STEMscopes Georgia Math Student Notebook Grade 3

Grade 3 Student Notebook

GEORGIA

GEORGIA

Student Notebook – Grade 3 ISBN: 978-1-64861-270-1 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.

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GEORGIA

Student Notebook - Grade 3

Scope Name

Table of Contents

Page Number

Place Value Relationships

1

Compare Numbers

15

Rounding

25

Addition and Subtraction Fluency

33

Addition and Subtraction Models

47

Arithmetic Patterns

59

Multiplication Models

69

Division Models

91

Multiplication and Division Strategies

109

Multiply Multiples of 10

121

Multiplication and Division Problem Solving

135

Area in Square Units

149

Apply the Area Formula

159

Perimeter

177

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iii

GEORGIA

Student Notebook - Grade 3

Table of Contents (Cont.)

Scope Name Page Number Lines and Angles

193

Two- and Three-Dimensional Figures

201

Represent and Compare Fractions

213

Equivalent Fractions

239

Time

255

Measurement

265

Represent and Interpret Data

285

Skills Quizzes

293

Glossary of Terms

365

Workspace

399

iv

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Place Value Relationships

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1

Place Value Relationships

Explore 1

Name: _______________________ Date: __________

Read and Write Numbers Read each Scenario Card, and represent the money you earned and that you want to deposit into the bank as a model with standard form, word form, and expanded form on the Bank Deposit Slip Work Mat and Place Value Chart. Then, record your work in the correct table.

January/February STANDARD FORM PAY TO THE ORDER OF

Georgia Second Bank

$ DOLLARS

WORD FORM

EXPANDED FORM March/April STANDARD FORM PAY TO THE ORDER OF

Georgia Second Bank

$ DOLLARS

WORD FORM

EXPANDED FORM

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Place Value Relationships | 3

Place Value Relationships

Explore 1 May/June

STANDARD FORM PAY TO THE ORDER OF

Georgia Second Bank

$ DOLLARS

WORD FORM EXPANDED FORM

July/August STANDARD FORM PAY TO THE ORDER OF

Georgia Second Bank

$ DOLLARS

WORD FORM EXPANDED FORM

September/October STANDARD FORM PAY TO THE ORDER OF

Georgia Second Bank

$ DOLLARS

WORD FORM EXPANDED FORM 4 | Place Value Relationships

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Place Value Relationships

Explore 1 November/December

STANDARD FORM PAY TO THE ORDER OF

Georgia Second Bank

$ DOLLARS

WORD FORM

EXPANDED FORM Refl ect After working with the place value disks, what do you notice about the values of each place? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can we use the given form of each number to help us write the other forms? For example, if we were given the standard form, how can we use the standard form to write the word form and the expanded form? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

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Place Value Relationships | 5

Name: _______________________ Date: __________

Expression 2: Expression 4:

Expression 1:

Expression 3:

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Model 2:

Model 1:

Clothes Shop

Place Value Relationships | 7

For each location, draw a visual representation of the number of signatures in two different ways. Then, write an expression for each of the numbers you drew (expressions 1 and 2). Challenge yourself to think of two different ways (expressions 3 and 4) to show the given number.

Compose and Decompose Whole Numbers

Explore 2

Place Value Relationships

Expression 2:

Expression 4:

Expression 1:

Expression 3:

8 | Place Value Relationships

Model 2:

Hardware Store

Model 1:

Explore 2

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Place Value Relationships

Expression 2:

Expression 4:

Expression 1:

Expression 3:

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Model 2:

Grocery Store

Model 1:

Explore 2

Place Value Relationships | 9

Place Value Relationships

Expression 2:

Expression 4:

Expression 1:

Expression 3:

10 | Place Value Relationships

Model 2:

Bakery

Model 1:

Explore 2

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Place Value Relationships

Expression 2:

Expression 4:

Expression 1:

Expression 3:

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Model 2:

Toy Store

Model 1:

Explore 2

Place Value Relationships | 11

Place Value Relationships

Expression 2:

Expression 4:

Expression 1:

Expression 3:

12 | Place Value Relationships

Model 2:

Restaurant

Model 1:

Explore 2

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Place Value Relationships

Expression 2:

Expression 4:

Expression 1:

Expression 3:

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Model 2:

Fun Zone

Model 1:

Explore 2

Place Value Relationships | 13

Place Value Relationships

14 | Place Value Relationships

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___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

Describe the process of decomposing a number.

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

If you look at the standard form of a number, how can you know the value of a specific digit within that number?

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

How do you know when you need to regroup a place value?

Reflect

Explore 2

Place Value Relationships

Compare Numbers

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15

Compare Numbers

Name: _______________________ Date: __________

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Riding the Rapids

Splashin’ Down

______

______

Thousands

,

,

______

______

Hundreds

______

______

Tens

Compare Numbers | 17

______

______

Ones

Using place value disks, compare the number of tickets that were sold for each ride during last year’s county fair.

Explore 1

Compare Numbers

7,500

8,000

8,500

9,000

9,500

10,000

18 | Compare Numbers

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–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Write a statement that compares the number of ticket sales for Splashin’ Down with the number of ticket sales for Riding the Rapids. Use the symbols >, <, or = in your statement. Explain how you know your statement is right.

7,000

Compare the number of tickets that were sold for each ride by placing the numbers on the number line.

Explore 1

Compare Numbers

7,550

7,600

7,650

Hundreds

7,700

7,750

7,800

Number Line

Thousands

7,850

7,900

Tens

7,950

8,000

Ones

–––––––––––

–––––––––––

–––––––––––

–––––––––––

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––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Compare Numbers | 19

Ferris Wheel

Bumper Cars

Statement 2

Bumper Cars

Ferris Wheel

Statement 1

Comparison Statements

Choose one comparison statement above, and write out how you would read the statement.

7,500

Bumper Cars

Ferris Wheel

Ride

Place Value Chart

Compare the number of tickets that were sold for each ride. Record the values in the place value chart, place the numbers on the number line, and write two comparison statements using the correct symbols.

Explore 1

Compare Numbers

9,100

9,200

9,300

Hundreds

9,400

9,500

9,600

Number Line

Thousands

Place Value Chart

9,700

9,800

Tens

9,900

10,000

Ones

–––––––––––

–––––––––––

Danger Drop –––––––––––

Loop de Loop –––––––––––

Statement 2

Loop de Loop

Danger Drop

Statement 1

Comparison Statements

20 | Compare Numbers

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–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Choose one comparison statement above, and write out how you would read the statement.

9,000

Loop de Loop

Danger Drop

Ride

Explore 1

Compare Numbers

2,500

Hundreds

3,000

3,500

Number Line

Thousands

Place Value Chart

4,000

Tens

4,500

Ones

–––––––––––

–––––––––––

–––––––––––

–––––––––––

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–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Compare Numbers | 21

Fun Slide

Swing n’ Spin

Statement 2

Swing n’ Spin

Fun Slide

Statement 1

Comparison Statements

Choose one comparison statement above, and write out how you would read the statement.

2,000

Swing n’ Spin

Fun Slide

Ride

Explore 1

Compare Numbers

7,100

7,200

7,300

Hundreds

7,400

7,500

7,600

Number Line

Thousands

Place Value Chart

7,700

7,800

Tens

7,900

8,000

Ones

–––––––––––

–––––––––––

Through the Chute –––––––––––

Faster than Light –––––––––––

Statement 2

Faster than Light

Through the Chute

Statement 1

Comparison Statements

22 | Compare Numbers

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–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Choose one comparison statement above, and write out how you would read the statement.

7,000

Faster than Light

Through the Chute

Ride

Explore 1

Compare Numbers

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Compare Numbers | 23

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Why can each comparison be shown using two statements?

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Describe the process you could use to compare two numbers.

Reflect

Explore 1

Compare Numbers

Rounding

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25

Explore 1

Rounding

Name: _______________________ Date: __________

Round Using a Number Line Draw where your group’s beanbags landed.

Describe where your beanbag landed.

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Where did your teammates’ beanbags land compared to yours?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– What number is the exact location of your beanbag? ––––––––––––––––––––––––––– Which multiple of 10 is your beanbag closest to? ––––––––––––––––––––––––––––––

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Rounding | 27

Explore 1

Rounding

On each number line, draw where your group’s beanbags landed. Then, fill in the answers on the chart.

Route: Actual Location Rounded Location

Route: Actual Location Rounded Location

28 | Rounding

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Explore 1

Rounding

Route: Actual Location Rounded Location

Route: Actual Location Rounded Location

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Rounding | 29

Explore 1

Rounding

Route: Actual Location Rounded Location

Refl ect How did you know what number to round to?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– How is rounding a number useful?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

30 | Rounding

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Rounding

Explore 2

Name: _______________________ Date: __________

Round to Justify Reasonableness Get ready for your camping trip! You are going on a camping trip for a week! Since this is your first time camping, you need to buy lots of supplies. At each station, estimate how much you will spend. Share your thinking with your group, and record your thinking below.

Station

Estimation

Actual Total

1

2

3

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Rounding | 31

Rounding

Explore 2 Station

Estimation

Actual Total

4

5

6

Refl ect What process did you use to estimate each amount?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Why is estimation helpful?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 32 | Rounding

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Addition and Subtraction Fluency

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33

Explore 1

Add Using Base-Ten Strategies

Name: _______________________ Date: __________

Addition and Subtraction Fluency

Value

Digit

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Value

Digit

Hundreds

Digit

Digit

Tens

Value

Value

Digit

Digit

Ones

Value

Value

Hundreds

Ones

Addition and Subtraction Fluency | 35

Tens

––––––––––––––––––––––––––––––––––– Henry’s Cards –––––––––––––––––––––––––––––––––––

Complete the following steps to find the total of each card collector’s purchase: • Record the equation in the place value chart on the right-hand side.

• Build a model for each number using base ten blocks on your work mat, and draw your model below.

• Write the value and the digit in each place value.

• Add together each column of expanded form to find the sum for each place value; then, add the place values together.

• Next, solve the standard algorithm on the right-hand side of the page.

Baseball Cards

Football Cards

Total

Baseball Cards

Football Cards

Addition and Subtraction Fluency

Value

Digit

Digit

Digit

Tens

Value

Value

Digit

Digit

Ones

Value

Value

Hundreds

Tens

Ones

Digit

36 | Addition and Subtraction Fluency

Value

Value

Hundreds

Digit

Digit

Tens

Value

Value

Digit

Digit

Ones

Value

Value

Tens

Ones

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Hundreds

––––––––––––––––––––––––––––––––––– Tarik’s Cards –––––––––––––––––––––––––––––––––––

Value

Digit

Hundreds

––––––––––––––––––––––––––––––––––– April’s Cards –––––––––––––––––––––––––––––––––––

Explore 1

Digit

Total

Baseball Cards

Football Cards

Total

Hundreds

Tens

Ones

Hundreds

Tens

Ones

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Addition and Subtraction Fluency | 37

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

What is the relationship between both strategies?

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Explain the differences between the equation on the right and the model on the left.

Reflect

Addition and Subtraction Fluency

––––––––––––––––––––––––––––––––––– José’s Cards –––––––––––––––––––––––––––––––––––

Explore 1

Try to find the sum of José’s cards without building the numbers with the blocks.

Baseball Cards

Football Cards

Total

Explore 2

Addition and Subtraction Fluency

Name: _______________________ Date: __________

Add Using Number Line Strategies To successfully complete each mission, complete each step below: • Use the number line to add.

• Write the partial sum above each jump.

• Write the expression that represents the mission solution.

• Try to get as close to the mission challenge as possible.

• Complete the final mission on your own.

Mission 1: Forest Friend

221 +

Equation:

Mission 2: Dino Delivery

31 +

Equation:

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Addition and Subtraction Fluency | 39

Explore 2

Addition and Subtraction Fluency

Mission 3: Delivery Drop

79 +

Equation: Mission 4: Submarine Adventure

367 +

Equation: Mission 5: Project Adopt-a-Pet

330 +

Equation:

40 | Addition and Subtraction Fluency

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Name: _______________________ Date: __________

Subtract Using Base-Ten Strategies

Explore 3

Addition and Subtraction Fluency

Value

Value

Value

Value

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Tens

Hundreds

Value

Value

Ones

Corn Dogs Hundreds

Ones

Addition and Subtraction Fluency | 41

Tens

Complete the following steps to find the difference of each carnival food: • Record the equation in the place value chart on the right-hand side.

• Build a model for the starting number using base ten blocks on your work mat, and draw your model below.

• Write the value of the digit in each place value to create the expanded form of each number.

• Subtract the number of items that were bought, and move them to the next row.

• Record how many items are left over in the last row.

• Record what happens to the digit in each place value in the equation on the right-hand side.

Number Made

Number Bought

Left Over

Number Made

Number Bought

Left Over

Number Made

Number Bought

Tens

Value

Value

Tens

Value

Value

Hundreds

Value

Value

Hundreds

Value

Value

Explore 3

42 | Addition and Subtraction Fluency

Left Over

Value

Value

Ones

Turkey Legs

Value

Value

Ones

Caramel Apples

Tens

Tens

Ones

Ones

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Hundreds

Hundreds

Addition and Subtraction Fluency

Number Made

Number Bought

Tens

Value

Value

Hundreds

Value

Value

Explore 3

Value

Value

Ones

Funnel Cakes Hundreds

Tens

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Addition and Subtraction Fluency | 43

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

What did you do if you didn’t have a large enough number to subtract from in a place value?

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Ones

Addition and Subtraction Fluency

Explain the relationship between the equation in the model on the left and the equation on the right.

Reflect

Left Over

Explore 4

Addition and Subtraction Fluency

Name: _______________________ Date: __________

Subtract Using Number Line Strategies Complete each step below to see the distance the hikers are traveling: • Use the number line to add up to find the difference between the two elevations.

• Show the partial sum above each jump, and add them together to find the difference.

• For each jump, write the number you landed on below the number line.

• Write an equation that represents the model.

Day 1: a.m.

Model the problem.

Equation:

Day 1: p.m.

Model the problem.

Equation:

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Addition and Subtraction Fluency | 45

Explore 4

Addition and Subtraction Fluency

Day 2: a.m.

Model the problem.

Equation: Day 2: p.m.

Model the problem.

Equation: Day 3 Model the problem.

Equation:

46 | Addition and Subtraction Fluency

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Addition and Subtraction Models

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47

Addition and Subtraction Models

Explore 1

Name: _______________________ Date: __________

Model Problems with Diagrams Use the space below to draw the model you built. Answer the questions based on your model.

Netherlands Diagram

Solution Information I need to know _________________________ _____________________________________ Equation: _____________________________ Solve it.

Solution statement: ____________________________________________________________________ Russia Diagram

Solution Information I need to know _________________________ _____________________________________ Equation: _____________________________ Solve it.

Solution statement: ____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Addition and Subtraction Models | 49

Addition and Subtraction Models

Explore 1 USA Diagram

Solution Information I need to know _________________________ _____________________________________ Equation: _____________________________ Solve it.

Solution statement: ____________________________________________________________________ 1. Describe your process for building a diagram.

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 2. How are diagrams helpful?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

50 | Addition and Subtraction Models

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Addition and Subtraction Models

Explore 1 China Diagram

Solution Information I need to know _________________________ _____________________________________ Equation: _____________________________ Solve it.

Solution statement: ____________________________________________________________________ Germany Diagram

Solution Information I need to know _________________________ _____________________________________ Equation: _____________________________ Solve it.

Solution statement: ____________________________________________________________________

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Addition and Subtraction Models | 51

Addition and Subtraction Models

Explore 1 Canada Diagram

Solution Information I need to know _________________________ _____________________________________ Equation: _____________________________ Solve it.

Solution statement: ____________________________________________________________________ 3. Describe your thought process for solving the Germany problem.

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 4. Did everyone’s diagrams look the same as yours? Explain why.

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

52 | Addition and Subtraction Models

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Model Problems with Number Lines

Name: _______________________ Date: __________

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What information do you have?

What is the problem asking for?

Addition and Subtraction Models | 53

___________________________________________

Solution statement: ___________________________

Equation: ___________________________________

Number line model:

Nonfiction Numbers

Organize the information for each problem, and model each problem by creating a number line. Draw the number line your group creates in the space below. Use the number line to build an equation using a letter for the unknown. Solve and record your answer as a statement, and then explain your reasoning.

Explore 2

Addition and Subtraction Models

54 | Addition and Subtraction Models

What information do you have?

What is the problem asking for?

What information do you have?

What is the problem asking for?

Explore 2

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___________________________________________

Solution statement: ___________________________

Equation: ___________________________________

Number line model:

Fiction Frenzy

___________________________________________

Solution statement: ___________________________

Equation: ___________________________________

Number line model:

Map Mess

Addition and Subtraction Models

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What information do you have?

What is the problem asking for?

What information do you have?

What is the problem asking for?

Explore 2

Addition and Subtraction Models | 55

___________________________________________

Solution statement: ___________________________

Equation: ___________________________________

Number line model:

Chapter-Book Challenge

___________________________________________

Solution statement: ___________________________

Equation: ___________________________________

Number line model:

Book Donations

Addition and Subtraction Models

Equation: ____________________________________

Number line model:

Back on the Shelves

Equation: ____________________________________

Number line model:

56 | Addition and Subtraction Models

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––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Explain your reasoning. ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Solution statement: ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

What information do you have?

What is the problem asking for?

Filling Bookshelves

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Explain your reasoning. ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Solution statement: ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

What information do you have?

What is the problem asking for?

Explore 2

Addition and Subtraction Models

Equation: ____________________________________

Number line model:

Book Sales

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Addition and Subtraction Models | 57

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

How did you know what equation to write for your number line?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

What process did you use to find your new location after each jump on the number line?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Reflect What did each jump on the number line represent?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Explain your reasoning. ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Solution statement: ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

What information do you have?

What is the problem asking for?

Explore 2

Addition and Subtraction Models

Arithmetic Patterns

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59

Arithmetic Patterns

Explore 1

Name: _______________________ Date: __________

Patterns on a Hundred Chart

Follow the instructions on the Assembly Line Cards, and record your answers below.

Outdoor Playhouse What multiplication expression is represented by your hundred chart? _____ × _____ What is the product represented by the length of the assembly line? _____ What patterns do you notice about the shaded numbers? __________________________ __________________________ __________________________ __________________________ __________________________

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Pedal Tractor What multiplication expression is represented by your hundred chart? _____ × _____ What is the product represented by the length of the assembly line? _____ What patterns do you notice about the shaded numbers? __________________________ __________________________ __________________________ __________________________ __________________________ © Accelerate Learning Inc. – All Rights Reserved

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Arithmetic Patterns | 61

Arithmetic Patterns

Explore 1 Toy Kitchen Set What multiplication expression is represented by your hundred chart? _____ × _____ What is the product represented by the length of the assembly line? _____ What patterns do you notice about the shaded numbers? __________________________ __________________________ __________________________ __________________________ __________________________

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Toy Roller Coaster What multiplication expression is represented by your hundred chart? _____ × _____ What is the product represented by the length of the assembly line? _____ What patterns do you notice about the shaded numbers? __________________________ __________________________ __________________________ __________________________ __________________________

62 | Arithmetic Patterns

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Explore 1

Arithmetic Patterns

Refl ect How is a hundred chart helpful when finding the multiples and product to a multiplication problem?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– How can a hundred chart be used to find patterns?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– What did you notice with the multiples when you extended the pattern?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

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Arithmetic Patterns | 63

Explore 2

Arithmetic Patterns

Name: _______________________ Date: __________

Patterns on a Multiplication Chart

Follow the instructions on the Pack the Boxes Cards, and record your answers.

Beans What multiplication expression is represented by your highlighted table? _____ × _____ What is the product for the total number of items needed in all of the boxes? _______ What pattern do you notice about the highlighted numbers? ________________________________ ________________________________ ________________________________ ________________________________ ________________________________

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Pasta What multiplication expression is represented by your highlighted table? _____ × _____ What is the product for the total number of items needed in all of the boxes? _______ What pattern do you notice about the highlighted numbers? ________________________________ ________________________________ ________________________________ ________________________________ ________________________________ © Accelerate Learning Inc. – All Rights Reserved

Arithmetic Patterns | 65

Arithmetic Patterns

Explore 2 Rice What multiplication expression is represented by your highlighted table? _____ × _____ What is the product for the total number of items needed in all of the boxes? _______ What pattern do you notice about the highlighted numbers? ________________________________ ________________________________ ________________________________ ________________________________ ________________________________

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Peanut Butter What multiplication expression is represented by your highlighted table? _____ × _____ What is the product for the total number of items needed in all of the boxes? _______ What pattern do you notice about the highlighted numbers? ________________________________ ________________________________ ________________________________ ________________________________ ________________________________

66 | Arithmetic Patterns

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Explore 2

Arithmetic Patterns

Refl ect What pattern do you notice when you multiply an even number by an even number?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– What pattern do you notice when you multiply an odd number by an even number?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– What pattern do you notice when you multiply an odd number by an odd number?

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

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Arithmetic Patterns | 67

Multiplication Models

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69

Equal Groups and Repeated Addition

Name: _______________________ Date: __________

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2.

1.

Model

Multiplication Models | 71

Corinne has ____________ diapers for her babies.

Multiplication sentence: _____ × _____ = _____

There are ____ groups of ______.

Repeated addition: __________________________

Waggin’ and Washing groomed ___________ pets.

Multiplication sentence: _____ × _____ = _____

There are ____ groups of ______.

Repeated addition: __________________________

Equations and Solution

Travel to different stations, and use the materials to build a model of each problem. Sketch what your model looks like, and complete each answer.

Explore 1

Multiplication Models

72 | Multiplication Models

4.

3.

Model

Explore 1

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Helen painted _______ nails on Tuesday.

Multiplication sentence: _____ × _____ = _____

There are ____ groups of ______.

Repeated addition: __________________________

Mrs. Sullivan has ___________ students.

Multiplication sentence: _____ × _____ = _____

There are ____ groups of ______.

Repeated addition: __________________________

Equations and Solution

Multiplication Models

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6.

5.

Model

Explore 1

Multiplication Models | 73

Lucita has _______ peonies in her garden.

Multiplication sentence: _____ × _____ = _____

There are ____ groups of ______.

Repeated addition: __________________________

Pablo stocked ___________ sodas.

Multiplication sentence: _____ × _____ = _____

There are ____ groups of ______.

Repeated addition: __________________________

Equations and Solution

Multiplication Models

74 | Multiplication Models

How are the models and repeated addition and multiplication sentences related?

What do you notice about each model? Explain how they’re similar and different.

Reflect

Explore 1

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Multiplication Models

Explore 2

Multiplication Models

Name: _______________________ Date: __________

Arrays and Area Models Part I: Grocery Store Stocking (Arrays) Use the Grocery Item Cards at each station to build the display described below. Record your work in the space provided.

Eggs The store has 6 shelves and wants 3 cartons of eggs on each shelf.

Draw the display.

Find the total number of items.

Multiplication sentence: There are ________ groups of ________ cartons of eggs.

Multiplication equation:

There are ________ egg cartons on display in the store.

Cupcakes The store has 2 shelves and wants 8 cupcakes on each shelf.

Draw the display.

Find the total number of items.

Multiplication sentence: There are ________ groups of ________ cupcakes.

Multiplication equation:

There are ________ cupcakes on display in the store. © Accelerate Learning Inc. – All Rights Reserved

Multiplication Models | 75

Multiplication Models

Explore 2 Water The store has 3 shelves and wants 5 water bottles on each shelf.

Draw the display.

Find the total number of items.

Multiplication sentence: There are ________ groups of ________ water bottles.

Multiplication equation:

There are ________ water bottles on display in the store.

Apples The store has 4 shelves and wants 9 apples on each shelf.

Draw the display.

Find the total number of items.

Multiplication sentence: There are ________ groups of ________ apples.

Multiplication equation:

There are ________ apples on display in the store.

76 | Multiplication Models

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Multiplication Models

Explore 2 Part II: USA Games, Inc. (Area Models) Request 1 Draw the game board.

Find the total number of square units.

Multiplication sentence: There are ________ rows of ______ units.

Multiplication equation:

Request 2 Draw the game board.

Find the total number of square units.

Multiplication sentence: There are ________ rows of ______ units.

Multiplication equation:

Request 3 Draw the game board.

Find the total number of square units.

Multiplication sentence: There are ________ rows of ______ units.

Multiplication equation:

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Multiplication Models | 77

Multiplication Models

Explore 2 Refl ect Explain how you determined the total number of items in each model.

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Describe how to find the total without counting each object. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How are these models similar to other multiplication models? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

78 | Multiplication Models

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Diagrams

Name: _______________________ Date: __________

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Card Number Tape Diagram

Multiplication Equation

Multiplication Models | 79

Solution Sentence

Record the card number from the bottom right of the card. Sketch a diagram that represents the problem, and write a multiplication equation to determine the solution.

Explore 3

Multiplication Models

80 | Multiplication Models

Card Number

Explore 3 Tape Diagram

Multiplication Equation

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Solution Sentence

Multiplication Models

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Multiplication Models | 81

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

How do you use the diagram model to represent a multiplication equation?

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

How do diagrams compare to other multiplication models?

Reflect

Explore 3

Multiplication Models

Multiplication Models

Explore 4

Name: _______________________ Date: __________

Number Lines and Skip Counting You’re almost ready for camp next week!

Open each envelope to see what essentials you have packed. Circle the multiples of each item on a meterstick, and place them on the number line model. Record how many of each item you have packed for camp! ____ Pairs of socks Model: Sketch the jumps on the number line, and write down the multiples.

0

Equation: ______ × ______ = ______ ____ Boxes of matches Model: Sketch the jumps on the number line, and write down the multiples.

0

Equation: ______ × ______ = ______

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Multiplication Models | 83

Multiplication Models

Explore 4 ____ Breathable bandages

Model: Sketch the jumps on the number line, and write down the multiples.

0

Equation: ______ × ______ = ______ ____ Batteries Model: Sketch the jumps on the number line, and write down the multiples.

0

Equation: ______ × ______ = ______ Refl ect How can a number line be used to multiply two numbers? _____________________________________________________________________ _____________________________________________________________________ What is the relationship between equal jumps on a number line and skip counting? _____________________________________________________________________ _____________________________________________________________________

84 | Multiplication Models

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Equalities

Name: _______________________ Date: __________

Expression 2: _________________________

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Multiplication Models | 85

_________________________________________________________________________________________

Solution: _________________________________________________________________________________

=

Value: ______

Value: ______

Expression 1: _________________________

Model:

Model:

You bought 5 bags of potting soil. Each bag of potting soil was $3. Garden World had a coupon for $3 off your potting soil purchase, so you only had to pay for 4 bags of potting soil. Write an equation with two expressions that shows how much money you spent on the potting soil.

Bags of Potting Soil

Read each gardening problem below. Create various models to represent each problem, and determine two expressions that represent those models and have values that make each equation equal. Then, write a solution to each problem.

Explore 5

Multiplication Models

Pieces of Lumber

Expression 2: _________________________

86 | Multiplication Models

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_________________________________________________________________________________________

Solution: _________________________________________________________________________________

=

Value: ______

Value: ______

Expression 1: _________________________

Model:

Model:

You bought 8 pieces of lumber. Each piece of lumber was $5. Garden World gave you two coupons. Each coupon took $5 off your lumber purchase, so you only had to pay for 6 pieces of lumber. Write an equation with two expressions that shows how much money you spent on lumber.

Explore 5

Multiplication Models

Bags of Seeds

Expression 2: _________________________

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Multiplication Models | 87

_________________________________________________________________________________________

Solution: _________________________________________________________________________________

=

Value: ______

Value: ______

Expression 1: _________________________

Model:

Model:

You bought 8 bags of potting seeds. Each bag of seeds was $2. Garden World had a coupon for $2 off your potting seeds purchase, so you only had to pay for 7 bags of seeds. Write an equation with two expressions that show how much money you spent on the bags of seeds.

Explore 5

Multiplication Models

Sprinklers

Expression 2: _________________________

88 | Multiplication Models

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_________________________________________________________________________________________

Solution: _________________________________________________________________________________

=

Value: ______

Value: ______

Expression 1: _________________________

Model:

Model:

You bought 3 sprinklers. Each sprinkler was $9. Garden World had a coupon for $9 off your sprinkler purchase, so you only had to pay for 2 sprinklers. Write an equation with two expressions that show how much money you spent on the sprinklers.

Explore 5

Multiplication Models

Garden Tools

Expression 2: _________________________

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Multiplication Models | 89

_________________________________________________________________________________________

Solution: _________________________________________________________________________________

=

Value: ______

Value: ______

Expression 1: _________________________

Model:

Model:

You bought 6 garden tools. Each garden tool was $7. Garden World gave you two coupons. Each coupon took $7 off your garden tool purchase, so you only had to pay for 4 garden tools. Write an equation with two expressions that show how much money you spent on garden tools.

Explore 5

Multiplication Models

90 | Multiplication Models

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___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

Why do both sides of an equality need to represent the same amount?

___________________________________________________________________________________________

___________________________________________________________________________________________

What can we determine if the expressions have different values? What can we determine if they have the same value?

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

Why is it important to determine the value of each expression in an equality?

Reflect

Explore 5

Multiplication Models

Division Models

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91

Division Models

Explore 1

Name: _______________________ Date: __________

Equal Groups and Shares Use the materials available to build a model of how to solve the problem at each station. Draw a picture of your model. Then, write the equation, and label what each part of the equation represents. Circle whether you found the number of objects in each group or the number of groups.

Station 1 Model

Equation

____________ ÷ ____________ = ____________ Dividend Divisor Quotient ___________ ___________

___________ ___________

___________ ___________

Circle one: Number of objects / number of groups How many cupcakes will each student get? __________________________________ Station 2 Model

Equation

____________ ÷ ____________ = ____________ Dividend Divisor Quotient ___________ ___________

___________ ___________

___________ ___________

Circle one: Number of objects / number of groups How many bows does she have in each color? ________________ © Accelerate Learning Inc. – All Rights Reserved

Division Models | 93

Division Models

Explore 1 Station 3

Model

Equation

____________ ÷ ____________ = ____________ Dividend Divisor Quotient ___________ ___________

___________ ___________

___________ ___________

Circle one: Number of objects / number of groups How many cars will each bin hold? _________________________________________ Station 4

Model

Equation

____________ ÷ ____________ = ____________ Dividend Divisor Quotient ___________ ___________

___________ ___________

___________ ___________

Circle one: Number of objects / number of groups How many pages are in the sticker book? ________________

94 | Division Models

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Division Models

Explore 1 Station 5

Model

Equation

____________ ÷ ____________ = ____________ Dividend Divisor Quotient ___________ ___________

___________ ___________

___________ ___________

Circle one: Number of objects / number of groups How many pairs of socks does he have? _____________________________________ Station 6

Model

Equation

____________ ÷ ____________ = ____________ Dividend Divisor Quotient ___________ ___________

___________ ___________

___________ ___________

Circle one: Number of objects / number of groups How many pieces of candy will she eat each day? _____________________________ Describe your process for solving these problems. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Division Models | 95

Explore 2

Division Models

Name: _______________________ Date: __________

Arrays Represent each problem from the Array Scenario Cards with an array. Complete the rest of the information.

Array 1.

Description

Division Equation

Number of rows: __________ Number in each row: _________

2.

Number of rows: __________ Number in each row: _________

3.

Number of rows: __________ Number in each row: _________

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Division Models | 97

Division Models

Explore 2

Array

Description

Division Equation

4.

Number of rows: __________ Number in each row: _________

5.

Number of rows: __________ Number in each row: _________

6.

Number of rows: __________ Number in each row: _________

98 | Division Models

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Explore 2

Division Models

Refl ect How does the array model help you write a division equation? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How does this model connect to multiplication? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

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Division Models | 99

Explore 3

Division Models

Name: _______________________ Date: __________

Diagrams and Repeated Subtraction Select a Task Card. Discuss the task with your group. Determine what information you need to find. Represent the task using a diagram, repeated subtraction, and a division sentence. Write a solution statement.

Task: _____

Diagram

What information do you need to find?

•

Number of groups

•

Number of items within a group

Repeated Subtraction

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Division Sentence

Solution Statement

Division Models | 101

Division Models

Explore 3 Task: _____

Diagram

What information do you need to find?

•

Number of groups

•

Number of items within a group

Repeated Subtraction

Division Sentence

Task: _____

Solution Statement

Diagram

What information do you need to find?

•

Number of groups

•

Number of items within a group

Repeated Subtraction

102 | Division Models

Division Sentence

Solution Statement

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Division Models

Explore 3 Task: _____

Diagram

What information do you need to find?

•

Number of groups

•

Number of items within a group

Repeated Subtraction

Division Sentence

Task: _____

Solution Statement

Diagram

What information do you need to find?

•

Number of groups

•

Number of items within a group

Repeated Subtraction

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Division Sentence

Solution Statement

Division Models | 103

Division Models

Explore 3 Task: _____

Diagram

What information do you need to find?

•

Number of groups

•

Number of items within a group

Repeated Subtraction

Division Sentence

Solution Statement

Refl ect Explain how a diagram can be drawn to represent and help solve a division problem. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Explain how repeated subtraction is related to division. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

104 | Division Models

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Explore 4

Division Models

Name: _______________________ Date: __________

Relate Multiplication and Division Equations Read all of the information about your party, and build a model.

Use your model to draw a picture of what you made. Write an equation to match your drawing, and answer the question.

1 – Tables Model:

Division equation (label the dividend, divisor, and quotient): ____________ ÷ ____________ = ____________ Missing factor equation: ____ × ____ = ______ What do you notice about your two equations? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Division Models | 105

Division Models

Explore 4 2 – Pizza Model:

Division equation (label the dividend, divisor, and quotient): ____________ ÷ ____________ = ____________

Write a new problem where we know the number of pizzas but not the number of slices in each pizza. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

Missing factor equation: ____ × ____ = ______

106 | Division Models

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Division Models

Explore 4 3 – Socks Model:

Division equation:

____________ ÷ ____________ = ____________

Missing factor equation:

____ × ____ = ______ 4 – Balloons

Model:

Division equation:

____________ ÷ ____________ = ____________

Restate the scenario as a multiplication problem with a missing factor. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Division Models | 107

Division Models

Explore 4 Refl ect What did you notice about the numbers in each set of equations? Why?

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can you use multiplication to help solve division problems? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

108 | Division Models

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Multiplication and Division Strategies

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109

Multiplication and Division Strategies

Explore 1

Name: _______________________ Date: __________

The Commutative Property Read each scenario, and use the manipulatives provided to build 3 different models that show the solution to the problem. Draw your models, and write an equation to describe those models.

Scenario 1

Frog and Toad are racing.

Frog hops 4 times. Each time, he hops 5 feet.

How far does Frog hop?

Toad hops 5 times. Each time, he hops 4 feet.

How far does Toad hop?

Number line:

Number line:

Array:

Array:

Equal groups:

Equal groups:

Equation:

Equation:

What is the same about the two situations? ______________________________________________________________________ What is different about the two situations? ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Strategies | 111

Multiplication and Division Strategies

Explore 1 Scenario 2 Rosa and Gwen have each planted a garden.

Rosa’s garden has 3 rows with 6 plants in each row. How many plants are in her garden?

Gwen’s garden has 6 rows with 3 plants in each row. How many plants are in her garden?

Number line:

Number line:

Array:

Array:

Equal groups:

Equal groups:

Equation:

Equation:

Who has more plants in her garden? ______________________________________________________________________ What do the two situations have in common? ______________________________________________________________________

112 | Multiplication and Division Strategies

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Multiplication and Division Strategies

Explore 1 Scenario 3 Ja’Von and Hugo are giving away candy.

Ja’Von gives 4 pieces of candy to each of his 7 friends. How much candy does he give away?

Hugo gives 7 pieces of candy to each of his 4 friends. How much candy does he give away?

Number line:

Number line:

Array:

Array:

Equal groups:

Equal groups:

Equation:

Equation:

Who gives away more candy? ______________________________________________________________________ What do your equations have in common? ______________________________________________________________________ Does the order of the factors matter when you multiply? Explain. ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Strategies | 113

Explore 1

Multiplication and Division Strategies

Refl ect What did you notice as you solved each scenario using the different models? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What did you notice about the equations for each model? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Does the order of the numbers matter when you are multiplying? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

114 | Multiplication and Division Strategies

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Explore 2

Multiplication and Division Strategies

Name: _______________________ Date: __________

The Associative Property Read each scenario. Use the manipulatives provided to model each scenario. Draw your models, and write an equation to describe those models.

Scenario 1

Scenario 2

Sydney purchased 3 containers of gummy bears. Each container had 5 bags of gummy bears, and each bag had 6 gummy bears inside. How many gummy bears did Sydney purchase?

Sydney purchased 5 containers of gummy bears. Each container had 6 rows of gummy bears, and there were 3 gummy bears in each row. How many gummy bears did Sydney purchase?

Draw your model.

Draw your model.

Equation: _______________________

Equation: _______________________

How many gummy bears did Sydney purchase in each scenario? ______________________________________________________________________ What do both equations have in common? ______________________________________________________________________ What is different about both equations? ______________________________________________________________________

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Multiplication and Division Strategies | 115

Explore 2

Multiplication and Division Strategies

Scenario 3

Scenario 4

Milo has 4 shelves for shoes in his closet. Each shelf has 3 boxes of shoes on it. There are 2 shoes in each box.

How many shoes does Milo have in his closet?

Milo has 3 shelves for shoes in his closet. Each shelf has 4 boxes of shoes on it. There are 2 shoes in each box.

How many shoes does Milo have in his closet?

Draw your model.

Draw your model.

Equation: _______________________

Equation: _______________________

How many shoes does Milo have in his closet for each scenario? ______________________________________________________________________ What do you notice about each model? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Refl ect Does the order of the factors matter when multiplying? Explain. ______________________________________________________________________ ______________________________________________________________________ 116 | Multiplication and Division Strategies

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Explore 3

Multiplication and Division Strategies

Name: _______________________ Date: __________

The Distributive Property Part I: The Distributive Property of Multiplication Draw the array models of each theater in the space provided, and label each section with a multiplication equation and partial products.

Theater 1: 4 rows, 6 seats in each row Large Array

Small Arrays Top section:

Lower section:

Complete the equations below to represent the array models above. ____ × ____ = =(____ + ____) × ____

____ × ____ = OR

= (____ × ____) + (____ × ____)

= ____ + ____

= ____ + ____

= __________

= __________

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Multiplication and Division Strategies | 117

Multiplication and Division Strategies

Explore 3

Theater 2: 4 rows, 8 seats in each row Large Array

Small Arrays Top section:

Lower section:

Complete the equations below to represent the array models above. ____ × ____ = =(____ + ____) × ____ = ____ + ____

____ × ____ = OR

= (____ × ____) + (____ × ____) = ____ + ____

= __________

= __________

Theater 3: 3 rows, 9 seats in each row Large Array

Small Arrays Top section:

Lower section:

Complete the equations below to represent the array models above. ____ × ____ = =(____ + ____) × ____ = ____ + ____ = __________ 118 | Multiplication and Division Strategies

____ × ____ = OR

= (____ × ____) + (____ × ____) = ____ + ____ = __________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Strategies

Explore 3 Part II: The Distributive Property of Division Draw the array models of each theater in the space provided, and label each section with the division equation and partial quotients.

Theater 4: 40 seats in the theater, 8 seats in each row.

How many rows of seats are in the theater?

Large Array

Small Arrays Top section:

Lower section:

Complete the equations below to represent the array models above. ____ ÷ ____ = ____ ÷ ____

OR

= (____ ÷ ____) + (____ ÷ ____) = ____ + ____

= __________

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= __________

Multiplication and Division Strategies | 119

Multiplication and Division Strategies

Explore 3

Theater 5: 42 seats in the theater, 7 seats in each row How many rows of seats are in the theater?

Large Array

Small Arrays Top section:

Lower section:

Complete the equations below to represent the array models above. ____ ÷ ____ = ____ ÷ ____

OR

= (____ ÷ ____) + (____ ÷ ____) = ____ + ____

= __________

= __________

Refl ect How are the larger arrays and smaller arrays similar? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How are the larger arrays and smaller arrays different? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ 120 | Multiplication and Division Strategies

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Multiply Multiples of 10

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121

Explore 1

Multiply Multiples of 10

Name: _______________________ Date: __________

Multiply Multiples of 10 Using Base Ten Blocks Insulated Coffee Cups Draw a model of your groups of ten in the space below.

___ groups of ___ tens = ___ tens ___ × ___ = _____ or _____ × ______ × 10 = _____ There are ______ cups in _________ packages.

Reusable Grocery Bags Draw a model of your groups of ten in the space below.

___ groups of ___ tens = ___ tens ___ × ___ = _____ or _____ × ______ × 10 = _____ There are ______ reusable bags in _________ packages. © Accelerate Learning Inc. – All Rights Reserved

Multiply Multiples of 10 | 123

Explore 1

Multiply Multiples of 10

Aluminum Cans Draw a model of your groups of ten in the space below.

___ groups of ___ tens = ___ tens ___ × ___ = _____ or _____ × ______ × 10 = _____ There are ______ cans in _________ packages.

Biodegradable Can Rings Draw a model of your groups of ten in the space below.

___ groups of ___ tens = ___ tens ___ × ___ = _____ or _____ × ______ × 10 = _____ There are ______ rings in _________ packages.

124 | Multiply Multiples of 10

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Explore 1

Multiply Multiples of 10

Egg Cartons Draw a model of your groups of ten in the space below.

___ groups of ___ tens = ___ tens ___ × ___ = _____ or _____ × ______ × 10 = _____ There are _______ cartons in _________ packages.

Glass Sauce Jars Draw a model of your groups of ten in the space below.

___ groups of ___ tens = ___ tens ___ × ___ = _____ or _____ × ______ × 10 = _____ There are _________ jars in _________ packages.

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Multiply Multiples of 10 | 125

Multiply Multiples of 10

Explore 1 Rubber Shoe Soles Draw a model of your groups of ten in the space below.

___ groups of ___ tens = ___ tens ___ × ___ = _____ or _____ × ______ × 10 = _____ There are _________ rubber soles in _________ packages.

Refl ect How does the number of base-ten rods relate to the total number of items in a package? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What strategies can be used to count the total number of items in a shipping order? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

126 | Multiply Multiples of 10

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Explore 2

Multiply Multiples of 10

Name: _______________________ Date: __________

Multiply Multiples of 10 Using Arrays Use the Grocery Item Cards at each station to take inventory of what you have. Make an array with your base-ten rods, and sketch your model. Solve for the total number of items.

Eggs Eggs aren’t just for breakfast! They are used in many recipes. In your inventory, you have 4 large cartons of 30 eggs in each.

Draw an array.

Find the total number of items.

_____ eggs

_____ groups of _____ tens or

____ groups

10 _____ × _____ × _____ _____ × _____ = _____

Multiplication sentence: ________________ There are ________ eggs.

Croissants Croissants can be breakfast or dessert! You made sure to have a good stock of this buttery treat. In your inventory, you have 5 boxes of 20 croissants each.

Draw an array.

Find the total number of items.

_____ croissants

_____ groups of _____ tens or

____ groups

_____ × _____ × _____ _____ × _____ = _____

Multiplication sentence: ________________ There are ________ croissants. © Accelerate Learning Inc. – All Rights Reserved

Multiply Multiples of 10 | 127

Explore 2

Multiply Multiples of 10

Juice Pouches Many families will stop by with their kids. Lots of kids love juice pouches. You made sure to get plenty; you have 7 boxes of 30 juice pouches each.

Draw an array.

Find the total number of items.

_____ juice pouches

_____ groups of _____ tens or

____ groups

_____ × _____ × _____ _____ × _____ = _____

Multiplication sentence: _______________ There are ________ juice pouches.

Coffee Creamer Guests love waking up to the smell of fresh coffee in the morning. Many people use creamer in their coffee. You have 3 large boxes of 50 creamers in each box.

Draw an array.

Find the total number of items.

_____ creamers

_____ groups of _____ tens or

____ groups

_____ × _____ × _____ _____ × _____ = _____

Multiplication sentence: ________________ There are ________ creamers.

128 | Multiply Multiples of 10

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Explore 2

Multiply Multiples of 10

Dish Soap Packs There will be lots of dishes to clean. Each box comes with 60 dish soap packs. You bought 8 boxes for the bed-and-breakfast.

Draw an array.

Find the total number of items.

_____ dish soap packs

_____ groups of _____ or _____ tens.

____ groups

_____ × _____ × _____ _____ × _____ = ______

Multiplication sentence: _____________ There are ________ dish soap packs.

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Multiply Multiples of 10 | 129

Multiply Multiples of 10

Explore 2 Refl ect Explain how you determined the total number of items in each model.

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Describe how to find the total without counting each object. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How do the equations relate to the array? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

130 | Multiply Multiples of 10

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Explore 3

Multiply Multiples of 10

Name: _______________________ Date: __________

Multiply Multiples of 10 Using Number Lines Record your number line models by drawing equal groups on the lines provided, and answer the questions that follow.

Shift 1: Tasty Taffy Size of each piece: _______ Number of pieces: _______ Total length: _______

0 Write two equations that represent your model. _________________________________

_________________________________

Shift 2: Tasty Taffy Size of each piece: _______ Number of pieces: _______ Total length: _______

0 Write two equations that represent your model. _________________________________ © Accelerate Learning Inc. – All Rights Reserved

_________________________________ Multiply Multiples of 10 | 131

Multiply Multiples of 10

Explore 3 Shift 3: Giant Raspberry Rods

Size of each piece: _______ Number of pieces: _______ Total length: _______

0 Write two equations that represent your model. _________________________________

_________________________________

Shift 4: Giant Raspberry Rods Size of each piece: _______ Number of pieces: _______ Total length: _______

0 Write two equations that represent your model. _________________________________

132 | Multiply Multiples of 10

_________________________________

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Multiply Multiples of 10

Explore 3 Shift 5: Silly ‘n Sweet Strips

Size of each piece: _______ Number of pieces: _______ Total length: _______

0

Write two equations that represent your model. _________________________________

_________________________________

Shift 6: Silly ‘n Sweet Strips Size of each piece: _______ Number of pieces: _______ Total length: _______

0 Write two equations that represent your model. _________________________________

_________________________________

Refl ect Explain how you found the total amount of candy made during each shift. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

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Multiply Multiples of 10 | 133

Multiplication and Division Problem Solving

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135

Explore 1

Multiplication and Division Problem Solving

Name: _______________________ Date: __________

Model and Solve One-Step Problems It’s time to get ready for lunch! It takes some math wizards to make sure everyone gets a healthy lunch. Because third grade is known for its amazing mathematicians, your principal has challenged you to make sure lunchtime runs smoothly!

Part I: Lunchtime Problems (Multiplication) Five kindergarten students in each of three kindergarten rooms order strawberry milk each day. How many cartons of strawberry milk need to be ordered?

Equation: ________________________

Ways we can solve this problem: 1. ___________________________________________________________________ 2. ___________________________________________________________________ 3. ___________________________________________________________________ How many cartons of strawberry milk need to be ordered? ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Problem Solving | 137

Explore 1

Multiplication and Division Problem Solving

Part II: Chicken-Finger Boxes (Division) First graders love chicken fingers! The teachers decided that 56 chicken fingers needed to be ordered for Wednesday’s lunch. There are 8 chicken fingers in a box.

How many boxes need to be ordered?

Model:

Equation: ___________________ How many boxes need to be ordered? ____________________________ Second graders prefer hot dogs. Tuesday is hot dog day, and you need to find out how many hot dogs are needed. You know that 45 students said they want hot dogs.

You have been told there are 9 boxes of hot dogs in the refrigerator, which should be enough. How many hot dogs must be in each box?

Model:

Equation: ___________________ How many hot dogs are in each box? ____________________________ 138 | Multiplication and Division Problem Solving

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Explore 1

Multiplication and Division Problem Solving

Part III: Model and Solve Everyone’s favorite dessert is the chocolate cupcakes. You decide to order 4 boxes of chocolate cupcakes. Each box contains 12 cupcakes. How many students will get a cupcake?

Model:

Equation: ___________________ How many students will get a cupcake? _____________________________________ Explain your reasoning. __________________________________________________ ______________________________________________________________________ You realize that is not nearly enough cupcakes, so you decide to order more boxes.

You want to make sure there are enough cupcakes for 30 more students. However, you realize that now you can order only 5 cupcakes per box. How many boxes are you going to need to order?

Model:

Equation: ___________________ How many boxes should you order? _____________________________________ Explain your reasoning. __________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Problem Solving | 139

Explore 2

Multiplication and Division Problem Solving

Name: _______________________ Date: __________

Model and Solve Two-Step Problems

Vacation is getting closer! Will you sleep in? Will you play with your friends? Will you go somewhere? Each card describes the dream vacation of other third-grade students. Represent and solve the problems together using diagrams, equations using a letter for the unknown, and base ten blocks. Get the answer correct, and you might be the first to reach your dream vacation!

Dream vacation: ________________________________________________________ Equation(s)

Model

Solution statement: ______________________________________________________ Dream vacation: ________________________________________________________ Equation(s)

Model

Solution statement: _____________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Problem Solving | 141

Explore 2

Multiplication and Division Problem Solving

Dream vacation: ________________________________________________________ Equation(s)

Model

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ Dream vacation: ________________________________________________________ Equation(s)

Model

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ 142 | Multiplication and Division Problem Solving

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Explore 2

Multiplication and Division Problem Solving

Dream vacation: ________________________________________________________ Equation(s)

Model

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ Dream vacation: ________________________________________________________ Equation(s)

Model

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Problem Solving | 143

Explore 3

Multiplication and Division Problem Solving

Name: _______________________ Date: __________

Model and Solve One- and Two-Step Problems 1. Start at one poster.

2. Read the problem, and select a model or strategy.

3. Use the model or strategy to build an equation using a letter for the unknown.

4. Use the model or strategy to solve the problem.

5. Record the solution as a statement, and explain your reasoning.

6. Find the poster that lists your answer at the top, and repeat.

Title: ______________________________________________ Model/Strategy

Equation(s)

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Problem Solving | 145

Explore 3

Multiplication and Division Problem Solving

Title: ______________________________________________ Model/Strategy

Equation(s)

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ Title: ______________________________________________ Model/Strategy

Equation(s)

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ 146 | Multiplication and Division Problem Solving

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Explore 3

Multiplication and Division Problem Solving

Title: ______________________________________________ Model/Strategy

Equation(s)

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ Title: ______________________________________________ Model/Strategy

Equation(s)

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Problem Solving | 147

Explore 3

Multiplication and Division Problem Solving

Title: ______________________________________________ Model/Strategy

Equation(s)

Solution statement: ______________________________________________________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ Refl ect How is using models or a strategy helpful? ______________________________________________________________________ ______________________________________________________________________ What strategies did you use to solve the problems? ______________________________________________________________________ ______________________________________________________________________

148 | Multiplication and Division Problem Solving

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Area in Square Units

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149

Area in Square Units

Explore 1

Name: _______________________ Date: __________

Recognize Unit Lengths and Tile the Area of Rectangles The Mystery of the Dripping Water Fountain Width: _________

Length: _________

Area: ______________________________ The Adventures of Measureman!

Width: _________

Length: _________

Area: ______________________________ Maxwell the Spider Width: _________

Length: _________

Area: ______________________________ How to Bake Cookies Width: _________

Length: _________

Area: ______________________________ Gilly the Unicorn Width: _________

Length: _________

Area: ______________________________ © Accelerate Learning Inc. – All Rights Reserved

Area in Square Units | 151

Area in Square Units

Explore 1 The Very Silly Rabbit Width: _________

Length: _________

Area: ______________________________ Poems About Dogs Width: _________

Length: _________

Area: ______________________________ All About Flowers Width: _________

Length: _________

Area: ______________________________ Mohammad Goes to Pluto!

Width: _________

Length: _________

Area: ______________________________ Gillespie: Hero of the Underworld Width: _________

Length: _________

Area: ______________________________

152 | Area in Square Units

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Explore 1

Area in Square Units

Refl ect How can you ensure your area is measured accurately? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What observations can you make about tiling? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What is the relationship of the length and width to the total area? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

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Area in Square Units | 153

Count Area in Square Units

Name: _______________________ Date: __________

____________________________ of computer board.

____________________________

of the cafeteria floor.

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Alejandra will have to work on

Mr. Liu will have to wax

5

of tiles.

Area in Square Units | 155

____________________________

Saffron will have to fill

6

of flooring.

of ceiling tiles.

of plastic laminate.

4

____________________________

____________________________

____________________________

Eric will have to wash

3

Selena will need

2

Fam Bam Games will need

1

Count the area for each of the scenarios. Write an answer statement, and complete the reflection questions.

Explore 2

Area in Square Units

156 | Area in Square Units

____________________________

____________________________. of soil.

The garden club needs to fertilize

The bulletin board is

10

11

____________________________.

____________________________

to display information.

The class quilt will be

8

The field day banner has

7

Explore 2

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____________________________.

Nimi’s mosaic art piece is

12

of paper for each book.

____________________________

Monae will need

9

Area in Square Units

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Area in Square Units | 157

___________________________________________________________________________________________

Will this work for all figures? Why or why not? ___________________________________________________________________________________________

___________________________________________________________________________________________

Do you think there is a different way of determining area without counting each tile based on your observations?

Explain. ___________________________________________________________________________________________

___________________________________________________________________________________________

What patterns did you observe? Explain. ___________________________________________________________________________________________

___________________________________________________________________________________________

How did you count the total area in each scenario? ___________________________________________________________________________________________

Reflect

Explore 2

Area in Square Units

Apply the Area Formula

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159

Explore 1

Apply the Area Formula

Name: _______________________ Date: __________

Relate Tiling to Multiplication Part I: Corn Plants Use your tiles to create a model of the corn plants. Draw your model of the garden with corn plants in the space below.

How many rows of corn are in the garden? ___________________________________ How many corn plants are in each row? ______________________________________ What operation can be used to find the total number of corn plants? Explain. ______________________________________________________________________ Write an equation that shows how to find the total number of corn plants. ______________________________________________________________________ Each corn plant takes up 1 square foot. What is the total area of the garden? ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Apply the Area Formula | 161

Apply the Area Formula

Explore 1

Part II: Garden Plans Use the tables below to draw a model of each garden section and record the equation that can be used to find the total area of the section.

Carrots Model

Equation

Area: __________________________ Lettuce Model

Equation

Area: __________________________ Wheat Model

Equation

Area: __________________________ 162 | Apply the Area Formula

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Apply the Area Formula

Explore 1 Tomatoes Model

Equation

Area: __________________________ Green Beans Model

Equation

Area: __________________________ Refl ect How did you find the total area of each garden section? ______________________________________________________________________ ______________________________________________________________________ Look at the length, width, and area of the wheat, tomatoes, and green beans. What do you notice about these sections? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Apply the Area Formula | 163

Name: _______________________ Date: __________

L = ________ W = ________

L = ________ W = ________

L = ________ W = ________

Model with Dimensions

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3 Rectangula City Bank

2 Toasty Mugs Coffee Shop

1 Easy Trims Barber Shop

Building

Equation

Apply the Area Formula | 165

Solution Sentence

For each scenario, sketch a model of the problem and its dimensions in the row that corresponds to the building.

Write an equation to represent the problem, and write a solution sentence with your findings.

Problem Solve for Area with Multiplication

Explore 2

Apply the Area Formula

166 | Apply the Area Formula

6 Sai’s Souvenir Shop

5 Abstract Art Gallery

4 Fernanda’s Florist Shop

Building

Model with Dimensions

L = ________ W = ________

L = ________ W = ________

L = ________ W = ________

Explore 2 Equation

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Solution Sentence

Apply the Area Formula

L = ________ W = ________

L = ________ W = ________

Model with Dimensions

Equation

Solution Sentence

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Apply the Area Formula | 167

____________________________________________________________________________________________

____________________________________________________________________________________________

Why would it be beneficial to know how to calculate area in your daily life?

Reflect

8 Rectangula City Hall

7 Crunch City Café

Building

Explore 2

Apply the Area Formula

Apply the Area Formula

Explore 3

Name: _______________________ Date: __________

Area and the Distributive Property Model how you broke up each exploration site over two days. Label the dimensions of the exploration site for each day.

Exploration Site: _____

Day 1 equation for area explored:

Day 2 equation for area explored:

Total area explored over two days:

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Apply the Area Formula | 169

Apply the Area Formula

Explore 3 Exploration Site: _____

Day 1 equation for area explored:

Day 2 equation for area explored:

Total area explored over two days:

Exploration Site: _____

Day 1 equation for area explored:

Day 2 equation for area explored:

Total area explored over two days:

170 | Apply the Area Formula

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Apply the Area Formula

Explore 3 Exploration Site: _____

Day 1 equation for area explored:

Day 2 equation for area explored:

Total area explored over two days:

Exploration Site: _____

Day 1 equation for area explored:

Day 2 equation for area explored:

Total area explored over two days:

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Apply the Area Formula | 171

Apply the Area Formula

Explore 3 Exploration Site: _____

Day 1 equation for area explored:

Day 2 equation for area explored:

Total area explored over two days: Refl ect How did you determine how to break up the exploration area into two days? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Was there only one way to break down the numbers? Explain your thinking. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Did breaking up the exploration site change the total area explored? Explain why or why not. ______________________________________________________________________ ______________________________________________________________________ 172 | Apply the Area Formula

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Apply the Area Formula

Explore 4

Name: _______________________ Date: __________

Solve for Area in Composite Figures Trabajo de retazos y acolchados

Trab

ajo

Part I: A Quilt for Your Puppy

de re

tazo

sy

acol

chad

os

What shape is each piece of fabric? ___________________________________ Draw your rectangles in the space below. Use a ruler to measure the length and width of each rectangle. Label the measurements in the spaces below your drawings.

Rectangle 1:

Rectangle 2:

Rectangle 3:

Length = ______ inches

Length = ______ inches

Length = ______ inches

Width = ______ inches

Width = ______ inches

Width = ______ inches

Explain how to find the area of a rectangle. _____________________________________________________________________ Write a number sentence to show how to find the area of each rectangle. Solve.

Rectangle 1: __________ × __________ = __________ square inches Rectangle 2: __________ × __________ = __________ square inches Rectangle 3: __________ × __________ = __________ square inches © Accelerate Learning Inc. – All Rights Reserved

Apply the Area Formula | 173

Explore 4

Apply the Area Formula

Arrange your rectangles to make the quilt for your puppy. There should be no overlapping edges or any edges sticking out. Draw your quilt in the space below.

What shape is your quilt? _____________________________________________________________________ Explain how you could find the area of your quilt. _____________________________________________________________________ _____________________________________________________________________ Find the area of your quilt. Be sure to include the units of measurement. Show your work in the space below.

What is the total length of your quilt? _____________________________________________________________________ What is the total width of your quilt? _____________________________________________________________________ Write a number sentence using these measurements to show how to find the area of the quilt. Use a calculator to multiply the length by the width to check if your answer matches the area you found previously. __________ × __________ = __________ square inches 174 | Apply the Area Formula

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Apply the Area Formula

Explore 4 Part II: Collage of Love

Complete the following steps for each fabric scrap: 1. Draw the scrap in the space below.

2. Cut the scrap into smaller rectangles. Mark on your drawing where you cut the scrap.

3. Find the area of each piece of the scrap. Label it on your drawing.

4. Find the total area of the whole scrap.

Fabric Scrap 1

Fabric Scrap 2

Drawing:

Drawing:

Total area: _______________________

Total area: _______________________

Fabric Scrap 3

Fabric Scrap 4

Drawing:

Drawing:

Total area: _______________________

Total area: _______________________

How can you find the area of your entire scrap of fabric? _____________________________________________________________________ Is there only one way to solve this type of problem? Explain. _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Apply the Area Formula | 175

Perimeter

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177

Perimeter

Explore 1

Name: _______________________ Date: __________

Solve for Perimeter Order A 1. Draw the shape of the table.

2. Label the length of each side.

What is the perimeter of this table? _________________________________________ What equation did you use to solve for the perimeter? ______________________________________________________________________ Order B 1. Draw the shape of the desk.

2. Label the length of each side.

What is the perimeter of this desk? _________________________________________ What equation did you use to solve for the perimeter? ______________________________________________________________________

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Perimeter | 179

Perimeter

Explore 1 Order C 1. Draw the shape of the desk.

2. Label the length of each side.

What is the perimeter of this desk? _________________________________________ What equation did you use to solve for the perimeter? ______________________________________________________________________

Order D 1. Draw the shape of the table.

2. Label the length of each side.

What is the perimeter of this table? _________________________________________ What equation did you use to solve for the perimeter? ______________________________________________________________________

180 | Perimeter

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Perimeter

Explore 1 Order E 1. Draw the shape of the nightstand.

2. Label the length of each side.

What is the perimeter of this nightstand? _____________________________________ What equation did you use to solve for the perimeter? ______________________________________________________________________

Order F 1. Draw the shape of the table.

2. Label the length of each side.

What is the perimeter of this table? _________________________________________ What equation did you use to solve for the perimeter? ______________________________________________________________________

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Perimeter | 181

Explore 2

Perimeter

Name: _______________________ Date: __________

Find the Missing Length Station 1: Welcome!

Drawing:

Equation:

How many feet of trim will Mr. Cranberry use for the banner? _____________________ How did you find the missing lengths of the trapezoid? ______________________________________________________________________ ______________________________________________________________________ Station 2: “Nest” Best Thing Drawing:

Equation:

How wide is the gate that farmer Rachel bought? _______________________________ Describe your process for finding the length of the gate. ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Perimeter | 183

Perimeter

Explore 2 Station 3: Concert Mania Drawing:

Equation:

How many more yards does Sean need to check? _____________________________ What other strategy could you use to find the length of the missing side? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Station 4: Rocky Mountain Adventure Drawing:

Equation:

How many miles of the tour are spent eating dinner? ___________________________ Could you solve for the missing length without knowing the total perimeter? Why or why not? ______________________________________________________________________ ______________________________________________________________________ 184 | Perimeter

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Perimeter

Explore 2 Station 5: Poolin’ Around Drawing:

Equation:

How many feet of tile will Aurora and Kai have laid when the tiling is finished? _____________________ How did you find the length of the other two sides of the pool? ______________________________________________________________________ ______________________________________________________________________ Station 6: “Wood” You Mind?

Drawing:

Equation:

How many inches of wood does Michelle need? _______________________________ If the length of the bottom side were not provided, how else could you figure it out?

How do you know this? ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Perimeter | 185

Explore 3

Perimeter

Name: _______________________ Date: __________

Rectangles with the Same Perimeter and Different Area

Work together with your group to find the area for how many tiles and the feet of ceiling molding you need to complete your project for the home. Draw and label the side lengths of each room. Each square tile represents a tile you will need to order.

Hallway

Area: ____________

Perimeter: ____________ Office

Area: ____________

Perimeter: ____________ Game Room

Area: ____________ © Accelerate Learning Inc. – All Rights Reserved

Perimeter: ____________ Perimeter | 187

Perimeter

Explore 3 Guest Bedroom

Area: ____________

Perimeter: ____________ Main Bedroom

Area: ____________

Perimeter: ____________ Living Room

Area: ____________ 188 | Perimeter

Perimeter: ____________ © Accelerate Learning Inc. – All Rights Reserved

Explore 3

Perimeter

Refl ect How is the method for finding the number of floor tiles different from the method for finding the number of feet needed for the ceiling molding? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What do you notice about each room’s area and perimeter? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

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Perimeter | 189

Perimeter

Explore 4

Name: _______________________ Date: __________

Rectangles with the Same Area and Different Perimeter

After using tiles to manipulate the area, sketch two ways you could design the pet kennels inside each pod in the dog shelter with a different perimeter.

Small Pod - 12 Square Feet Kennel 1

Kennel 2

Perimeter = ________

Perimeter = ________

Area = ________

Area = ________ Medium Pod - 16 Square Feet

Kennel 1

Kennel 2

Perimeter = ________

Perimeter = ________

Area = ________

Area = ________

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Perimeter | 191

Perimeter

Explore 4 Large Pod - 20 Square Feet Kennel 1

Kennel 2

Perimeter = ________

Perimeter = ________

Area = ________

Area = ________

Refl ect How is the method for finding the amount of space inside the kennel different from the method for finding the number of feet needed for the fence? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What do you notice about the area and perimeter of the kennels in each of the pods? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ 192 | Perimeter

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Lines and Angles

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193

Explore 1

Lines and Angles

Name: _______________________ Date: __________

Identify Lines and Right Angles Part I: Creating Frames Determine whether each shape matches the criteria to frame Alani’s paintings. Label each shape with the following attributes: • Pairs of parallel line segments • Pairs of perpendicular line segments • Right angle(s)

A ____ parallel line segments ____ perpendicular line segments ____ right angle(s)

C ____ parallel line segments ____ perpendicular line segments ____ right angle(s)

E ____ parallel line segments ____ perpendicular line segments ____ right angle(s) © Accelerate Learning Inc. – All Rights Reserved

B ____ parallel line segments ____ perpendicular line segments ____ right angle(s)

D ____ parallel line segments ____ perpendicular line segments ____ right angle(s)

F ____ parallel line segments ____ perpendicular line segments ____ right angle(s) Lines and Angles | 195

Lines and Angles

Explore 1

G ____ parallel line segments ____ perpendicular line segments ____ right angle(s)

H ____ parallel line segments ____ perpendicular line segments ____ right angle(s)

Refl ect How did you determine whether the shape had a right angle? ______________________________________________________________________ ______________________________________________________________________ How did you determine whether the shape had parallel line segments? ______________________________________________________________________ ______________________________________________________________________ How did you determine whether the shape had perpendicular line segments? ______________________________________________________________________ ______________________________________________________________________ Which shapes meet the criteria for the frames? ______________________________________________________________________ ______________________________________________________________________ In order to make a frame, do they have to have right angles? ______________________________________________________________________ ______________________________________________________________________ 196 | Lines and Angles

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Lines and Angles

Explore 1 Part II: Lines and Angles Are All Around

Look around your classroom for examples of parallel line segments, perpendicular line segments, and right angles. Draw an example of each in the chart below, and label your drawings.

Parallel Line Segments

Perpendicular Line Segments

Right Angles

Refl ect What did you notice about perpendicular line segments in relation to right angles? ______________________________________________________________________ ______________________________________________________________________ What examples of parallel lines do you see in the real world? ______________________________________________________________________ ______________________________________________________________________ What would your classroom look like if it had no right angles or perpendicular line segments? ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Lines and Angles | 197

Explore 2

Lines and Angles

Name: _______________________ Date: __________

Identify Lines of Symmetry • Take all of the 2-D shapes out of the bag.

• Fold each shape into as many equal halves as possible.

• Trace the folds that make equal halves. These folds are called “lines of symmetry.” Some shapes might have more than one line of symmetry, and some shapes might have none at all.

• Draw and label how many lines of symmetry there are on each shape below.

2 1

A

B ____ line(s) of symmetry

C ____ line(s) of symmetry

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____ line(s) of symmetry

D

____ line(s) of symmetry

Lines and Angles | 199

Lines and Angles

Explore 2

E

F

____ line(s) of symmetry

____ line(s) of symmetry

H

G

____ line(s) of symmetry

____ line(s) of symmetry

Refl ect Use at least three of the following words to write a statement or two about the lines you drew on your shapes.

Mirror

Half/Halves Same

Congruent Symmetry Image Divide

Equal

______________________________________________________________________ ______________________________________________________________________ Follow the directions below to create a greeting card: • Choose one of the shapes provided with at least one line of symmetry.

• Trace that shape onto your drawing paper.

• Cut out your shape.

• Fold your shape in half along one of the lines of symmetry.

• Decorate the card, and write your message.

200 | Lines and Angles

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Two- and Three-Dimensional Figures

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201

Explore 1

Two- and Three-Dimensional Figures

Name: _______________________ Date: __________

Classify Two-Dimensional Shapes Part I: Shape Hunt Name each shape, and list its attributes using the word bank.

Attributes:

Attributes:

Attributes:

Attributes:

Attributes:

Attributes:

Word Bank Parallel lines Perpendicular lines Symmetry Right angle Acute angle Obtuse angle Congruent Pentagon Trapezoid Rhombus Kite Hexagon Octagon Triangle Square Parallelogram Rectangle © Accelerate Learning Inc. – All Rights Reserved

Two- and Three-Dimensional Figures | 203

Two- and Three-Dimensional Figures

Explore 1

Attributes:

Attributes:

Attributes:

Attributes:

Refl ect What type of angle(s) does a rhombus have? How do you know? ______________________________________________________________________ ______________________________________________________________________ How do you identify parallel or perpendicular lines in polygons? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What shape do you see the most in your classroom? ____________________ Why do you think that is the one you see most? ______________________________________________________________________ ______________________________________________________________________

204 | Two- and Three-Dimensional Figures

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Explore 1

Two- and Three-Dimensional Figures

Part II: Classifying Shapes Draw how you classified your shapes below. Name each group with its common attribute.

Group 1: _____________________________

Group 2: _____________________________

Group 3: _____________________________

Refl ect What is an example of a shape with zero right angles? How do you know? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What do you notice about the lines on the shapes with right angles? ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Two- and Three-Dimensional Figures | 205

Explore 2

Two- and Three-Dimensional Figures

Name: _______________________ Date: __________

Compare and Contrast Quadrilaterals Part I: Customer Orders Order 1: Hello! I am looking for a frame with exactly one set of parallel sides, one line of symmetry, and two obtuse angles.

Choice 1:

Choice 2:

Order 2: I love your frames! Would you please create a frame for me that has four right angles and two sets of parallel sides?

Choice 1:

Choice 2:

Order 3: Cool frames! I’d like one that has acute and obtuse angles and at least two pairs of equal sides, please!

Choice 1:

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Choice 2:

Two- and Three-Dimensional Figures | 207

Two- and Three-Dimensional Figures

Explore 2

Order 4: Your frames are so funky! Please make a frame for me that has four sides that are equal lengths.

Choice 1:

Choice 2:

Order 5: Cool frames! I’d like one that has at least one acute angle and two pairs of equal sides, please!

Choice 1:

Choice 2:

Refl ect Which frames could fit more than one order? ______________________________________________________________________ ______________________________________________________________________

Compare a kite and a rhombus. How are they different? ______________________________________________________________________ ______________________________________________________________________

208 | Two- and Three-Dimensional Figures

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Two- and Three-Dimensional Figures

Explore 2 Part II: Leftover Frames

Compare the frames, and group them according to the listed attributes below. Draw the frames in the correct box below, and title the group with a keyword from the word bank.

Some frames will go in more than one group.

Rhombus

Word Bank Trapezoid Rectangle Parallelogram

Square

Fabulous Funky Frames website keyword: ________________ A quadrilateral with two sets of parallel lines and no right angles

Fabulous Funky Frames website keyword: ________________ A quadrilateral with two sets of parallel lines and four right angles

Fabulous Funky Frames website keyword: ________________ A quadrilateral with two adjacent sides that are equal in length

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Two- and Three-Dimensional Figures | 209

Explore 2

Two- and Three-Dimensional Figures

Fabulous Funky Frames website keyword: ________________ A quadrilateral with two sets of parallel lines and four equal sides

Fabulous Funky Frames website keyword: ________________ A quadrilateral with four right angles and four equal sides

Fabulous Funky Frames website keyword: ________________ A quadrilateral with only one set of parallel lines

Refl ect What do you notice about parallelograms, rectangles, rhombuses, and squares? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What makes trapezoids and kites different from parallelograms? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ 210 | Two- and Three-Dimensional Figures

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Explore 3

Two- and Three-Dimensional Figures

Name: _______________________ Date: __________

Three-Dimensional Solids Part I: Viewing a City Record the attributes of the cityscape shapes in the chart below.

3-D Figure

Number of Faces

2-D Shape of Faces

Number Number of of Edges Vertices

Cityscape Example

Triangular prism Rectangular prism Cube Square pyramid Refl ect What is a face of a three-dimensional solid? ______________________________________________________________________ ______________________________________________________________________ What is similar about the faces of a cube and the faces of a rectangular prism? ______________________________________________________________________

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Two- and Three-Dimensional Figures | 211

Two- and Three-Dimensional Figures

Explore 3 Part II: Building a City

Buildings must have the following attributes: 6 faces 12 edges 8 vertices

Section 2

Section 3

Section 4

212 | Two- and Three-Dimensional Figures

Buildings must have the following attributes: 5 faces 9 edges 6 vertices

Section 1

Buildings must have the following attributes: 5 faces 8 edges 5 vertices

Buildings must have the following attributes: 6 faces 12 edges 8 vertices

Draw your cityscape. Be sure to label each section with the three-dimensional solid name and its attributes, including the shape of the faces.

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Represent and Compare Fractions

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213

Explore 1

Represent and Compare Fractions

Name: _______________________ Date: __________

Represent and Compare Unit Fractions Part I: Mystery Puzzles Once the puzzles are all put together, complete the report below. Use each circle to sketch one of the puzzles. Name the puzzle, and label what fraction of the whole each piece equals.

Name: ___________________

Name: ___________________

Name: ___________________

Name: ___________________

Name: ___________________

What did you notice about all of the fractions within one puzzle? Explain. ______________________________________________________________________ ______________________________________________________________________ What did you notice about the fraction of each piece of all the puzzles? Explain. ______________________________________________________________________ ______________________________________________________________________ What is a unit fraction? ___________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Compare Fractions | 215

Explore 1

Represent and Compare Fractions

Part II: Puzzle Contest With your group, read each situation, and find the solution. Write the comparison with symbols, and use a drawing to represent how manipulatives were used.

Situation 1 vs.

Decision of the contest: ________________________________________________________ ________________________________________________________ Drawing

Situation 2 vs.

Symbols

(Write 2 different ways, using > and <.)

Decision of the contest: ________________________________________________________ ________________________________________________________ Drawing

216 | Represent and Compare Fractions

Symbols

(Write 2 different ways, using > and <.)

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Explore 1 Situation 3 vs.

Decision of the contest: ________________________________________________________ ________________________________________________________ Drawing

Situation 4 vs.

Represent and Compare Fractions

Symbols

(Write 2 different ways, using > and <.)

Decision of the contest: ________________________________________________________ ________________________________________________________ Drawing

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Symbols

(Write 2 different ways, using > and <.)

Represent and Compare Fractions | 217

Explore 1

Represent and Compare Fractions

Refl ect 1. Are all fractions with the same numerators but different denominators equal?

Explain. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 2. What happens to the size of the pieces as the denominator gets smaller? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 3. What happens to the size of the pieces as the denominator gets larger? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

218 | Represent and Compare Fractions

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Represent and Compare Fractions

Explore 2

Name: _______________________ Date: __________

Combine Fractional Parts 1. Egg-cellent Units Fraction for the whole carton:

Draw a model of the egg carton. Label each egg with the fraction it represents.

_______ Unit fraction for each egg: _______ Numerical equation that represents the whole carton of eggs: _____________________________

Challenge: Write a numerical equation for the eggs Solange needs. _____________________________

2. Racing to the Whole Fraction for the total laps in the race:

Draw each lap of the race. Label each lap with the fraction it represents.

_______ Unit fraction for each lap: _______ Numerical equation that represents the whole race: _____________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Compare Fractions | 219

Represent and Compare Fractions

Explore 2 3. Dunking Units Fraction of all of the balls that need to be tossed in the basket:

Draw the balls. Label each ball with the fraction of the set it represents.

_______ Unit fraction for each ball: _______ Numerical equation that represents the set of balls that need to be made into the basket:

Challenge: Write a numerical equation showing what fraction of the balls you made.

_____________________________

____________________________

4. I Want a Pizza That!

Fraction for the total number of pizza pieces: _______

Draw the pizza you made. Label each piece with the fraction it represents.

Unit fraction for each pizza piece: _______ Numerical equation that represents the whole pizza:

_____________________________ 220 | Represent and Compare Fractions

Challenge: Write a numerical equation for the slices of pizza with veggies. _____________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Compare Fractions

Explore 2 5. Show Me the Money Fraction of quarters in a whole dollar:

Draw the quarters. Label each quarter with the fraction of the dollar it represents.

_______ Unit fraction for each quarter: _______ Numerical equation that represents the whole dollar:

Challenge: Write a numerical equation for the fraction of a dollar Dr. Kim needs to purchase her snack.

_____________________________

____________________________

Refl ect What do you notice about the fractions that represent each whole? Explain. ______________________________________________________________________ ______________________________________________________________________ What do you notice about the fractions that represent each piece of the whole? ______________________________________________________________________ ______________________________________________________________________

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Represent and Compare Fractions | 221

Represent and Compare Fractions

Explore 3

Name: _______________________ Date: __________

Parts of a Whole Welcome to your special dinner! Use the materials provided to model each part of your dinner. Draw your model, and record the details to share with your friends.

RESTAURANT

Card 1: The Windows Draw your model of the window. In your model, shade in the pieces that have been washed.

Complete the statement below. _______ of _______ windowpanes were washed.

Write this as a fraction.

Washed windowpanes Total windowpanes

Card 2: The Menu Draw your model of the menu. In your model, shade in the sections that listed dinner items.

Complete the statement below. _______ of _______ menu sections listed dinner items.

Write this as a fraction.

Dinner sections Total sections © Accelerate Learning Inc. – All Rights Reserved

Represent and Compare Fractions | 223

Represent and Compare Fractions

Explore 3

Card 3: The Caramel Apple Draw your model of the caramel apples. In your model, shade in the total pieces that the family ate if they each ate 1 piece.

Complete the statement below.

The family members ate _______ _______ pieces of a caramel apple.

Write this as a fraction.

Total pieces the family ate Total for each apple

Write another way this fraction could be read. _________________________________ Card 4: The Napkin Draw your model of the napkin. In your model, shade in the pieces that are embroidered.

Complete the statement below. _______ of _______ parts of the napkin are embroidered.

Write this as a fraction.

Embroidered pieces Total pieces Write another way this fraction could be read. _________________________________

224 | Represent and Compare Fractions

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Represent and Compare Fractions

Explore 3

For the rest of the cards, be sure to complete the following steps: 1. Create a model of what is described on the card.

2. Read the question in the box below.

3. Draw your model by shading in the part the question indicates.

4. Complete two statements that answer the question. Use the word bank below to help you describe the number of parts in the whole.

5. Write the fraction that represents your answer.

Word Bank Half

Halves

Third

Fourth

Card 5: The Bread How much of the bread loaf was eaten?

Sixth

Eighth

Card 6: The Butter How much butter did you take?

Model:

Model:

Each loaf is partitioned into ________.

The girls ate _____ pieces.

I took ______ of ______ pieces of the butter.

___________________ of the bread was eaten.

I took _____________________ of the butter.

Fraction:

Fraction:

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Represent and Compare Fractions | 225

Represent and Compare Fractions

Explore 3 Card 7: The Steak

Card 8: The Cake

How much steak did your friends take?

How much cake did you and your siblings eat?

Model:

Model:

My friends ate ______ of ______ pieces of the steak.

We ate ______ of ______ pieces of the cake.

My friends ate ____________________ of the steak.

We ate _____________________ of the cake.

Fraction:

Fraction:

Refl ect How are fractions helpful? ______________________________________________________________________ ______________________________________________________________________ Where is the numerator, and what does it tell you? ______________________________________________________________________ ______________________________________________________________________ Where is the denominator, and what does it tell you? ______________________________________________________________________ ______________________________________________________________________

226 | Represent and Compare Fractions

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Represent and Compare Fractions

Explore 4

Name: _______________________ Date: __________

Parts of a Set

Build a model of what is happening at each station. Be sure to complete the following steps: 1. Create a model of what is described at the station.

2. Read the question in the box for that station.

3. Draw your model by shading in the part the question is asking for.

4. Complete the statement that answers the question. Use the word bank below to help you describe the number of parts in the whole set.

5. Write the fraction that represents your answer.

Word Bank Half

Third

Fourth

Sixth

Station 1

Eighth

Station 2

What fraction of the cars are empty?

What fraction of people ahead of you are girls?

Model:

Model:

______ of the ______ cars are empty.

_____________________ of the people ahead of me are girls.

Fraction:

Fraction:

Empty cars

Total number of cars © Accelerate Learning Inc. – All Rights Reserved

Girls Total people Represent and Compare Fractions | 227

Represent and Compare Fractions

Explore 4 Station 3

Station 4

What fraction of places to eat are popcorn or hot dog stands?

What fraction of the colors available did you choose for your cotton candy?

Model:

Model:

______ of the ______ stands are popcorn or hot dog stands.

I chose _____________________ of the colors for my cotton candy.

Fraction:

Fraction:

Station 5

Station 6

What fraction of wild carousel animals did you not choose to ride on?

What fraction represents the number of cars that have 6 seats?

Model:

Model:

I did not ride on ______ of the ______ wild animals.

_____________________ of the cars can hold 6 people.

Fraction:

Fraction:

228 | Represent and Compare Fractions

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Represent and Compare Fractions

Explore 4 Station 7

Station 8

What fraction of the items available could you choose to buy?

What fraction of activities on your list are rides?

Model:

Model:

I could choose to buy______ of the ______ items.

______ of the ______ items on my list are rides.

Fraction:

Fraction:

Refl ect How can fractions be used to describe a set of objects? ______________________________________________________________________ ______________________________________________________________________ What did you notice about Station 8? ______________________________________________________________________ ______________________________________________________________________ Look at the model below. What fraction of the group is shaded?

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Represent and Compare Fractions | 229

0

1

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10. Complete the statements for each station.

9. Place a point on the number line where you land after the last hop.

Represent and Compare Fractions | 231

8. To find the point on the number line that represents the fraction, let each piece you shaded on the bar equal one “hop” on the number line.

7. Partition the number line, and label it the same way your model is partitioned.

6. Cut out and glue one of the number line models directly below your drawing so 0 and 1 line up with the edges of your drawing.

5. Build the fraction that represents the situation using these pieces, and shade in that many pieces of your drawing. Label the parts of your drawing.

4. Use the pieces to create sections in your drawing so the whole bar is divided up into the right number of equal parts.

3. Trade out the whole fraction bar for one that is divided into the number of equal pieces you need based on the situation. Note that some situations may have more than one whole.

2. Trace the “whole” fraction bar in the box below for that station.

1. Act out the situation described at the station.

1 2

Name: _______________________ Date: __________

Diagrams and Number Lines

Repeat the following procedure at each station.

Explore 5

Represent and Compare Fractions

232 | Represent and Compare Fractions

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I made _______ of the laps around the table. I still need to make _______ of the laps around the table.

Station 2

Another way to write this is _______.

Station 1

My egg rolled _______ of the distance.

Explore 5

Represent and Compare Fractions

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I did not score _______ of the points.

Represent and Compare Fractions | 233

I did score _______ of the points.

Station 4

I still need to make _______ of the designs.

Station 3

I was able to finish _______ of the designs.

Explore 5

Represent and Compare Fractions

234 | Represent and Compare Fractions

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Another way to write this is ________________.

Station 6

I still have _______ of the distance to go until I return to the start.

Station 5

I knocked down a total of _______ pins.

I went _______ of the distance.

Explore 5

Represent and Compare Fractions

Station 7

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I swatted the fly _______ of the time.

Represent and Compare Fractions | 235

I did not swat the fly _______ of the time.

Station 8

of the votes.

Lucius got _______ of the votes and won / tied / lost the position of class president. Lucius did not get _______

Explore 5

Represent and Compare Fractions

236 | Represent and Compare Fractions

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____________________________________________________________________________________________

____________________________________________________________________________________________

How was the number line similar to the diagram? ____________________________________________________________________________________________

____________________________________________________________________________________________

____________________________________________________________________________________________

How did you figure out what fraction would complete each statement? ____________________________________________________________________________________________

Reflect

Explore 5

Represent and Compare Fractions

1 1 1 1 2

1 1

0

0

0

0

0

0

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1

0

Represent and Compare Fractions | 237

2

1

Number Lines

0

Explore 5

Represent and Compare Fractions

Equivalent Fractions

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239

Equivalent Fractions

Explore 1

Name: _______________________ Date: __________

Model Equivalence with Visual Models

Part I: Apples and Oranges

Akari and Mila like to share their fruit at lunch. Akari brings an apple, and Mila brings an orange. The apple and the orange are the same size. Their moms slice their fruit into different sizes each day, and then the girls have to figure out how to equally trade their fruit.

Fraction of an Apple Akari Shares with Mila

Draw a model of the fraction of an apple Akari shares with Mila.

Find a Fraction Card that is equivalent to Akari’s fraction. Glue the card in this column.

This represents the fraction of an orange Mila gives to Akari.

Draw a model of the fraction of an orange Mila gives to Akari.

1 4 2 4 1 3 4 6 Can two fractions with different digits be equal? Explain. ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Equivalent Fractions | 241

Equivalent Fractions

Explore 1 Part II: Lolita’s Fraction Salad Record your work for each ingredient.

Ingredient:

Sketch and label the models of the fractions.

____________________

Equivalent fractions:

Ingredient:

Sketch and label the models of the fractions.

____________________

Equivalent fractions:

Ingredient:

Sketch and label the models of the fractions.

____________________

Equivalent fractions:

242 | Equivalent Fractions

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Equivalent Fractions

Explore 1 Ingredient:

Sketch and label the models of the fractions.

____________________

Equivalent fractions:

Ingredient:

Sketch and label the models of the fractions.

____________________

Equivalent fractions:

Refl ect How can you know if two fractions are equivalent? ______________________________________________________________________ ______________________________________________________________________ 6 What did you notice about the fractions equivalent to ?

6 ______________________________________________________________________ ______________________________________________________________________

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Equivalent Fractions | 243

Model Equivalence with Number Lines

Name: _______________________ Date: __________

1

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Equivalent Fractions | 245

____________________________________________________________________________________________

____________________________________________________________________________________________

Does this fraction mean that people got bigger pieces or smaller pieces? Explain.

____________________________________________________________________________________________

How did you determine what fraction was equivalent to the amount left over? Explain. ____________________________________________________________________________________________

0

Write the dish name in the gray box. Using different colors, create and label the number line with the fractions for last year’s amount and this year’s amount of food. Put a dot on the indicated fraction.

Explore 2

Equivalent Fractions

1

246 | Equivalent Fractions

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____________________________________________________________________________________________

Does this fraction mean that people got bigger pieces or smaller pieces? Explain. ____________________________________________________________________________________________

____________________________________________________________________________________________

How did you determine what fraction was equivalent to the amount eaten? Explain. ____________________________________________________________________________________________

0

Explore 2

Equivalent Fractions

1

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Equivalent Fractions | 247

____________________________________________________________________________________________

Does this fraction mean that people got bigger pieces or smaller pieces? Explain. ____________________________________________________________________________________________

____________________________________________________________________________________________

How did you determine what fraction was equivalent to the amount eaten? Explain. ____________________________________________________________________________________________

0

Explore 2

Equivalent Fractions

1

248 | Equivalent Fractions

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____________________________________________________________________________________________

Does this fraction mean that people got bigger pieces or smaller pieces? Explain. ____________________________________________________________________________________________

____________________________________________________________________________________________

How did you determine what fraction was equivalent to the amount eaten? Explain. ____________________________________________________________________________________________

0

Explore 2

Equivalent Fractions

1

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Equivalent Fractions | 249

____________________________________________________________________________________________

Does this fraction mean that people got bigger pieces or smaller pieces? Explain. ____________________________________________________________________________________________

____________________________________________________________________________________________

How did you determine what fraction was equivalent to the amount eaten? Explain. ____________________________________________________________________________________________

0

Explore 2

Equivalent Fractions

1

250 | Equivalent Fractions

© Accelerate Learning Inc. – All Rights Reserved

____________________________________________________________________________________________

Does this fraction mean that people got bigger pieces or smaller pieces? Explain. ____________________________________________________________________________________________

____________________________________________________________________________________________

How did you determine what fraction was equivalent to the amount eaten? Explain. ____________________________________________________________________________________________

0

Explore 2

Equivalent Fractions

Explore 3

Equivalent Fractions

Name: _______________________ Date: __________

Whole Numbers as Fractions Choose a way to represent the kinds of windows you are washing. Create and draw a model for each job. Write the total number of parts in the window and how many you washed in fraction form. Think about what each number in a fraction represents. Prove your answer using a number line in order to get paid for the job.

Train Car Panes

Fraction of windows washed:

Label the number line with the whole numbers and fractions to show how many whole windows you washed.

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Equivalent Fractions | 251

Equivalent Fractions

Explore 3 Sky Scraping

Fraction of windows washed:

House Hunters

Fraction of windows washed:

252 | Equivalent Fractions

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Equivalent Fractions

Explore 3 Float on a Boat

Fraction of windows washed:

Reptile Exhibit

Fraction of windows washed:

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Equivalent Fractions | 253

Equivalent Fractions

Explore 3 Cozy Cabin

Fraction of windows washed:

Refl ect Does making a whole number change the amount of the number? Why or why not? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What is the role of the numerator and denominator in these jobs? Explain. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Can all whole numbers be made into fractions? How do you know? ______________________________________________________________________ ______________________________________________________________________ 254 | Equivalent Fractions

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Time

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255

Explore 1

Time

Name: _______________________ Date: __________

Time on an Analog Clock

Part I: Telling Time to the Nearest Minute Under each part of your class’s daily routine, draw what an analog clock would read at that time and what a digital clock would say.

Start of Our Day

Science Lab

Math

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Time | 257

Time

Explore 1 Lunch

Recess

Special Areas

258 | Time

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Time

Explore 1 Reading and Writing

Dismissal

Refl ect What observations did you make about the way the minute hand versus the hour hand moved? ______________________________________________________________________ ______________________________________________________________________ Does the hour hand stay on the number the entire hour? Why do you think this is? ______________________________________________________________________ ______________________________________________________________________ How does the minute hand show specific minutes? ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Time | 259

Time

Explore 1

Part II: Estimating Time to the Nearest 15 Minutes Use the hour hand on the clock to estimate the new time each activity will begin to the nearest fifteen minutes. Write your estimation below the clock.

Reading and Writing

Close to or at

Math

Close to or at

Science Lab

Close to or at

Recess

Close to or at

Lunch

Close to or at

Special Areas

Close to or at

Refl ect How were you able to estimate the time using only the hour hand? ______________________________________________________________________ ______________________________________________________________________

260 | Time

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Explore 2

Time

Name: _______________________ Date: __________

Problem Solve with Time on a Number Line For each scenario, place the Time Interval Cards on the floor time line.

Draw your group’s number line. Record the jumps and final solution to each scenario below. Be sure to label your number line with time intervals.

Scenario 1

What time did the movie start? _________________ Scenario 2

What time did the game start? _________________ Scenario 3

How long did it take for the pizza to be delivered? _________________

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Time | 261

Time

Explore 2 Scenario 4

What time did Raj finish playing video games? _________________

Use the number lines below to solve scenarios 5 and 6 without building the number line.

Scenario 5

6:00 a.m. 6:15 a.m. 6:30 a.m. 6:45 a.m. 7:00 a.m. 7:15 a.m. 7:30 a.m. 7:45 a.m.

What time should Alana wake up? _________________

Scenario 6

10:00 a.m. 10:15 a.m. 10:30 a.m. 10:45 a.m. 11:00 a.m. 11:15 a.m. 11:30 a.m. 11:45 a.m.

How long did George stay at the library? _________________

262 | Time

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Explore 2

Time

Refl ect How do you know whether to add or subtract time intervals? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How does thinking about time as a number line help you? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How did you know what time intervals to count by? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

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Time | 263

Measurement

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265

Measurement

Explore 1

Name: _______________________ Date: __________

Select Tools to Measure Examine each measurement tool, and label what attribute each tool is used to measure.

Measurement Tools

16 oz.

2 cups 1 2

12 oz.

1

8 oz.

1 cup

4 oz.

1 2

Name each tool in the boxes below.

Label what each tool measures in the boxes below.

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Measurement | 267

Measurement

Explore 1

Select the appropriate measurement tool for each tea party scenario. Then, use that tool to accurately measure the length, volume, or weight of each item at the tea party.

Pigs in a Blanket Estimation: __________ Draw a line above the measurement tool to represent the length of the pig in a blanket.

1

INCH

2

3

What tool was used to measure the length of this item?

4

5

6

What is the length of the item?

Teapot Estimation: __________ Shade the measurement tool below to represent the volume of the liquid in the teapot.

16 oz.

2 cups 1 2

12 oz.

1

8 oz.

1 cup

4 oz.

1 2

268 | Measurement

What tool was used to measure the volume of this liquid?

What is the volume of the liquid?

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Measurement

Explore 1 Plate and Silverware Estimation: __________ Shade the measurement tool below to represent the weight of the plate and silverware.

What tool was used to measure the weight of the plate and silverware?

What is the weight of the plate and silverware?

Teacup Estimation: __________ Shade the measurement tool below to represent the volume of the liquid in the teacup.

16 oz.

What tool was used to measure the volume of this liquid?

2 cups 1 2

12 oz.

1

8 oz.

1 cup

4 oz.

1 2

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What is the volume of the liquid?

Measurement | 269

Measurement

Explore 1 Tea Sandwich Estimation: __________ Draw a line above the measurement tool to represent the length of the tea sandwich.

INCH

1

2

What tool was used to measure the length of this item?

3

4

5

6

What is the length of the item?

Refl ect What would happen if we used the incorrect tool to measure an attribute of an object? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Why is it important to correctly label the unit of measurement for an object? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Why is it important to accurately measure the attributes of an object? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ 270 | Measurement

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Explore 2

Measurement

Name: _______________________ Date: __________

Length Read each Nature Card, and work with your group to determine the correct operation in order to solve. Show your work through solving equations that represent the problem and a model or picture representing what is happening in the scenario. Write your answer for each card in the correct box below.

A

Answer:

B

Answer:

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Measurement | 271

Explore 2

Measurement

C

Answer:

D

Answer:

E

Answer:

272 | Measurement

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Explore 2

Measurement

F

Answer:

G

Answer:

H

Answer:

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Measurement | 273

Measurement

Explore 2 I

Answer:

Refl ect How did you determine what operation to use for each problem? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How can a model help you solve a word problem? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

274 | Measurement

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Measurement

Explore 3

Name: _______________________ Date: __________

Mass and Weight Part I: Packing Genevieve Help Genevieve pack for her family trip! It is important that she stays within the limits of weight for safety. Create a model to justify your answer.

Tuck It in the Pocket Determine two ways in which Genevieve can pack this bag. Use a model to prove your answer.

Numerical expression:

Numerical expression:

How did you determine which operation to use? ______________________________________________________________________ ______________________________________________________________________ How did you decide which items to help Genevieve pack? Were there more options? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Measurement | 275

Explore 3

Measurement

Too Much?

Show how you determined which clothing item needed to be packed in a different place.

Which clothing item needs to be removed? ___________________________________ How did you determine this? ______________________________________________________________________ ______________________________________________________________________ Outfit Conundrum Show how you determined if she was able to pack all three outfits she planned.

276 | Measurement

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Explore 3

Measurement

Was she able to pack all three outfits? _______________ How did you determine the solution? ______________________________________________________________________ ______________________________________________________________________

Sharing the Weight Show how you determined the weight of each suitcase.

What is the weight of each suitcase? _______________ How did you determine the solution? ______________________________________________________________________ ______________________________________________________________________

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Measurement | 277

Measurement

Explore 3 Part II: Scenarios

Help Genevieve figure out different weights during her day at the happiest theme park in the country by creating a model and writing an equation to help solve the problem.

Scenario 1 Model:

Solution:

Will the family be able to ride the Whirl-o-Master together?

Yes

278 | Measurement

No

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Measurement

Explore 3 Scenario 2 Model:

Solution:

How many pounds over the limit are the girls and their dad?

Scenario 3 Model:

Solution:

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How many ounces of slushie should Genevieve give each person?

Measurement | 279

Measurement

Explore 3 Scenario 4 Model:

Solution:

What weight should Genevieve guess?

Refl ect How did you determine which operation to use for each word problem? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How did using models help you solve the problems? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

280 | Measurement

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Explore 4

Measurement

Name: _______________________ Date: __________

Liquid Volume Read each Station Card. Model each question, and write an equation to solve the problem.

Bathroom Cleaner

Perfect for almost any cleaning job!

Migh Clea ty n

Use in : · Ki · Batchens · An throom y room s Fo surfa r use on an ce ex cept y glass

1

2

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Measurement | 281

Explore 4

Measurement

Laundry Cleaner

3

4

282 | Measurement

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Explore 4

Measurement

Window Cleaner

5

6

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Measurement | 283

Explore 4

Measurement

Floor Cleaner

7

8

284 | Measurement

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Represent and Interpret Data

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285

Represent and Interpret Data

Explore 1

Name: _______________________ Date: __________

Frequency Tables and Line Plots Part I: How Tall Are We? Complete the frequency table and the line plot based on the class data collected.

Title:

Height

Tally

Frequency

Title:

Key:

Part II: Line Plot Stations

Follow the instructions on each Station Card to build a frequency table and a line plot.

Rolling a Die Number Rolled

Tally

Frequency

Title:

Line Plot

Title:

Compare the greatest frequency with the second greatest frequency for the numbers rolled using the symbols >, <, or =. ________ © Accelerate Learning Inc. – All Rights Reserved

Key:

________ Represent and Interpret Data | 287

Represent and Interpret Data

Explore 1 Rainy Days Activities Activity

Tally

Frequency

Title:

Line Plot

Title:

What is the total number of times the spinner landed on Board game and Reading? ______________________________________

Key:

Summer Heat Temp.

Tally

Frequency

Title:

Line Plot

Title:

Key: What is the difference between the highest and lowest temperatures? ______________ What temperature occurred the most often? __________________________________ Refl ect How can organizing data this way be helpful? ______________________________________________________________________ 288 | Represent and Interpret Data

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Represent and Interpret Data

Explore 2

Name: _______________________ Date: __________

Pictographs and Bar Graphs Follow the instructions at each station. Use the space below to represent the data collected, and answer the questions that follow.

Station 1: Bouncing Putty Stretch Name

Length Bouncing Putty Stretched (in.)

Label:

Title:

Label: What is the difference between the longest stretch and the shortest stretch? ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Interpret Data | 289

Explore 2

Represent and Interpret Data

Key:

Station 2: Animal Populations Title:

Compare the sums of the animals with the two lowest populations to the animals with the two highest populations using the symbols >, <, or =. _________ ________ Station 3: Local Food Drive Title:

Label:

How many more corn and tuna items were donated than beans? ______________________________________________________________________ 290 | Represent and Interpret Data

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Explore 2

Represent and Interpret Data

Station 4: Gummy Bear Inventory Title:

Key:

Which color did you have the most of? ____________________________ You are planning for a holiday party and only want to keep the red and green bears.

How many bears can you keep? ___________________ How many bears will you throw out? ___________________ You want to give your two guests an equal number of red and green bears. How many bears could each guest get? ________________________ Refl ect What are the similarities and differences between a bar graph and pictograph? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Interpret Data | 291

Skills Quizzes

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293

Skills Quiz

Place Value Relationships

Name: _______________________ Date: __________

Place Value Relationships Write the number in standard form by using the information given.

1.

2.

3.

Two thousand one hundred ninety-six

4.

Four hundred fifty-eight

5.

4,000 + 90 + 1

6.

3,000 + 500 + 40 + 1

7.

9 thousands + 6 hundreds + 17 ones

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Place Value Relationships | 295

Place Value Relationships

Skills Quiz Write each number below in expanded form and word form.

8. 9,307 Expanded form: __________________________________

Word form: ___________________________________________

9.

5,840 Expanded form: __________________________________ Word form: ___________________________________________

Represent the given number by writing a number sentence and by using base ten blocks to model. (A square represents a 100 flat, a line represents a 10 rod, and a dot represents a unit cube.)

10.

783

296 | Place Value Relationships

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Compare Numbers

Skills Quiz

Name: _______________________ Date: __________

Compare Numbers Show the approximate location of each number on the number line, and write >, <, or = on the line to make a true statement.

1.

546 __________ 564

530

540

2.

873 __________ 782

3.

1,085 __________ 1,085

4.

3,067 __________ 3,607

5.

9,465 __________ 9,645

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550

560

570

Compare Numbers | 297

Compare Numbers

Skills Quiz

Analyze each comparison statement, and determine whether it is true or false. Use the number line to prove your answer. Circle the correct responses for each comparison below.

6.

514

<

415

The comparison statement is true / false.

514 is greater than / less than / equal to 415.

7.

2,790

<

6,736

The comparison statement is true / false.

2,790 is greater than / less than / equal to 6,736.

8.

4,746

>

4,746

The comparison statement is true / false.

4,746 is greater than / less than / equal to 4,746.

298 | Compare Numbers

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Compare Numbers

Skills Quiz

The approximate locations of a set of numbers are represented on the number lines below. Analyze the location of each set of numbers, and complete the comparison statement. Then, write out how you would read the statement.

9.

611

359

Write out how you would read the above comparison statement.

––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 10.

1,189

2,517

Write out how you would read the above comparison statement.

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––

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Compare Numbers | 299

Rounding

Skills Quiz

Name: _______________________ Date: __________

Rounding 1.

Round 642 to the nearest ten.

2.

Round 289 to the nearest hundred.

3.

Which of the following numbers would round to 70 if rounding to the nearest ten?

Choose all that apply.

78

68

75

72

4.

Round 250 to the nearest hundred.

5.

Round the temperature to the nearest 10 degrees Fahrenheit.

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Rounding | 301

Rounding

Skills Quiz 6.

Use the number line to represent the number 625. Round the number 625 to the nearest ten.

600 7.

610

620

630

640

650

Using the number line, what number would point A be rounded to if rounding to the nearest ten?

A 120 8.

140

The Rogers family is going on a road trip to visit their cousins. They have driven 108 miles. Use the number line to represent 108, and round to the nearest ten to estimate how far they have driven.

90 9.

130

100

110

120

130

140

Kyle’s teacher passed out number cards to the class in order to practice estimation. The teacher instructed the students to round their numbers to the nearest ten and put the rounded number on the number line. Mark where Kyle should place his card.

216 200 10.

210

220

230

240

Use the number line to represent the number 731. Round the number 731 to the nearest hundred.

600 302 | Rounding

700

800

900 © Accelerate Learning Inc. – All Rights Reserved

Skills Quiz

Addition and Subtraction Fluency

Name: _______________________ Date: __________

Addition and Subtraction Fluency Solve the following addition and subtraction sentences. Show your work.

1.

145 + 645

2.

945 + 50

3.

268 + 547

4.

47 + 365 + 148

5.

565 – 24

6.

850 – 347 – 135

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Addition and Subtraction Fluency | 303

Skills Quiz

Addition and Subtraction Fluency

7.

Prinith is playing a video game. He scored 78 points in his first game, 98 points in his second game, and 357 points in his third game. How many total points did Prinith score?

8.

Mrs. Paek gave her class a 167-page book to read. José read 34 pages on Monday and 23 pages on Tuesday. How many pages of the book does José still need to read?

304 | Addition and Subtraction Fluency

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Addition and Subtraction Models

Skills Quiz

Name: _______________________ Date: __________

Addition and Subtraction Models For each problem below, write an equation with a letter standing for the unknown value. Then, solve by using addition, subtraction, or both.

1.

During a fundraiser, the third graders raised $274 on Friday, $442 on Saturday, and $501 on Sunday. Write an equation to represent how much total money the third graders raised in those 3 days. Use the diagram. m $274

$442

$501

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: –––––––––––––––––––––––––––––––––––––––––– 2.

There were 8,542 people at the championship football game. Some of the people left during halftime. There were 6,931 people watching the second half of the game. Write an equation to represent how many people left at halftime.

8,542 p

6,931

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: –––––––––––––––––––––––––––––––––––––––––– 3.

Write two equations represented by the number line. +1,323

n 1,323

4,902

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: ––––––––––––––––––––––––––––––––––––––––––

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Addition and Subtraction Models | 305

Addition and Subtraction Models

Skills Quiz 4.

Write an equation for the number line.

+3,420

− 782 3,420

x

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: –––––––––––––––––––––––––––––––––––––––––– 5.

Zack had 2,187 baseball cards. He sold 1,016 at the baseball card expo. Using the diagram, write two equations to find out how many cards he has left.

2,187 1,016

c

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: –––––––––––––––––––––––––––––––––––––––––– 6.

The elementary school hosted a used book sale.

• On the first day, 1,509 books were sold.

• On the second day, 2,093 books were sold.

• On the last day, 1,981 books were sold.

Write an equation that represents how many books were sold during the sale.

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: ––––––––––––––––––––––––––––––––––––––––––

7.

Max earned 4,367 points during the first level of his video game. While playing the second level, he lost 1,793 points. His final game was disappointing because he lost another 974 points. Write an equation that represents the number of points Max earned while playing the video game.

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: ––––––––––––––––––––––––––––––––––––––––––

306 | Addition and Subtraction Models

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Addition and Subtraction Models

Skills Quiz 8.

Write an equation that represents the diagram below.

7,821 2,574

3,501

k

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: –––––––––––––––––––––––––––––––––––––––––– 9.

Hank needs $9,040 for a car he has been wanting to buy. He had saved $7,097, but he needed to use $1,203 to fix his roof. Write an equation that represents how much money he still has left to save. Use the number line. +7,097 −1,203 5,894

+s

7,097

9,040

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: –––––––––––––––––––––––––––––––––––––––––– 10.

There were 6,230 people at the zoo in the morning. In the afternoon, 4,425 people left and 3,029 people arrived. Write an equation that represents how many people are now at the zoo.

Equation: ––––––––––––––––––––––––––––––––––––––––– Solution: ––––––––––––––––––––––––––––––––––––––––––

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Addition and Subtraction Models | 307

Arithmetic Patterns

Skills Quiz

Name: _______________________ Date: __________

Arithmetic Patterns Use the hundred chart below to answer questions 1–5.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

Determine the pattern of each set of numbers, and continue the pattern.

1.

4, 8, 12, 16, _____, _____, _____, _____ Pattern: ___________________

2.

6, 12, 18, _____, _____, _____, _____ Pattern: ___________________

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Arithmetic Patterns | 309

Arithmetic Patterns

Skills Quiz 3.

Determine the multiples of 5 using the hundred chart. What patterns do you notice? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________

4.

Hannah eats 3 strawberries each day. Write a multiplication expression to determine how many strawberries Hannah will eat in 7 days, and write it below. _____ × _____ What pattern do you notice on the hundred chart for the multiples of 3? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________

5.

Ginny makes $2 for every chore that she finishes around the house. She completes 8 chores. Using the hundred chart, write out the multiples for how much money Ginny made, and circle the product. _____, _____, _____, _____, _____, _____, _____, _____ What pattern do you notice for the multiples of 2? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________

310 | Arithmetic Patterns

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Arithmetic Patterns

Skills Quiz Use the multiplication table to answer questions 6–10.

6.

X

1

2

3

4

5

6

7

8

9

10

1

1

2

3

4

5

6

7

8

9

10

2

2

4

6

8

10

12

14

16

18

20

3

3

6

9

12

15

18

21

24

27

30

4

4

8

12

16

20

24

28

32

36

40

5

5

10

15

20

25

30

35

40

45

50

6

6

12

18

24

30

36

42

48

54

60

7

7

14

21

28

35

42

49

56

63

70

8

8

16

24

32

40

48

56

64

72

80

9

9

18

27

36

45

54

63

72

81

90

10

10

20

30

40

50

60

70

80

90 100

When you multiply by 2, is the product odd or even? How do you know this? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________

7.

Josh ran 3 days this week. He ran 5 miles each day. Use the multiplication table to find how many miles Josh ran, and write it below. _____________ If he runs for 3 more days this week, write what that extended pattern would look like: ____, ____, ____

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Arithmetic Patterns | 311

Arithmetic Patterns

Skills Quiz 8.

When you multiply by an odd number, is the product odd or even? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________

9.

When you multiply by 7, is the product odd or even? How do you know this? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________

10.

David sleeps for 8 hours a day. How many hours has David slept over the past 4 days? Use the multiplication table to find how many hours David has slept, and write it below. _____________ If he sleeps the same number of hours over the next 3 days, write what that extended pattern would look like: ____, ____, ____

312 | Arithmetic Patterns

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Multiplication Models

Skills Quiz

Name: _______________________ Date: __________

Multiplication Models Solve the multiplication problems.

1.

Jenna drew 3 rows of shapes. There were 8 shapes in each row. How many shapes did Jenna draw? Draw a model, and write an equation to represent the model.

2.

Write an equation that represents the model shown below.

3.

Ted created the array below. He made 4 rows of 7 items each. Write the equation that represents the model below.

4.

Casey used stickers to make a rectangular array. She made 6 rows with 9 stickers in each row. Draw Casey’s array to answer how many stickers she used.

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Multiplication Models | 313

Multiplication Models

Skills Quiz 5.

Judy drew the area model below to represent a multiplication problem. Charlie had to write the equation and solve it. What multiplication equation did Charlie write on the board?

Complete the expressions to make the equations true. Then, write the value of each expression on each side of the equation.

6.

5 × 9 = (____ × ____) – 9 Value: ______

7.

7 + 7 + 7 + 7 = _____ × _____ Value: ______

8.

Value: ______

4 × 5 = _____ + _____ + _____ + _____ Value: ______

10.

Value: ______

_____ × _____ = (5 × 6) – 6 Value: ______

9.

Value: ______

Value: ______

3 × 3 = (4 × _____) – _____ Value: ______

314 | Multiplication Models

Value: ______

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Skills Quiz

Division Models

Name: _______________________ Date: __________

Division Models Write a division equation for each model below.

1.

Division equation: ___ ÷ ___ = ___

2.

Division equation: ___ ÷ ___ = ___

3.

Division equation: ___ ÷ ___ = ___

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Division Models | 315

Division Models

Skills Quiz Make a model to go with each division equation.

4.

24 ÷ 6 = 4

5.

21 ÷ 3 = 7

Fill in the missing divisor for each division equation. Then, complete the multiplication equation.

6.

7.

81 ÷ ___= 9 ___ × ___ = ___

54 ÷ ___ = 9 ___ × ___ = ___

Write four different equations that represent the relationship between the three numbers in each of the boxes below.

8.

4

36

9

9.

6

18

3

10.

5

40

8

___ ÷ ___ = ___

___ ÷ ___ = ___

___ ÷ ___ = ___

___ ÷ ___ = ___

___ ÷ ___ = ___

___ ÷ ___ = ___

___ × ___ = ___

___ × ___ = ___

___ × ___ = ___

___ × ___ = ___

___ × ___ = ___

___ × ___ = ___

316 | Division Models

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Skills Quiz

Multiplication and Division Strategies

Name: _______________________ Date: __________

Multiplication and Division Strategies Solve the problems below by using any strategy.

1.

5×6

2.

9×4

3.

7×8

4.

What are two ways to write the dimensions of the array?

5.

Find the value of n.

8×5×2=2×8×n

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Multiplication and Division Strategies | 317

Skills Quiz 6.

Write an expression that is equal to 10 × 9 × 4.

7.

Find the value of n.

Multiplication and Division Strategies

n×6×9=9×6×7

8.

Fill in the blank to make the equation true. ___ ÷ 7 = (21 ÷ 7) + (21 ÷ 7)

9.

Fill in the blank to make the equation true.

(5 + 2) × 7 = (___ × 7) + (2 × 7)

10.

Create a model of each equation, and fill in the product.

4 × 5 = ___

318 | Multiplication and Division Strategies

5 × 4 = ___

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Multiply Multiples of 10

Skills Quiz

Name: _______________________ Date: __________

Multiply Multiples of 10 Solve the problems below.

1.

2 × 60

2.

50 × 6

3.

70 × 8

4.

7 × 20

5.

4 × 30

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Multiply Multiples of 10 | 319

Skills Quiz 6.

9 × 30

7.

40 × 2

8.

6 × 30

9.

6 × 10

10.

7 × 30

320 | Multiply Multiples of 10

Multiply Multiples of 10

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Multiplication and Division Problem Solving

Skills Quiz

Name: _______________________ Date: __________

Multiplication and Division Problem Solving For each problem below, write an equation with a letter standing for the unknown value, and solve by using a multiplication or division strategy.

1.

A neuroscientist is growing cells in 6 different Petri dishes. Each Petri dish has 15 cells in it. Write the expression modeled by the diagram, and solve for the total number of cells.

t (total number of cells) 15

15

15

15

15

15

Equation: __________________________________ Solution: __________________________________

2.

Mrs. Smith left an unfinished area model on the whiteboard for the students in her class to finish. Fill in the missing parts of the area model, and find the solution to the math problem it represents.

10

7

4 40

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Equation: ____________________________ Solution: ____________________________

Multiplication and Division Problem Solving | 321

Skills Quiz 3.

Multiplication and Division Problem Solving

Sam has a total of 49 coins. He wants to put 7 coins in each row. How many rows of coins will Sam have?

Use the space below to draw circles to represent a model of what Sam’s coins will look like for the picture.

Equation: __________________________________ Solution: __________________________________

Jodie created an array of smiley-face emojis. She knows that the array is made of a total of 36 emojis. She also knows that the array has 4 rows. How many emojis are in each row?

Equation: __________________________________ Solution: __________________________________

322 | Multiplication and Division Problem Solving

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Multiplication and Division Problem Solving

Skills Quiz

Read each problem below. Using the equations given, match the correct equation with a letter representing the unknown to each problem. Then, find the solution.

8×7=t 4.

(8 × 7) + 4 = t

(8 × 7) – 4 = t

Frank has 8 boxes of toys. Each box contains 7 toys. He removes 4 toys from a box to play with them. How many toys are still in all of the boxes?

Equation:

Solution: 5.

Frank has 8 boxes of toys. Each box contains 7 toys. How many toys are in all of the boxes?

Equation:

Solution: 6.

Frank has 8 boxes of toys. Each box contains 7 toys. He buys 4 more toys and puts them in one of the boxes. How many toys does Frank have?

Equation:

Solution: © Accelerate Learning Inc. – All Rights Reserved

Multiplication and Division Problem Solving | 323

Multiplication and Division Problem Solving

Skills Quiz

Read each problem below. Determine which model from the chart represents each problem, and write the corresponding letter in the space given. Then, find the solution.

A

0

5

10

15

B t (total)

C 7.

7

7

7

Monica has 10 heart erasers. She wants to give each of her 5 friends the same number of heart erasers. How many heart erasers will each friend receive?

Model Solution

8.

Rachel has 3 pieces of ribbon. Each piece of ribbon is 5 inches long. If she ties each piece of ribbon together, how long will all of Rachel’s ribbon be?

Model Solution

9.

Joey has 3 packages of baseball cards. Each package contains 7 baseball cards.

How many total baseball cards does Joey have?

Model Solution

324 | Multiplication and Division Problem Solving

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Area in Square Units

Skills Quiz

Name: _______________________ Date: __________

Area in Square Units Find the area of each shaded region. Each block is 1 square unit.

1.

2.

Area = ______ square units

Area = ______ square units

3.

Area = ______ square units

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Area in Square Units | 325

Area in Square Units

Skills Quiz Find the area of each figure below. Each block is 1 square unit.

4.

5.

Area = ______ square units

6.

Area = ______ square units

Create a figure that has an area of 20 square units. Label the side lengths.

326 | Area in Square Units

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Skills Quiz

Area in Square Units

Find the area of each figure below. Each block is 1 square unit.

7.

Area = ______square units

8.

Area = ______ square units

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Area in Square Units | 327

Area in Square Units

Skills Quiz Find the area of each shaded region. Each block is 1 square unit.

9.

Area = ______ square units

10.

Area = ______ square units

328 | Area in Square Units

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Skills Quiz

Apply the Area Formula

Name: _______________________ Date: __________

Apply the Area Formula Write a multiplication expression to find the area of each rectangle. _____ rows 1.

_____ units in each row ______ × ______ = ______ Area: _______________

_____ rows 2.

_____ units in each row ______ × ______ = ______ Area: _______________

_____ rows 3.

_____ units in each row ______ × ______ = ______ Area: _______________

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Apply the Area Formula | 329

Apply the Area Formula

Skills Quiz _____ rows 4.

_____ units in each row ______ × ______ = ______ Area: _______________

_____ rows 5.

_____ units in each row ______ × ______ = ______ Area: _______________

330 | Apply the Area Formula

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Apply the Area Formula

Skills Quiz Find the area of each composite figure.

Area of rectangle 1 _____ × _____ = ______ 6.

Area of rectangle 2 _____ × _____ = ______ Area of rectangle 1 ______ + Area of rectangle 2 ______ Area: _________________

7.

Area of rectangle 1 _____ × _____ = ______ Area of rectangle 2 _____ × _____ = ______ Area of rectangle 1 ______ + Area of rectangle 2 ______ Area: _________________

8.

Area of rectangle 1 _____ × _____ = ______ Area of rectangle 2 _____ × _____ = ______ Area of rectangle 3 _____ × _____ = ______ Area of rectangle 1 ______ + Area of rectangle 2 ______ + Area of rectangle 3 ______ Area: _________________

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Apply the Area Formula | 331

Skills Quiz

Apply the Area Formula

Use an addition expression to find the area of each composite figure. Show your work in the box provided.

9.

Area: _____________

10.

Area: _____________

332 | Apply the Area Formula

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Perimeter

Skills Quiz

Name: _______________________ Date: __________

Perimeter Find the perimeter of the following polygons.

1.

7 ft.

Perimeter: ____________________ 8 ft.

2.

5 in.

5 in.

Perimeter: ____________________

2 in.

3 in.

3 in.

3.

6 in.

6 in.

Perimeter: ____________________

2 in.

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Perimeter | 333

Perimeter

Skills Quiz Given the perimeter, find the missing side length of the polygon.

4.

Perimeter = 36 ft.

Side length: ____________________

?

4 ft.

7 ft.

5.

A polygon has side lengths of 36 ft., 45 ft., 18 ft., and 28 ft. What is the perimeter of the polygon?

Perimeter: ____________________

6.

A polygon has side lengths of 125 in., 74 in., 8 in., and 63 in. What is the perimeter of the polygon?

Perimeter: ____________________

7.

A triangle has a perimeter of 163 in. One leg is 85 in., and another leg is 21 in.

What is the length of the third leg?

Third leg: ____________________

334 | Perimeter

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Skills Quiz

Perimeter

Solve each problem.

8.

The rectangle below has the dimensions 4 × 10. Create a rectangle with the same area but a different perimeter.

9.

The rectangle below has the dimensions 3 × 3. Create a rectangle with the same area but a different perimeter.

10.

The rectangle below has the dimensions 5 × 7. Create a rectangle with the same perimeter but a different area.

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Perimeter | 335

Lines and Angles

Skills Quiz

Name: _______________________ Date: __________

Lines and Angles Write the vocabulary word that best describes each picture.

Word Bank Parallel line segments Right angle

Line of symmetry

1.

_________________________

2.

_________________________

3.

_________________________

4.

_________________________

5.

_________________________

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Perpendicular line segments Polygon

Lines and Angles | 337

Lines and Angles

Skills Quiz Use the quadrilaterals below to answer questions 6 and 7.

6.

Do the quadrilaterals above have perpendicular sides?____ Explain how you know this.

7.

How many pairs of parallel sides does each quadrilateral have? _________ Use the polygon below to answer question 8.

8.

How many lines of symmetry does the polygon have? _________ Use the quadrilateral below to answer questions 9 and 10.

9.

How many lines of symmetry does the quadrilateral have? _________ Draw any lines of symmetry on the quadrilateral.

10.

How many pairs of perpendicular sides does the quadrilateral have? _________ How many pairs of parallel sides does the quadrilateral have? _________

338 | Lines and Angles

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Two- and Three-Dimensional Figures

Skills Quiz

Name: _______________________ Date: __________

Two- and Three-Dimensional Figures Use the two-dimensional shapes below to answer questions 1–5.

1

6

2

3

7

8

4

5

9

1.

Every shape is a __________________________________

2.

Which shapes are classified as quadrilaterals? ___________________________

3.

Which shapes have right angles? __________________________________

4.

Which shapes have four congruent sides? _______________________________

5.

Which shapes are classified as trapezoids? ___________________________

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.

Two- and Three-Dimensional Figures | 339

Two- and Three-Dimensional Figures

Skills Quiz

Use the three-dimensional solids below to answer questions 6–10.

2

3

1

5

4

6

7

8

6.

Which solids have triangular faces? _______________________________

7.

Which solids do NOT have square faces? _______________________________

8.

Which shapes are classified as prisms? _______________________________

9.

What two-dimensional shape do all of these solids contain? _________________

10.

Which shapes are classified as cubes? _______________________________

340 | Two- and Three-Dimensional Figures

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Two- and Three-Dimensional Figures

Skills Quiz 11.

Draw a quadrilateral that does not fit into any of the groups of parallelograms, trapezoids, rectangles, squares, or rhombuses.

12.

The shape below has _____ edges, _____ vertices, and _____ faces.

13.

All squares are _______________________________

14.

What is the difference between a rectangular prism and a triangular prism?

15.

Name the shape that has one square face and four triangular faces.

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.

Two- and Three-Dimensional Figures | 341

Represent and Compare Fractions

Skills Quiz

Name: _______________________ Date: __________

Represent and Compare Fractions For questions 1–5, use the models to represent or compare the given fractions.

1.

Shade the figure below to represent

2.

Use the models to compare

1 4

and

1 2

.

1 2

using the <, >, or = symbol.

1 4

3.

1 2

Sammie cut her sandwich into 4 equal parts. She ate 1 part of her sandwich.

What fraction of the sandwich did Sammie eat?

Sammie ate ________ of her sandwich.

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Represent and Compare Fractions | 343

Represent and Compare Fractions

Skills Quiz 4.

Write the fraction as the sum of unit fractions.

5.

Compare the fractions using the <, >, or = symbol.

_______

_______

For questions 6–10, write the fraction represented in each model.

x

6.

0

1

7.

8.

344 | Represent and Compare Fractions

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Represent and Compare Fractions

Skills Quiz 9.

x

10.

0

1

Create a model represented by the problem. Write the fraction or comparison.

11.

Sara ate 14 of a pizza. Kendra ate 18 of a pizza. Who ate less pizza?

1 4

12.

1 8

Four friends are going to split a candy bar equally with each other. Draw and write the fraction of the candy bar that each friend will get.

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Represent and Compare Fractions | 345

Represent and Compare Fractions

Skills Quiz 13.

There are 6 pencils in a package. Sara took 5 of the pencils to school. Draw a model, and write the fraction of pencils that Sara took to school.

14.

Chocolate chip cookies use 16 of a cup of sugar. Oatmeal raisin cookies use 1 3

of a cup of sugar. Which kind of cookie uses less sugar? Draw a model,

and compare the fractions using the <, >, or = symbol.

1 6 15.

1 3

A dollar can be split into 4 quarters. Herb has 1 quarter. Draw a model, and write the fraction of a dollar Herb has.

346 | Represent and Compare Fractions

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Equivalent Fractions

Skills Quiz

Name: _______________________ Date: __________

Equivalent Fractions Use the number lines to answer the questions.

1.

Using the number lines shown, what is the equivalent fraction to 14 ?

0

2.

Using the number lines shown, what is the equivalent fraction to 36 ?

0

3.

1

1

8

Using the number lines shown, what is the equivalent fraction to 8 ?

0

5.

1

Using the number lines shown, what is the equivalent fraction to 2 ?

0

4.

1

1

Using the number lines shown, what is the equivalent fraction to 13 ?

0

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1

Equivalent Fractions | 347

Skills Quiz

Equivalent Fractions

Write an equivalent fraction by using the model to shade in the equivalent parts.

6.

7.

8.

9.

10.

3 6 2 6

___________

___________

3 4

___________

1 2

___________

6 8

___________

348 | Equivalent Fractions

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Equivalent Fractions

Skills Quiz Express the following whole numbers as fractions.

11.

1 ___________

3

12.

___________

13.

5 ___________

Mark the fraction on the number line.

14.

2 1

1

2

3

4

15.

8 2

1

2

3

4

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Equivalent Fractions | 349

Skills Quiz

Time

Name: _______________________ Date: __________

Time Draw the hour and minute hands on the clocks to match the times shown.

1.

3:47

2.

6:22

Write the time shown on each clock.

3.

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4.

Time | 351

Time

Skills Quiz Estimate the time shown on each clock to the nearest 15 minutes.

5.

6.

For scenarios 7–10, show the time jumps on the number line, and write the solutions.

Include a.m. or p.m. in your answer where needed.

7.

Mr. Phelps’s class usually goes to the library at 9:15 a.m. Because of the book fair this week, they will go to the library at 8:45 a.m. By how much did their library time change?

8:15

8:30

8:45

9:00

9:15

9:30

9:45

10:00

10:15

10:30

Mr. Phelps’s class will go to the library _________________________ earlier / later than usual. _____________ 352 | Time

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Time

Skills Quiz 8.

Steven has to set up his project at the science fair by 11:30 a.m. If it takes him 15 minutes to check in and find his table and 30 minutes to set up his display, what time does he need to arrive at the science fair?

9:45

10:00

10:15

10:30

10:45

11:00

11:15

11:30

11:45

12:00

Steven needs to arrive at the science fair at __________________________.

9.

Every day, it takes Jorge 2 hours to complete his homework. If he starts working at 3:30 p.m., what time will he finish?

3:15

3:30

3:45

4:00

4:15

4:30

4:45

5:00

5:15

5:30

Jorge will finish his homework at __________________________.

10.

Tara’s class is making posters for field day. Their teacher says they need to finish the posters by 11:00 a.m. They start working on them at 9:45 a.m. How long is Tara’s class given to work on the posters?

9:30

9:45

10:00

10:15

10:30

10:45

11:00

11:15

11:30

11:45

Tara’s class is given __________________________ to work on their posters.

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Time | 353

Measurement

Skills Quiz

Name: _______________________ Date: __________

Measurement Use a ruler to find the length to the nearest half-inch.

1.

The fork is _______ in.

The crayon is _______ in.

2.

Use the scale to measure the weight to the nearest pound.

3.

4.

The weight is ________.

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The weight is ________.

Measurement | 355

Measurement

Skills Quiz

Use the beaker to measure the volume of the liquid to the nearest 12 of a cup or to the nearest ounce. Be sure to include the correct unit of measure.

5.

6.

The liquid volume is ________.

The liquid volume is ________.

Solve the problems. Be sure to include the correct unit of measure in your answer.

7.

Chester is making an obstacle course for his dog. The first obstacle will be 15 feet from the start, the middle obstacle will be 26 feet from the first obstacle, and the finish will be 18 feet from the middle obstacle. How long is the entire obstacle course from the start?

356 | Measurement

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Skills Quiz

Measurement

8.

Mariella has 4 guinea pigs that each weigh 24 ounces. She also has a guinea pig that weighs 39 ounces. How much do the guinea pigs weigh altogether?

9.

Mr. Thomas is putting together a jigsaw puzzle. He has 64 ounces of a special glue that he uses to make the whole puzzle stick together. He uses the same amount of glue on each of the 8 sections of the puzzle. How many ounces of glue does Mr. Thomas use on each section of the puzzle?

10.

A student measured the weight of three objects. One object weighed 43 pounds.

The second object weighed 29 pounds, and the third object weighed 17 pounds.

How much more did the first and second objects combined weigh compared to the third object?

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Measurement | 357

Represent and Interpret Data

Skills Quiz

Name: _______________________ Date: __________

Represent and Interpret Data 1.

Create a frequency table using the data below.

Dog

Cat

Dog

Bird

Fish

Fish

Dog

Cat

Rabbit

Dog

Bird

Cat

Dog

Turtle

Dog

Cat

Bird

Dog

Bird

Cat

Frequency of Household Pets Pets

2.

Tally Marks

Frequency

Create a line plot of the data below.

83

82

84

81

89

88

85

85

80

85

86

88

83

87

84

88

88

83

87

83

86

81

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Represent and Interpret Data | 359

Represent and Interpret Data

Skills Quiz 3.

Create a bar graph using the data in the frequency table.

Frequency of Color in a Bag of Candy Color Choices

Tally Marks

Frequency

Purple

4

Yellow

8

Red

7

Green

9

Blue

5

Orange

4 Title:

9 8 7

Frequency

6 5 4 3 2 1

Purple

Yellow

Red

Green

Blue

Orange

Colors

360 | Represent and Interpret Data

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Represent and Interpret Data

Skills Quiz

Use the line plot to answer questions 4–6. (Each dot represents 1 third grader.)

Number of Hours Third Graders Played Video Games This Weekend

0

1

2

3

4

5

6

7

8

9

10

4.

How many third graders played video games this weekend?

5.

How many third graders played video games for more than 6 hours last weekend?

6.

What is the difference between the number of third graders playing 6 or more hours and the number of third graders playing less than 6 hours?

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Represent and Interpret Data | 361

Represent and Interpret Data

Skills Quiz Use the bar graph to answer questions 7–9.

Students’ Birthdays by Month

Number of Students

10 8 6 4 2

r

r ec

em

be

be D

em

er N

ov

ct

ob

r O

em

be

st Se

pt

gu

ly

Au

Ju

ne Ju

ay M

ril Ap

ch M

ar

ua br

Fe

Ja

nu

ar

y

ry

0

Months

7.

Which month has the most birthdays? Which month has the least birthdays?

8.

How many students have a birthday in the last 2 months of the year?

9.

How many months have birthdays of 4 or more students?

362 | Represent and Interpret Data

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Represent and Interpret Data

Skills Quiz Use the pictograph to answer questions 10–12.

Donuts Sold at the Donut Hut Monday Tuesday Wednesday Thursday Friday Saturday Sunday

= 6 donuts

10.

How many donuts were sold on the weekend?

11.

On which days of the week were more than 24 donuts sold?

12.

Compare the number of donuts sold on Friday and Saturday with the number of donuts sold on Sunday and Monday using the symbol >, <, or =.

________

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________

Represent and Interpret Data | 363

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.

acute triangle: a three-sided geometric shape adjacent: next to something else in which each angle is less than 90 degrees © Accelerate Learning Inc. – All Rights Reserved

365

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

366

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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

367

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 368

clock: a tool for measuring time in numbers and symbols © Accelerate Learning Inc. – All Rights Reserved

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

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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 371

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 372

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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 374

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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

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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

halves: two equal parts © Accelerate Learning Inc. – All Rights Reserved

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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 378

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

key: the part of a graph, chart, or map that helps to explain it by showing the symbols and what they stand for © Accelerate Learning Inc. – All Rights Reserved

lend: to give money or goods and expect it to be returned 379

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 381

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) 382

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

number: a word or symbol used to show an amount or quantity © Accelerate Learning Inc. – All Rights Reserved

numerator: the top number in a fraction; represents part of a whole 383

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 384

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 386

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

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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 388

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

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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 389

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.

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scaling: comparing the size of the product to the size of one factor based on the other factor; predicting products based on factors © Accelerate Learning Inc. – All Rights Reserved

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 392

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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 393

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: 978-1-64861-270-1

9 781648 612701