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Grade 4 Student Notebook

GEORGIA

Student Notebook – Grade 4 ISBN: 978-1-64861-271-8 Published by Accelerate Learning Inc. 5177 Richmond Ave, Suite 800, Houston, TX 77056. Copyright © 2023 by Accelerate Learning Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written consent of Accelerate Learning Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

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GEORGIA

Student Notebook - Grade 4

Scope Name

Table of Contents

Page Number

Place Value of Whole Numbers

Compare and Order Numbers

Rounding

Addition and Subtraction Algorithms

Prime and Composite Numbers

Multiplicative Comparisons

Multiplication Models and Strategies

Division Models and Strategies

Generate Patterns

107

Problem Solve Using the Four Operations

121

Compare Fractions

139

Equivalent Fractions

159

Compose and Decompose Fractions and Mixed Numbers

179

Add and Subtract Fractions and Mixed Numbers

187

iii

GEORGIA

Student Notebook - Grade 4

Table of Contents (Cont.) Scope Name Page Number Represent and Compare Decimals

205

Area and Perimeter

217

Angles

225

Points, Lines, and Angles

235

Properties of Two-Dimensional Figures

249

Measurement

257

Represent Measurement with Line Plots

279

Skills Quizzes

287

Glossary of Terms

345

Workspace

379

Place Value of Whole Numbers

Place Value Relationships

Name: _______________________ Date: __________

Number Collected

Donation from Money Matchers

Number Collected

Donation from Money Matchers

Number Collected

Donation from Money Matchers

Place Value of Whole Numbers | 3

Multiplication: ______________________________ Division: ______________________________

Day

Multiplication: ______________________________ Division: ______________________________

Day

Multiplication: ______________________________ Division: ______________________________

Day

Use the tables below to record the donations for each day. Record the day, the number of pennies that are collected, and the donation from the Money Matchers Company. For each day, write one multiplication equation and one division equation showing the relationship between the number collected and the donation from the Money Matchers Company.

Explore 1

Place Value of Whole Numbers

Number Collected

Penny Palooza! Donation from Money Matchers

Number Collected

Donation from Money Matchers

Number Collected

Donation from Money Matchers

4 | Place Value of Whole Numbers

Multiplication: ______________________________ Division: ______________________________

Day

Multiplication: ______________________________ Division: ______________________________

Day

Multiplication: ______________________________ Division: ______________________________

Day

Explore 1

Place Value of Whole Numbers

Number Collected

Penny Palooza! Donation from Money Matchers

Number Collected

Donation from Money Matchers

Place Value of Whole Numbers | 5

___________________________________________________________________________________________

How does multiplying a number by 10 affect the digits in the number? ____________________________________

___________________________________________________________________________________________

In each scenario, what is the relationship between the number collected and the donation from the Money Matchers Company? __________________________________________________________________________

On day 8, what is the relationship between the digit 1 in the number collected and the digit 1 in the donation amount? _____________________________________________________________________________________

Reﬂect

Multiplication: ______________________________ Division: ______________________________

Day

Multiplication: ______________________________ Division: ______________________________

Day

Explore 1

Place Value of Whole Numbers

Name: _______________________ Date: __________

Your Personal Notes: Standard Form

Diamonds

Emeralds

Amethysts

Gemstone

Coding for News Website: Expanded Form

Place Value of Whole Numbers | 7

Reporter Teleprompter Script: Word Form

4. Write the number in word form so it is prepared for the reporter’s teleprompter script.

3. Write the number in expanded form for the news website to have coded.

2. Build a model of the number on each card with place value disks, and then record the number in standard form.

1. Use the table below to record the number of each gemstone discovered.

Read and Write Multi-Digit Whole Numbers

Explore 2

Place Value of Whole Numbers

Your Personal Notes: Standard Form

8 | Place Value of Whole Numbers

Topaz

Rubies

Sapphires

Opals

Gemstone

Explore 2

Coding for News Website: Expanded Form

Reporter Teleprompter Script: Word Form

Place Value of Whole Numbers

Your Personal Notes: Standard Form

Coding for News Website: Expanded Form

Reporter Teleprompter Script: Word Form

Place Value of Whole Numbers | 9

___________________________________________________________________________________________

You’re given an 11th gemstone that has 7 ten thousands and 5 tens. How many digits is this number? What is this number in standard form? ______________________________________________________________________

___________________________________________________________________________________________

What is the relationship between standard form and expanded form? ____________________________________

Reﬂect

Aquamarines

Moonstones

Garnets

Gemstone

Explore 2

Place Value of Whole Numbers

Compare and Order Numbers

Explore 1

Name: _______________________ Date: __________

Compare Numbers Which movie was the biggest hit? Your mission is to compare the all-time ticket sales of eight movies using the symbols >, <, and = to determine which movie made the most money. Part I: The Big Reveal! Record the digits of each number as your teacher reveals them.

HTh

TTh

Backyard Adventures Fish Tales

, ,

Use the number lines to compare the two ticket sales. Backyard Adventures

Fish Tales

200,000 220,000 240,000 260,000 280,000 300,000 320,000 340,000 360,000 380,000 400,000

Write two comparison statements that show the relationship between the two numbers. _________________________

_________________________

Compare and Order Numbers | 13

Explore 1

Compare and Order Numbers

Which place values are the most helpful when comparing numbers? ______________________________________________________________________ ______________________________________________________________________ Explain your process for comparing two numbers. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

14 | Compare and Order Numbers

Compare and Order Numbers

Explore 1 Part II: Movie Ticket Sales!

Use the Place Value Mat and number lines to compare the movie ticket sales for the movies listed below. Write two comparison statements, and state which movie made more money. The Fourth-Grade Genius vs. Math Marvels The Fourth-Grade Genius: 300,000 301,000 302,000 303,000 304,000 305,000 306,000 307,000 308,000 309,000 310,000

Math Marvels: 300,000 301,000 302,000 303,000 304,000 305,000 306,000 307,000 308,000 309,000 310,000

Statement 1: _________________________

_________________________

Statement 2: _________________________

_________________________

Which movie won? ________________________________ How do you know? __________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Compare and Order Numbers | 15

Compare and Order Numbers

Explore 1

In The Greatest Place vs. The Greatest Comparison In The Greatest Place: 900,000 910,000 920,000 930,000 940,000 950,000 960,000 970,000 980,000 990,000 1,000,000

The Greatest Comparison: 900,000 910,000 920,000 930,000 940,000 950,000 960,000 970,000 980,000 990,000 1,000,000

Statement 1: _________________________

_________________________

Statement 2: _________________________

_________________________

Which movie won? ________________________________

More than Most vs. The Value More than Most: 400,000 410,000 420,000 430,000 440,000 450,000 460,000 470,000 480,000 490,000 500,000

The Value: 400,000 410,000 420,000 430,000 440,000 450,000 460,000 470,000 480,000 490,000 500,000

Statement 1: _________________________

_________________________

Statement 2: _________________________

_________________________

Which movie won? ________________________________ 16 | Compare and Order Numbers

Compare and Order Numbers

Explore 1

From Left to Right vs. Your Number Is Up! From Left to Right: 700,000 720,000 740,000 760,000 780,000 800,000 820,000 840,000 860,000 880,000 900,000

Your Number Is Up!: 700,000 720,000 740,000 760,000 780,000 800,000 820,000 840,000 860,000 880,000 900,000

Statement 1: _________________________

_________________________

Statement 2: _________________________

_________________________

Which movie won? ________________________________

Reﬂ ect What could you do if you didn’t have a Place Value Mat to help you? _____________________________________________________________________ _____________________________________________________________________ Why is place value important when comparing numbers? _____________________________________________________________________ _____________________________________________________________________ How did the number line help you when comparing numbers? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare and Order Numbers | 17

Compare and Order Numbers

Explore 2

Name: _______________________ Date: __________

Order Numbers Part I: Which Spacecraft to Buy? Record the cost of each spacecraft in the place value chart below as the values are revealed. HTh

TTh

, , ,

Spacecraft 1 Spacecraft 2 Spacecraft 3

Use the number line to compare the costs of the spacecrafts.

433,000

433,100

433,200

433,300

433,400

433,500

433,600

433,700

433,800

433,900

434,000

Record the costs of the spacecrafts in order from greatest to least. Draw the correct symbol in between each value. ____________________

____________________

Which spacecraft was the most expensive? __________________________________ Describe your process for placing numbers in order from greatest to least or least to greatest. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare and Order Numbers | 19

Compare and Order Numbers

Explore 2 Part II: Explore the New Universe Complete the sections below about each scenario.

How are you ordering the population of the planets: greatest to least or least to greatest?

Which planet is the most populated?

Record the work your group did on the Place Value Mat.

Record each planet’s population on the number line.

50,000

100,000

150,000

200,000

250,000

300,000

Write the numbers in order, using the symbol <, >, or =. _____________

_____________

Label the values above by planet. 20 | Compare and Order Numbers

Compare and Order Numbers

Explore 2 2: Buildings on Planet Flunu How are you ordering the number of buildings: greatest to least or least to greatest?

Which month had the least buildings?

Record the work your group did on the Place Value Mat.

Record each month’s number of buildings on the number line.

246,000

246,100

246,200

246,300

246,400

246,500

246,600

246,700

246,800

246,900

247,000

247,100

Write the numbers in order, using the symbol <, >, or =. _____________

_____________

Label the values above by month.

Compare and Order Numbers | 21

Compare and Order Numbers

Explore 2 3: Xeuess and Its Sun How are you ordering the distance between Xeuess and its sun: greatest to least or least to greatest?

When is Xeuess farthest from its sun?

Record the work your group did on the Place Value Mat.

Record each season’s distance on the number line.

300,000

350,000

400,000

450,000

500,000

Write the numbers in order, using the symbol <, >, or =. _____________

_____________

Label the values above by season. Draw the symbol in the circle below that completes the statement. Distance in fall

distance in spring

How are place values and number lines helpful when ordering numbers? _____________________________________________________________________ _____________________________________________________________________ 22 | Compare and Order Numbers

Rounding

Explore 1

Name: _______________________ Date: __________

Round Using a Number Line Part I Draw where your group’s beanbags landed on number line 1. Number Line 1

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000 10,000

Describe where your beanbag landed. _____________________________________________________________________ _____________________________________________________________________ Where did your teammates’ beanbags land compared to yours? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What actual number do you think your beanbag landed on? ______________________ Which multiple of 1,000 is your beanbag closest to? ____________________________ What strategy did you use to ﬁnd the nearest rounded number?___________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

Rounding | 25

Rounding

Explore 1 Part II Draw where your group’s beanbags landed. Number Line 2

210,000 220,000 230,000 240,000 250,000 260,000 270,000 280,000 290,000 300,000

Teammate Name Actual Amount Rounded Amount

Number Line 3

10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

Teammate Name Actual Amount Rounded Amount

26 | Rounding

Rounding

Explore 1 Draw where your group’s beanbags landed. Number Line 4

10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000 19,000

Teammate Name Actual Amount Rounded Amount Number Line 5

100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000

Teammate Name Actual Amount Rounded Amount

Rounding | 27

Rounding

Explore 1 Draw where your group’s beanbags landed. Number Line 6

100,000 101,000 102,000 103,000 104,000 105,000 106,000 107,000 108,000 109,000

Teammate Name Actual Amount Rounded Amount

Reﬂ ect How did you know what number to round to? _____________________________________________________________________ _____________________________________________________________________ How is rounding a number useful? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

28 | Rounding

Rounding

Explore 2

Name: _______________________ Date: __________

Round Using Reasoning Use your reasoning skills to choose which place value it makes more sense to round to. Use your mental strategies to ﬁnd the total miles traveled as well as the difference between those distances. Record your strategies. Month

Mental Calculation Total distance traveled:

September

Difference between the miles:

Mental Calculation Total distance traveled:

October

Difference between the miles:

Rounding | 29

Rounding

Explore 2 Month

Mental Calculation Total distance traveled:

November

Difference between the miles:

What place value did you round to? Explain your reasoning. _____________________________________________________________________ _____________________________________________________________________

Month

Mental Calculation Total distance traveled:

December

Difference between the miles:

What place value did you round to? Explain your reasoning. _____________________________________________________________________ _____________________________________________________________________

30 | Rounding

Rounding

Explore 2 Month

Mental Calculation Total distance traveled:

January

Difference between the miles:

What place value did you round to? Explain your reasoning. _____________________________________________________________________ _____________________________________________________________________ Reﬂ ect How did you estimate the numbers in these scenarios using mental math? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Did you always have to round to the nearest thousand, ten thousand, or hundred thousand? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Rounding | 31

Addition and Subtraction Algorithms

Multi-Digit Addition

Your strategy:

------------------------- Atlanta

Trip 1

Philippines

Addition and Subtraction Algorithms | 35

Standard algorithm:

Australia -------------------------

Name: _______________________ Date: __________

Complete the following steps to ﬁnd the total distance traveled. • Find the two boarding passes that match with the trip. • Use a strategy of your choosing as well as the standard algorithm to solve for the sum of each trip. • Use these strategy options: open number line or partial sums. • For the last question, ﬁnd the total distance traveled for all 3 trips.

Explore 1

Addition and Subtraction Algorithms

36 | Addition and Subtraction Algorithms

Your strategy:

--------------------- Canada

Trip 3

Your strategy:

---------------------- Los Angeles

Trip 2

Explore 1

Dubai

Paris

Standard algorithm:

New Zealand ----------------------

Standard algorithm:

Mexico -----------------------

Addition and Subtraction Algorithms

____________________________

____________________________ ____________________________ ____________________________ ____________________________

____________________________

Addition and Subtraction Algorithms | 37

____________________________

Is the standard algorithm always the most efﬁcient way to solve addition problems?

Standard algorithm:

How are the open number line, partial sums, and the standard algorithm similar?

Explain the reason you chose a certain strategy on a trip and why.

Reﬂect

Your strategy:

------------------------------------------------- Total Travel -------------------------------------------------

Explore 1

Addition and Subtraction Algorithms

Multi-Digit Subtraction

Name: _______________________ Date: __________

Your strategy:

Addition and Subtraction Algorithms | 39

Standard algorithm:

----------------------------------------- Soda Can Ring -----------------------------------------

Booth 1

Complete the following steps to find the number on the raffle ticket. • Locate each carnival booth, and complete the problems in the spaces below. • Use a strategy of your choosing as well as the standard algorithm to solve. • Use these strategy options: open number line or partial differences. • Write your answer in each blank raffle ticket for each game booth.

Explore 2

Addition and Subtraction Algorithms

Standard algorithm:

40 | Addition and Subtraction Algorithms

Your strategy:

Standard algorithm:

------------------------------------------- Gone Fishing -------------------------------------------

Booth 3

Your strategy:

------------------------------------------- Balloon Pop -------------------------------------------

Booth 2

Explore 2

Addition and Subtraction Algorithms

____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________

____________________________

Which subtraction strategy had a similar way of regrouping as the standard algorithm?

In a subtraction equation or expression, what does the subtraction sign mean?

Reﬂect

Your strategy:

Addition and Subtraction Algorithms | 41

____________________________

Which subtraction strategy did you ﬁnd to be the most efﬁcient way to solve each problem?

Standard algorithm:

------------------------------------------ Beanbag Toss -----------------------------------------

Booth 4

Explore 2

Addition and Subtraction Algorithms

Explore 3

Addition and Subtraction Algorithms

Name: _______________________ Date: __________

Addition and Subtraction Strategies To successfully complete each question, complete each step below. • Write an expression to represent the problem. • Solve each problem using two strategies of your choice: open number line, partial sums or differences, and the standard algorithm. • Write a solution statement, and justify which strategy you found to be most efﬁcient. I. I would rather _______________________________________________________ Equation: First strategy:

Second strategy:

Addition and Subtraction Algorithms | 43

Explore 3

Addition and Subtraction Algorithms

2. I would rather ______________________________________________________ ______________________________________________________________________ Equation: First strategy:

Second strategy:

Explore 3

Addition and Subtraction Algorithms

3. I would rather ______________________________________________________ ______________________________________________________________________ Equation: First strategy:

Second strategy:

Addition and Subtraction Algorithms | 45

Explore 3

Addition and Subtraction Algorithms

4. I would rather ______________________________________________________ ______________________________________________________________________ Equation: First strategy:

Second strategy:

Solution statement: ___________________________________________________ ___________________________________________________________________ Justify the most efﬁcient strategy. ________________________________________ ___________________________________________________________________ ___________________________________________________________________ Reﬂ ect How did you determine whether to use addition or subtraction? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Why do you think there are multiple strategies we can choose from? ______________________________________________________________________ ______________________________________________________________________ 46 | Addition and Subtraction Algorithms

Prime and Composite Numbers

Explore 1

Prime and Composite Numbers

Name: _______________________ Date: __________

Find Factor Pairs Draw a model of each of your tile arrangements. Label each of the dimensions with the number of blocks used.

Tomatoes Draw and label each possible arrangement.

List all of the possible factor pairs.

Bell Peppers Draw and label each possible arrangement.

List all of the possible factor pairs.

Prime and Composite Numbers | 49

Prime and Composite Numbers

Explore 1 Corn Draw and label each possible arrangement.

List all of the possible factor pairs.

Carrots Draw and label each possible arrangement.

List all of the possible factor pairs.

Reﬂ ect How can you be sure to ﬁnd all the factor pairs for a large number? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What is the relationship between each factor pair in your list? ______________________________________________________________________ ______________________________________________________________________ 50 | Prime and Composite Numbers

Prime and Composite Numbers

Explore 2

Name: _______________________ Date: __________

Determine Multiples Work with your group to help Mrs. Buckman order new items for the library.

Fiction Books Use the space below to ﬁnd whether Mrs. Buckman can order exactly 96 ﬁction books.

Can she order exactly 96 books? Explain. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Use the space below to ﬁnd whether Mrs. Buckman can order exactly 86 ﬁction books.

Can she order exactly 86 books? Explain. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Prime and Composite Numbers | 51

Prime and Composite Numbers

Explore 2 Bookmarks

Use the space below to ﬁnd whether Mrs. Buckman should order packs of 6 or 8.

What would you recommend to Mrs. Buckman? Explain your thinking. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Nonﬁction Books Use the space below to ﬁnd several ways the books could be shipped.

What did you notice about all of the ways the books could be grouped into boxes? __________________________________________________________________ __________________________________________________________________ Complete the statement below. 36 is a _______________________ of each of its ________________________.

52 | Prime and Composite Numbers

Prime and Composite Numbers

Explore 2 Magazines

Use the space below to ﬁnd whether Mrs. Buckman can order exactly 91 magazines.

Can she order exactly 91 magazines? Explain your thinking. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Reﬂ ect Describe the relationship between factors and multiples. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How can you know if number A is a multiple of number B? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

Prime and Composite Numbers | 53

Explore 3

Prime and Composite Numbers

Name: _______________________ Date: __________

Prime and Composite Numbers Part I Use color tiles to show how the desks can be arranged. Then, draw arrays showing all of the ways 12 desks can be arranged on your graph paper.

What are the factors of 12? _______________________________________________ Is 12 prime or composite? ________________________________________________ Part II Use color tiles to show how the desks can be arranged. Then, draw arrays showing all of the ways the desks can be arranged on the graph paper on the next two pages. Organize and label your arrays based on the total number of desks.

Prime and Composite Numbers | 55

Explore 3

Prime and Composite Numbers

My group was assigned to ﬁnd arrangements for these numbers of desks: Graph paper 1

56 | Prime and Composite Numbers

Explore 3

Prime and Composite Numbers

Use the graph paper below for drawing additional arrays. Graph paper 2

Prime and Composite Numbers | 57

Prime and Composite Numbers

Explore 3 Record the data from each group in the table below. Number of Desks

Factors

Prime or Composite?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 58 | Prime and Composite Numbers

Prime and Composite Numbers

Explore 3 Number of Desks

Factors

Prime or Composite?

20 21 22 23 24 25 Reﬂ ect What other prime numbers did you ﬁnd? _____________________________________________________________________ How do you know if a number is prime or composite? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Name a number greater than 25. Prove in words and pictures whether it is prime or composite.

Prime and Composite Numbers | 59

Multiplicative Comparisons

Explore 1

Multiplicative Comparisons

Name: _______________________ Date: __________

Model Multiplicative Comparisons

Part I: Farm Wars For two of your matches, record a multiplication sentence, write a description using the phrase times as many, and sketch your model. Model Farmer Joe’s ______________

Farmer Susan’s _____________

Equation

Description

Model Farmer Joe’s ______________

Farmer Susan’s _____________

Equation

Description

Multiplicative Comparisons | 63

Multiplicative Comparisons

Explore 1

Part II: Farm Scenario Cards Use the Farm Scenario Cards to represent a model of each scenario. Then, complete the sentence stem to explain the model. Scenario 1 Model of Joe’s pigs in pens:

Model of Susan’s pigs in pens:

Joe has __________ pigs. Susan has ________ pigs. _____________ has _______ times as many pigs as ___________. Joe needs ___ pens. Scenario 2 Model of chickens fed in one serving:

Model of each group of chickens fed for all of the servings:

Susan has ______ chickens. This is ______ times as many as _______. Equation: ______________________ 64 | Multiplicative Comparisons

Multiplicative Comparisons

Explore 1 Scenario 3 Model of horses each barn can hold:

Model of all of the barns of horses:

Each barn can hold ______ horses. 24 is ____ times as many as 4. Equation: ___________________ Scenario 4 Model of Joe’s cows in the pasture:

Model of Susan’s cows in the pastures:

Multiplicative Comparisons | 65

Multiplicative Comparisons

Explore 1 Scenario 5 Model of groups of sheep:

Model of donkeys:

Donkeys can protect ______ sheep. 54 is ____ times as many as 6. Scenario 6 Model of Joe’s ducks in pools:

Model of Susan’s ducks in pools:

Joe has __________ ducks. Susan has ________ ducks. _____________ has _______ times as many ducks as ___________. Susan needs ___ pools. Reﬂ ect What operations did you use to solve each scenario? ___________________________ ______________________________________________________________________ Why do you think we call these scenarios “multiplicative comparisons”? ______________________________________________________________________ ______________________________________________________________________ 66 | Multiplicative Comparisons

Name: _______________________ Date: __________

Equation: Solution statement: ___________________________________________ ___________________________________________ Circle one:

Equation:

Solution statement:

___________________________________________

Circle one:

Multiplicative Comparisons | 67

Additive or Multiplicative

Model:

Additive or Multiplicative

Part of the meal:

Read each Dinner Card, and develop a diagram to model the problem. Create an equation, and solve to ﬁnd the solution. Record the solution statement, and determine whether the situation is an additive comparison or a multiplicative comparison.

Additive and Multiplicative Comparisons

Explore 2

Multiplicative Comparisons

Solution statement: ___________________________________________ ___________________________________________ Circle one:

Solution statement:

___________________________________________

Circle one:

68 | Multiplicative Comparisons

___________________________________________________________________________________________

What helped you determine whether a problem was an additive comparison or a multiplicative comparison?

Reﬂect

Equation:

Additive or Multiplicative

Model:

Additive or Multiplicative

Part of the meal:

Explore 2

Multiplicative Comparisons

Explore 3

Multiplicative Comparisons

Name: _______________________ Date: __________

Solve Problems with Multiplicative Comparisons

1. Read the information on each Shopping Card. 2. Draw a diagram to model the problem. A model can be built with play money, if needed. 3. Write an equation that could be used to ﬁnd the solution using a letter in place of the unknown. 4. Solve, and explain your solution. 5. Complete the ﬁnal statement to show which item you would rather purchase.

Purchase 1 Diagram:

Multiplicative Comparisons | 69

Multiplicative Comparisons

Explore 3 Purchase 2 Diagram:

70 | Multiplicative Comparisons

Multiplicative Comparisons

Explore 3 Purchase 4 Diagram:

Multiplicative Comparisons | 71

Multiplicative Comparisons

Explore 3 Purchase 6 Diagram:

Equation: Solution statement: ___________________________________________________ ___________________________________________________________________ I would purchase the ___________________ because _______________________ ___________________________________________________________________ Reﬂ ect How did you ﬁgure out the missing information? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How is a model, such as a diagram, helpful for solving problems? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 72 | Multiplicative Comparisons

Multiplication Models and Strategies

Explore 1

Name: _______________________ Date: __________

Multiply up to Four-Digit by One-Digit Numbers – Arrays Cra-Z-Crafts needs your help with their quarterly inventory. They need your help ﬁguring out how many craft supplies they have in stock. At each station, build an array to model the number of items. Describe your model by writing how many groups of thousands, hundreds, tens, and ones you have. Then, write an equation for each group, and use the products to ﬁnd the total number of items. Glue Sticks Model:

Write an expression for your model: _______ × _______ Hundreds

Tens

Ones

Total

_____ groups of _____

Equation:

_____ × _____ = _____

Solution statement:

Multiplication Models and Strategies | 75

Multiplication Models and Strategies

Explore 1 Paint Bottles Model:

Write an expression for your model: _______ × _______ Hundreds

Tens

Ones

_____ groups of _____

Equation:

_____ × _____ = _____

Total

Solution statement: Jars of Glitter Model:

Write an expression for your model: _______ × _______ Hundreds

Tens

Ones

_____ groups of _____

Equation:

_____ × _____ = _____

Total

Solution statement: 76 | Multiplication Models and Strategies

Multiplication Models and Strategies

Explore 1 Poster Board Model:

Write an expression for your model: _______ × _______ Find the partial products for each place value, and use them to ﬁnd the ﬁnal product:

Solution statement: Gel Pens Model:

Write an expression for your model: _______ × _______ Solve using partial products.

Multiplication Models and Strategies | 77

Multiplication Models and Strategies

Explore 1 Scrapbook Paper Model:

Write an expression for your model: _______ × _______ Solve using partial products.

Solution statement: Refl ect How can models be used to multiply large numbers? _____________________________________________________________________ _____________________________________________________________________ How did you find the final total? _____________________________________________________________________ _____________________________________________________________________ What connections did you make during this activity? _____________________________________________________________________ _____________________________________________________________________

78 | Multiplication Models and Strategies

Multiplication Models and Strategies

Explore 2

Name: _______________________ Date: __________

Multiply up to Four-Digit by One-Digit Numbers – Area Models Draw the area model of each amphitheater in the space provided, and label each section with the equation and partial product.

Theater 1: 5 rows, 628 seats in each row

Complete the equations below to represent the area model above. _____ × _____ = = (______ × ______) + (______ × ______) + (______ × ______) = ______ + ______ + ______ = ___________

Multiplication Models and Strategies | 79

Multiplication Models and Strategies

Explore 2

Theater 2: 3 rows, 216 seats in each row

Complete the equations below to represent the area model above. ______ × ______ = = (_____ × _____) + (_____ × _____) + (____ × ____) = _______ + _______ + _______ = ___________

Theater 3: 7 rows, 1,235 seats in each row

Complete the equations below to represent the area model above. ______ × ______ = = (_____ × _____) + (_____ × _____) + (_____ × _____) + (____ × ____) = _______ + _______ + _______ + _______ = ___________

80 | Multiplication Models and Strategies

Multiplication Models and Strategies

Explore 2

Theater 4: 6 rows, 2,543 seats in each row

Reﬂ ect What is the relationship between an array and an area model? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What is the relationship between the equation and the area model? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication Models and Strategies | 81

Explore 3

Multiplication Models and Strategies

Name: _______________________ Date: __________

Multiply Two-Digit by Two-Digit Numbers – Arrays Part I: Measurement Tools Use the space below to trace each base ten block. These blocks will be used as measuring tools for each flower bed. Label the flat, the rod, and the unit with the length, width, and area if the flat is 100 square feet.

How did you know the width of the rod? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How did you know the length and width of the unit cube? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication Models and Strategies | 83

Multiplication Models and Strategies

Explore 3 Part II: Measuring Orders Use the base ten blocks as measurement tools to build a model of each ﬂower bed. Then, write the measurements in expanded notation and an equation that represents the model.

Flower Bed Size

Array

Expanded Notation

Equation

Length: 15 ft. Width: 23 ft.

Length: 21 ft. Width: 47 ft.

Length: 13 ft. Width: 13 ft.

84 | Multiplication Models and Strategies

Multiplication Models and Strategies

Explore 3 Flower Bed Size

Array

Expanded Notation

Equation

Length: 12 ft. Width: 12 ft.

Length: 34 ft. Width: 18 ft.

Refl ect How did you know which size piece to use in each section of your model? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What connections did you make during this activity? _____________________________________________________________________ _____________________________________________________________________ How did you use your model to find the final product? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication Models and Strategies | 85

Explore 4

Multiplication Models and Strategies

Name: _______________________ Date: __________

Multiply Two-Digit by Two-Digit Numbers – Area Models Part I: Small Party Pizza Use the base ten blocks to build a model of each pizza. Create an area model based on the blocks. Use the models to ﬁgure out the total size of each pizza.

Pizza Size

Partial Products Area Model

Equation

Length: 22 in. Width: 16 in.

Length: 15 in. Width: 15 in.

Multiplication Models and Strategies | 87

Multiplication Models and Strategies

Explore 4 Part II: Monster Pizza

As a group, draw an area model that represents each pizza. Record the area models below, and ﬁnd the area of each section. Use the partial products to ﬁgure out the total amount of pizza. Pizza Size

Partial Products Area Model

Equation

Paciano’s Pizza Parlor Length: 55 in. Width: 24 in.

Papa’s Pizza Length: 43 in. Width: 36 in.

Pedro’s Pizza Length: 63 in. Width: 18 in.

88 | Multiplication Models and Strategies

Multiplication Models and Strategies

Explore 4 Pizza Size

Partial Products Area Model

Equation

Penelope’s Pizza Length: 51 in. Width: 35 in.

Joe’s Pizza Length: 29 in. Width: 49 in.

Which pizza parlor made the biggest pizza? __________________________________ Reﬂ ect How are area models similar to arrays? _____________________________________________________________________ _____________________________________________________________________ How is an area model helpful? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiplication Models and Strategies | 89

Explore 5

Multiplication Models and Strategies

Name: _______________________ Date: __________

Multiply Two-Digit by Two-Digit Numbers – Area Models and Partial Products Read each scenario. Use the Area Model Template to create an area model and ﬁnd the solution. Record your work below. Write each partial product in the box on the right. ---------------------------------------------- Scenario 1 ---------------------------------------------Area model:

Partial products: ____ ____ ____ ____ ×____________ ____ ____ ____ ____ (____ ×____) ____ ____ ____ ____ (____ ×____) ____ ____ ____ ____ (____ ×____) ____ ____ ____ ____ (____ ×____) _____________________ ____ ____ ____ ____ square ft.

---------------------------------------------- Scenario 2 ---------------------------------------------Area model:

Multiplication Models and Strategies | 91

Explore 5

Multiplication Models and Strategies

---------------------------------------------- Scenario 3 ---------------------------------------------Area model:

---------------------------------------------- Scenario 4 ---------------------------------------------Area model:

Reﬂ ect Describe the relationship between area models and partial products. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 92 | Multiplication Models and Strategies

Division Models and Strategies

Explore 1

Name: _______________________ Date: __________

Share Equally

Part 1 Use the materials available to complete the following tasks. The fourth-grade department at your school received a new shipment of school supplies! Each of the three fourth-grade classes should get the same number of supplies. Use the space below to show how you will share the supplies evenly.

Part II Scenario 1: Cake-Decorating Competition Describe the problem in your own words. ____________________________________________________ ____________________________________________________ Use the space below to draw and label your solution.

Division Models and Strategies | 95

Explore 1

Division Models and Strategies

Scenario 2: Youth Soccer Camp Describe the problem in your own words. ______________________ _______________________________________________________ Use the space below to draw and label your solution.

Describe the solution in a sentence. __________________________________________________________________ __________________________________________________________________ Equation: ________________________ Scenario 3: The Great Lemonade Gulp Describe the problem in your own words. ______________________ _______________________________________________________ Use the space below to draw and label your solution.

Describe the solution in a sentence. __________________________________________________________________ __________________________________________________________________ Equation: ________________________ Explain your process for splitting up large amounts evenly. _____________________________________________________________________ _____________________________________________________________________ 96 | Division Models and Strategies

Explore 2

Division Models and Strategies

Name: _______________________ Date: __________

Arrays

Use the blocks to model your solutions to the problems below. Draw and label your models, and write the equations that represent the quotients. 1. Rice Elementary is hosting 84 people for a kindergarten graduation. They want the parents in the audience to be able to hear the names called, so they only want 4 rows of chairs. Plan how the chairs will be arranged, and draw your plan below.

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________ 2. A local band wants to host a concert under a park pavilion. They are expecting around 280 people to attend. The pavilion is narrow, and they need to leave walking space around the chairs. Only 8 chairs can ﬁt in each row. Use the space below to plan how the chairs will be arranged.

Division Models and Strategies | 97

Explore 2

Division Models and Strategies

3. Sargent County is planning a strawberry festival with live music. They want to put 6 rows of chairs at the front of the stage, but they need to make sure they can seat 1,284 people at a time. How many chairs can they set up in each row? Use the space below to arrange the chairs.

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________ 4. Congratulations on your new car dealership! You have a shipment of 238 cars on its way to your lot. You only have enough space for 7 rows of cars. How many cars do you need to park in each row so that they all ﬁt?

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________

98 | Division Models and Strategies

Explore 2

Division Models and Strategies

5. Your school is raising money for new computers in the computer lab. The school raised $2,210 selling rafﬂe tickets. Each ticket cost $5. How many tickets did the school sell?

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________ 6. The Washington County youth baseball teams received 272 baseballs to use during practices. There are 6 teams in the league, and each team should get the same number of baseballs. How many baseballs should each team get?

Division Models and Strategies | 99

Explore 3

Division Models and Strategies

Name: _______________________ Date: __________

Area Models Use the Area Model Cards to model your solutions to the problems below. Draw and label your models, and write the equations that represent the quotients. 1. Jill wanted to buy a rug for her bedroom. She knew her rug could not be larger than 96 square feet. She measured 6 feet for the length of the ﬂoor where her rug would be. How wide of a rug could she buy? Use the space below to create an area model to show Jill’s rug.

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________ 2. Adam built a garden in his backyard that was 448 square feet. He planted 8 rows of vegetables in his garden, leaving 1 foot between each plant. How many plants can Adam plant in each row?

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________

Division Models and Strategies | 101

Explore 3

Division Models and Strategies

3. Jake is installing a new tile ﬂoor in his house. He has 1,165 tiles to put down. He will lay 5 rows of tile. How many tiles will he lay in each row?

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________

4. Derrick loves to collect baseball cards. He wants to place the cards in a binder in which each page can hold 9 cards. He has collected a total of 1,479 baseball cards. How many pages will Derrick need to hold all of his baseball cards?

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________

102 | Division Models and Strategies

Explore 3

Division Models and Strategies

5. The ice cream factory made 2,346 ice pops on Tuesday. All of the ice pops were made in batches. That day, 3 batches were done. How many ice pops were in a batch?

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________ 6. Sweet Treats Candy Store has a display of 7,272 jelly beans. There are 4 large jars of jelly beans, and each jar holds the same amount. How many jelly beans are in each jar?

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________ Describe how to use an area model to divide large numbers. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Division Models and Strategies | 103

Division Models and Strategies

Explore 4

Name: _______________________ Date: __________

Partial Quotients Scenario 1 Draw an area model. Use one color to label the divisor, a different color to label the areas, and a third color to label the top dimensions.

After using the Partial Quotients Work Mat, record the partial quotients workspace below. Use the same colors for the same parts you used above in your area model. You will need a fourth color for the differences.

What is the relationship between an area model and the partial quotients strategy? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Division Models and Strategies | 105

Explore 4

Division Models and Strategies

Use the Partial Quotients Work Mat to solve scenarios 2 and 3. Record your work below. Try to solve scenarios 4 and 5 without using place value disks. Scenario 2

Scenario 3

Scenario 4

Scenario 5

In your own words, describe how to divide a four-digit number by a one-digit number. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 106 | Division Models and Strategies

Generate Patterns

107

Generate Patterns

Explore 1

Name: _______________________ Date: __________

Shape Patterns Part 1: Playing the Games Block’d Stage 1

Stage 2

Stage 3

What is the rule to get to the next stage? _____________________________________ How many blocks would stage 4 have? ______________________________________ Draw a model of what stage 4 would look like.

Running in Circles Stage 1

Stage 2

Stage 3

What is the rule to get to the next stage? _____________________________________ How many circles would stage 5 have? ______________________________________ Draw a model of what stage 5 would look like.

Generate Patterns | 109

Generate Patterns

Explore 1 Heart Drop Stage 1

Stage 2

Stage 3

What is the rule to get to the next stage? _____________________________________ How many hearts would stage 4 have? ______________________________________ Draw a model of what stage 4 would look like.

Stair Steppin’ Stage 1

Stage 2

Stage 3

What is the rule to get to the next stage? _____________________________________ How many squares would stage 4 have? _____________________________________ Draw a model of what stage 4 would look like.

110 | Generate Patterns

Generate Patterns

Explore 1 Say Cheese! Stage 1

Stage 2

Stage 3

What is the rule to get to the next stage? _____________________________________ How many smiley faces would stage 4 have? _________________________________ Draw a model of what stage 4 would look like.

Cloudy with a Chance of WINNING! Stage 1

Stage 2

Stage 3

What is the rule to get to the next stage? _____________________________________ What is another rule that could be used to get to the next stage that uses two operations? ___________________________________________________________

How many clouds would stage 5 have? _______________ Draw a model of what stage 5 would look like.

Generate Patterns | 111

Generate Patterns

Explore 1 Reﬂ ect

What can you say about the pattern in each game going from stage to stage? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What strategy did you use to determine the rule and the pattern for each game? _____________________________________________________________________ _____________________________________________________________________ What strategy did you use to ﬁnd another rule for Cloudy with a Chance of WINNING!? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Part II: New Game

Stage 1

Stage 2

Stage 3

What is the rule to get to the next stage? _____________________________________ How did you determine the pattern and rule for this game? _______________________ _____________________________________________________________________ 112 | Generate Patterns

Generate Patterns

Explore 2

Name: _______________________ Date: __________

Number Patterns Birthday Buddies Fynn’s Age

Expression

Amari’s Age

Last year: This year: Next year: If you know how old Fynn is, how can you ﬁnd Amari’s age? ______________________________________________________________________ If you know how old Amari is, how can you ﬁnd Fynn’s age? ______________________________________________________________________ Decorations Number of Balloon Sets

Expression

Total Cost

How can you ﬁgure out how much 3 sets of balloons would cost? ______________________________________________________________________ Why does the total cost alternate between even and odd? ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Generate Patterns | 113

Generate Patterns

Explore 2 Party Horns Number of Bags

Expression

Party Horns

How can you ﬁnd out how many bags of party horns you will need for your guests? ______________________________________________________________________ ______________________________________________________________________ Why is the number of party horns always even? ______________________________________________________________________ ______________________________________________________________________ Treasure Hunt Chest

Expression

Coins

If the trend continues, how can you ﬁgure out how many coins will be in chest 5? ______________________________________________________________________ How many coins do you think will be in chest 7? _______________________________ What can you say about the answers in the coins column? _______________________ ______________________________________________________________________ 114 | Generate Patterns

Generate Patterns

Explore 2 Hot Dogs Package(s)

Expression

Hot Dogs

How can you ﬁnd out if you have enough hot dogs? ______________________________________________________________________ What can you say about the answers in the hot dogs column? ____________________ ______________________________________________________________________ Ice Cream Scoop

Expression

Ounces

How can you determine how many ounces there are in the number of scoops? ______________________________________________________________________ What can you say about the answers in the ounces column? ______________________________________________________________________

Generate Patterns | 115

Generate Patterns

Explore 2 Pin the Tail on the Donkey Tails on the Donkey

Expression

Turns

How can you determine the number of turns he took using the number of tails he pinned to the donkey? ___________________________________________________ How many turns would it take for Amari to get 8 tails on the donkey? _______________ ______________________________________________________________________ Refl ect What strategies did you use to figure out the patterns in these scenarios? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How could you tell which operation to use? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ When might finding a number pattern be useful? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ 116 | Generate Patterns

Generate Patterns

Explore 3

Name: _______________________ Date: __________

Input-Output Tables Uncle Santiago uses wood scraps from his woodworking shop to make toys. When children can answer his riddles, he gives the toys to them for free! Find the toy that matches the riddle. Then, help Uncle Santiago ﬁnd the rule, and complete the table to get the toy! My variables: Plane Rule: __________________ _____ = _________________________ Input: Number of Planes

Output: Number of Wings

_____ = _________________________ What equation could be used to ﬁnd the input if you have the output? ________________________________

6 8 15 90

Car Rule: _______________ Input: Number of Cars Output: Number of People

8 9

10 36

My variables: _____ = __________________________

_____ = __________________________

Generate Patterns | 117

Generate Patterns

Explore 3 My variables: Dog Rule: __________________ Input: Order Dog Was Made

Output: Number of Wood Scraps

3rd

_____ = _________________________ _____ = _________________________ What equation could be used to ﬁnd the input if you have the output? ________________________________

4th 12 15th 23

My variables: Blocks Rule: __________________ Input: Number of Packages

Output: Number of Blocks

_____ = _________________________ _____ = _________________________ What equation could be used to ﬁnd the input if you have the output? ________________________________

42 11 78 102 118 | Generate Patterns

Generate Patterns

Explore 3 Train Rule: _______________ Input: Number of Cars

Output: Number of Parts

My variables: _____ = __________________________

_____ = __________________________

What equation could be used to ﬁnd the input if you have the output? _____________ Elephant Rule: _______________ Input: Length of Pulling String

Output: Length to Cut

14 14

30 28

My variables: _____ = __________________________

_____ = __________________________

What equation could be used to find the input if you have the output? ______________ Refl ect How is using input-output tables useful? _____________________________________________________________________ _____________________________________________________________________ When would knowing the rule that shows the relationship between numbers be helpful? _____________________________________________________________________ _____________________________________________________________________ If you have one number in the relationship, how can you find the other number? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Generate Patterns | 119

Problem Solve Using the Four Operations

121

Explore 1

Problem Solve Using the Four Operations

Name: _______________________ Date: __________

Interpret Remainders

Part I Bryson collects toy trains. He has 186 trains in his collection. He wants to display them on 8 shelves in his room, with the same number of trains on each shelf. How many trains can he ﬁt on each shelf? What operation should be used? ___________________________________________ Write an equation, and solve. ______________________________________________________________________

How many trains will be on each shelf? ______________________________________ Will there be an equal number of trains on each shelf? __________________________ How many trains will not ﬁt on the shelves? ___________________________________ Solution: ______________________________________________________________

Problem Solve Using the Four Operations | 123

Explore 1

Problem Solve Using the Four Operations

Read each Problem Card, and answer the questions below. Workspace:

1 How many bracelets can she make? _____________________________ How many beads will be left over, if any? _________________________ Write the solution as a quotient. _____________________________

Workspace:

2 How many full piles will he make? _____________________________ How many pieces will be left over, if any? _________________________ Write the solution as a quotient. _____________________________

Workspace:

3 How many cages are full? _____________________________ How many guinea pigs are not in a cage with another guinea pig? _____________________________ Write the solution as a quotient. _____________________________

124 | Problem Solve Using the Four Operations

Problem Solve Using the Four Operations

Explore 1

Part II Read each problem, and solve it in the space given below. Decide how the remainder will affect your solution by circling whether you needed to ignore it or round up your solution.

Workspace:

Circle one: Round it!

Circle one: Ignore it!

Round it!

Solution: _________________________

Workspace:

Circle one: Round it!

Ignore it!

Solution: _________________________

Workspace:

Circle one: Ignore it!

Round it!

Solution: _________________________

Workspace:

Circle one: Round it!

Workspace:

Ignore it!

Solution: _________________________

Workspace:

Circle one: Ignore it!

Solution: _________________________

Round it!

Ignore it!

Solution: _________________________

Problem Solve Using the Four Operations | 125

Explore 1

Problem Solve Using the Four Operations

Reﬂ ect Explain how a remainder can affect your solution. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

126 | Problem Solve Using the Four Operations

Problem Solve Using the Four Operations

Explore 2

Name: _______________________ Date: __________

Problem Solve Using the Four Operations — Level 1

Problem: _________________________________ Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem.

Estimate the solution(s).

Solve the equation(s).

Write the solution as a statement.

Problem Solve Using the Four Operations | 127

Problem Solve Using the Four Operations

Explore 2 Problem: _________________________________ Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem.

Estimate the solution(s).

Solve the equation(s).

Write the solution as a statement.

128 | Problem Solve Using the Four Operations

Problem Solve Using the Four Operations

Explore 2 Problem: _________________________________ Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem.

Estimate the solution(s).

Solve the equation(s).

Write the solution as a statement.

Reﬂ ect What are the different ways you represented the problems? _____________________________________________________________________ _____________________________________________________________________ What does a letter represent in an equation? _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Problem Solve Using the Four Operations | 129

Problem Solve Using the Four Operations

Explore 3

Name: _______________________ Date: __________

Problem Solve Using the Four Operations – Level 2 Problem: _________________________________ Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem.

Estimate the solution(s).

Solve the equation(s).

Write the solution as a statement.

Problem Solve Using the Four Operations | 131

Problem Solve Using the Four Operations

Explore 3 Problem: _________________________________ Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem.

Estimate the solution(s).

Solve the equation(s).

Write the solution as a statement.

132 | Problem Solve Using the Four Operations

Problem Solve Using the Four Operations

Explore 3 Problem: _________________________________ Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem.

Estimate the solution(s).

Solve the equation(s).

Write the solution as a statement.

Problem Solve Using the Four Operations | 133

Problem Solve Using the Four Operations

Explore 3 Create Your Own! Problem:

Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem.

Estimate the solution(s).

Solve the equation(s).

Write the solution as a statement.

134 | Problem Solve Using the Four Operations

Explore 4

Problem Solve Using the Four Operations

Name: _______________________ Date: __________

Problem Solve Using the Four Operations – Level 3

Flower Shop

Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem using a letter to represent the unknown.

Estimate the solution(s).

Solve the equation(s).

How many flowers will be in each vase? _______________________________ How many flowers will be left over, if any? _____ What kind of flower are they? ___________

Problem Solve Using the Four Operations | 135

Problem Solve Using the Four Operations

Explore 4 Recess Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem using a letter to represent the unknown.

Estimate the solution(s).

Solve the equation(s).

How many students did not earn extra recess time? _________

136 | Problem Solve Using the Four Operations

Problem Solve Using the Four Operations

Explore 4 Rafﬂ e Tickets Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem using a letter to represent the unknown.

Estimate the solution(s).

Solve the equation(s).

How many parents bought rafﬂe tickets? _________ How much money was spent on rafﬂe tickets? _________

Problem Solve Using the Four Operations | 137

Problem Solve Using the Four Operations

Explore 4 Survey Rewards Draw the diagram(s) that represent(s) the problem.

Write the equation(s) that represent(s) this problem using a letter to represent the unknown.

Estimate the solution(s).

Solve the equation(s).

How many points did Molly earn from just taking surveys? _________ How many total points does she have? _________

138 | Problem Solve Using the Four Operations

Compare Fractions

139

Explore 1

Compare Fractions

Name: _______________________ Date: __________

Compare Fraction Wholes

Layers of Onion Draw a model of each onion, and shade each customer’s portion.

What fraction of the onion did each customer receive? ________ Did both tacos get the same amount of onion? ___________ Explain your reasoning. __________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Beeftastic Draw a model of each beefsteak, and shade each customer’s portion.

What fraction of the steak did each customer receive? ________ Did both tacos get the same amount of steak? ___________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare Fractions | 141

Compare Fractions

Explore 1 Lettuce Heads Draw a model of each lettuce head, and shade each customer’s portion.

What fraction of the lettuce did each customer receive? ________ Did both tacos get the same amount of lettuce? ___________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ Feelin’ Cheesy Draw a model of each cheese cube, and shade each customer’s portion.

What fraction of the cheese did each customer receive? ________ Did both tacos get the same amount of cheese? ___________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ 142 | Compare Fractions

Explore 1

Compare Fractions

Ta-may-toe/Ta-mah-toe Draw a model of each tomato, and shade each customer’s portion.

What fraction of the tomato did each customer receive? ________ Did both tacos get the same amount of tomato? ___________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ Make It Spicy! Draw a model of each jalapeño, and shade each customer’s portion.

What fraction of the jalapeño did each customer receive? ________ Did both tacos get the same amount of jalapeño? ___________ Explain your reasoning. ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare Fractions | 143

Name: _______________________ Date: __________

Fractions

Fraction Models (number line, bars, or circles)

Riddle

Comparison Statement

Compare Fractions | 145

Answer and Reasoning

For each recipe riddle, complete the following steps: 1. Write the fractions you are comparing. 2. Draw a model to represent each fraction. 3. Write a comparison statement using symbols. 4. Answer the question on the Recipe Riddles Card, and explain your reasoning.

Compare Fractions with the Same Numerator or Denominator

Explore 2

Compare Fractions

lle

Fractions

Fraction Models (number line, bars, or circles)

Comparison Statement

Answer and Reasoning

146 | Compare Fractions

___________________________________________________________________________________________

Explain your process for comparing two fractions.

Reﬂect

a Ch

5nge!

Riddle

Explore 2

Compare Fractions

Explore 3

Compare Fractions

Name: _______________________ Date: __________

Compare Fractions with Models

Read each Would You Rather Card, and complete the steps below. 1. Build or draw a model of the fractions. 2. Find a way to create equivalent fractions that have the same numerator or the same denominator. 3. Draw your models in the space provided, and write a comparison statement using symbols. 4. Discuss and record which option you would rather have. Explain your answer. Card 1 Draw and label the models you built. Show any equivalent fractions you created to compare them.

I would rather _____________________________________ because _________________________________________

Comparison statement:

________________________________________________. Why is it helpful to create equivalent fractions with the same numerator or the same denominator? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare Fractions | 147

Compare Fractions

Explore 3 Card 2

Draw and label the models you built. Show any equivalent fractions you created to compare them.

I would rather _____________________________________ because _________________________________________

Comparison statement:

________________________________________________. Card 3 Draw and label the models you built. Show any equivalent fractions you created to compare them.

I would rather _____________________________________ because _________________________________________

Comparison statement:

________________________________________________. 148 | Compare Fractions

Compare Fractions

Explore 3 Card 4

Draw and label the models you built. Show any equivalent fractions you created to compare them.

I would rather _____________________________________ because _________________________________________

Comparison statement:

________________________________________________. Describe the process you used to make each choice. ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ How could you compare the two fractions without models? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What connections did you make while working on this activity? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare Fractions | 149

Explore 4

Compare Fractions

Name: _______________________ Date: __________

Compare Fractions with Number Lines Look at your road signs. Compare the fractions by creating models using your fraction tiles and a number line showing each fraction. Find a common numerator or a common denominator between the two fractions to further prove which one is greater or less. Write two comparison statements using the symbols <, >, or = to compare the restaurants’ distances.

Where

go?

Road Sign 1 Draw the fraction tile model of each fraction.

Find a common denominator.

Draw the number line model for each fraction. 0

Write two comparison statements using symbols.

_______________________________ restaurant is closer.

Compare Fractions | 151

Compare Fractions

Explore 4 Road Sign 2 Draw the fraction tile model of each fraction.

Find a common denominator.

Draw the number line model for each fraction. 0

Write two comparison statements using symbols.

_______________________________ restaurant is farther. Road Sign 3 Draw the fraction tile model of each fraction.

Find a common denominator.

Draw the number line model for each fraction. 0

Write two comparison statements using symbols.

_______________________________ restaurant is closer. 152 | Compare Fractions

Compare Fractions

Explore 4 Road Sign 4 Draw the fraction tile model of each fraction.

Find a common denominator.

Draw the number line model for each fraction. 0

Write two comparison statements using symbols.

_______________________________ restaurant is farther. Road Sign 5 Draw the fraction tile model of each fraction.

Find a common denominator.

Draw the number line model for each fraction. 0

Write two comparison statements using symbols.

Compare Fractions | 153

Compare Fractions

Explore 4 Road Sign 6 Draw the fraction tile model of each fraction.

Find a common denominator.

Draw the number line model for each fraction. 0

Write two comparison statements using symbols.

_______________________________ restaurant is closer. Reﬂ ect What is the relationship between the fraction tiles and the number line? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Explain how you can compare two fractions when the numerators or denominators are not equal. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

154 | Compare Fractions

Explore 5

Compare Fractions

Name: _______________________ Date: __________

Compare Fractions Using Benchmarks Part I 1 Cecia is taking the 10-day, 2 -mile walking challenge. Use fraction circles to show whether she met her goal each day for the ﬁrst 5 days. Walk Day

Total Miles

Day 1

4 10

Day 2

1 3

Day 3

6 8

Day 4

4 8

Day 5

4 12

Model

Goal Met?

How can you know a fraction is more or less than half without using fraction circles? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare Fractions | 155

Compare Fractions

Explore 5

Part II For the second 5 days, Cecia wants to see how she does compared to her friend Jill. Compare Cecia’s miles to Jill’s miles, and explain how you determined which was greater.

Walk Day

Cecia’s Miles

Comparison (<, >, =)

Day 6

3 5

4 10

2 4

4 6

4 4

10 12

2 5

3 4

9 10

4 5

Jill’s Miles

Explain: Day 7 Explain: Day 8 Explain: Day 9 Explain: Day 10 Explain: 156 | Compare Fractions

Explore 5

Compare Fractions

Reﬂ ect How does knowing whether a fraction is greater than or less than a half help you compare fractions? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ For the day 10 comparison, how does knowing your unit fractions help you decide who walked farther that day? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Are benchmark fractions similar to another math concept used before? How? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Compare Fractions | 157

Equivalent Fractions

159

Explore 1

Equivalent Fractions

Name: _______________________ Date: __________

Model Equivalence with Area Models Part I Model the different ways your pie could be served by building the fractions below. Draw a model of each one, and use the chart to list how they are similar and how they are different. 1 1

2 2

Similarities

4 4

Differences

Equivalent Fractions | 161

Equivalent Fractions

Explore 1

Use fraction circles and fraction tiles to build the fraction of cookie cake the customer ordered, and draw it in the Model 1 column. Use the size of the pieces the Task Card says the cake has been cut into to build an equivalent fraction by laying them over the model of the order. Draw this in the Model 2 column. Record your work below. Save the Equation column for later. Order 1 Model 1

Model 2

Equation

2 3

Order 2 Model 1

Model 2

Equation

1 4

162 | Equivalent Fractions

Equivalent Fractions

Explore 1 Order 3 Model 1

Model 2

Equation

2 6 Order 4 Model 1

Model 2

Equation

3 4 What did you notice about the models you drew for each order? _____________________________________________________________________ _____________________________________________________________________ Explain how the equation represents the change from the ﬁrst model to the second model. _____________________________________________________________________ _____________________________________________________________________ Why does multiplying the numerator and the denominator by the same digit create an equivalent fraction? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Equivalent Fractions | 163

Equivalent Fractions

Explore 1

Part II Fold your paper in half. Trace the crease with a dark-colored marker. Shade in onehalf of your paper with a pencil to represent how much of the cake you will serve your guests. Draw the model of your cake below. Model

Fold your paper back in half the way it was, and then fold it in half again. Trace the new creases with your dark marker, and draw your cake model below. Fill in the missing pieces of the equation to represent how your new model changed. Second Cut Model

Equation

Fold your paper back the way it was, and then fold it in half again. Repeat the same process. Third Cut Model

164 | Equivalent Fractions

Equation

Equivalent Fractions

Explore 1

Fold your paper back the way it was, and then fold it in half again. Repeat the same process. Fourth Cut Model

Equation

Complete the table below by recording the equivalent fractions you found using your cake model. Numerator

Denominator

What patterns do you notice in the table above? _____________________________________________________________________ _____________________________________________________________________ Explain why all of the fractions in the table are equivalent. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Equivalent Fractions | 165

Explore 2

Equivalent Fractions

Name: _______________________ Date: __________

Model Equivalence on a Number Line Read each detail about the color run. Use the Number Line Work Mat and the Number Line Spacers to ﬁnd the location described. Find other ways the location could be described. Sketch your number line model in the ﬁrst box for each location. Record the equivalent fractions and an equation to prove they are equivalent in the second box for each location.

Bubble Machine: Located at

2 5

of a Mile

Other Ways to Describe the Location

Equivalent Fractions | 167

Equivalent Fractions

Explore 2

Pit of Paint: Located at

5 4

of a Mile

Other Ways to Describe the Location

Blue Blaster: Located at

3 2

of a Mile

Other Ways to Describe the Location

168 | Equivalent Fractions

Equivalent Fractions

Explore 2

Salty Snacks: Located at

4 12

of a Mile

Other Ways to Describe the Location

Reﬂ ect What connections did you make between this activity and what you have done before in class? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can we know if two fractions are equivalent on a number line? _____________________________________________________________________ _____________________________________________________________________ How did you know what equation you could use to show your fractions were equivalent? _____________________________________________________________________ _____________________________________________________________________

Equivalent Fractions | 169

Equivalent Fractions

Explore 3

Name: _______________________ Date: __________

Recognize and Generate Equivalent Fractions 1. For each animal, ﬁll in the scoop fraction. 2. Find three matches per animal. 3. Prove the matches are equivalent by sketching a visual model of your choice. 4. Write an equation proving the matches are equivalent.

Dogs

Scoop Fraction:

Equivalent scoop:

Model:

Equation:

Cats

Scoop Fraction:

Equivalent scoop:

Model:

Equation:

Equivalent Fractions | 171

Equivalent Fractions

Explore 3 Hamsters

Scoop Fraction:

Equivalent Scoop

Model

Birds

Scoop Fraction:

Equivalent Scoop

Model

172 | Equivalent Fractions

Equation

Equivalent Fractions

Explore 3 Bunnies

Scoop Fraction:

Equivalent scoop:

Model:

Equation:

Reﬂ ect What connections did you make during this activity? _____________________________________________________________________ _____________________________________________________________________ How did you know if two fractions were equivalent? _____________________________________________________________________ _____________________________________________________________________ What is the relationship between the model you drew and the equation you wrote? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Equivalent Fractions | 173

Equivalent Fractions

Explore 4

Name: _______________________ Date: __________

Equivalent Fractions with Denominators of 10 and 100

1. Record the weights of the items in each package. 2. Add all fractional parts together to ﬁnd the total weight of each package, using equivalent fractions as needed. 3. Decide how much postage you will need to send each package using the table below. Package Weight (lb.) Postage Cost

1 100

to 100

$0.47

51 100

to 1

1 100 to 1 100

1 100 to 2

$1.41

$1.88

$0.94

Package 1 Item weights:

Workspace:

Final package weight:

Cost of postage:

Equivalent Fractions | 175

Equivalent Fractions

Explore 4 Package 2 Item weights:

Workspace:

Final package weight:

Cost of postage:

Package 3 Item weights:

Workspace:

Final package weight:

Cost of postage:

176 | Equivalent Fractions

Equivalent Fractions

Explore 4 Package 4 Item weights:

Workspace:

Final package weight:

Cost of postage:

Reﬂ ect How did you combine fractional parts that were not the same-sized pieces? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Explain your process for adding the fractions after you found common denominators. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can equivalent fractions be helpful when adding fractional values? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Equivalent Fractions | 177

Compose and Decompose Fractions and Mixed Numbers

179

Explore 1

Compose and Decompose Fractions and Mixed Numbers

Name: _______________________ Date: __________

Compose and Decompose Unit Fractions At each station, assemble the pie pieces into as many whole pies as possible, and complete the table below. Serving Station 1: Cherry Pie Each cherry pie is sliced into 6 equal pieces. The bakery handed out 5 slices. Assemble the slices of pie that were given away, and draw the slices below.

What fractional part of the whole is each slice of pie?

Write an equation to represent how much pie was given away.

How much cherry pie was given away?

How many more slices do they need to hand out to make a whole pie?

Compose and Decompose Fractions and Mixed Numbers | 181

Compose and Decompose Fractions and Mixed Numbers

Explore 1

Serving Station 2: Pumpkin Pie Each pumpkin pie is sliced into 8 equal pieces. The bakery handed out 12 slices. Assemble the slices of pie that were given away, and draw the slices below.

What fractional part of the whole is each slice of pie?

Write an equation to represent how much pie was given away.

How many whole pumpkin pies were given away?

Write the total amount of pie given away as a mixed number.

Serving Station 3: Apple Pie Each apple pie is sliced into 5 equal pieces. The bakery handed out 13 slices. Assemble the slices of pie that were given away, and draw the slices below.

What fractional part of the whole is each slice of pie?

Write an equation to represent how much pie was given away.

How many whole apple pies were given away?

Write the total amount of pie given away as a mixed number.

182 | Compose and Decompose Fractions and Mixed Numbers

Explore 1

Compose and Decompose Fractions and Mixed Numbers

Serving Station 4: Chocolate Pie Each chocolate pie is sliced into 4 equal pieces. The bakery handed out 7 slices. Assemble the slices of pie that were given away, and draw the slices below.

What fractional part of the whole is each slice of pie?

Write an equation to represent how much pie was given away.

How many whole chocolate pies were given away?

Write the total amount of pie given away as a mixed number.

Reﬂ ect What can you determine from a fraction that has a numerator greater than the denominator? What is it called? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Explain why the equation you wrote represents the amount of pie that was given away. _____________________________________________________________________ _____________________________________________________________________ How could you develop a mixed number from an improper fraction with no model? _____________________________________________________________________ _____________________________________________________________________

Compose and Decompose Fractions and Mixed Numbers | 183

Explore 2

Compose and Decompose Fractions and Mixed Numbers

Name: _______________________ Date: __________

Compose and Decompose Fractions in Multiple Ways

Bag 1: Cookie Cakes Assemble each cookie cake. Draw a model of the cakes in the circles below. Label the names of the cakes on each line. Be sure to draw lines to show how many pieces each cake was cut into.

How many slices make up each cookie cake? _____________ Write a fraction that represents 1 slice of cookie cake. _______________ Seventeen slices of cookie cake were handed out at the grand opening. What fraction of cookie cake was handed out? _____________________ Count out 17 slices of cookie cake using any combination of the 3 flavors. Write an equation that represents the fractional amount of cookie cake for each flavor combined. Label each fraction by the flavor it represents.

Choose a new combination of 17 slices, and write another equation to represent the combination.

Describe how each combination is the same and how they are different. _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compose and Decompose Fractions and Mixed Numbers | 185

Explore 2

Compose and Decompose Fractions and Mixed Numbers

Bag 2: Mini-Cheesecakes Assemble each mini-cheesecake. Draw models of the cakes in the circles below. Label the name of the cheesecake on each line. Be sure to draw lines to show how many pieces each cake was cut into.

How many slices make up each cheesecake? _____________ Write a fraction that represents 1 slice of cheesecake. _______________ In the first hour, 3 slices were handed out. There were at least 2 flavors handed out. Create 2 combinations of flavors that could have been handed out in the first hour. Record an equation, and label what each fraction represents. Combination 1:

Combination 2:

By the end of the day, 10 slices had been handed out. At least 1 slice of each ﬂavor had been handed out. Create 2 combinations of ﬂavors that could have been handed out. Record an equation, and label what each fraction represents. Combination 1:

186 | Compose and Decompose Fractions and Mixed Numbers

Combination 2:

Add and Subtract Fractions and Mixed Numbers

187

Explore 1

Add and Subtract Fractions and Mixed Numbers

Name: _______________________ Date: __________

Join and Separate Parts of a Whole

Part I: Mixing Syrup

Draw a model of each recipe. Write a number sentence that represents your model. Marvelous Marshmallow model:

Total syrup:

Number sentence:

No Monkey Business model:

Total syrup:

Number sentence:

Punch-O model:

Total syrup:

Number sentence:

Add and Subtract Fractions and Mixed Numbers | 189

Explore 1 Summer Forever model:

Add and Subtract Fractions and Mixed Numbers

Total syrup:

Number sentence:

Not Birthday Cake model:

Total syrup:

Number sentence:

Ice-Ice Maybe model:

Total syrup:

Number sentence:

190 | Add and Subtract Fractions and Mixed Numbers

Explore 1 Summer Vampire model:

Add and Subtract Fractions and Mixed Numbers

Total syrup:

Number sentence:

Splash-It Good model:

Total syrup:

Number sentence:

Why did only some of the sums need to be rewritten as mixed numbers? _____________________________________________________________________ _____________________________________________________________________ How did the pattern blocks help you ﬁnd the sums? _____________________________________________________________________ _____________________________________________________________________ What do you notice about the denominators within a number sentence? Explain. _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Add and Subtract Fractions and Mixed Numbers | 191

Add and Subtract Fractions and Mixed Numbers

Explore 1 Part II: Syrup Inventory

Using the models from Part I, write number sentences to ﬁnd how much of each syrup is left. Use the table below to create your report to your manager.

Flavor

How Much Was Sold Today

Marvelous Marshmallow

2 6

cup

No Monkey Business

1 3

cup

Punch-O

4 6

cup

Summer Forever

1 2

cup

192 | Add and Subtract Fractions and Mixed Numbers

Equation

Amount Left

Add and Subtract Fractions and Mixed Numbers

Explore 1

Flavor

How Much Was Sold Today

Not Birthday Cake

1 23 cups

Ice-Ice Maybe

2 6

Equation

Amount Left

cup

Summer Vampire

1 12 cups

Splash-It Good

1 3

cup

How did you use the pattern blocks to subtract? _____________________________________________________________________ _____________________________________________________________________ How could you add or subtract fractions with no models? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Add and Subtract Fractions and Mixed Numbers | 193

Explore 2

Add and Subtract Fractions and Mixed Numbers

Name: _______________________ Date: __________

Add Fractions and Mixed Numbers with Like Denominators

Part I Read each Training Card, and use the fraction models, equivalent fractions, or equations to help you solve. Record your work in the correct spaces below. Megan Model:

Solve:

Solution statement: __________________________________________________ __________________________________________________________________

Calvin Model:

Solve:

Add and Subtract Fractions and Mixed Numbers | 195

Add and Subtract Fractions and Mixed Numbers

Explore 2

Part II Read each Racing Scenario Card, and use a strategy of your choice to solve. Record your work in the correct space below. Scenario 1 Solve:

Solution statement: __________________________________________________ __________________________________________________________________

Scenario 2 Solve:

Solution statement: __________________________________________________ __________________________________________________________________ 196 | Add and Subtract Fractions and Mixed Numbers

Add and Subtract Fractions and Mixed Numbers

Explore 2 Scenario 3 Solve:

Solution statement: __________________________________________________ __________________________________________________________________

Scenario 4 Solve:

Solution statement: __________________________________________________ __________________________________________________________________

Add and Subtract Fractions and Mixed Numbers | 197

Add and Subtract Fractions and Mixed Numbers

Explore 2 Scenario 5 Solve:

Solution statement: __________________________________________________ __________________________________________________________________

Scenario 6 Solve:

Solution statement: __________________________________________________ __________________________________________________________________ Reﬂ ect How could you solve each addition scenario without a model? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 198 | Add and Subtract Fractions and Mixed Numbers

Explore 3

Add and Subtract Fractions and Mixed Numbers

Name: _______________________ Date: __________

Subtract Fractions and Mixed Numbers with Like Denominators

Part I Use the provided fraction tiles or circles to help you solve for each hiking scenario. Water Model:

Solve:

Solution statement: __________________________________________________ __________________________________________________________________ Use a different strategy from the ﬁrst scenario in order to solve the next scenario. Trail Mix Model:

Solve:

Solution statement: __________________________________________________ __________________________________________________________________

Add and Subtract Fractions and Mixed Numbers | 199

Add and Subtract Fractions and Mixed Numbers

Explore 3

Part II Use fraction tile models, equivalent fractions, or the standard algorithm to help you solve each scenario. Record your work in the correct spaces below. Mt. Fangtooth Draw your model, and solve.

Solution statement: __________________________________________________ __________________________________________________________________ Mt. Bearclaw Draw your model, and solve.

Solution statement: __________________________________________________ __________________________________________________________________ 200 | Add and Subtract Fractions and Mixed Numbers

Add and Subtract Fractions and Mixed Numbers

Explore 3

Mt. Crooked Thumb Solve:

Solution statement: __________________________________________________ __________________________________________________________________ Mt. Camel’s Back Solve:

Solution statement: __________________________________________________ __________________________________________________________________ Mt. Lakeview Solve:

Add and Subtract Fractions and Mixed Numbers | 201

Add and Subtract Fractions and Mixed Numbers

Explore 3

Mt. Pumice Rock Solve:

Solution statement: __________________________________________________ __________________________________________________________________

Reﬂ ect How can you use a model to help you solve each scenario? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How could you solve similar problems without a model? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

202 | Add and Subtract Fractions and Mixed Numbers

Explore 4

Add and Subtract Fractions and Mixed Numbers

Name: _______________________ Date: __________

Solve Addition and Subtraction Fraction Problems

Create a diagram to model each problem. Use the diagram to create an equation, and then use a strategy of your choice to solve. Write a solution statement that answers the question from each Scenario Card.

Card 1 Diagram:

Equation and solution:

Solution statement: __________________________________________________ __________________________________________________________________

Card 2 Diagram:

Equation and solution:

Solution statement: __________________________________________________ __________________________________________________________________

Add and Subtract Fractions and Mixed Numbers | 203

Add and Subtract Fractions and Mixed Numbers

Explore 4 Card 3 Diagram:

Equation and solution:

Solution: ___________________________________________________________ __________________________________________________________________

Card 4 Diagram:

Equation and solution:

Solution: ___________________________________________________________ __________________________________________________________________ Reﬂ ect What connections did you make during this activity? _____________________________________________________________________ _____________________________________________________________________ How were your tape diagrams helpful? _____________________________________________________________________ _____________________________________________________________________ 204 | Add and Subtract Fractions and Mixed Numbers

Represent and Compare Decimals

205

Explore 1

Represent and Compare Decimals

Name: _______________________ Date: __________

Decimal Notation for Denominators of 10 Record how many sculptures you were able to build in each round by shading in the model and writing the value in fraction notation and decimal notation. Record how the value is read. 30-Second Round Shade in the model below to show how many sculptures you were able to build.

Fraction notation:

Decimal notation:

Word form:

If a ﬂat is one whole, which block could we use to show one-tenth? Explain. _____________________________________________________________________

Represent and Compare Decimals | 207

Represent and Compare Decimals

Explore 1 45-Second Round

Shade in the model below to show how many sculptures you were able to build.

Fraction notation:

Decimal notation:

Word form:

Describe the relationship between fraction notation and decimal notation. _____________________________________________________________________ _____________________________________________________________________

208 | Represent and Compare Decimals

Name: _______________________ Date: __________

Fraction Notation

Decimal Notation

Card Number

Length (meters)

Number Line

Represent and Compare Decimals | 209

For each Scenario Card, measure using a meterstick to the nearest hundredth. Write this measurement in fraction notation and decimal notation. Sketch the measurement on a number line.

Decimal Notation for Denominators of 100

Explore 2

Represent and Compare Decimals

Fraction Notation

210 | Represent and Compare Decimals

Card Number Decimal Notation

Length (meters)

Explore 2

Number Line

Represent and Compare Decimals

Fraction Notation

Decimal Notation

Number Line

Represent and Compare Decimals | 211

___________________________________________________________________________________________

What is the relationship between fractions and decimals?

___________________________________________________________________________________________

How could you show 100 as a decimal?

___________________________________________________________________________________________

What connections did you make during this activity?

Reﬂect

Card Number

Length (meters)

Explore 2

Represent and Compare Decimals

Explore 3

Name: _______________________ Date: __________

Represent and Compare Decimals Sketch a model of the features from both parks either with base ten block grids or on a number line. Use comparison symbols (<, >, =) to make two comparison statements. Write a justiﬁcation that compares each feature statistic of the two parks and explains how you know your statement is correct.

Distance from City Center Splashing Wild

Screaming Good Time

Model

Comparison Statement

Justiﬁcation

Represent and Compare Decimals | 213

Represent and Compare Decimals

Explore 3 Entrance Fee

Number Line

Comparison Statement Justiﬁcation

Average Ride Wait Time (Minutes) Splashing Wild

Screaming Good Time

Model

Comparison Statement

Justiﬁcation

214 | Represent and Compare Decimals

Represent and Compare Decimals

Explore 3

Average Ride Time (Minutes)

Number Line

Comparison Statement Justiﬁcation

Reﬂ ect Describe the process you could use to compare two decimals. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why can each comparison be shown using two statements? _____________________________________________________________________ _____________________________________________________________________ How can you prove your comparison is correct? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Which park would you choose to build? Explain. _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Compare Decimals | 215

Area and Perimeter

217

Area and Perimeter

Explore 1

Name: _______________________ Date: __________

Area and Perimeter Formulas

Part I: Framing Material

Use the table below to draw each frame and label the length and width. Write a number sentence, and record the amount of framing material needed for each piece of art. Painting

Drawing

Number Sentence

Total Framing Material

4 Record two formulas that could be used to ﬁnd the perimeter of any rectangle. Formula 1

Formula 2

Why do both of these formulas work to ﬁnd the perimeter of a rectangle? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Area and Perimeter | 219

Area and Perimeter

Explore 1 Part II: Backing Material

Use the table below to draw each frame and label the length and width. Write a number sentence, and record the amount of backing material needed for each piece of art. Painting

Drawing

Number Sentence

Total Backing Material

4 Record the formula that could be used to ﬁnd the area of any rectangle. Formula

Why does this formula work to ﬁnd the area? _____________________________________________________________________ _____________________________________________________________________

220 | Area and Perimeter

Area and Perimeter

Explore 2

Name: _______________________ Date: __________

Apply the Formulas Congratulations! You are on the design team to plan out the new zoo in your city! Your task is to create a blueprint of the zoo in the space below. You will need to use the following criteria: • Include at least ﬁve exhibits. One of them must be a square. You must include the hippos and zebras exhibits. • Label the length and width of each exhibit.

Area and Perimeter | 221

Area and Perimeter

Explore 2

Use the table below to plan the materials needed for each zoo exhibit. Be sure to write the equation you use to calculate the ground cover and fencing material.

Exhibit

Dimensions

Ground Cover (sq. ft. or sq. yd.) Formula: __________________

Fencing Material (ft. or yd.) Formula: __________________

Length: ____________ Width: ____________ Length: ____________ Width: ____________ Length: ____________ Width: ____________ Shape 1

Hippos

Length/width: ______ / ______ Shape 2 Length/width: ______ / ______ Shape 1

Zebras

Length/width: ______ / ______ Shape 2 Length/width: ______ / ______

222 | Area and Perimeter

Explore 2

Area and Perimeter

Refl ect When you found the amount of ground cover needed, were you finding the area or the perimeter of the space? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ When you found the amount of fencing material needed, were you finding the area or the perimeter of the space? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How did you find the area or the perimeter of the space? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Area and Perimeter | 223

Angles

225

Explore 1

Angles

Name: _______________________ Date: __________

Angles as Fractions of a Circle

Part I: The 360 Use the circle below to record the pieces of your paper plate. Record the measure of each angle in degrees.

Angles | 227

Angles

Explore 1 Part II: Dance Moves Draw and label your dance design. Dance Move Model Angle Name Degree Measure Fraction of a Circle Reﬂ ect Where do you see angles in everyday life?

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What jobs might you have in which you would need to use angle measurements? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

228 | Angles

Explore 2

Angles

Name: _______________________ Date: __________

Determine the Angle Measure Use your fraction circle wedges to create each play set using the given paper plates. Represent the model you created for each problem below. Then, write a division and multiplication equation to ﬁnd the solution for each angle measure. Write a solution statement that explains the angle measure for each model. Supreme-Pizza Play Set Division equation and solution: ____ ÷ ____ = ____

Multiplication equation and solution: ____ × ____ = ____

Solution statement: __________________________________________________ __________________________________________________________________

Angles | 229

Angles

Explore 2 Apple-Pie Play Set Division equation and solution: ____ ÷ ____ = ____

Multiplication equation and solution: ____ × ____ = ____

Solution statement: __________________________________________________ __________________________________________________________________ Birthday-Cake Play Set Division equation and solution: ____ ÷ ____ = ____

Multiplication equation and solution: ____ × ____ = ____

Solution statement: __________________________________________________ __________________________________________________________________

230 | Angles

Angles

Explore 2 Pepperoni-Pizza Play Set Division equation and solution: ____ ÷ ____ = ____

Multiplication equation and solution: ____ × ____ = ____

Solution statement: __________________________________________________ __________________________________________________________________ Reﬂ ect How can we use division or multiplication to determine the measure of an angle within a circle? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What do you notice about the measure of each angle when a circle is divided into equal pieces? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Angles | 231

Angles

Explore 3

Name: _______________________ Date: __________

Measure Angles Record the measurement and direction of each turn below in order to code the robot toy to follow the appropriate pathway.

Robot 1 Turn Name

Measurement

Direction

Robot 2 Turn Name

Measurement

Direction

Robot 3 Turn Name

Measurement

Direction

Angles | 233

Angles

Explore 3 Robot 4 Turn Name

Measurement

Direction

Reﬂ ect How can you measure an angle? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ When would it be helpful to know the measurement of an angle? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

234 | Angles

Points, Lines, and Angles

235

Explore 1

Points, Lines, and Angles

Name: _______________________ Date: __________

Investigate and Draw Points, Lines, Rays, and Angles Draw the constellations in the spaces provided. Label each of the points with a letter. Name two of each attribute listed below. If needed, continue any pieces of the constellation with dashed lines and arrows.

Libra

Attribute

Example 1

Example 2

Point Line Line segment Ray Angle

Points, Lines, and Angles | 237

Points, Lines, and Angles

Explore 1 Leo

Attribute

Example 1

Example 2

Point Line Line segment Ray Angle What makes a line segment different from a line? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 238 | Points, Lines, and Angles

Points, Lines, and Angles

Explore 1 Cancer

Attribute

Example 1

Example 2

Point Line Line segment Ray Angle What is the relationship between a ray and an angle? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Points, Lines, and Angles | 239

Points, Lines, and Angles

Explore 1 Aquarius

Attribute

Example 1

Example 2

Point Line Line segment Ray Angle Where in our classroom do you see examples of angles? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 240 | Points, Lines, and Angles

Explore 2

Points, Lines, and Angles

Name: _______________________ Date: __________

Investigate and Draw Types of Angles Parts I and II: Angler Theory and Angler Reality Record the information about each angle below. Angler

Angle Drawing

Measurement Estimate

Angle Type

Actual Measurement

Points, Lines, and Angles | 241

Points, Lines, and Angles

Explore 2

Part III: The Perfect Boat Your boat needs to have obtuse angles so that you can easily move around, but it also needs acute angles so it glides smoothly and quietly through the water. Measure the angles of each boat, and identify whether they are acute (A), right (R), or obtuse (O). Circle the boats that ﬁt the criteria. B B A

C A ABC = _________

D ABC = _______ DAB = ________

BCA = _________

BCD = _______

CAB = _________

CDA = _______ B

A D ABC = ________

C DEA = _______

BCD = ________

EAB = _______

CDA = ________

CDE = ________

ABC = ________

D DAB = _______

Describe how you can classify angles. _____________________________________________________________________ 242 | Points, Lines, and Angles

Explore 3

Points, Lines, and Angles

Name: _______________________ Date: __________

Investigate and Draw Types of Lines Part 1.a: Create Perpendicular Lines Use the tape to create a four-square court. Draw your model in the space below.

Name the two interior lines. _____________________________________________________________________ Use symbols to show their relationship. _____________________________________________________________________ What types of lines make a four-square court? _____________________________________________________________________ What kind of angles are made when these lines intersect? _____________________________________________________________________ What would happen to the spaces if the lines were not like this? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Points, Lines, and Angles | 243

Points, Lines, and Angles

Explore 3

Part 1.b: Create Parallel Lines Draw a model of your parallel tape lines in the ﬁrst box. In the next box, change one line to show that the model is no longer parallel.

Name the lines. _____________________________________________________________________ Use symbols to show the relationship between the parallel lines in the ﬁrst box. _____________________________________________________________________ What types of lines make the racetrack? _____________________________________________________________________ Does the distance between these types of lines matter? Explain. _____________________________________________________________________ _____________________________________________________________________ How are these lines different from the lines needed to create a four-square court? _____________________________________________________________________ _____________________________________________________________________ 244 | Points, Lines, and Angles

Points, Lines, and Angles

Explore 3

Part II: Lines Are All around Us Take a walk around your school or playground. Look for two examples of perpendicular lines, two examples of parallel lines, and two examples of lines that are neither of these. Draw and label your examples in the chart below.

Perpendicular Lines

Parallel Lines

Non-perpendicular or Nonparallel Lines

Points, Lines, and Angles | 245

Points, Lines, and Angles

Explore 3

Part III: A New Track Evaluate the design options for the new playground track by completing the report below. Place a check mark in the table for each criteria met by the track. The track must meet the following criteria: • Contain at least 1 set of perpendicular sides • Contain at least 2 sets of parallel sides • Contain no acute angles • Contain at least 1 line of symmetry 1 Set of Track Perpendicular Number Sides

2 Sets of Parallel Sides

No Acute Angles

Line of Symmetry

Meets All Criteria?

1 2 3 4 5 6

246 | Points, Lines, and Angles

Points, Lines, and Angles

Explore 3 Reﬂ ect

How did you know if the track contained parallel or perpendicular sides? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How did you know if the track contained any acute angles? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How did you know if the track contained at least 1 line of symmetry? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Points, Lines, and Angles | 247

Properties of TwoDimensional Figures

249

Properties of Two-Dimensional Figures

Explore 1

Name: _______________________ Date: __________

Classify Shapes by Lines and Angles An artist at a local museum creates colorful mosaics out of various shapes. At a recent art showing, one of the mosaics was accidentally broken. Using your knowledge of twodimensional shapes and their lines and angles, can you help the artist put the broken mosaic back together? Part I: Classifying Shapes Take all of your shapes out of the bag. Use the categories in the table below to help you classify the shapes. Draw the shapes that belong in each category in the table. Some shapes may belong to more than one category. Shapes with One or More Lines of Symmetry

Shapes with One or More Pairs of Congruent Sides or Angles

Shapes with Shapes One or More with One or Sets of More Sets Perpendicular of Parallel Lines Lines

Shapes with One or More Acute Angles

Shapes with One or More Obtuse Angles

Shapes with One or More Right Angles

Properties of Two-Dimensional Figures | 251

Properties of Two-Dimensional Figures

Explore 1

Part II: Mosaic Reassembly The artist needs help putting the broken mosaic back together. He cannot remember the exact shapes he used, but he does remember what some of the lines and angles looked like. Read the artist’s clues below. Find the shape that matches each clue, and create a mosaic. Once you have assembled it, draw and color a model of it in the space below. Artist’s Clues • There were seven shapes with right angles. • There were thirteen shapes with at least one line of symmetry. • There were nine shapes with at least one set of parallel lines. • There were three triangles with congruent angles. • There were two shapes with one acute angle and four obtuse angles. • There were fourteen shapes with at least one set of congruent sides.

Draw and color a model of your mosaic.

Reﬂ ect Is there only one way to reassemble the mosaic? Explain. _____________________________________________________________________ _____________________________________________________________________ How did knowing about properties of two-dimensional shapes help you reassemble the mosaic? _____________________________________________________________________ _____________________________________________________________________ 252 | Properties of Two-Dimensional Figures

Explore 2

Properties of Two-Dimensional Figures

Name: _______________________ Date: __________

Identify Types of Triangles Part I: Identifying Types of Triangles Use the craft sticks to model equilateral triangles. Sketch your triangles below. Equilateral Triangles Right

Acute

Obtuse

Which triangles cannot possibly exist? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What attributes do all equilateral triangles share? _____________________________________________________________________ _____________________________________________________________________ Deﬁne the following terms in your own words. Equilateral: ___________________________________________________________ Equiangular: __________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Properties of Two-Dimensional Figures | 253

Properties of Two-Dimensional Figures

Explore 2

Use the geoboards to model isosceles and scalene triangles. Sketch your triangles below. Right

Acute

Obtuse

Isosceles (At least two sides are the same length.)

Scalene (Each side is a different length.)

What is the difference between isosceles triangles and scalene triangles? _____________________________________________________________________ _____________________________________________________________________ How can you tell if a triangle is right, acute, or obtuse? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 254 | Properties of Two-Dimensional Figures

Properties of Two-Dimensional Figures

Explore 2

Part II: Choosing the Best Triangle Read the music teacher’s request for the type of triangular roof to be built for each pig’s house. Draw a picture of the triangle that best ﬁts the description. Identify each type of triangular roof. Roof Model Request

Drawing of Roof

Triangle Identiﬁcation

Pig 1’s House

I would like a triangular roof with two congruent sides and one right angle. Pig 2’s House

I would like a triangular roof with all acute angles and congruent sides. Pig 3’s House

Properties of Two-Dimensional Figures | 255

Measurement

257

Measurement

Explore 1

Name: _______________________ Date: __________

Length Part I: Find the Relationship Using your measurement tools, ﬁnd out how many smaller units equal the larger units in the tables below. As you complete each table, write a rule for each relationship.

Meters

Centimeters Model:

1 2

Number of meters ___ _______ = number of centimeters

Kilometers

Number of centimeters ___ _______ = number of meters

Meters

Model:

1 2 3

Number of kilometers ___ _______ = number of meters Number of meters ___ _______ = number of kilometers

Measurement | 259

Measurement

Explore 1 Part II: Who Will Win at Field Day? Read each Event Card. Show your work in the boxes below to convert units. Toy-Hoop Race What was team 1’s total distance?

What was team 2’s total distance?

Winning team:

How much farther did the winning hoop travel? ________________________________

________________________________

Flying-Disk Throw What was team 1’s total distance?

What was team 2’s total distance?

Winning team:

How much farther did the winning ﬂying disk travel? ________________________________

________________________________ 260 | Measurement

Measurement

Explore 1 Straw Bridge How many centimeters long was team 1’s bridge?

How many centimeters long was team 2’s bridge?

Winning team:

What was the combined length of the bridges in meters?

________________________________

Toilet-Paper Mummies What was team 1’s total distance?

What was team 2’s total distance?

Winning team:

How much longer was the winning team’s toilet paper distance?

________________________________

Measurement | 261

Measurement

Explore 1 Egg Race What was the combined distance for team 1?

What was the combined distance for team 2?

Winning team:

What was team 1’s and team 2’s combined distance in cm?

________________________________

Marble Wars What was team 1’s total combined marble ﬂicks?

What was team 2’s total combined marble ﬂicks?

Winning team:

How much longer was the winning team’s marble ﬂicks?

________________________________

262 | Measurement

Explore 1

Measurement

Reﬂ ect Explain how using a table is helpful when converting length. _____________________________________________________________________ _____________________________________________________________________ What could you do if you had to convert centimeters to kilometers? _____________________________________________________________________ _____________________________________________________________________ What process did you use to change, or convert, from one unit to another? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can you check your measurements? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Measurement | 263

Measurement

Explore 2

Name: _______________________ Date: __________

Mass

Part I: Find the Relationship Using your measurement tools, ﬁnd out how many smaller units equal the larger units in the table below. As you complete the table, write a rule for each relationship. Kilograms

Grams

Model:

1 2 3

Number of kilograms ___ _______ = number of grams Number of grams ___ ________ = number of kilograms

Reﬂ ect Look at each of your rules for the tables. What do you notice? _____________________________________________________________________ _____________________________________________________________________ Why do you think we are using multiplication and division? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Measurement | 265

Measurement

Explore 2

Part II: Farmers’ Market Read each Scenario Card. Show your work in the boxes below to convert units. Cherrylicious!

Orangelic!

_______ kilograms = ________ grams

Hatchy!

Let’s Salsa!

________ kilograms = ________ grams

_______ kilograms = ________ grams

Ring in the Onions!

Excilantric!

_______ grams = ________ kilograms

Reﬂ ect Explain how using a table is helpful when converting units of mass. _____________________________________________________________________ _____________________________________________________________________ Explain your process for converting an amount from one unit to another. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 266 | Measurement

Measurement

Explore 3

Name: _______________________ Date: __________

Liquid Volume Part I: Find the Relationship Using your measurement tools, ﬁnd out how many smaller units equal the larger units in the table below. As you complete the table, write a rule for each relationship. Liters

Milliliters

Model:

1 2 3

Number of liters ___ _______ = number of milliliters Number of milliliters ___ _______ = number of liters

Reﬂ ect What operation helps you convert a larger unit to a smaller unit? _____________________________________________________________________ What operation helps you convert a smaller unit to a larger unit? _____________________________________________________________________

Measurement | 267

Measurement

Explore 3

Part II: Smoothie Sam’s Read each Station Card. Show your work in the boxes below to convert units.

Delicious Choices

Family with the largest order:

Crazy Coconut

Best-selling smoothie:

__________

Berry Blaster

Ice-Cold Drinks

Day most Berry Blasters sold:

Day the most water was used:

__________

Strawberry Surprise

Pineapple Passion

Company with the better value: __________ 268 | Measurement

Measurement

Explore 4

Name: _______________________ Date: __________

Intervals of Time Part I: Find the Relationship Using your measurement tools, ﬁnd out how many smaller units equal the larger units in the tables below. Draw a number line or diagram to show your conversions. As you complete each table and model, write a rule for each relationship. Minutes

Seconds

Number line model:

1 2 Number of minutes ___ _____ = number of seconds 3

Hours

Number of seconds ___ _____ = number of minutes Minutes

Diagram model:

1 2 Number of hours ___ ______ = number of minutes 3

Number of minutes ___ ______ = number of hours

How are these two sets of conversions similar? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Measurement | 269

Measurement

Explore 4 Part II: Family Reunion Fun! Read each Game Card. Show your work in the boxes below to convert units. Ring Toss What was the boys’ total combined time?

What was the girls’ total combined time?

Winning team:

How much faster was the winning team?

________________________________

Video Game Madness What was the boys’ total combined time?

What was the girls’ total combined time?

Winning team:

How much less time would the losing team have needed to beat the winners?

________________________________ 270 | Measurement

Measurement

Explore 4 Human Tower What was the boys’ total combined time?

What was the girls’ total combined time?

Winning team:

How much faster was the winning team?

________________________________

Half-Marathon Run How long did it take the boys’ team to cross the ﬁnish line?

How long did it take the girls’ team to cross the ﬁnish line?

Winning team:

What was the winning team’s time in hours?

________________________________

Measurement | 271

Measurement

Explore 4 Tissue-Box Explosion What was the boys’ total combined time?

What was the girls’ total combined time?

Winning team:

How many seconds short of one minute was Pearl’s time?

________________________________

Tennis-Ball Toss What was the boys’ total combined time?

What was the girls’ total combined time?

Winning team:

What was the girls’ total time in hours?

________________________________

272 | Measurement

Measurement

Explore 4 Reﬂ ect How did your conversion tables help you ﬁnd out who won each competition?

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What similarities are there between converting time, length, mass, and liquid volume? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Measurement | 273

Measurement

Explore 5

Name: _______________________ Date: __________

Elapsed Time Look at several ﬂight schedules. Some of the schedules have times that are missing. Travel to each station, and use your ﬂight schedule to answer the questions on your Station Cards. Solve each problem by using an open number line. There are two problems on each Station Card. Flight I A)

The ﬂight leaves at __________ B)

The family needs to leave their house at __________ What information helped you solve question A? _____________________________________________________________________ _____________________________________________________________________ Describe how you found the time the family needed to leave their house. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Measurement | 275

Explore 5

Measurement

Flight II A)

The ﬂight from Sacramento to Phoenix lasts _____ hour(s) and _____ minutes. B)

Keegan can watch _____ full shows. Flight III A)

The ﬂight to Dallas will land at _________ B)

The Schumanns will arrive home at _________ 276 | Measurement

Explore 5

Measurement

Flight IV A)

What time will Aroosh arrive at the airport? _______ Will he make his ﬂight? _______ B)

The ﬂight lasts _______ hours and _______ minutes. Flight V A)

The ﬂight departs at _______ B)

Ricardo arrived at the airport at _______ How was the number line helpful? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Measurement | 277

Represent Measurement with Line Plots

279

Explore 1

Represent Measurement with Line Plots

Name: _______________________ Date: __________

Create Line Plots to Display Data Part I: Arm Length Measure the length of your arm, from your shoulder to the tip of your longest ﬁnger, to the nearest 18 of an inch. Record the arm length of each group member in the group’s Data Display Chart as well as in the table below. Rotate to each table, and record each student’s measurement in the appropriate column. Group 1

Group 2

Group 3

Group 4

Group 5

Represent Measurement with Line Plots | 281

Explore 1

Represent Measurement with Line Plots

Use the masking tape, two-colored counters, and a dry-erase marker to create a line plot for your data on your table. Then, draw a model of your line plot in the box to the right. Be sure to give your line plot a title, and label the line. What do you know about the measurement(s) on your line plot with the most dots? ___________________________________ ___________________________________

What do you know about the measurement(s) with the fewest dots? ___________________________________ ___________________________________

Arm Length

___________________________________

___________________________________ How many students participated in this data collection? How can you use your line plot to ﬁnd your answer? ___________________________________ ___________________________________ ___________________________________ ___________________________________ What is the difference between the longest arm length and the shortest arm length?

282 | Represent Measurement with Line Plots

Represent Measurement with Line Plots

Explore 1 Part II: Hand Length

Measure the length of your hand, from your wrist to the tip of your longest ﬁnger, to the nearest 18 of an inch. Record the hand length of each group member in the group’s Data Display Chart as well as in the table below. Rotate to each table, and record each student’s measurement in the appropriate column. Group 1

Group 2

Group 3

Group 4

Group 5

Represent Measurement with Line Plots | 283

Explore 1

Represent Measurement with Line Plots

What do you know about the measurement(s) with the fewest dots? ___________________________________ ___________________________________

Hand Length

___________________________________

284 | Represent Measurement with Line Plots

Represent Measurement with Line Plots

Explore 2

Name: _______________________ Date: __________

Problem Solve Using Line Plots Use the space below to show your work for each Station Card.

Client A – Insect Lengths How long was the longest insect? ____________ How long was the shortest insect? _____________ What is the difference in length between the longest insect and the shortest insect? _____________ How many insects were measured in this study? ____________

Client B – High Temperatures in July What was the lowest temperature recorded? ____________ What was the highest temperature recorded? _____________ How many days had a temperature of 33°C or higher? _____________ What is the difference in temperature between the highest temperature and the lowest temperature? ____________

Client C – Crayon Lengths How many crayons were between 1 12 and 3 inches long? ____________ What was the length of the crayon that was less than 1 inch? _____________ What is the difference in length between the longest crayon and the shortest crayon? ____________ If you laid all of the crayons end to end, how long would the line of crayons be? ______________ © Accelerate Learning Inc. – All Rights Reserved

Represent Measurement with Line Plots | 285

Represent Measurement with Line Plots

Explore 2

Client D – Lengths of Seashells How long was the longest seashell? ____________ How long was the shortest seashell? _____________ What is the difference in length between the longest seashell and the shortest seashell? ___________ List the lengths of seashells that were between 4 and 5 cm. _________________

Client E – Distances of Baseball Throws How many baseball throws were measured? ____________ What distance was the most common? _____________ What is the difference between the longest distance and the shortest distance? ___________ To qualify for a medal in the baseball throw, students needed to throw farther than 64 feet. How many students qualiﬁed? ______________ Reﬂ ect What connections did you make during this activity? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What are some other ways you have seen data displayed? _____________________________________________________________________ _____________________________________________________________________ Why is it important to analyze data? _____________________________________________________________________ _____________________________________________________________________ 286 | Represent Measurement with Line Plots

Skills Quizzes

287

Skills Quiz

Place Value of Whole Numbers

Name: _______________________ Date: __________

Place Value of Whole Numbers For questions 1–3, write each number in expanded form. 1.

501,674 ________________________________________________________________

Ninety-eight thousand, one hundred twenty-three ________________________________________________________________

Seven hundred thirty-six thousand, one ________________________________________________________________

For questions 4–6, write each number in standard form. 4.

(4 × 100,000) + (2 × 10,000) + (8 × 1,000) + (3 × 100) + (1 × 10) + (9 × 1) ________________________________________________________________

Six hundred four thousand, eight hundred ﬁve ________________________________________________________________

80,000 + 7,000 + 400 + 10 + 7 ________________________________________________________________

Place Value of Whole Numbers | 289

Skills Quiz

Place Value of Whole Numbers

For questions 7–9, write each number in word form. 7.

490,212 ________________________________________________________________

700,000 + 50,000 + 40 + 9 ________________________________________________________________

(3 × 10,000) + (4 × 1,000) + (2 × 100) + (4 × 10) ________________________________________________________________

For questions 10–12, ﬁll in the blanks. 10.

70 is _______________ of 700.

11.

54 tens is the same as _________________________________________.

12.

The 4 in 524,365 is ___________________ the 4 in 525,465.

290 | Place Value of Whole Numbers

Compare and Order Numbers

Skills Quiz

Name: _______________________ Date: __________

Compare and Order Numbers For questions 1–5, plot both numbers on the number line, and then write >, <, or = on the line to make a true statement. 1.

4,847 _______ 3,908

1,000

2,000

50,000

100,000

500,000

1,000,000

27,298 _______ 27,299

27,000

5,000

827,463 _______ 827,463

4,000

9,432 _______ 98,432

3,000

27,100

27,200

27,300

27,400

214,376 _______ 174,120

100,000

200,000

300,000

Compare and Order Numbers | 291

Compare and Order Numbers

Skills Quiz

Order each set of numbers below from greatest to least. Use symbols to show the comparison. 6.

34,083

310,279

98,371

102,385

3,083

______________________________________________________________ 7.

540,139

987,452

640,389

54,212

4,108

______________________________________________________________ Order each set of numbers below from least to greatest. Use symbols to show the comparison. 8.

39,018

9,237

139,212

43,643

813,937

______________________________________________________________ 9.

870,964

87,900

870,954

8,209

400,819

______________________________________________________________

10.

Tyron got ﬁve cards with numbers on them. He put them in order from greatest to least and wrote them below. Was he correct? Why or why not? 201,367

321,364

50,245

49,843

6,999

______________________________________________________________ ______________________________________________________________

292 | Compare and Order Numbers

Skills Quiz

Rounding

Name: _______________________ Date: __________

Rounding Round each number to the place value indicated. 1.

Round 174,246 to the nearest ten thousand.

Round 559,441 to the nearest hundred thousand.

Round 67,133 to the nearest ten thousand.

Round 923,219 to the nearest hundred thousand.

Round 346,713 to the nearest ten thousand.

Round 6,172 to the nearest thousand.

Round 55,555 to the nearest thousand.

Round 86,367 to the nearest ten thousand.

Round 369,471 to the nearest hundred thousand.

10.

Round 2,934 to the nearest thousand.

Rounding | 293

Addition and Subtraction Algorithms

Skills Quiz

Name: _______________________ Date: __________

Addition and Subtraction Algorithms Solve each problem. 1.

6,037 + 4,510 _______

6,199 + 4,832 = _______

41,712 + 24,375 =

24,156 + 10,631 =

3,006 + 2,872 _______

8,512 + 4,284 _______

4,622 + 1,307 = _______

Addition and Subtraction Algorithms | 295

Addition and Subtraction Algorithms

Skills Quiz Solve each problem. 8.

1,041 – 1,040 _______

11.

40,002 – 2,930 = _______

13.

18,959 – 10,788 =

14.

92,677 – 92,328 =

15.

52,673 – 23,601 =

296 | Addition and Subtraction Algorithms

10.

4,453 – 3,102 _______

12.

5,988 – 3,952 _______

10,006 – 4,662 = _______

Skills Quiz

Prime and Composite Numbers

Name: _______________________ Date: __________

Prime and Composite Numbers List factor pairs for each whole number below. 1.

Determine if the whole number listed is a multiple of the one-digit number. Circle your answer. 6.

Is 60 a multiple of 5?

Yes No

Is 34 a multiple of 4?

Yes No

Is 72 a multiple of 7?

Yes No

Is 64 a multiple of 8?

Yes No

10.

Is 25 a multiple of 6?

Yes No

Prime and Composite Numbers | 297

Prime and Composite Numbers

Skills Quiz

Determine if each number below is prime or composite. Circle your answer. 11.

Prime

Composite

12.

Prime

Composite

13.

Prime

Composite

14.

Prime

Composite

15.

Prime

Composite

298 | Prime and Composite Numbers

Multiplicative Comparisons

Skills Quiz

Name: _______________________ Date: __________

Multiplicative Comparisons Fill in the blanks, and write the matching equation with n as the unknown. 1.

6 times as much as 3 is ___.

Equation: ______________ 3.

8 times as much as 3 is ___. Equation: ______________

2 times as much as 7 is ___. Equation: ______________

7 times as much as 6 is ___. Equation: ______________

Use the information below to help answer questions 5–8. Janis checked out 6 books from the library. Amie checked out 3 more books than Janis. How many books did Amie check out? 5.

Model the problem.

Write the equation. _________________________

Write a solution statement. ________________________________________________________________

Is this situation an additive or multiplicative comparison? (Circle one.) Additive

Multiplicative

Multiplicative Comparisons | 299

Multiplicative Comparisons

Skills Quiz Use the information below to answer questions 9 and 10.

A video game costs $64. It costs 8 times as much as a video game controller. How much does the video game controller cost? $64 Video Game ?

Use the two numbers and the variable in the box to write an equation that matches the model. Then, solve for the variable. 64 9.

Equation: __________________

8 10.

d d = _____________

Use the information below to answer questions 11 and 12. Rosie had 6 erasers. Siddharth had 7 times as many erasers as Rosie. How many erasers did Siddharth have? Make a model to match the equation. Then, solve for the variable. 6×7=e 11.

Model:

12.

e = ______________

300 | Multiplicative Comparisons

Skills Quiz

Multiplication Models and Strategies

Name: _______________________ Date: __________

Multiplication Models and Strategies Solve the equations below by using the area models. 1.

34 × 12 = ______

56 × 25 = ______

23 × 42 = ______

48 × 16 = ______

Multiplication Models and Strategies | 301

Multiplication Models and Strategies

Skills Quiz

Solve the equations below by using models or partial products. 5.

324 × 5 = ______

1,465 × 6 = ______

137 × 2 = ______

2,078 × 3 = ______

22 × 14 = ______

10.

1,010 × 5 = ______

302 | Multiplication Models and Strategies

Skills Quiz

Division Models and Strategies

Name: _______________________ Date: __________

Division Models and Strategies Solve the equations below by using the area models provided. 1.

398 ÷ 2 = ______

1,050 ÷ 5 = ______

567 ÷ 9 = ______

8,888 ÷ 4 = ______

921 ÷ 3 = ______

5,128 ÷ 8 = ______

Division Models and Strategies | 303

Division Models and Strategies

Skills Quiz Use partial quotients to solve the equations below. 7.

324 ÷ 3 = ______

2,546 ÷ 2 = ______

540 ÷ 5 = ______

10.

4,104 ÷ 9 = ______

11.

224 ÷ 4 = ______

12.

6,312 ÷ 8 = ______

Use an area model or partial quotients to solve the equations below. 13.

336 ÷ 6 = ______

304 | Division Models and Strategies

14.

6,048 ÷ 7 = ______

Generate Patterns

Skills Quiz

Name: _______________________ Date: __________

Generate Patterns Apply the given rule to continue the pattern and ﬁnd the sixth term. Rule 1.

Pattern

Sixth Term

The ﬁrst number in the pattern is 5. The pattern rule is to add 4.

5, __, __, __, __, ?

The ﬁrst shape in the pattern is a triangle. The pattern rule is to add a side to each shape.

The ﬁrst number in the pattern is 2. The pattern rule is to multiply each number by 2.

2, 4, __, __, __, ?

Start with 1 star. Add 3 dots around the star for each term.

Start with the number 3, and add 6 each time.

Start with the number 7. Add 7 more to each number in the pattern.

, __, __, __, ?

3, __, __, __, __, ?

7, __, __, __, __, ?

Generate Patterns | 305

Generate Patterns

Skills Quiz Use the pattern below to answer questions 7 and 8. 7.

Draw the next ﬁgure in the pattern.

Determine whether the following statement is true or false: each ﬁgure has twice as many parts as the ﬁgure before it in the pattern. ________________________

Find the relationship between the position and the value. Use the tables to answer questions 9 and 10. Position

Value

What is the value of position 5? ________________________________________ Position

10.

Numerical Expression

Value

What is the value of position 6? ________________________________________

306 | Generate Patterns

Skills Quiz

Problem Solve Using the Four Operations

Name: _______________________ Date: __________

Problem Solve Using the Four Operations Solve the problems below. 1.

Bianca is buying bookshelves for her books. She has 115 books that she needs to shelve. If each bookshelf has 4 shelves and each shelf can hold 12 books, how many bookshelves will Bianca need to buy to shelve all of her books?

Equation with unknown variable:

Workspace:

Solution:

A stadium was sold out for four nights in a row for a concert series. The stadium can hold 1,805 people. About how many people attended the concerts over the four days?

Equation with unknown variable:

Workspace:

Solution:

Problem Solve Using the Four Operations | 307

Problem Solve Using the Four Operations

Skills Quiz 3.

Mrs. Warner’s sewing class is making T-shirt blankets. The class has 304 shirts, and each blanket uses 9 shirts. How many shirts will be left over after all of the blankets are made?

Equation with unknown variable:

Workspace:

Solution:

Robert and his ﬁve friends are going to evenly split 100 toy race cars. If each boy gets the same number of cars, how many cars will each boy get?

Equation with unknown variable:

308 | Problem Solve Using the Four Operations

Workspace:

Solution:

Problem Solve Using the Four Operations

Skills Quiz 5.

The Spencer family went on a road trip to visit their grandparents. It took 4 days to travel to their grandma’s house. They drove 354 miles on day 1, 213 miles on day 2, 334 miles on day 3, and 150 miles on day 4. About how many more miles did they drive on days 1 and 2 than on days 3 and 4?

Equation with unknown variable:

Workspace:

Solution:

Jo and her friends were doing a cup-stacking challenge. They used 148 cups in all. Jo stacked 23 cups, one of her friends stacked 55 cups, and her other friend stacked the rest of the cups. How many cups did the third friend stack for the cup-stacking challenge?

Equation with unknown variable:

Workspace:

Solution:

Problem Solve Using the Four Operations | 309

Compare Fractions

Skills Quiz

Name: _______________________ Date: __________

Compare Fractions Write the appropriate comparison symbol (<, >, or =) and the correct fractions for each set of models below. 1.

Write the appropriate comparison symbol (<, >, or =) for each fraction below. You may draw fraction models to help you answer. 5 6

2 6

1 4

1 2

Tony ﬁnished 38 of his homework. Matilda ﬁnished 36 of her homework. Who completed more of their homework?

Chocolate chip cookies use 8 of a cup of sugar. Oatmeal raisin cookies use 6 of a cup of sugar. Which kind of cookie uses less sugar?

Sara ate

2 3

of a pizza. Kendra ate 1 of a pizza. Who ate less pizza?

Compare Fractions | 311

Compare Fractions

Skills Quiz

Use <, >, or = to solve each problem. Show your work on the number lines by using labels. 8.

3 5

6 10

4 12

4 8

3 4

10.

8 10

Determine if the fraction shown is more than, less than, or equal to half. Label and use the number lines to justify your answer.

11.

9 12

12.

2 8

312 | Compare Fractions

Equivalent Fractions

Skills Quiz

Name: _______________________ Date: __________

Equivalent Fractions Shade the first figure to represent the fraction. Partition the second figure. Use the identity property of multiplication to help you. Then, shade the second figure to help you write an equivalent fraction for each question. 1.

2. 3 4

2 2

1 3

4 4

2 5

2 2

3 4

3 3

Equivalent Fractions | 313

Equivalent Fractions

Skills Quiz

Use the shaded models and the identity property of multiplication to determine the fraction needed to make the two fractions equivalent. 5.

5 6

10 12

1 5

3 15

1 8

3 24

3 4

12 16

1 2

4 8

10.

3 5

9 15

Fill in the missing numerator to make the two fractions equivalent. 11.

7 = 10 100

13. 90 = 100 10

314 | Equivalent Fractions

12.

2 = 10 100

14. 40 = 100 10

Equivalent Fractions

Skills Quiz

Write the fraction for each visual equation below, and then add the fractions.

15.

16.

17.

Equivalent Fractions | 315

Skills Quiz

Compose and Decompose Fractions and Mixed Numbers

Name: _______________________ Date: __________

Compose and Decompose Fractions and Mixed Numbers Decompose the given fraction into the sum of its unit fractions. 1.

3 5

= ___________________________________________

7 4

= ___________________________________________

8 8

= ___________________________________________

4 12 = ___________________________________________

5. 1 26 = ___________________________________________

Compose and Decompose Fractions and Mixed Numbers | 317

Compose and Decompose Fractions and Mixed Numbers

Skills Quiz

Fill in the fraction or mixed number that makes the equation true.

2 5

+ ___ =

5 5

___ + 9 = 9

5 7 11 + 11

= _____

9. + ____ =

10.

3 6 4 12 + 12 = _____ + 12

318 | Compose and Decompose Fractions and Mixed Numbers

Skills Quiz

Compose and Decompose Fractions and Mixed Numbers

Write two different addition equations to decompose each fraction.

11.

7 10 = _______________________

12.

9 9

= _______________________

9 9

= _______________________

13.

6 6

= _______________________

6 6

= _______________________

14. = _________________

= _________________

15.

= ______________________

Compose and Decompose Fractions and Mixed Numbers | 319

Skills Quiz

Add and Subtract Fractions and Mixed Numbers

Name: _______________________ Date: __________

Add and Subtract Fractions and Mixed Numbers 1.

Which answer choice below does not equal 2 ? 10

A. B. C. D. 2.

Which answer choice below does not equal 7 ? 8

A. B. C. D. 3.

10 8 10 – 10 = 1 1 10 + 10 = 5 3 10 – 10 = 2 1 10 + 10 =

1 8 8 8 3 8 8 8

+ – + –

6 8 1 8 4 8 5 8

= = = =

Which answer choice below does not equal 11 ? 12

A. B. C. D.

3 8 12 + 12 1 10 12 + 12 6 6 12 + 12 6 5 12 + 12

= = = =

Add and Subtract Fractions and Mixed Numbers | 321

Add and Subtract Fractions and Mixed Numbers

Skills Quiz 4.

Write an addition sentence to represent each of the following fractions. __________________________________________________ =

4 5

__________________________________________________ =

3 6

__________________________________________________ =

9 10

Write a subtraction sentence to represent each of the following fractions. __________________________________________________ =

1 3

__________________________________________________ =

4 12

__________________________________________________ =

5 8

Replace each mixed number with an equivalent fraction. 9

4 4 = ____

3 6 = ____

5 10 = ____ 9 5 = ____

Answer each mixed-number addition sentence below. 4

2 5

10.

3 4 +4 4 =

12.

2 3 +3 3 =

5 10 + 3 10 =

1 5 +1 5 =

11.

5 10 + 10 =

322 | Add and Subtract Fractions and Mixed Numbers

+9 5 = 3

Represent and Compare Decimals

Skills Quiz

Name: _______________________ Date: __________

Represent and Compare Decimals Use the number lines below to answer the questions. 1.

Which letter best represents the location of 0.7?

1 A B

Which letter best represents the location of 0.27?

1 A

Convert each decimal to a fraction. 3.

0.1 = ____

0.42 = ____

0.05 = ____

0.85 = ____

0.06 = ____

0.2 = ____

Represent and Compare Decimals | 323

Represent and Compare Decimals

Skills Quiz Convert each fraction to a decimal.

91 = ____ 100

10.

9 10

= ____

11.

1 100

= ____

Use <, >, or = to compare the numbers.

12.

2.5 ____ 2.1

13.

7.03 ____ 7.3

Draw models to compare the decimals, and write comparison sentences. 14.

2.5 and 2.1

___________________________

324 | Represent and Compare Decimals

15.

7.03 and 7.3

___________________________

Area and Perimeter

Skills Quiz

Name: _______________________ Date: __________

Area and Perimeter Find the perimeter and area of each shape.

____ + ____ + ____ + ____ = ________

_____ rows _____ units in each row ______ × ______ = ______

Area: _______________

____ + ____ + ____ + ____ = ________

_____ rows _____ units in each row ______ × ______ = ______

Area and Perimeter | 325

Area and Perimeter

Skills Quiz 5 units 5 units 10 units

10 units 5 units 15 units

Perimeter: ______________

Area: _________________

9 inches 13 inches

Perimeter: ______________

326 | Area and Perimeter

Area: _________________

Area and Perimeter

Skills Quiz 2 feet 5 feet 3 feet 4 feet

Perimeter: ______________

10.

Area: _________________

7 cm

This is a square.

11.

Perimeter: ______________

12.

Area: _________________

Area and Perimeter | 327

Angles

Skills Quiz

Name: _______________________ Date: __________

Angles 1.

Use a protractor to ﬁnd the measure of PRQ.

PRQ: __________

Use a protractor to ﬁnd the measure of LOM.

LOM: __________

Angles | 329

Angles

Skills Quiz

Use each equation below to model and determine each angle measure within a circle.

Equation

Model with a Circle

Angle Measure

3. 360° ÷ 8 = a

4. 2 × a = 360°

5. 3 × a = 360°

6. 360° ÷ 9 = a

7. 360° ÷ 4 = a

330 | Angles

Angles

Skills Quiz The measure of a circle is 360°.

Angle ABC is a straight angle. What is the measure, in degrees, of angle ABC?_______

Angle ABD is a right angle. What is the measure, in degrees, of angle ABD?_______

For questions 10 and 11, tell what fractional part of the circle is shaded. What is the measure of the angle in degrees? 10.

11.

Fraction: ______

Degrees: ______°

Angles | 331

Skills Quiz

Points, Lines, and Angles

Name: _______________________ Date: __________

Points, Lines, and Angles Draw an angle to match the given measurement. Label the angle as either right, acute, or obtuse. 1.

45°

____________________

120°

____________________

24°

____________________

90°

____________________

165°

____________________

Points, Lines, and Angles | 333

Skills Quiz

Points, Lines, and Angles

Draw an example of each of the following items. 6.

Parallel lines

Line segment

Ray

Perpendicular lines

10.

Line

334 | Points, Lines, and Angles

Points, Lines, and Angles

Skills Quiz Write your answer to each question. 11.

What type of angles are present in the quadrilaterals below? _____________

12.

How many of each type of angle are in the ﬁgure below? Acute angles: __________ Obtuse angles: _________ Right angles: ___________

13.

What types of angles are present in the trapezoid below? ______ and ________

14.

Draw any lines of symmetry on the pentagon below. How many lines of symmetry does the pentagon have? _________________

Points, Lines, and Angles | 335

Properties of Two-Dimensional Figures

Skills Quiz

Name: _______________________ Date: __________

Properties of Two-Dimensional Figures 1.

Sort the shapes below into the appropriate categories. You may not use all of the shapes.

2 or More Sets of Parallel Sides

No Sets of Parallel Lines

List one shape from above that did not ﬁt into one of the categories. List one attribute of the shape. Shape

Attribute

Write the number of lines of symmetry for each shape below.

______

______ Properties of Two-Dimensional Figures | 337

Properties of Two-Dimensional Figures

Skills Quiz 4.

Classify this shape by checking the boxes of the properties it has.

Lines of symmetry

Parallel lines

Perpendicular lines

Acute angles

Obtuse angles

Right angles

Look at the shape below. What makes it an obtuse scalene triangle?

_____________________________________________________________________ _____________________________________________________________________

Draw a shape that has two lines of symmetry, two different pairs of congruent sides, and four pairs of perpendicular lines in the box below.

338 | Properties of Two-Dimensional Figures

Measurement

Skills Quiz

Name: _______________________ Date: __________

Measurement Use your mathematics measurement chart to help you answer the questions below. 1.

120 seconds = __________ min.

2 km = __________ m

16,000 mL = __________ L

35 m = __________ cm

4 kg = __________ g

5 min. = __________ seconds

4,000 cm = __________ m

3 hr. = __________ min.

Measurement | 339

Skills Quiz

Measurement

Jaime completed her chores. She spent 45 minutes doing laundry, 22 minutes walking the dog, and 17 minutes emptying the dishwasher. How much time did Jaime spend doing chores?

10.

The Garcias packed 4 suitcases for their trip. Each suitcase weighed 15,000 grams. The airline weight limit for the family’s luggage was 70 kilograms. Did the family meet the weight limit for their luggage?

11.

Lain got up for school in the morning and spent 10 minutes in the shower, 23 minutes eating breakfast, and 5 minutes packing his backpack. He left for school at 7:45 a.m. What time did Lain get up?

12.

Vivian takes her dog for a walk to her mailbox every day. Vivian’s mailbox is 1,500 meters from her house. How many kilometers do Vivian and her dog walk in a week?

340 | Measurement

Represent Measurement with Line Plots

Skills Quiz

Name: _______________________ Date: __________

Represent Measurement with Line Plots 1.

Create a line plot for the given data. Pansy asked each kid in her class their shoe size. The results are in the table below. Create a line plot to represent this data. Shoe Size Frequency

3 12

4 12

5 12

6 12

Title: _____________________________

Create and label the line plot by using the set of numbers provided. 4 4

2 4

4 4

3 1

2 1

3 2

2 1

4 3 1

Represent Measurement with Line Plots | 341

Represent Measurement with Line Plots

Skills Quiz 3.

Create and label the line plot by using the set of numbers provided. 7

1 2

7 6

7 1 2

1 2

6 2

7 12

Create and label the line plot by using the set of numbers provided. 2

2 4

3 4

3 14

2 24

3 14

342 | Represent Measurement with Line Plots

Represent Measurement with Line Plots

Skills Quiz Use the line plots to answer each question.

The line plot shows the distance, in miles, that children live from the pool.

What is the difference in distance between the children who live the closest to and the farthest from the pool?

The line plot shows the height, in inches, of different plants.

What is the difference in height between the shortest plant and tallest plant?

Represent Measurement with Line Plots | 343

Represent Measurement with Line Plots

Skills Quiz Use the line plots to answer each question.

The line plot shows the amount of water, in ounces, in students’ water bottles.

What is the difference between the most amount of water and the least amount of water?

The line plot shows the distance, in miles, that students ran in PE over a month.

What is the difference in distance between the shortest and farthest distance that students ran?

344 | Represent Measurement with Line Plots

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.

345

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

346

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

347

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 348

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

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

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

component: a part or element of a larger whole

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

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

compose: to put pieces together

349

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

350

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 351

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 352

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

353

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 354

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

355

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

356

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

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

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

357

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 358

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

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

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

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

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

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

ledger: a record of all income and expenses

justify: to explain your thinking

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

lend: to give money or goods and expect it to be returned 359

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 361

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) 362

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

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

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

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

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

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

numeral: a symbol used to show an amount or quantity

note: to notice and observe carefully

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

numerator: the top number in a fraction; represents part of a whole 363

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 364

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 366

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

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

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

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

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GLOSSARY OF TERMS quarter ‘til quarter ‘til: a time that ends in 45, that shows 15 minutes until the hour; 3:45 or a quarter ‘til 4:00 quarter after: a time that ends in 15, that shows 15 minutes after the hour; 4:15 or a quarter after 4:00 quarter of an hour: 15 minutes; one-fourth of an hour (60 minutes) quarter past: a time that ends in 15, that shows 15 minutes past the hour; 4:15 or a quarter past 4:00 quarter to: a time that ends in 45 and that shows 15 minutes to the hour; 3:45 or a quarter to 4:00 quarter-circle: one-fourth of a circle question: a sentence that requires an answer gained through knowledge, research, calculation, and/or reasoning quotient: the answer to a division problem range: (1) A set of values; (2) the difference between the values of least and greatest numbers in a data set 368

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

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

repeated subtraction

record: to write

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

rectangle: a polygon with exactly 4 sides and 4 vertices

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

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

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

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

relative position (location): a point established with reference to another position that is either moving or fixed relative size: how big or small something is in comparison to another object remainder: the amount that is left over after dividing repeated addition: a pattern of adding the same amount over and over; can be shown with a multiplication sentence repeated subtraction: a pattern of subtracting the same amount over and over; can be used to solve some types of division problems 369

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. 370

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 372

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 373

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

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