 100 multiplicand: the number that gets multiplied (one of the factors) 208

being multiplied by (one of the factors) multiply: to create a product by making equal groups, repeating addition, or forming arrays multistep (word) problem: a mathematical question written with words that requires more than one step to complete name: (1) a word used to refer to or address people, places, or things; (2) to recognize or identify nearest: the closest nearest 10: rounding a number to the closest 10 above or the closest 10 below © Accelerate Learning Inc. – All Rights Reserved

GLOSSARY OF TERMS net income net income: the total amount of money left after taxes and expenses are subtracted nickel: a coin with a value of 5 cents nonagon: a polygon with exactly 9 sides and 9 vertices nonexample: a representation that does not follow a rule or does not have certain characteristics non-parallelograms: two–dimensional shapes that do not have two sets of parallel sides non-standard unit: any unit or item that is not a standard metric or customary unit that can be used to measure an object

numerator number line: a line with evenly spaced tick marks to show the position of a number in relation to other numbers number name: a word used to identify a number number pattern: a group of numbers that follow a pattern or rule number sense: a person’s ability to use and understand numbers; knowing relative values and how to use them appropriately to perform operations; developing helpful strategies for estimation, measurement, and counting number sentence: a mathematical sentence written by using numbers; an equation

non-unit fraction: a fraction that represents more than one part of the whole

number string: a set of related math problems or numbers in a pattern

not equal: the state of being different in value, number, amount, or size ≠

numeral: a symbol used to show an amount or quantity

note: to notice and observe carefully

numeral-word form: a way to write a number using a symbol for a number and words

numerator: the top number in a fraction; represents part of a whole 209

GLOSSARY OF TERMS numerical data numerical data: data composed of numbers, measurements, or quantities

ordered pair one-digit number: a number in the ones place — 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 only

numerical expression: a sentence one-hundred dollar bill: a paper bill that has containing only numerals and the symbols for a value of 100 dollars operations ones (place): the place value created when o’clock: the hour position on the clock; there is a group with a value of 0–9; one-tenth example: six o’clock the value of the tens place object: a thing that can be seen, touched, grouped, counted, and manipulated

open figure: a figure where all the sides do not meet

observation: an act of noticing or perceiving

open number line: a number line without tick marks

observe: to notice obtuse angle: an angle that measures more than 90 degrees obtuse triangle: a triangle with two acute angles (less than 90 degrees) and one obtuse angle (larger than 90 degrees) octagon: a polygon with exactly 8 sides and 8 vertices odd: a whole number that is not divisible by 2; odd numbers end with 1, 3, 5, 7, or 9 one: a single unit used for counting 210

operations: math processes, such as addition, subtraction, multiplication, and division order: to arrange into a sequence order of operations: the order in which computations should be done within an expression ordered pair: a pair of numbers written in parentheses in a specific order used to show a numerical relationship with a point’s x-coordinate and y-coordinate on a graph (x, y) © Accelerate Learning Inc. – All Rights Reserved

GLOSSARY OF TERMS organize organize: to arrange orientation: the direction or position of an object origin: the point on the coordinate plane where the x-axis and the y-axis intersect, found at (0, 0) overlap: a part that extends and partly covers another part p.m.: half of the day from beginning at noon and ending at midnight, also called afternoon/evening pack: to fill pair: (1) a group of 2; (2) join or connect to form a pair parallel line segments: line segments that do not intersect parallel lines: two lines that never touch

pentagon parentheses, brackets, and braces: symbols used in pairs to group terms together allowing operations to be performed in the correct order part: a piece of something part-part-whole model: a visual model for showing the relationship among numbers in addition and subtraction situations partial products: multiplying decomposed factors and putting together those products to get a final product partition: to divide into equal parts pattern: an arrangement of numbers or shapes that repeats pattern rule: a rule that states the process for generating a pattern payroll tax: tax that an employer is required to subtract from a person’s gross income

parallelogram: a polygon with exactly 4 sides penny: a coin with a value of 1 cent and 2 sets of sides that will never meet pentagon: a polygon with exactly 5 sides and 5 vertices © Accelerate Learning Inc. – All Rights Reserved

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GLOSSARY OF TERMS perform perform: to carry out a task perimeter: the total distance around a shape

power of ten place value strategy: decomposing two numbers by place value to add or subtract

perpendicular line segments: two line segments that intersect at a right angle

place value system: the framework that dictates the numerical value that a digit has based on its position within a number

perpendicular lines: two lines that intersect and form 90-degree angles at the intersection

placement: putting something (such as a decimal point) in a specific location

pictograph: a graph that uses symbols to show data

plane: a flat surface on which lines lie

pictorial model: a picture or representation of (a) real object(s)

plane figures: closed figures with straight or curved lines; also called two-dimensional shapes

picture: a painting, drawing, photograph, or image

plot: to put points on a graph based on their x- and y-values

picture graph: a graph that uses pictures of the data it shows

point: an exact location usually represented by a small, filled-in circle

place: a designated location for the value of a digit (e.g., the tens place)

polygon: a closed shape with at least three straight sides

place value: the value of a digit that depends on its location within a number

position: a specific location

place value mat: a graphic organizer to help students organize numbers to the thousandths 212

power of ten: ten multiplied by itself a certain number of times

GLOSSARY OF TERMS predict predict: to guess what might happen in the future by using information prediction: a statement about what will or might happen in the future prime number: a whole number greater than 1 with exactly two factors: 1 and itself principle: an idea that explains how to do something prism: a three-dimensional solid with at least two congruent polygon faces (bases) problem: a hypothetical, real-world situation that requires mathematical reasoning or a number sentence using mathematical operations to solve produce: to create or make producer: someone who makes goods, such as a farmer product: (1) a good that is for sale; (2) the result of multiplying two or more numbers together

quarter proper fraction: a fraction less than one whole properties of operations: mathematical rules that always work and help you solve equations property: a characteristic or quality that something has (like shape, number of sides, length of sides, etc.) property tax: money paid to the local government based on the value of someone’s house or land protractor: an instrument used to draw or measure angles in degrees pyramid: a solid with a polygon base and 3 or more triangles as faces that meet at a vertex quadrant: one of four areas made when drawing an x-axis and a y-axis on a graph quadrilateral: a polygon with exactly 4 sides quantity: the amount of something

quarter: (1) a coin with a value of 25 cents; (2) profit: amount of money left after subtracting one part of a whole that is divided into four taxes and expenses from income equal pieces © Accelerate Learning Inc. – All Rights Reserved

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GLOSSARY OF TERMS quarter ‘til quarter ‘til: a time that ends in 45, that shows 15 minutes until the hour; 3:45 or a quarter ‘til 4:00 quarter after: a time that ends in 15, that shows 15 minutes after the hour; 4:15 or a quarter after 4:00 quarter of an hour: 15 minutes; one-fourth of an hour (60 minutes) quarter past: a time that ends in 15, that shows 15 minutes past the hour; 4:15 or a quarter past 4:00 quarter to: a time that ends in 45 and that shows 15 minutes to the hour; 3:45 or a quarter to 4:00 quarter-circle: one-fourth of a circle question: a sentence that requires an answer gained through knowledge, research, calculation, and/or reasoning quotient: the answer to a division problem range: (1) A set of values; (2) the difference between the values of least and greatest numbers in a data set 214

recipient rational number: any number that can be shown as a fraction ray: an endpoint that extends indefinitely in one direction read: to look at and comprehend the meaning of written letters, numbers, and symbols real-object graph: a graph that is created using real-life objects, such as shoes, or manipulatives, such as linking cubes, counting bears, colored counters, etc. real-world problem: a hypothetical situation and question that require mathematical knowledge, strategies, and an equation to be solved rearrangement: the process of changing the position or order of something reason: to logically think, understand, and form judgments about something reasonableness: the solution to a problem makes sense and can be checked with estimation recipient: a person or thing that receives something © Accelerate Learning Inc. – All Rights Reserved

GLOSSARY OF TERMS recognize recognize: to identify from having prior knowledge or experience

repeated subtraction

record: to write

related division fact: a division fact that helps us find the answer to a multiplication fact; related facts use the same numbers in a different order.

rectangle: a polygon with exactly 4 sides and 4 vertices

related facts: equations that share the same set of numbers to show number relationships

rectangular array: objects or numbers that are arranged into rows or columns

relationship: (1) the way two numbers are connected by a rule; (2) opposite operations; they undo each other

rectangular prism: a solid with 4 rectangular faces, 2 rectangular or square bases, 8 vertices, and 12 edges refer: to allude to something reflex angle: an angle in a circle greater than 180° but less than 360° regrouping: changing groups of one place value into a different place value to help with adding or subtracting regular shape: a shape where all the sides are the same length relate: to make a connection

relative position (location): a point established with reference to another position that is either moving or fixed relative size: how big or small something is in comparison to another object remainder: the amount that is left over after dividing repeated addition: a pattern of adding the same amount over and over; can be shown with a multiplication sentence repeated subtraction: a pattern of subtracting the same amount over and over; can be used to solve some types of division problems 215

GLOSSARY OF TERMS replace

scaling

replace: to put something in the place of something else

row: objects that are lined up next to each other; a horizontal arrangement of objects

represent: to show in some way; to stand for something

rule: (1) a guideline; (2) a pattern applied to a set of numbers or shapes

representation: a picture or symbol that portrays something else

ruler: a measuring tool used to measure both customary and metric units of length, width, and height

restate: to say again or in a new way result: an outcome or answer to a question

sales tax: a tax added to the price of goods and services

rewrite: to write again

save: to put away for later

rhombus: a four-sided shape with four equal sides and opposite angles that are equal

say: to speak or express in words

right angle: an angle that measures 90 degrees

scale: a tool used to measure weight scale (on a graph): what the graph is counting by on each axis

right triangle: a triangle that has two acute angles and one angle that measures 90 degrees scaled intervals: intervals on the axes of a graph that are spaced by an equal value round: to raise or lower a number to a specific place value position; to represent an scalene triangle: a triangle with no equal approximate worth sides rounding: finding a number that is close to the original number by changing it to the closest multiple of 10, 100, 1,000, etc. 216

GLOSSARY OF TERMS scarce

sold

scarce: a small amount of materials or goods; side: a straight line joining 2 vertices of a can sometimes result in a higher price polygon scatterplot: plotted points on a graph that show a relationship between two sets of data

side length: the measured distance of a line segment on a two-dimensional shape

section: a part or piece of a whole thing select: to make a choice

simplify: to combine the terms of an expression and create an equivalent expression

separate: to take apart or remove

situations: different types of problems

sequence: numbers or shapes in a set order

size: how large something is

sequence of operations: when multiple steps are performed in the specific order in which computations should be done within an expression

sketch: to draw

set: a group shape: a form or outline shapes: two-dimensional closed figures with straight or curved lines share: to split or divide something show: to be capable of doing something by explanation or demonstration © Accelerate Learning Inc. – All Rights Reserved

skip count by 100s: to count 100 at a time skip count by 10s: to count 10 at a time skip count by 2s: to count 2 at a time skip count by 5s: to count 5 at a time skip counting: a counting technique where you repeatedly add the same number to the previous number; counting by multiples sold: gave away in exchange for money

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GLOSSARY OF TERMS solid

subtract

solid: a 3-D shape that has length, width, and height

standard unit: a unit chosen as most common and used by most people

solution: the answer to a problem

statement: a written or verbal way of communicating information

solve: to find an answer or solution to a problem

stem-and-leaf plot: a way to separate data by place value

sort: to group or arrange according to specific characteristics straight angle: an angle that measures 180° and looks like a straight line spend: to use money to buy goods and services straight side: a side that is made by a straight line sphere: a 3-D solid with no faces, edges, or vertices strategy: a plan or way of solving a problem or finding an answer square: a polygon with exactly 4 sides and 4 vertices, with all sides congruent (same length) strip diagram: a model used to solve word problems that shows the relationship square unit: the space covered by creating between known and unknown amounts a square with each side being 1 unit; used to measure area subcategories: groups within groups of specific shared attributes into which objects standard algorithm: a systematic procedure can be sorted of computation used to solve a particular type of mathematical problem subtract: to take away an amount from a larger amount; to find the difference between standard form: the most common way to two numbers write a number; a number shown in digits 218

GLOSSARY OF TERMS subtraction

tens (place)

subtraction: taking away an amount from a tax: money that the government requires all larger amount; finding the difference between citizens to pay two numbers technique: a method used to complete a sum: the total amount; the result in addition task summarize: to give a brief statement of main points

tell: to look at and comprehend the meaning of written letters, numbers, and symbols

supplementary angles: two angles that can be combined to equal 180°

tell time: to read a clock or watch and understand what time of day it is

symbol: a character used to represent a value temperature: measure of the heat in an object or process ten: a group of ten ones symmetry: when two halves are identical after a fold t-chart: a graphic organizer divided into two or more categories table: a chart containing data that is displayed in columns and rows tally mark: a way to represent data that has been collected using a vertical or diagonal line tape diagram: a model used to solve word problems that shows the relationship between known and unknown amounts © Accelerate Learning Inc. – All Rights Reserved

ten-dollar bill: a paper bill that has a value of 10 dollars ten thousands: the place value created when a group of 10 thousands are combined; ten times greater than the thousands place, onetenth the hundred thousands place tens: skip counting by adding 10 to get the next number tens (place): the place value created when a group of 10 ones are combined; ten times greater than the ones place, one-tenth the hundreds place 219

GLOSSARY OF TERMS tenth tenth: an equal part of a group of 10 tenths: parts of a whole divided into 10 equal pieces thermometer: a tool used to measure temperature in degrees Celsius or Fahrenheit third : one of three equal parts thirds: three equal parts thousand: a group of ten hundreds thousands (place): the place value created when a group of 10 hundreds are combined; ten times greater than the hundreds place, one-tenth the ten thousands place thousands period: any digit in the hundred thousands, ten thousands, or one thousands place thousandths: parts of a whole divided into 1,000 equal pieces thousandths (place): the place value that is three places to the right of the decimal

tool three-digit number: a number with a digit in the hundreds place, a digit in the tens place, and a digit in the ones place three-dimensional: having length, width, and height tiling: filling a plane surface with square tiles laid side by side with no overlapping sides or gaps time: how the past, present, and future are measured; uses units such as seconds, minutes, hours, days, and years time interval: a distinct and consistent measure of time between two things; a unit of time such as a second, a minute, an hour, etc. time units: different-sized units used to measure how long an event lasts timeline: a list of events in the order in which they happened times: multiply; repeated addition title: a name or heading tool: an instrument used or worked by hand or machine to perform a task

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GLOSSARY OF TERMS total total: how many there are in all transfer: to move money from one account to another trapezoid: a two-dimensional shape that has four sides with at least one set of opposite sides being parallel triangle: a polygon with exactly 3 sides and 3 vertices triangular prism: a 3-D solid with 3 rectangular faces, 2 triangular bases, 6 vertices, and 9 edges triple: a group multiplied by three true: exact or accurate

unit square two-dimensional: flat; having only length and width twos: skip counting by adding 2 to get the next number understand: to interpret or view in a particular way; to grasp the meaning of understanding: comprehension unit: a single item unit cube: a cube that has each edge one unit long and with a volume of one cubic unit unit fraction: a fraction that represents only one part of the whole or set

turn: to move in a circular direction

unit of measurement: a standard amount that is used to measure

twenty-dollar bill: a paper bill that has a value of 20 dollars

unit period: numbers in the ones, tens, and hundreds place

two-digit number: a number with a digit in the tens place and a digit in the ones place

unit segments: units of measure used to find the length around a two-dimensional figure unit square: a single square used to measure area

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GLOSSARY OF TERMS units of length units of length: measure lengths and distances. Customary units: inches, feet, yards, and miles. Metric units: millimeters, centimeters, and meters. units of length: inches (in.): unit for measuring the length of small items; inches allow for measuring by ½ inch and ¼ inch increments units of liquid and volume: different-sized units used to measure how much liquid a container can hold units of mass and weight: measure weight and mass. Customary units: pounds and ounces. Metric units: grams and kilograms. units of time: different-sized units used to measure how much time has passed unknown: a missing piece of information

withdraw verbal statement: a clear expression said out loud vertex (2-D): a point where 2 sides meet on a polygon vertex (3-D): a point where edges meet on a solid figure visual model (representation): a representation that can be seen volume: the space inside an object; calculated by counting how many cubic units take up the space of an object wage: money that is earned by working weight: how heavy something is whole: a complete object or set of objects

use: to employ or utilize for a purpose

whole number: a numerical value with no decimal or fractional part

value: total amount of something; how much something is worth

width: measurement of the distance between two opposite sides

variable expense: an expense that might change each month

withdraw: to take money out of an account

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GLOSSARY OF TERMS word form

zero

word form: a representation of a number written with words

yardstick: a measuring tool that is a linear stick that measures 1 yard long

word problem: a hypothetical situation and question that require mathematical knowledge, strategies, and an equation to be solved

zero: the absence of all size or quantity

write: to make marks that represent letters, words, or numbers written numeral: how a number is written x-axis: the horizontal axis; all points on it have a Y-value of zero. x-coordinate: the horizontal value of a point on a graph shown by the first number in an ordered pair y-axis: the vertical axis; all points on it have an X-value of zero. y-coordinate: the vertical value of a point on a graph shown by the second number in an ordered pair yard: a unit of measure (length, width, height) that represents 3 feet; abbreviated as “yd.”

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Workspace

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A Part of STEMscopes Math Developed by Accelerate Learning Inc. 800-531-0864

ISBN: 978-1-64861-269-5

9 781648 612695