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Grade 5 Student Notebook

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Student Notebook – Grade 5 ISBN: 978-1-64861-272-5 Published by Accelerate Learning Inc. 5177 Richmond Ave, Suite 800, Houston, TX 77056. Copyright © 2023 by Accelerate Learning Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written consent of Accelerate Learning Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

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GEORGIA

Student Notebook - Grade 5

Scope Name

Table of Contents

Page Number

Place Value Relationships

Read and Write Decimals

Compare and Order Decimals

Round Decimals

Add and Subtract Decimals

Multiply Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers

Numerical Expressions

Compare and Order Fractions and Mixed Numbers

105

Add and Subtract Fractions

123

Multiply Fractions

141

Fractions as Division

161

Divide Fractions

173

Classify Two-Dimensional Figures

189

iii

GEORGIA

Student Notebook - Grade 5

Table of Contents (Cont.) Scope Name Page Number Unit Conversions

203

Volume

227

Graph in the First Quadrant

237

Generate and Graph Numerical Patterns

247

Represent and Interpret Data

261

Skills Quizzes

279

Glossary of Terms

335

Workspace

369

Place Value Relationships

Explore 1

Place Value Relationships

Name: _______________________ Date: __________

Place Value Relationships

Part I: Whole Numbers Use the Clue Cards to help you solve the missing numbers to open the locks. Lock 1 Lock code: Clues

Expression

Clue 1

( __________ × __________ )

Clue 2

( __________ × __________ )

Clue 3

( __________ × __________ )

Clue 4

( __________ × __________ )

Clue 5

( __________ ÷ __________ )

Clue 6

( __________ × __________ )

Value

Lock 2 Lock code: Clues

Expression

Clue 1

( __________ × __________ )

Clue 2

( __________ × __________ )

Clue 3

( __________ × __________ )

Clue 4

( __________ ÷ __________ )

Value

Place Value Relationships | 3

Place Value Relationships

Explore 1 Lock 3 Lock code:

Clues

Expression

Clue 1

( __________ × __________ )

Clue 2

( __________ × __________ )

Clue 3

( __________ ÷ __________ )

Clue 4

( __________ ÷ __________ )

Clue 5

( __________ × _________ )

Value

Lock 4 Lock code:

Clues

Expression

Clue 1

( __________ × __________ )

Clue 2

( __________ × __________ )

Clue 3

( __________ ÷ __________ )

Clue 4

( __________ × __________ )

Clue 5

( __________ ÷ __________ )

4 | Place Value Relationships

Value

Place Value Relationships

Explore 1

Part II: Decimals Label the place value disk with the value of each base ten block. Then, circle the correct title of the ancient coins found inside the treasure chests.

Base Ten Block

Place Value Disk

Value

Ancient Coin

One-tenth One One-hundredth One-thousandth

Dime Silver dollar Penny Mill

One-tenth One One-hundredth One-thousandth

Dime Silver dollar Penny Mill

One-tenth One One-hundredth One-thousandth

Dime Silver dollar Penny Mill

One-tenth One One-hundredth One-thousandth

Dime Silver dollar Penny Mill

Place Value Relationships | 5

Place Value Relationships

Explore 1

Read each Treasure Card, and use your Place Value Chart and place value disks to help you solve. Record your answers below. Treasure Chest 1 Money amount:

$ Clues

Expression

Clue 1

( __________ × __________ )

Clue 2

( __________ ÷ __________ )

Clue 3

( __________ × __________ )

Clue 4

( __________ × __________ )

Value

Treasure Chest 2 Money amount:

$ Clues

Expression

Clue 1

( __________ × __________ )

Clue 2

( __________ ÷ __________ )

Clue 3

( __________ × __________ )

Clue 4

( __________ × __________ )

6 | Place Value Relationships

Value

Explore 1

Place Value Relationships

Reﬂ ect How does the value of a number change as it moves to the left on the Place Value Chart? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How does the value of a number change as it moves to the right on the Place Value Chart? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How do you determine the change in value of a digit that is more than one place to the left or right? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Place Value Relationships | 7

Powers of Ten 10 Houses

Each Employee’s Earnings

1 House

Value

Expression

Model

Scenario 2

Value

Expression

Model

Scenario 1

Place Value Relationships | 9

Each Purchase Cost

10 Houses on 10 Streets in 10 Neighborhoods

Each Family Member’s Money

10 Houses on 10 Streets

10 Houses on 10 Streets in 10 Neighborhoods in 10 Cities

Name: _______________________ Date: __________

Part I Read each Business Card, and represent it using place value disks. Record your observations.

Explore 2

Place Value Relationships

Trees in Each City

1 Dog

Trees in Each Park

10 Dogs

Trees in Each Section

10 Dogs for 10 Days

Trees in Each Row

10 Dogs for 10 Days for 10 Months

10 | Place Value Relationships

___________________________________________________________________________________________

What pattern do you notice in each scenario when you divide a value by multiple 10s?

___________________________________________________________________________________________

What pattern do you notice in each scenario when you multiply a value by multiple 10s?

Value

Expression

Model

Scenario 4

Value

Expression

Model

Scenario 3

Explore 2

Place Value Relationships

Value

Expression

Model

Pennies

Value

Expression

Model

Dimes

1 Penny

1 Dime

10 Pennies

10 Dimes

Part II Read each Coin Card, and represent it using coins. Record your observations.

Explore 2

Place Value Relationships | 11

10 Pennies in 10 Rolls

10 Dimes in 10 Rolls

Place Value Relationships

10 Rolls

10 Stacks

10 Customers

12 | Place Value Relationships

___________________________________________________________________________________________

What pattern do you notice in each scenario when you divide a decimal value by multiples of 10?

___________________________________________________________________________________________

What pattern do you notice in each scenario when you multiply a decimal value by multiples of 10?

Value

Expression

Model

Quarters

Value

Expression

Model

Nickels

Explore 2

Place Value Relationships

Place Value Relationships | 13

___________________________________________________________________________________________

What observations have you made about each place in our place value system based off of this activity?

___________________________________________________________________________________________

Why does a value lose a zero or shift the decimal to the left when you divide by 10?

___________________________________________________________________________________________

Why does the value gain a zero or shift the decimal to the right when you multiply a whole number by 10?

___________________________________________________________________________________________

Did multiplying a decimal number by 10 have the same outcome as multiplying a whole number by 10? Explain.

Reﬂect

Explore 2

Place Value Relationships

Exponents

The bacteria grew to 1,000 cells.

The bacteria grew to 100 cells.

The bacteria starts as 10 cells.

Bacteria Growth

Model

Place Value Relationships | 15

Name: _______________________ Date: __________

Part I Bacteria Growth Read each bacteria growth scenario. Create a model for each scenario.

Explore 3

Place Value Relationships

Word Form

Powers of Ten Expression

Expression

Exponent

16 | Place Value Relationships

___________________________________________________________________________________________

What relationship do you notice between the exponent and the multiples of 10 in the powers of ten expression?

1,000

100

Value

Match the Bacteria Growth Sort cards that represent each value.

Explore 3

Place Value Relationships

Powers of Ten Expression

Expression

Exponent

Place Value Relationships | 17

___________________________________________________________________________________________

What relationship do you notice between the exponent and how many places the decimal moved during division?

The food bacteria is reduced to 3.5 cells.

The food bacteria is reduced to 35 cells.

The food bacteria is reduced to 350 cells.

The food bacteria starts as 3,500 cells.

Value

Bacteria Reduction Read each bacteria reduction scenario. Match the Bacteria Reduction Sort cards that represent that scenario.

Explore 3

Place Value Relationships

4.6 × ( ______________ ) 2,674 ÷ ( ____________ )

Bacteria sample from chair

Bacteria sample from couch

194 × ( ______________ ) 684 ÷ ( _____________ )

Bacteria sample from pencil

Bacteria sample from pillow

18 | Place Value Relationships

56 ÷ ( ________ )

Bacteria sample from carpet

Bacteria sample 0.88 × ( _________________ ) from door handle

Powers of Ten Expression

Value

684 ÷ _________

194 × __________

56 ÷ _______

0.88 × ________

2,674 ÷ ________

4.6 × _________

Expression

Answer

684 ÷ _____

194 × _____

56 ÷ _____

0.88 × ____

2,674 ÷ ____

4.6 × ____

Exponent

Part II: Bacteria Scenario Cards Read each Bacteria Scenario Card, and use multiple strategies to ﬁnd your answer. Record your work in the space below.

Explore 3

Place Value Relationships

Place Value Relationships | 19

___________________________________________________________________________________________

How can an exponent represent multiples of ten?

___________________________________________________________________________________________

What does the exponent represent when it is being used to divide by a power of ten?

___________________________________________________________________________________________

What does the exponent represent when it is being used to multiply a power of ten?

Reﬂect

Explore 3

Place Value Relationships

Read and Write Decimals

Explore 1

Name: _______________________ Date: __________

Read and Write Decimals Read each Meal Card, and correctly prepare the weight of each meal using the Place Value Mat and base ten blocks. Then, represent each value as a numeral, as a base ten block model, and with a number name. Coconut Shrimp

Ones

Tenths

Hundredths

Thousandths

Ones

Tenths

Hundredths

Thousandths

Numeral

Base ten blocks model Number name:

Salmon Numeral

Base ten blocks model Number name:

Read and Write Decimals | 23

Read and Write Decimals

Explore 1 Fried Chicken

Ones

Tenths

Hundredths

Thousandths

Ones

Tenths

Hundredths

Thousandths

Base ten blocks model

Numeral Number name:

Chicken Alfredo Pasta

Base ten blocks model

Numeral Number name:

24 | Read and Write Decimals

Read and Write Decimals

Explore 1 Steak

Ones

Tenths

Hundredths

Thousandths

Numeral

Base ten blocks model Number name:

Reﬂ ect How can you use a numeral to help write a decimal in number name form? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can you use number names to write numbers in numeral form? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What examples of decimals have you seen in the real world? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Read and Write Decimals | 25

Explore 2

Read and Write Decimals

Name: _______________________ Date: __________

Decimals in Expanded Form Take a look at the Baseball Cards provided to see some players’ stats. For each player’s batting average, do the following tasks: • Represent the player decimal using your base ten blocks and place value disks. • Draw a model of each batting average using each manipulative. • Write an expression to represent the value of each digit in decimal and fraction form. • Write the decimal as a number name. • Then, use the expressions to show the decimal in expanded form. Neil Farney

Ones

Tenths

Hundredths

Thousandths

Fraction expression

_____ × _____

Decimal expression

_____ × _____

Numeral Base ten blocks model Place value disks model

Number name How do you write the decimal expression in expanded form? _____________________________________________________________________ How do you write the fraction expression in expanded form? _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Read and Write Decimals | 27

Read and Write Decimals

Explore 2 Tina Minio

Ones

Tenths

Hundredths

Thousandths

Fraction expression

_____ × _____

Decimal expression

_____ × _____

Tenths

Hundredths

Thousandths

Fraction expression

_____ × _____

Decimal expression

_____ × _____

Numeral Base ten blocks model Place value disks model

Number name Martha Loewe

Ones

Numeral Base ten blocks model Place value disks model

Number name 28 | Read and Write Decimals

Read and Write Decimals

Explore 2

How do you write the decimal expression for Tina Minio in expanded form? _____________________________________________________________________ How do you write the fraction expression for Martha Loewe in expanded form? _____________________________________________________________________

Jules Shaw

Ones

Tenths

Hundredths

Thousandths

Fraction expression

_____ × _____

Decimal expression

_____ × _____

Numeral Base ten blocks model Place value disks model

Number name Write the expanded notation of the number above using decimal expressions. _____________________________________________________________________ Write the expanded notation of the number above using fraction expressions. _____________________________________________________________________

Read and Write Decimals | 29

Read and Write Decimals

Explore 2 Matt Becker

Ones

Tenths

Hundredths

Thousandths

Fraction expression

_____ × _____

Decimal expression

_____ × _____

Numeral Base ten blocks model Place value disks model

Number name

Write the expanded notation of the number above using decimal expressions. _____________________________________________________________________ Write the expanded notation of the number above using fraction expressions. _____________________________________________________________________

30 | Read and Write Decimals

Explore 2

Read and Write Decimals

Reﬂ ect How can a model or picture help us write a number in expanded form? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What do you notice in your expanded form about the difference in the value of each place as you go from left to right? _____________________________________________________________________ What do you notice in your expanded form about the difference in the value of each place as you go from right to left? _____________________________________________________________________

Read and Write Decimals | 31

Compare and Order Decimals

Explore 1

Name: _______________________ Date: __________

Compare Decimals Using place value disks, compare the time it took the champions Justify and Always Dreaming to get to the ﬁnish line. Then, plot and label each horse’s name and time on the number line below and compare. Ones

Tenths

Hundredths

Thousandths

______

Justify

Always Dreaming

Number Line

2.030

2.031

2.032

2.033

2.034

2.035

2.036

2.037

2.038

2.039

2.040

2.041

2.042

Write a statement that compares Justify’s time with Always Dreaming’s time. Use the symbol >, <, or = in your statement. Explain how you know your statement is right. _____________________________________________________________________

2.014 2.010 2.018 2.022 2.026 2.030 2.034 _____________________________________________________________________ 2.012

2.016

2.020

2.024

2.028

2.032

Compare and Order Decimals | 35

Compare and Order Decimals

Explore 1

Compare these horse champions’ ﬁnish times using the Place Value Chart and number line. Then, write two comparison statements using the correct symbols.

2.030

2.031

2.032

2.034 vs. American 2.036 2.038 Nyquist Pharoah

2.033

2.035

2.037

2.039

2.040

2.041

2.042

Plot and label each horse’s name and time on the number line below, and compare.

2.014 2.010 2.018 2.022 2.026 2.030 2.034 2.030 2.012 2.032 2.016 2.034 2.020 2.036 2.024 2.038 2.028 2.040 2.032 2.042 2.031 2.033 2.035 2.037 2.039 2.041 Comparison Statements

Statement 1 American Nyquist Pharoah ________________________

Statement 2 American Pharoah Nyquist _________________________

2.031 2.029 2.033 2.035 2.037 2.039 2.041 2.010 2.030 2.014 2.032 2.018 2.034 2.022 2.036 2.026 2.038 2.030 2.040 2.034 vs. Orb 2.028 2.012 2.016 California 2.020 Chrome 2.024 2.032 Plot and label each horse’s name and time on the number line below, and compare.

2.012 2.010 2.014 2.016 2.018 2.020 2.022 2.011 2.013 2.015 2.017 2.019 2.021 2.031 2.029 2.033 2.035 2.037 2.039 2.041 2.030 2.032 2.034 2.036 2.038 2.040

Comparison Statements

Statement 1 California Orb Chrome ________________________

Statement 2 California Chrome Orb _________________________

2.012 2.010 2.014 2.016 2.018 2.020 2.022 1.550 2.011 1.650 2.013 1.750 2.015 1.850 2.017 1.950 2.019 2.250 2.021 2.350 1.600 Choose one comparison statement1.800 above, and1.900 write out how you would2.300 read the 1.700 2.000 statement.

_____________________________________________________________________ 36 | Compare and Order Decimals

1.650 1.550 1.750 1.850 1.950 2.250 2.350 2.000 1.600 2.100 1.700 2.200 1.800 2.300 1.900 2.400 2.000 2.500 2.300 2.600 2.050 2.150 2.250 2.350 2.450 2.550

2.010

2.012

2.014

2.016

2.018

2.020

2.022

2.024

2.026

2.028

2.030

2.031

2.032

2.034

Compare and Order Decimals

Explore 1 2.029

2.030

2.033

2.035

2.037

Street Sense 2.032 2.034 vs. Animal 2.036 Kingdom 2.038

2.039

2.040

2.041

Plot and label each horse’s name and time on the number line below, and compare.

2.010

2.011

2.012

2.013

2.014

2.015

2.016

2.017

Statement 1

Comparison Statements

1.550

1.600

Street Animal Sense Kingdom ________________________

1.650

1.700

1.750

1.800

1.850

1.900

2.018

2.019

2.020

2.021

2.022

Statement 2

Animal Street Kingdom Sense _________________________

1.950

Big Brown vs. Monarchos

2.000

2.250

2.300

2.350

Plot and label each horse’s name and time on the number line below, and compare.

1.550 2.000

1.600 2.050

1.650 2.100

1.700 2.150

1.750 2.200

1.800 2.250

1.850 2.300

Statement 1

Comparison Statements

1.900 2.350

Big Brown Monarchos ________________________

1.950 2.400

2.000 2.450

2.050 2.500

2.100 2.550

2.150 2.600

Statement 2

Big Monarchos Brown _________________________

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

Compare and Order Decimals | 37

Compare and Order Decimals

Explore 1

1.550

1.600

1.650

1.700

1.750

1.800

1.850

1.900

1.950

2.000

2.250

2.300

2.350

Chant vs. Smarty Jones Plot and label each horse’s name and time on the number line below, and compare.

2.000

2.050

Comparison Statements

2.100

2.150

2.200

2.250

2.300

2.350

Statement 1 Smarty Chant Jones ________________________

2.400

2.450

2.500

2.550

2.600

Statement 2

Smarty Jones Chant ________________________

Write out how you would read one of the comparison statements above. _____________________________________________________________________ Reﬂ ect Describe the process you could use to compare two numbers. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can a number line help us compare decimals? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why can each comparison be shown using two statements? _____________________________________________________________________ _____________________________________________________________________ 38 | Compare and Order Decimals

Compare and Order Decimals

Explore 2

Name: _______________________ Date: __________

Order Decimals Use the tables below to record the race times in the order requested. Boys’ 100 m Dash Plot and label each boy’s name and time on the number line below, and order from least to greatest.

0.425 0.450

0.475 0.500

0.525 0.550 0.575

Least

0.600

0.625 0.650

0.675 0.700 0.725

Greatest

Name Race Time What digit and place value helped you determine what decimal was the greatest? _____________________________________________________________________ _____________________________________________________________________ Order Dion’s, Edgar’s, and Steven’s times from greatest to least using symbols. _____________________________________________________________________ Whose race time was the fastest? Explain. _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare and Order Decimals | 39

Compare and Order Decimals

Explore 2 Girls’ 100 m Dash

Plot and label each girl’s name and time on the number line below, and order from greatest to least.

0.550 0.580

0.610 0.640

0.670 0.700 0.730

0.760

0.790 0.820

Greatest

0.850 0.880

0.910

Least

Name Race Time Whose time is less than Tarianna’s but greater than Lucea’s? _____________________________________________________________________

40 | Compare and Order Decimals

Compare and Order Decimals

Explore 2 Boys’ 400 m Dash

Plot and label each boy’s name and time on the number line below, and order from least to greatest.

0.850 0.900

0.950 1.000

Least

1.050 1.100 1.150

1.200

1.250 1.300

1.350 1.400

1.450

Greatest

Name Race Time

Compare and Order Decimals | 41

Compare and Order Decimals

Explore 2

Use symbols to write a comparison statement showing the names of the racers in order from least race time to greatest race time. _____________________________________________________________________ _____________________________________________________________________ Whose race time is the greatest? _____________________________________________________________________ Whose race time is the least? _____________________________________________________________________ Girls’ 400 m Dash Plot and label each girl’s name and time on the number line below, and order from greatest to least.

1.465 1.468

1.471 1.474

Greatest

1.477 1.480 1.483

1.486

1.489 1.492

1.495 1.498

1.501

Least

Name Race Time Order Kailee’s, Ruby’s, and Monica’s race times from least to greatest using symbols. _____________________________________________________________________

42 | Compare and Order Decimals

Compare and Order Decimals

Explore 2 Boys’ and Girls’ Long Jump

Plot and label each name and distance jumped on the number line below, and order from longest to shortest.

16.800 16.900 17.000 17.100 17.200 17.300 17.400 17.500 17.600 17.700 17.800 17.900 18.000

Longest

Shortest

Name Race Time Whose jump was the shortest?

Whose jump was longer than 16.923 but shorter than 17.538?

Reﬂ ect Draw and describe your process for ordering decimals.

If you have numbers in order from least to greatest, how could you order them from greatest to least? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Compare and Order Decimals | 43

Round Decimals

Explore 1

Name: _______________________ Date: __________

Round Decimals Part I In 2009, Usain Bolt set the current world record in the 100 m dash with a time of 9.576 seconds. The ofﬁcial time is only recorded to the hundredths place. Round this decimal to a hundredth of a second. A number line has been started below. Label Usain Bolt’s time. Write the two decimals that belong in the boxes.

9.571

9.572

9.573

9.574

9.575

9.576

9.577

9.578

9.579

Which two hundredths is your point between? _________________________________ Which hundredth is your point closest to? ____________________________________ What was Usain Bolt’s ofﬁcial time in the 100 m dash? __________________________ How does the number line help you when rounding? ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ What would the time be rounded to the tenths place? ___________________________ What would the time be rounded to the ones place? ____________________________

Round Decimals | 47

Round Decimals

Explore 1 Part II

Complete each event. Use a stopwatch to record your time for each event. Round that number to the closest hundredths, tenths, and ones places. Shoelace Race Name

Time

Time Rounded to Hundredths

Time Rounded to Tenths

Time Rounded to Ones

Round your time to the hundredths.

Round your time to the tenths.

Round your time to the ones.

48 | Round Decimals

Round Decimals

Explore 1 Puzzle Put Together Name

Time

Time Rounded to Hundredths

Time Rounded to Tenths

Time Rounded to Ones

Round your time to the hundredths.

Round your time to the tenths.

Round your time to the ones.

Round Decimals | 49

Round Decimals

Explore 1 Pattern Block Picture Name

Time

Time Rounded to Hundredths

Time Rounded to Tenths

Time Rounded to Ones

Round your time to the hundredths.

Round your time to the tenths.

Round your time to the ones.

50 | Round Decimals

Round Decimals

Explore 1 ABC Song Showdown Name

Time

Time Rounded to Hundredths

Time Rounded to Tenths

Time Rounded to Ones

Round your time to the hundredths.

Round your time to the tenths.

Round your time to the ones.

Round Decimals | 51

Round Decimals

Explore 1 Hidden Items Name

Time

Time Rounded to Hundredths

Time Rounded to Tenths

Time Rounded to Ones

Round your time to the hundredths.

Round your time to the tenths.

Round your time to the ones.

52 | Round Decimals

Explore 1

Round Decimals

Reﬂ ect What happened to the accuracy of your numbers as you rounded them to a greater place value versus a lower place value? Explain why that is. _____________________________________________________________________ ____________________________________________________________________ _____________________________________________________________________ How do you determine the benchmark numbers on a number line? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How would you determine which place value is the best to round to? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Round Decimals | 53

Add and Subtract Decimals

Explore 1

Part I: The Games

Name: _______________________ Date: __________

Add Decimals Cornhole

Grid Model Method Use two different colors to represent the decimal amount of your beanbag throws.

Partial Sums + +

+ Sum = Standard Algorithm

Equation: ______ + ______ = ______ Bobbing for Apples Grid Model Method Use two different colors to represent the decimal amount of apples collected.

Partial Sums + +

+ Sum = Standard Algorithm Equation:

Add and Subtract Decimals | 57

Explore 1

Add and Subtract Decimals

Tug-of-War

Grid Model Method Use two different colors to represent the decimal amount of rope pulled.

Partial Sums + +

+ Sum = Standard Algorithm Equation:

______ + ______ = ______ Sack Races Grid Model Method Use two different colors to represent the distance completed in decimals.

Partial Sums + +

+ Sum = Standard Algorithm Equation:

______ + ______ = ______

58 | Add and Subtract Decimals

Add and Subtract Decimals

Explore 1

Part II: The Food Work with your group to solve each problem below, and record your work in the space provided. Your Aunt Juanita brings a cheese pizza for the children. You eat 0.25 of the pizza, and Maria eats 0.52 of the pizza. How much pizza did you eat altogether? Equation: ______ + ______ = ______ Partial Sums

Standard Algorithm

+ +

Sum =

Aunt Paula has brought a pan of brownies. Miranda eats 0.31 of the brownies, and Mateo eats 0.59 of the brownies. What decimal represents the amount of brownies that was eaten? Equation: ______ + ______ = ______ Partial Sums

Standard Algorithm

+ +

Add and Subtract Decimals | 59

Add and Subtract Decimals

Explore 1

Your mother made three cakes for the reunion, but you ate 0.14 of one of the cakes before you leave home. At the reunion, Gabriel eats 0.76 of one of the cakes, and your mother gives 0.94 of one of the cakes to your grandfather and grandmother to take home and eat. What decimal represents the amount of cake eaten? Partial Sums

Standard Algorithm

+ + +

+ +

Sum = Reﬂ ect How did you use the grid models to add your decimals? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How is the partial sums method similar to the standard algorithm? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What strategy did you ﬁnd most helpful when adding decimals? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 60 | Add and Subtract Decimals

Add and Subtract Decimals

Explore 2

Name: _______________________ Date: __________

Subtract Decimals Part I: Silent Auction 1. Sally won the toy kitchen from the silent auction. How much money does Sally have left? Diagram: Show Your Work

Equation: _____

_____ = _____ Solution statement:

2. Justin won the toy cars collection from the silent auction. How much money does Justin have left? Diagram: Show Your Work

Equation: _____

_____ = _____ Solution statement:

Add and Subtract Decimals | 61

Add and Subtract Decimals

Explore 2

3. You won the sports basket from the silent auction. How much money do you have left? Diagram: Show Your Work

Equation: _____

_____ = _____ Solution statement:

4. Kelly won the stuffed animal basket from the silent auction. How much money does Kelly have left?

Diagram: Show Your Work

Equation: _____

_____ = _____ Solution statement:

62 | Add and Subtract Decimals

Add and Subtract Decimals

Explore 2 Part II: Contest Craze 1. How many more pies did Justin eat than you? Diagram:

Show Your Work

Equation: _____

_____ = _____ Solution statement:

2. How many more pies did Sally eat than Kelly? Diagram: Show Your Work

Equation: _____

_____ = _____ Solution statement:

Add and Subtract Decimals | 63

Add and Subtract Decimals

Explore 2 3. How many more hot dogs did you eat than Sally? Diagram:

Show Your Work

Equation: _____

_____ = _____

Solution statement:

4. How many more hot dogs did Kelly eat than Justin? Diagram:

Show Your Work

Equation: _____

_____ = _____

Solution statement:

Reﬂ ect How is solving a subtraction problem with whole numbers similar to solving a subtraction problem with decimals? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How is a diagram helpful in solving a real-world problem? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 64 | Add and Subtract Decimals

Multiply Multi-Digit Whole Numbers

Explore 1

Multiply Multi-Digit Whole Numbers

Name: _______________________ Date: __________

Partial Products and the Standard Algorithm Part I: Partial Products • Look at the length and width of each building. • Use the Area Model Template to create an area model, and solve the problem. • Record your work below. Write each partial product in the box below it. Electrifying Electronics Store Books Galore Length = 184 yards; width = 52 yards Length = 313 yards; width = 28 yards Area model:

Area model:

Partial products:

____ ____ ____ ____ ____ × ____________ ____ ____ ____ ____ ____ (____ × ____) ____ ____ ____ ____ ____ (____ × ____) ____ ____ ____ ____ ____ (____ × ____) ____ ____ ____ ____ ____ (____ × ____) ____ ____ ____ ____ ____ (____ × ____) ____ ____ ____ ____ ____ (____ × ____) + _________________________ ____ ____ ____ ____ ____

Multiply Multi-Digit Whole Numbers | 67

Multiply Multi-Digit Whole Numbers

Explore 1 Rosie’s Clothing Store Length = 548 yards; width = 46 yards

West Bend Mall Length = 679 yards; width = 73 yards

Area model:

Partial products:

Reﬂ ect Describe the relationship between the area model and the partial products. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 68 | Multiply Multi-Digit Whole Numbers

Multiply Multi-Digit Whole Numbers

Explore 1

Part II: The Standard Algorithm • Read each problem, and set up the equation. • Use the Standard Algorithm Work Mat and Digit Cards to solve each problem. • Record your work in the space provided. Remnant 1

Remnant 2

Remnant 3

Length: 362 feet Width: 27 feet

Length: 436 feet Width: 16 feet

Length: 154 feet Width: 34 feet

____ ____ ____ ____ ____ × _______________ ___ ___ ___ ___ ___ + ___ ___ ___ ___ ___ ___________________ ___ ___ ___ ___ ___

square feet

Reﬂ ect How are the partial products and standard algorithm strategies similar? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Multiply Multi-Digit Whole Numbers | 69

Divide Multi-Digit Whole Numbers

Explore 1

Name: _______________________ Date: __________

Rectangular Arrays Use base ten blocks or digital manipulatives to model your solution to the problems on each Scenario Card in the space below. Draw and label your model, and write the equations that represent the quotient.

Scenario 1 – Dealership 1

Describe the solution in a sentence. __________________________________________________________________ Equations: __________________________________________________________________ Did you ﬁnd the number of groups or the size of each group? __________________________________________________________________

Divide Multi-Digit Whole Numbers | 73

Divide Multi-Digit Whole Numbers

Explore 1

Scenario 2 – Dealership 2

74 | Divide Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers

Explore 1

Scenario 3 – Dealership 3

Divide Multi-Digit Whole Numbers | 75

Divide Multi-Digit Whole Numbers

Explore 1

Scenario 4 – Dealership 4

76 | Divide Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers

Explore 1

Scenario 5 – Dealership 5

Divide Multi-Digit Whole Numbers | 77

Explore 1

Divide Multi-Digit Whole Numbers

Reﬂ ect How did you decompose each total and use your knowledge of base ten to build each array? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What is the relationship between the array and your equations? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How could you use your arrays to help check your work? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

78 | Divide Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers

Explore 2

Name: _______________________ Date: __________

Area Models Use the Area Model Cards to model your solution to the problems on each Crop Design Card in the space below. Draw and label your model, and write the equations that represent the quotient.

Crop Design 1 – Corn

Divide Multi-Digit Whole Numbers | 79

Divide Multi-Digit Whole Numbers

Explore 2 Crop Design 2 – Carrots

80 | Divide Multi-Digit Whole Numbers

Explore 2

Divide Multi-Digit Whole Numbers

Crop Design 3 – Strawberries

Divide Multi-Digit Whole Numbers | 81

Divide Multi-Digit Whole Numbers

Explore 2 Crop Design 4 – Potatoes

82 | Divide Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers

Explore 2 Crop Design 5 – Tomatoes

Divide Multi-Digit Whole Numbers | 83

Divide Multi-Digit Whole Numbers

Explore 2 Reﬂ ect Describe how to use an area model to divide larger numbers.

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How are your area models similar to your base-ten arrays? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why should we start with the greatest place value ﬁrst when building an area model? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

84 | Divide Multi-Digit Whole Numbers

Explore 3

Divide Multi-Digit Whole Numbers

Name: _______________________ Date: __________

Algorithms Part I: Division Strategies The concert for this year’s hottest band just let out, and there are so many people! There are 1,134 people waiting for a shuttle to the train station, 2,464 people waiting for a bus, and 1,325 cars sitting in the parking lots, waiting for their owners. • Each shuttle can hold only 18 people. • Each bus can hold only 16 people. • There are 25 parking lots. You need to help the people in charge of trafﬁc ﬂow determine how many shuttles they need, how many buses they need, and how many cars are in each parking lot. Shuttle Riders Area model:

Partial quotients model:

Divide Multi-Digit Whole Numbers | 85

Explore 3

Divide Multi-Digit Whole Numbers

Use the Algorithms Work Mat to solve the bus and car problems, and record your work below. Partial quotients models: Bus Riders

How many buses are needed? ______

Car Riders

How many lots are needed to hold all the cars? ______

In your own words, describe how to divide a four-digit number by a two-digit number. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 86 | Divide Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers

Explore 3 Part II: Division Algorithm

Use the partial quotients you found in Part I to help you solve each problem using the standard algorithm. Standard algorithm: Shuttles

Number of shuttles needed:

Buses

Number of buses needed:

Cars

Number of cars in each parking lot:

How can you use estimation to help you ﬁnd partial quotients? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What is the relationship between using partial quotients and the standard algorithm? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Divide Multi-Digit Whole Numbers | 87

Numerical Expressions

Explore 1

Name: _______________________ Date: __________

Order Matters Part I: Cows Model the scenario. Then, create an expression that represents the word problem, and evaluate and describe the process you used to evaluate. Write a solution statement to answer the question in your scenario. Draw a model to represent the scenario.

First expression:

Evaluate from left to right.

Second expression:

Evaluate using order of operations.

Process description:

Solution statement:

Numerical Expressions | 91

Numerical Expressions

Explore 1 Part II: Working on the Farm

Work with your group to create a model for each scenario. Then, create an expression that represents the word problems, evaluate and describe the process you used to evaluate, and write a solution statement. Carrots Expression:

Process description:

Evaluate from left to right.

Evaluate using order of operations. Solution statement:

Apples Expression:

Process description:

Evaluate from left to right.

Evaluate using order of operations. Solution statement:

92 | Numerical Expressions

Numerical Expressions

Explore 1 Eggs Expression:

Process description:

Evaluate from left to right.

Evaluate using order of operations.

Solution statement:

Potatoes Expression:

Process description:

Evaluate from left to right.

Evaluate using order of operations.

Solution statement:

Numerical Expressions | 93

Numerical Expressions

Explore 1 Cotton

Corn

Expression:

Evaluate from left to right.

Evaluate using order of operations.

Process description:

Solution statement:

Reﬂ ect Why is it important to solve using the correct order of operations? _____________________________________________________________________ _____________________________________________________________________ How can creating a model help you determine the correct order of operations? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 94 | Numerical Expressions

Numerical Expressions

Explore 2

Name: _______________________ Date: __________

Grouping Symbols Catie owns a catering company. She shops at a kitchen supply store. She bought three mixers for $74 each and two pans for $26 each. How much did she spend at the kitchen supply store? Write an expression that represents this problem. Then, evaluate the expression.

For each scenario, write the expression that represents the problem, and evaluate the expression. If given an expression, evaluate.

Farmers Market

Trendy Tablecloths

Numerical Expressions | 95

Explore 2

Numerical Expressions

Station 3

Station 4

Station 5

Station 6

96 | Numerical Expressions

Explore 2 Station 7

Numerical Expressions

Station 8

Numerical Expressions | 97

Numerical Expressions

Explore 2 Reﬂ ect Were the expressions in station 7 equivalent? Why or why not?

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Were the expressions in station 8 equivalent? Why or why not? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What is the purpose of parentheses for evaluating expressions? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Describe the process for evaluating expressions. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 98 | Numerical Expressions

Numerical Expressions

Explore 3

Name: _______________________ Date: __________

Interpret Expressions Help Mrs. López sort through the sales, and make sure you match the correct sales slip with Mrs. López’s records. Not all slips will be used. Part I Carrots by the Carton Rainbow Carrots

Round Carrots

8 less than the sum of 51 and 19

25 × (5 × 8)

Matching numerical expression:

Matching interpretation in words:

Describe how to interpret the expression in order to determine the value.

________________________________

Numerical Expressions | 99

Numerical Expressions

Explore 3 Bunches of Beets Golden Beets

Chioggia Beets

(9 + 33) ÷ 3

13 times the sum of 7 and 8

Matching interpretation in words:

Matching numerical expression:

Describe how to interpret the expression in order to determine the value.

________________________________

100 | Numerical Expressions

Numerical Expressions

Explore 3 Tomatoes by the Tub Cherry Tomatoes

Juliet Tomatoes

2 × (729 ÷ 9)

5 groups of the sum of 9 and 13

Matching interpretation in words:

Matching numerical expression:

Describe how to interpret the expression in order to determine the value.

________________________________

Numerical Expressions | 101

Numerical Expressions

Explore 3 Pomegranates by the Pound Granada Pomegranates

Foothill Pomegranates

Half of 72 more than 8

3 × (78 – 15)

Matching numerical expression:

Matching interpretation in words:

Describe how to interpret the expression in order to determine the value.

________________________________

102 | Numerical Expressions

Numerical Expressions

Explore 3 Part II

Help the López family double-check their fruit inventory. If their inventory has a numerical expression, interpret it using words. Use a numerical expression to interpret an inventory that is written in words. Oranges Interpret using words. 3 × (532 – 27)

Apples Interpret into a numerical expression. 532 more than 27 increased by 3

What relationships do you observe in this expression? __________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Numerical Expressions | 103

Numerical Expressions

Explore 3 Watermelons Triple the sum of 532 and 27

Interpret into a numerical expression.

Use the expression to explain how to ﬁnd the value. __________________________________________________________________ __________________________________________________________________

Cucumbers 3 + (532 × 27)

Interpret using words.

Use the expression to explain how to ﬁnd the value. __________________________________________________________________ __________________________________________________________________ How did you use your understanding of operations to determine either a word interpretation or a numerical expression? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What were some challenges that you had as you were interpreting different expressions? What would you caution other students about? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 104 | Numerical Expressions

Compare and Order Fractions and Mixed Numbers

105

Compare and Order Fractions and Mixed Numbers

Explore 1

Name: _______________________ Date: __________

Compare Fractions with Models Read each Roadway Station Card, and complete the steps below: 1. Build or draw a model of the fractions in the space provided. 2. Find a way to create and model equivalent fractions that have the same numerator or same denominator. 3. Determine whether the construction crew is on, ahead of, or behind schedule. Explain your answer. 4. Write a comparison statement using symbols. Gold Gator Way Draw and label the models you built. Show any equivalent fractions you created to compare them.

The construction crew is (circle one) on schedule / ahead of schedule / behind schedule

Comparison statement:

because _________________________________________ ________________________________________________.

Compare and Order Fractions and Mixed Numbers | 107

Compare and Order Fractions and Mixed Numbers

Explore 1

Georgia Parkway Roundabout Draw and label the models you built, including any equivalent fractions.

The construction crew is (circle one) on schedule / ahead of schedule / behind schedule

Comparison statement:

because _________________________________________ ________________________________________________. Featherstone Road Draw and label the models you built, including any equivalent fractions.

The construction crew is (circle one) on schedule / ahead of schedule / behind schedule

Comparison statement:

because _________________________________________ ________________________________________________.

108 | Compare and Order Fractions and Mixed Numbers

Compare and Order Fractions and Mixed Numbers

Explore 1

Bulldog Trail Roundabout Draw and label the models you built, including any equivalent fractions.

The construction crew is (circle one) on schedule / ahead of schedule / behind schedule

Comparison statement:

because _________________________________________ ________________________________________________. Eagle Landing Trail Draw and label the models you built, including any equivalent fractions.

The construction crew is (circle one) on schedule / ahead of schedule / behind schedule

Comparison statement:

because _________________________________________ ________________________________________________.

Compare and Order Fractions and Mixed Numbers | 109

Compare and Order Fractions and Mixed Numbers

Explore 1

Yellow Jacket Roundabout Draw and label the models you built, including any equivalent fractions.

The construction crew is (circle one) on schedule / ahead of schedule / behind schedule

Comparison statement:

because _________________________________________ ________________________________________________. Reﬂ ect Describe the process you used to make each choice. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How could you compare the two fractions without models? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why is it helpful to create equivalent fractions with the same numerator or denominator? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 110 | Compare and Order Fractions and Mixed Numbers

Compare and Order Fractions and Mixed Numbers

Explore 2

Name: _______________________ Date: __________

Compare Fractions with Number Lines Look at your Paint Checklist, and complete the steps below: 1. Compare the fractions and mixed numbers using the number lines to show each fraction. 2. Find a common numerator or denominator between the two fractions to further prove which one is greater or less. 3. Write two comparison statements using symbols. 4. Determine whether you have enough paint, not enough paint, or more than enough paint. Explain your answer. Morning Fog Gray Draw the number line model for each amount. 0

Find a common numerator or denominator.

You have (circle one)

Write two comparison statements using symbols.

not enough / more than enough / just the right amount of

paint because _________________________________________________________.

Compare and Order Fractions and Mixed Numbers | 111

Compare and Order Fractions and Mixed Numbers

Explore 2 Black Suede Draw the number line model for each amount. 0

Find a common numerator or denominator.

You have (circle one)

Write two comparison statements using symbols.

not enough / more than enough / just the right amount of

paint because _________________________________________________________. Polar Bear White Draw the number line model for each amount. 0

Find a common numerator or denominator.

You have (circle one)

Write two comparison statements using symbols.

not enough / more than enough / just the right amount of

paint because _________________________________________________________. 112 | Compare and Order Fractions and Mixed Numbers

Compare and Order Fractions and Mixed Numbers

Explore 2

Gale Force Blue Draw the number line model for each amount. 0

Find a common numerator or denominator.

You have (circle one)

Write two comparison statements using symbols.

not enough / more than enough / just the right amount of

paint because _________________________________________________________. Dusty Rose Pink Draw the number line model for each amount. 0

Find a common numerator or denominator.

You have (circle one)

Write two comparison statements using symbols.

not enough / more than enough / just the right amount of

Compare and Order Fractions and Mixed Numbers | 113

Explore 2

Compare and Order Fractions and Mixed Numbers

Reﬂ ect Explain how you can compare two fractions when the numerators or denominators are not equal. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why is it helpful to use number lines to compare fractions? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why is it helpful to ﬁnd a common numerator or denominator? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

114 | Compare and Order Fractions and Mixed Numbers

Explore 3

Compare and Order Fractions and Mixed Numbers

Name: _______________________ Date: __________

Compare Fractions with Benchmarks Read each Screen Time Station Card, and complete the steps below: 1. Represent each fraction or mixed number using a number line or fraction tiles. 2. Use benchmark numbers of 0, 1, and 2 to explain the comparison of the fractions and mixed numbers. 3. Write two comparison statements using symbols. 4. Determine which child used the most or least amount of screen time. Explain your answer. The Johnson Family Model your fractions and mixed numbers in the space below.

Use benchmarks to explain the comparison.

Write two comparison statements using symbols.

_____________ used the most screen time because ___________________________ ____________________________________________________________________.

Compare and Order Fractions and Mixed Numbers | 115

Compare and Order Fractions and Mixed Numbers

Explore 3

The Watson Family Model your fractions and mixed numbers in the space below.

Use benchmarks to explain the comparison.

Write two comparison statements using symbols.

_____________ used the least screen time because ___________________________ ____________________________________________________________________. The Ramirez Family Model your fractions and mixed numbers in the space below.

Use benchmarks to explain the comparison.

Write two comparison statements using symbols.

_____________ used the least screen time because ___________________________ ____________________________________________________________________. 116 | Compare and Order Fractions and Mixed Numbers

Compare and Order Fractions and Mixed Numbers

Explore 3

The Robinson Family Model your fractions and mixed numbers in the space below.

Use benchmarks to explain the comparison.

Write two comparison statements using symbols.

_____________ used the most screen time because ___________________________ ____________________________________________________________________. The Rose Family Model your fractions and mixed numbers in the space below.

Use benchmarks to explain the comparison.

Write two comparison statements using symbols.

Compare and Order Fractions and Mixed Numbers | 117

Compare and Order Fractions and Mixed Numbers

Explore 3

The Swanson Family Model your fractions and mixed numbers in the space below.

Use benchmarks to explain the comparison.

Write two comparison statements using symbols.

_____________ used the most screen time because ___________________________ ____________________________________________________________________. Reﬂ ect How does knowing whether a fraction is greater or less than a benchmark number help you compare fractions? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What other math concepts are similar to using benchmark numbers? How? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

118 | Compare and Order Fractions and Mixed Numbers

Order Fractions with Number Lines

Name: _______________________ Date: __________

Whose class won the pizza party?

List your fractions from least to greatest.

Plot and label your fractions and mixed numbers on the number line.

Kindergarten

Compare and Order Fractions and Mixed Numbers | 119

Plot each teacher’s fraction on its given number line, and label that point with the teacher’s last name initial. Then, list the fractions in order from least to greatest, and ﬁnd the teacher who won the pizza party by collecting the most canned goods.

Explore 4

Compare and Order Fractions and Mixed Numbers

First Grade

Second Grade

120 | Compare and Order Fractions and Mixed Numbers

Whose class won the pizza party?

List your fractions from least to greatest.

Plot and label your fractions and mixed numbers on the number line.

Whose class won the pizza party?

List your fractions from least to greatest.

Plot and label your fractions and mixed numbers on the number line.

Explore 4

Compare and Order Fractions and Mixed Numbers

Third Grade

Fourth Grade

Whose class won the pizza party?

List your fractions from least to greatest.

Plot and label your fractions and mixed numbers on the number line.

Whose class won the pizza party?

List your fractions from least to greatest.

Plot and label your fractions and mixed numbers on the number line.

Explore 4

Compare and Order Fractions and Mixed Numbers | 121

Compare and Order Fractions and Mixed Numbers

Fifth Grade

122 | Compare and Order Fractions and Mixed Numbers

___________________________________________________________________________________________

How can a number line be used to order fractions?

___________________________________________________________________________________________

Reﬂect How can you use equivalent fractions to help you plot your points on a number line?

Whose class won the pizza party?

List your fractions from least to greatest.

Plot and label your fractions and mixed numbers on the number line.

Explore 4

Compare and Order Fractions and Mixed Numbers

Add and Subtract Fractions

123

Explore 1

Add and Subtract Fractions

Name: _______________________ Date: __________

Addition and Subtraction Using Benchmark Fractions Part I After using your fraction tiles to ﬁnd which benchmark fraction your paint bottles are closer to, write the fraction and draw the model in the correct columns below. Color Bottle

Fraction

Benchmark Fraction

Model

Blue Red Green Yellow Orange Purple How is using benchmark fractions like rounding? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Add and Subtract Fractions | 125

Add and Subtract Fractions

Explore 1

Part II Model how you used estimation, addition, and subtraction to solve each scenario. Then, write a number sentence and solution sentence for each scenario. The Blue Paint Estimated fraction 1:

Estimated fraction 2:

Solve:

Number sentence:

Solution sentence:

The Red Paint Estimated fraction 1:

Estimated fraction 2:

Solve:

Number sentence:

126 | Add and Subtract Fractions

Solution sentence:

Add and Subtract Fractions

Explore 1 The Orange Paint Estimated fraction 1:

Estimated fraction 2:

Solve:

Number sentence:

Solution sentence:

The Purple Paint Estimated fraction 1:

Estimated fraction 2:

Solve:

Number sentence:

Solution sentence:

Add and Subtract Fractions | 127

Explore 2

Add and Subtract Fractions

Name: _______________________ Date: __________

Addition with Unlike Denominators Using Equivalent Fractions Model how you created equivalent fractions. Add fractions and write an addition sentence to solve. The East Orchard

Addition sentence: __________________________________________ The Meadow

Addition sentence: __________________________________________

Add and Subtract Fractions | 129

Add and Subtract Fractions

Explore 2 The West Orchard

Addition sentence: __________________________________________

The Acres

Addition sentence: __________________________________________

130 | Add and Subtract Fractions

Explore 2

Add and Subtract Fractions

Reﬂ ect How did you determine the common denominator to create an equivalent fraction? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can you use multiplication to determine a common denominator? Why does it work? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Add and Subtract Fractions | 131

Explore 3

Add and Subtract Fractions

Name: _______________________ Date: __________

Subtraction with Unlike Denominators Using Equivalent Fractions For each ingredient, draw a model of the original fractions and the equivalent fractions. Create an equation and solution that represent the problem. Sugar Original fractions:

Equivalent fractions:

Equation and solution:

Salt Original fractions:

Equivalent fractions:

Equation and solution:

Add and Subtract Fractions | 133

Add and Subtract Fractions

Explore 3 Flour Original fractions:

Equivalent fractions:

Equation and solution:

Chocolate Candy Original fractions:

Equivalent fractions:

Equation and solution:

134 | Add and Subtract Fractions

Add and Subtract Fractions

Explore 3 Butter Original fractions:

Equivalent fractions:

Equation and solution:

Baking Powder Original fractions:

Equivalent fractions:

Equation and solution:

Add and Subtract Fractions | 135

Explore 3

Add and Subtract Fractions

Reﬂ ect How is subtracting fractions similar to adding fractions? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What happens to the size of the pieces when the fraction is multiplied to ﬁnd a common denominator? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

136 | Add and Subtract Fractions

Add and Subtract Fractions

Explore 4

Name: _______________________ Date: __________

Problem Solve with Visual Models For each problem, draw and label the model. Write an equation and a solution statement that represent the problem. Hydration Station Model:

Equation: Solution:

Add and Subtract Fractions | 137

Add and Subtract Fractions

Explore 4 Fill Me Up, Scotty Model:

Equation: Solution:

Running to the Rhythm Model:

Equation: Solution:

138 | Add and Subtract Fractions

Add and Subtract Fractions

Explore 4 Go for Gold Model:

Equation: Solution:

Find the Line Model:

Equation: Solution:

Add and Subtract Fractions | 139

Add and Subtract Fractions

Explore 4 Go the Extra Mile Model:

Equation: Solution:

Reﬂ ect How does drawing a model help you when ﬁnding equivalent fractions? _____________________________________________________________________ _____________________________________________________________________

When looking at the fractions you added or subtracted, what is the relationship between the original denominators and the common denominators? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

140 | Add and Subtract Fractions

Multiply Fractions

141

Multiply Fractions

Explore 1

Name: _______________________ Date: __________

Equal Groups

Station 1

Milk in Cookie Batches ________ groups of ________ Model:

Mrs. Johnson needs __________ cups of milk to bake the cookies. Addition expression:

Multiplication expression:

Baking Chocolate in Cupcake Batches ________ groups of ________ Model:

Mrs. Johnson needs __________ cups of chocolate to bake the cupcakes. Addition expression:

Multiplication expression:

Multiply Fractions | 143

Multiply Fractions

Explore 1 Station 2 Pecans in Blondie Batches ________ groups of ________ Model:

Mrs. Johnson needs __________ cups of pecans to bake the blondies. Addition expression:

Multiplication expression:

Walnuts in Brownie Batches ________ groups of ________ Model:

Mrs. Johnson needs __________ cups of walnuts to bake the brownies. Addition expression:

144 | Multiply Fractions

Multiplication expression:

Multiply Fractions

Explore 1 Station 3 Flour in Pie Crusts ________ groups of ________ Model:

Mrs. Johnson needs __________ cups of ﬂour to bake the pie crusts. Addition expression:

Multiplication expression:

Butter in Pastry Batches ________ groups of ________ Model:

Mrs. Johnson needs __________ sticks of butter to bake the pastries. Addition expression:

Multiplication expression:

Multiply Fractions | 145

Multiply Fractions

Explore 1 Reﬂ ect What does repeated addition of a fraction mean?

_____________________________________________________________________ How does multiplication represent another way to write a fraction with repeated addition? _____________________________________________________________________ Think about one of the baking problems, and answer the questions below. When you add to solve for the total cups of an ingredient, what values are added? _____________________________________________________________________ What happens to the denominator in the addition problem? _____________________________________________________________________ When you multiply by the number of batches, what values are multiplied? _____________________________________________________________________ What stays the same? _____________________________________________________________________ Why do you think this is so? _____________________________________________________________________ _____________________________________________________________________

146 | Multiply Fractions

Multiply Fractions

Explore 2

Name: _______________________ Date: __________

Fractions of a Group Scenario 1 How many counters will you need to represent Makayla’s candles? ________________ If we categorized the candles, what categories would we have? _____________________________________________________________________ Draw the model you created with your group below.

How many of Makayla’s candles are burned out? ________________ How do you know this? _____________________________________________________________________ _____________________________________________________________________ Scenario 2 Draw the model you created.

How many of Makayla’s candles are not burned out? ________________ How does it differ from the model in Scenario 1? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Multiply Fractions | 147

Multiply Fractions

Explore 2 Scenarios 3–6

In the table below, draw the model for each scenario using the counters; ﬁnd the total number of each collection; and explain your solution. Model

Total

Explanation

Scenario 3:

Scenario 4:

Scenario 5:

Scenario 6:

148 | Multiply Fractions

Explore 2

Multiply Fractions

Reﬂ ect How did you and your group know how many items to place in each group? _____________________________________________________________________ _____________________________________________________________________ As you and your group solved each scenario, did you see any evidence of repeated addition? Explain what evidence you saw. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Use your own words to explain this statement: 6 is 25 of 15. _____________________________________________________________________ _____________________________________________________________________ Explain why we are actually multiplying a fraction and a whole number but our answer is less than the whole number. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Multiply Fractions | 149

Explore 3

Multiply Fractions

Name: _______________________ Date: __________

Area Models Read the Scenario Cards, and answer the questions about each scenario. Scenario 1 Use the Grid Paper to represent the scenario. Draw the model you created in the space below.

Write an expression to represent the scenario. ________________________________ Of the 9 dozen cupcakes, how many dozens needed to be gluten-free? ____________

Multiply Fractions | 151

Explore 3

Multiply Fractions

Scenario 2 Use the Grid Paper to represent the scenario. Draw the model you created in the space below.

Write an expression to represent the scenario. ________________________________ How many of the 20 fruit pies were mistakenly sold to customers in the store? _______ Explain how you know your solution is reasonable. _____________________________________________________________________ _____________________________________________________________________

152 | Multiply Fractions

Explore 3

Multiply Fractions

Scenario 3 Use the Grid Paper to represent each of the sheet cakes. Represent the amount of time each of the sheet cakes takes to bake, and work with your group members to ﬁnd the total time. Draw your model below.

Write the expression your model represents. __________________________________ How many whole hours are represented in your model? _________________________ Is there a fractional portion left after regrouping the whole hours? _________________ What fractional part is left? ___________________ What is the total time that it will take the baker to make all 6 sheet cakes? __________

Multiply Fractions | 153

Multiply Fractions

Explore 3 Scenario 4 Use the Grid Paper to represent and draw scenario 4.

Write the expression your model represents. ____________________________ How much of the cake was eaten in all? _______________________ How do you know your solution is reasonable? _____________________________________________________________________ _____________________________________________________________________

154 | Multiply Fractions

Explore 4

Multiply Fractions

Name: _______________________ Date: __________

Scaling You and your business partner are in charge of planning the new look of the farm. Each of you has written a different business plan that lays out the area of each section of the farm. Use pictures, models, or manipulatives to help plan. Be prepared to justify your reasoning and ﬁnd some similarities and differences with your business partner. Corn vs. Peppers Model:

How do both business plans compare? How do you know? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ Explain the similarities and differences in your and your partner’s reasoning and strategies.

Multiply Fractions | 155

Multiply Fractions

Explore 4

Barn vs. Coop Model:

156 | Multiply Fractions

Multiply Fractions

Explore 4

Corral vs. Pen Model:

How do both business plans compare? How do you know? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ Explain the similarities and differences in your and your partner’s reasoning and strategies.

Multiply Fractions | 157

Multiply Fractions

Explore 4

Animals vs. Crops Model:

How do both business plans compare? How do you know? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ Explain the similarities and differences in your and your partner’s reasoning and strategies.

158 | Multiply Fractions

Explore 4

Multiply Fractions

Reﬂ ect What connections did you make during this activity? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How were you able to determine the answer without multiplying? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Explain the process for how you determined the resizing. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Multiply Fractions | 159

Fractions as Division

161

Explore 1

Fractions as Division

Name: _______________________ Date: __________

Fractions as Division without Remainders Read each scenario, and help Scoop-tastic ﬁgure out the fractional amount of product each customer received. Record your work below with a model, an operation to solve, and an inverse operation to check your work. Vanilla Ice Cream Model:

Equation from scenario:

Inverse operation check:

Solution statement: Strawberry Ice Cream Model:

Equation from scenario:

Inverse operation check:

Fractions as Division | 163

Fractions as Division

Explore 1 Chocolate Ice Cream Model:

Equation from scenario:

Inverse operation check:

Solution statement:

Chocolate Sauce Model:

Equation from scenario:

Inverse operation check:

Solution statement:

164 | Fractions as Division

Fractions as Division

Explore 1 Cookie Dough Bites Model:

Equation from scenario:

Inverse operation check:

Solution statement:

Brownies Model:

Equation from scenario:

Inverse operation check:

Solution statement:

Fractions as Division | 165

Fractions as Division

Explore 1 Mint Ice Cream Model:

Equation from scenario:

Inverse operation check:

Solution statement:

Sprinkles Model:

Equation from scenario:

Inverse operation check:

Solution statement:

166 | Fractions as Division

Explore 1

Fractions as Division

Reﬂ ect What did you notice when you partitioned a smaller number by a larger number? _____________________________________________________________________ _____________________________________________________________________ How did the model help you solve each scenario? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How did the model help you use an inverse operation to check your work? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Fractions as Division | 167

Explore 2

Fractions as Division

Name: _______________________ Date: __________

Fractions as Division with Remainders Use your knowledge to solve each scenario during your babysitting weekend. Use the manipulatives to help you draw a model and answer the questions for each scenario. Pizza Night Model:

Solution equation:

Solution statement:

What two whole numbers is your answer in between? ________________________ Candy Jar Model:

Solution equation:

Solution statement:

Fractions as Division | 169

Fractions as Division

Explore 2 Toy Box Model:

Solution equation:

Solution statement:

What two whole numbers is your answer in between? ________________________ Crayons Model:

Solution equation:

Solution statement:

What two whole numbers is your answer in between? ________________________ 170 | Fractions as Division

Fractions as Division

Explore 2 Feeding Ducks Model:

Solution equation:

Solution statement:

What two whole numbers is your answer in between? ________________________ Books Model:

Solution equation:

Solution statement:

Fractions as Division | 171

Fractions as Division

Explore 2 Reﬂ ect How did you determine what to do with the remainder?

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ When is the answer a fraction or a mixed number? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What does that fraction represent? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can you determine what two wholes an answer falls between? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

172 | Fractions as Division

Divide Fractions

173

Explore 1

Divide Fractions

Name: _______________________ Date: __________

Divide a Whole Number by a Unit Fraction Part I: Sharing Pizza Split each of the 4 pizzas into thirds. Draw your model in the space below, and write the equation the model represents.

Equation: Predict what will happen to the size of each piece and the number of pieces when you divide the pizza into a greater number of pieces. _____________________________________________________________________ Split each of the 4 pizzas into fourths. Draw your model in the space below, and write the equation the model represents.

Divide Fractions | 175

Divide Fractions

Explore 1

Split each of the 4 pizzas into eighths. Draw your model in the space below, and write the equation the model represents.

Equation: Reﬂ ect As you split the pizza into smaller fractions, how did the size of each slice change? _____________________________________________________________________ Morgan said that if you split the pizza into smaller fractions, you will have more pieces of pizza to share. Freddy said that if you split the pizza into smaller fractions, you will not have more pieces. Who is correct: Freddy or Morgan? Explain your reasoning. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 176 | Divide Fractions

Divide Fractions

Explore 1 Part II: Sharing a Candy Bar

Mack wants to see what it would look like if he divided his 3 candy bars into halves. Make a model with the fraction tiles that would show Mack how many parts he would make when dividing by 1 . Label the number of parts in each candy bar. 2

1 candy bar = 1 whole

Equation: Mack is still not quite convinced that if he divides his 3 candy bars by 12 he will create more parts. Use the number line to show Mack that when you divide a whole number by a fraction, you make smaller parts, but there are actually more of them.

3 1

Show Mack what would happen if he divided his 3 candy bars by 4 . 1 candy bar = 1 whole

Divide Fractions | 177

Divide Fractions

Explore 1 Prove your answer on the number line below.

3 1

Show Mack what would happen if he divided his 3 candy bars by 5 . 1 candy bar = 1 whole

Equation: Prove your answer on the number line below.

Reﬂ ect

What similarities did you ﬁnd in these problems? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ When we split up the whole, what happened to the size of the parts? _____________________________________________________________________ _____________________________________________________________________ 178 | Divide Fractions

Explore 2

Divide Fractions

Name: _______________________ Date: __________

Divide a Unit Fraction by a Whole Number Scenario 1: Dividing Land Offer 1: After cutting the ﬁrst Fraction Card, draw the model you created.

Draw a star on one of the shaded pieces. What fraction of the square mile is the piece with the star? ________ Describe what your model shows. _____________________________________________________________________ _____________________________________________________________________ Generate an expression that matches your model. ______________________________ 1

If Kristen’s 4 of a square mile is divided by 2, what is the size of each part? _________ 1

Predict how the size of each piece will change when Kristen’s 4 piece of land is divided into 3 equal parts instead of just 2. _____________________________________________________________________

Divide Fractions | 179

Divide Fractions

Explore 2 Offer 2: Cut the second Fraction Card. Draw the model you created.

If Kristen’s 4 of a square mile is divided by 3, what is the size of each part? _________

180 | Divide Fractions

Explore 2

Divide Fractions

Offer 3: Cut the third Fraction Card. Draw the model you created.

Draw a star on one of the shaded pieces. What fraction of the square mile is the piece with the star? ________ Generate an expression that matches your model. _____________________________ 1

If Kristen’s 4 of a square mile is divided by 4, what is the size of each part? _________

Divide Fractions | 181

Divide Fractions

Explore 2 Offer 4: Cut the fourth fraction card. Draw the model you created.

Draw a star on one of the shaded pieces. What fraction of the square mile is the piece with the star? ________ Generate an expression that matches your model. _____________________________ 1

If Kristen’s 4 of a square mile is divided by 8, what is the size of each part? _________ As Kristen’s land is divided into more pieces, what happens to the size of each piece? _____________________________________________________________________

182 | Divide Fractions

Divide Fractions

Explore 2 Scenario 2: Sharing Brownies

Help Mr. Cooper by completing the table below. Divide each circle into equal sections. Draw a star on one of the shaded sections. Write the expression, and determine the fractional size of each brownie in the container. Area Model

Expression

Fractional Size of Each Brownie in the Container

What do the lines that you drew represent? _____________________________________________________________________ After you divided the 12 brownie piece, what did the small shaded parts represent? _____________________________________________________________________ Which containers held the biggest brownies? _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Divide Fractions | 183

Divide Fractions

Explore 2 Scenario 3: Making Napkins

Help Sew-It-All Fabrics by completing the table below. Use the number line to divide the fabric into equal sections. Draw a star on one of the shaded sections. Write the expression, and determine the fractional size of each napkin. Number Line

Expression

Fractional Size of Each Napkin

Reﬂ ect What similarities did you ﬁnd in these problems? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ When we split up the fraction, what happened to the size and number of pieces? _____________________________________________________________________ _____________________________________________________________________ 184 | Divide Fractions

Explore 3

Divide Fractions

Name: _______________________ Date: __________

Develop Models to Solve Problems Scenario 1: Dividing the Gym Rectangular Area Model

Equation

Scenario 2: Dividing the Cafeteria Number Line Model

Equation

Scenario 3: Dividing the Computer Lab Rectangular Area Model

Equation

Divide Fractions | 185

Explore 3

Divide Fractions

Scenario 4: Dividing the Library Model (your choice)

Equation

Scenario 5: Dividing the Classrooms Number Line Model

Equation

Scenario 6: Dividing Science Lab Tables Circular Area Model

186 | Divide Fractions

Equation

Explore 3

Divide Fractions

Reﬂ ect Make a general statement about the result of dividing whole units by a unit fraction. _____________________________________________________________________ _____________________________________________________________________ What did you notice about the relationship between the dividend and the divisor compared to the quotient when whole units were divided by a fraction unit? _____________________________________________________________________ _____________________________________________________________________ Make a general statement about the result of dividing a unit fraction by whole units. _____________________________________________________________________ _____________________________________________________________________ What did you notice about the relationship between the dividend and the divisor compared to the quotient when a fraction unit was divided by whole units? _____________________________________________________________________ _____________________________________________________________________ How is division with fractions similar to and different from division with whole numbers? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Divide Fractions | 187

Classify Two-Dimensional Figures

189

Classify Two-Dimensional Figures

Explore 1

Name: _______________________ Date: __________

Classify Polygons Part I: Number of Sides and Lines of Symmetry

enta l Pa rty R re! o Superst

Fill in the table with the correct term that describes each group of tables. Then, ﬁll in the table with the numbers from the Table Shapes. There are 24 tables. Make sure each table is classiﬁed. Number of Sides

Name

Table Numbers

3 4 5 6 8

If a table has 5 corners, what shape is it? How do you know? _____________________________________________________________________ _____________________________________________________________________ What do you think the preﬁx tri- means? Explain why. _____________________________________________________________________

Classify Two-Dimensional Figures | 191

Classify Two-Dimensional Figures

Explore 1

Use the polygon sort for Part I to identify how many lines of symmetry each type of shape can have. Lines of Symmetry Polygon

Number of Sides

Triangles Quadrilaterals Pentagons Hexagons Octagons Can a shape have the same number of lines of symmetry as their number of sides? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why do you think a polygon can have a different number of lines of symmetry? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

192 | Classify Two-Dimensional Figures

Classify Two-Dimensional Figures

Explore 1 Part II: Angle Size

Fill in the table with the correct term that describes each group of tables. Then, fill in the table with the numbers from Table Shapes. There are 24 tables. Make sure each one is classified in the table. Some may be classified into more than one group. Angle Size

Names of Angles

Table Numbers

All smaller than 90° All larger than 90° All exactly 90° Some exactly 90° Some greater and some smaller than 90° At least one pair of congruent angles If all the sides of a shape are congruent, are all the angles congruent too? _____________________________________________________________________ _____________________________________________________________________ Is it possible to draw a triangle with all obtuse angles? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Classify Two-Dimensional Figures | 193

Classify Two-Dimensional Figures

Explore 1 Part III: Parallel Sides

Fill in the table with the numbers from the table cards. There are 24 tables. Make sure each table is classiﬁed. Tables with No Parallel Sides

Tables with at Least 1 Pair of Parallel Sides

Tables with No Perpendicular Sides

Tables with at Least 1 Pair of Perpendicular Sides

Tables with at Least 1 Pair of Congruent Sides

What do all the shapes with at least 1 pair of perpendicular sides have in common? _____________________________________________________________________ Why are we able to classify shapes in different ways? _____________________________________________________________________ 194 | Classify Two-Dimensional Figures

Classify Two-Dimensional Figures

Explore 2

Name: _______________________ Date: __________

Classify Quadrilaterals Use the category headings you created to ﬁll out the table below.

Attribute

Shapes That Have the Characteristic

Four-sided polygon

No parallel sides

At least one pair of parallel sides Two pairs of parallel sides Two opposite sets of congruent sides Exactly four congruent sides

Exactly four sets of perpendicular sides

Classify Two-Dimensional Figures | 195

Explore 2

Classify Two-Dimensional Figures

Reﬂ ect What categories does a square belong to? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Are all trapezoids quadrilaterals? Justify your answer. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Is every parallelogram a rhombus? Justify your answer. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

196 | Classify Two-Dimensional Figures

Classify Two-Dimensional Figures

Explore 2

Use the category headings from your chart paper model, the word bank, and the space below to represent the relationship between different types of quadrilaterals. Word Bank Trapezoid

Quadrilateral

Rectangle

Rhombus

Parallelogram

Square

Classify Two-Dimensional Figures | 197

Classify Two-Dimensional Figures

Explore 3

Name: _______________________ Date: __________

Classify Triangles Part I: Classify Types of Triangles Based on Side Lengths and Angles Use the Category Headings and your chart paper model to ﬁll out the table below. Shapes That Have the Characteristic

Attribute

Three-sided polygon Equilateral (All three sides are the same length.) Isosceles (Two sides are the same length.) Scalene (Each side is a different length.) Represent and label how you classiﬁed the triangles on your chart paper in the space below. Triangle

Equilateral

Isosceles

Scalene

Classify Two-Dimensional Figures | 199

Classify Two-Dimensional Figures

Explore 3

Record how each triangle was classiﬁed based on its side lengths and angles in the space below: Acute

Right

Obtuse

Equilateral Triangles (All three sides are the same length.) Isosceles Triangles (At least two sides are the same length.) Scalene Triangles (Each side is a different length.)

Explain how a triangle can be named after two different classiﬁcations. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can you determine whether a triangle is right, acute, or obtuse? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 200 | Classify Two-Dimensional Figures

Classify Two-Dimensional Figures

Explore 3 Part II: Choosing the Best Triangle

Read each customer request for the type of triangular sail they need for their sailboat. Draw a picture of the triangle that best ﬁts the description. Identify each type of triangular sail. Customer Request

Drawing of Sail

Triangle Identiﬁcation

Sailboat 1 I would like a triangular sail with two congruent sides and one obtuse angle. Sailboat 2 I would like a triangular sail with a right angle and no congruent sides. Sailboat 3 I would like a triangular sail with all acute angles and all congruent sides.

Classify Two-Dimensional Figures | 201

Unit Conversions

203

Unit Conversions

Explore 1

Name: _______________________ Date: __________

Convert Units of Length Record your work for each Task Card in the space below.

Task 1 When converting _______ to _______, I need to __________________________. Feet

Inches

Step 1:

1 12 13

Step 2 (if needed):

Inches between the buildings: ___________________________

Task 2 When converting _______ to _______, I need to __________________________. Meters

Centimeters

Step 1:

1 9 7.5

Step 2 (if needed):

Unit Conversions | 205

Unit Conversions

Explore 1 Task 3

When converting _______ to _______, I need to __________________________. Yards

Step 1:

Inches

1 55 Is the stadium far enough? Why?

Step 2 (if needed):

___________________________ ___________________________

Task 4 When converting _______ to _______, I need to __________________________. Meters

Kilometers

Step 1:

1,000 15,000 12,500 Is the hospital close enough? Why?

Step 2 (if needed):

___________________________ ___________________________

206 | Unit Conversions

Unit Conversions

Explore 1 Task 5

When converting _______ to _______, I need to __________________________. mm

Step 1:

10 60 Total length of hoses:

Step 2 (if needed):

___________________________

Task 6 When converting _______ to _______, I need to __________________________. Miles

Feet

Step 1:

1 1 2

Feet to the museum:

Step 2 (if needed):

___________________________

Unit Conversions | 207

Explore 1

Unit Conversions

Reﬂ ect What do you notice about the numbers when converting smaller measurement units to larger measurement units? _____________________________________________________________________ _____________________________________________________________________ What do you notice about the numbers when converting larger measurement units to smaller measurement units? _____________________________________________________________________ _____________________________________________________________________ Even though the numbers change when converting units of measurement, what can you say about the distance they represent? _____________________________________________________________________ _____________________________________________________________________ Why do some conversions require only one step while other conversions require two steps? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

208 | Unit Conversions

Explore 2

Unit Conversions

Name: _______________________ Date: __________

Convert Units of Weight and Mass Part I How are ounces related to pounds? How are pounds related to tons? _____________________________________________________________________ _____________________________________________________________________ How are milligrams related to grams? How are grams related to kilograms? _____________________________________________________________________ _____________________________________________________________________ Use your scale or balance to complete the table below to show the number of smaller units in relation to the larger units. Larger Unit

Smaller Unit

1 pound

______ ounces

1 ton

______ pounds

1 kilogram

______ grams

1 gram

______ milligrams

Unit Conversions | 209

Unit Conversions

Explore 2 Part II

Station 1

Pounds

Ounces

1 18 12 When converting _______ to _______, I need to ___________________________. Write an equation that will help you solve the problem. Show your work for solving the problem. Solution:

Station 2

Tons

Pounds

1 3 When converting _______ to _______, I need to ___________________________. Write an equation that will help you solve the problem. Show your work for solving the problem. Solution:

210 | Unit Conversions

Unit Conversions

Explore 2 Station 3

Grams

Kilograms

1,000 10,000 When converting _______ to _______, I need to ___________________________. Write an equation that will help you solve the problem. Show your work for solving the problem. Solution:

Station 4

Milligrams

Grams

1,000 200,000 When converting _______ to _______, I need to ___________________________. Write an equation that will help you solve the problem. Show your work for solving the problem.

Solution:

Unit Conversions | 211

Unit Conversions

Explore 2 Station 5

Kilograms

Grams

1 1

2 10 When converting _______ to _______, I need to ___________________________. Write an equation that will help you solve the problem. Show your work for solving the problem.

Solution:

Station 6

Tons

Pounds

1 1

5 2 When converting _______ to _______, I need to ___________________________. Write an equation that will help you solve the problem. Show your work for solving the problem.

Solution:

212 | Unit Conversions

Explore 2

Unit Conversions

Reﬂ ect Describe your process for converting units. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Even though the numbers change when converting units of measurement, what can you say about the weight they represent? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Why do some conversions require only one step while other conversions require two steps? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Unit Conversions | 213

Unit Conversions

Explore 3

Name: _______________________ Date: __________

Convert Units of Liquid Volume Part I Record your work in the space provided. Gallon

Quart

Pint

Cup

Fluid Ounce

1 1 1 1 Kiloliter

Liter

Milliliter

1 Give an example of needing to multiply to convert. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Give an example of needing to divide to convert. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________

Unit Conversions | 215

Unit Conversions

Explore 3 Part II Water Station

When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Baked Goods Station When converting ___________ to ___________, I __________________________. Solve the problem.

216 | Unit Conversions

Solution and explanation:

Unit Conversions

Explore 3 Milkshake Station

When converting ___________ to ___________, I __________________________. When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Drink Station When converting ___________ to ___________, I __________________________. When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Unit Conversions | 217

Unit Conversions

Explore 3 Bread Station

When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Chocolate Fountain Station When converting ___________ to ___________, I __________________________. Solve the problem.

218 | Unit Conversions

Solution and explanation:

Explore 3

Unit Conversions

Reﬂ ect If someone asked you how it is possible that you found 16 pints to be equal to 2 gallons, how would you explain this is true using what you learned from your measurement tools? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How do you know when more than one step is needed to convert units? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Unit Conversions | 219

Explore 4

Unit Conversions

Name: _______________________ Date: __________

Convert Units of Time Part 1

Hours

Minutes

Seconds

1 1

If you are given a number of minutes, how would you ﬁnd the number of seconds that are equivalent? __________________________________________________________________ __________________________________________________________________ How do you know the relationship between seconds and minutes? __________________________________________________________________ __________________________________________________________________ If you are given a number of minutes, how would you ﬁnd the number of hours that are equivalent? __________________________________________________________________ __________________________________________________________________ How do you know the relationship between minutes and hours? __________________________________________________________________ __________________________________________________________________

Unit Conversions | 221

Unit Conversions

Explore 4 Part II Setting up Chairs

When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Icing Cookies When converting ___________ to ___________, I __________________________. Solve the problem.

222 | Unit Conversions

Solution and explanation:

Unit Conversions

Explore 4 Leaving for the Party

When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Party Events When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Unit Conversions | 223

Unit Conversions

Explore 4 Bidding on Dessert Timing

When converting ___________ to ___________, I __________________________. Solve the problem.

Solution and explanation:

Final Touches When converting ___________ to ___________, I __________________________. Solve the problem.

224 | Unit Conversions

Solution and explanation:

Explore 4

Unit Conversions

Reﬂ ect Explain how you can use your knowledge of fractions to efﬁciently solve problems related to a fraction of an hour or minute. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ In which task did you need to convert twice? Why? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ If you were given seconds, minutes, and hours and told to convert each time to the same unit, which unit of time would you choose? Why? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

Unit Conversions | 225

Volume

227

Explore 1

Volume

Name: _______________________ Date: __________

Cubic Units Part I: Boxing Hats Shipping Box 1 How many cubes fit the length of the box? _________________________________ How many cubes fit the width of the box? _________________________________ How many cubes fit the height of the box? _________________________________ Measure, using centimeters. Box length

Elf-hat box length

Box width

Elf-hat box width

Box height

Elf-hat box height

The volume of the shipping box is ______________________________________. Shipping Box 2 How many cubes fit the length of the box? _________________________________ How many cubes fit the width of the box? _________________________________ How many cubes fit the height of the box? _________________________________ Measure, using centimeters. Box length

Elf-hat box length

Box width

Elf-hat box width

Box height

Elf-hat box height

The volume of the shipping box is ______________________________________.

Volume | 229

Volume

Explore 1 Part II: Missing Boxes Shipping Box 3 Three elf-hat boxes will ﬁt in the length of this shipping box. What is the length of shipping box 3 in centimeters?

__________

Two elf-hat boxes will ﬁt in the width of this shipping box. What is the width of shipping box 3 in centimeters?

__________

Two elf-hat boxes will ﬁt in the height of this shipping box. What is the height of shipping box 3 in centimeters?

__________

What is the volume of shipping box 3? _____________________ Shipping Box 4 Six elf-hat boxes will ﬁt in the length of this shipping box. What is the length of shipping box 4 in centimeters?

__________

Five elf-hat boxes will ﬁt in the width of this shipping box. What is the width of shipping box 4 in centimeters?

__________

Four elf-hat boxes will ﬁt in the height of this shipping box. What is the height of shipping box 4 in centimeters?

__________

What is the volume of shipping box 4? _____________________ Reﬂ ect What conclusion can you draw about the volume of a container and the number of cubic units that ﬁt into it? _____________________________________________________________________ _____________________________________________________________________ 230 | Volume

Volume

Explore 2

Name: _______________________ Date: __________

Discover Volume Part I: Skyscraper Design Create two rectangular prism-shaped buildings with the same volume. Building 1

Building 2

Base is 4 units long by 3 units wide.

Base is 5 units long by 2 units wide.

Area of the base = _________________

Volume with 1 ﬂoor = _____________________

Volume with 2 ﬂoors = _____________________

Volume with 3 ﬂoors = _____________________

Volume with 4 ﬂoors = _____________________

Volume with 5 ﬂoors = _____________________

Volume with 6 ﬂoors = _____________________

Volume with 7 ﬂoors = _____________________

Final building size:

Height = _________________________

Volume = ________________________

Volume | 231

Volume

Explore 2 Part II: Buildings in All Shapes Construct as many buildings as you can out of the cubes. All buildings need to be equal to the given volume. Your group must come up with all possibilities of the different buildings with the same volume. Volume = 36 cubic units

How many buildings did your group create? _______________________________ What are the dimensions of your different buildings? ________________________ __________________________________________________________________ __________________________________________________________________ Volume = 24 cubic units How many buildings did your group create? _______________________________ What are the dimensions of your different buildings? ________________________ __________________________________________________________________ __________________________________________________________________ Reﬂ ect How can there be two formulas for ﬁnding volume of a rectangular prism? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What did you notice about the relationship between the area of the base and the height of the skyscraper when you had two skyscrapers with the same volume? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 232 | Volume

Explore 3

Volume

Name: _______________________ Date: __________

Volume of Rectangular Prisms Part I: Small Pet Crates MeWOW’s Pet Store wants to set up a new small pet crate display. Only certain size crates will ﬁt on the top shelf of the display. • The crate must have a volume of at least 10 cubic feet. • There is only enough space on the top shelf for a crate that has a base area of 7 square feet or less. Which crate or crates will ﬁt? Show all of your work. Crate A Length = 3 feet Width = 2 feet Height = 2 feet

Crate B Length = 2 feet Width = 4 feet Height = 2 feet

Crate C Length = 2 feet Width = 3 feet Height = 3 feet

Area of the base =

____________________

V=B×h=

____________________

V=l×w×h=

____________________

Which small pet crate or crates did you choose? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Volume | 233

Volume

Explore 3 Part II: Cat Toy Display

MeWOW’s has an area in their store to place cube-shaped bins for cat toys. Because their space is limited, they must make sure the bin is big enough to hold all the cat toys and tall enough so that customers can easily look through the sides of the bin to see the toys. • The bin must have a volume of at least 25 cubic feet. • The bin must be 3–5 feet tall. Which bin or bins will work in MeWOWs’ display? Show all of your work. Bin A Side length = 2 feet

Bin B Side length = 3 feet

Bin C Side length = 4 feet

Area of the base =

____________________

V=B×h=

____________________

V=s×s×s=

____________________

Which bin or bins did you choose? Explain. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

234 | Volume

Volume

Explore 3 Part III: Cat Food Display Shape: Rectangular Prism Length = 3 feet Width = 2 feet Height = ___________ Volume = 6 cu. ft.

Shape: Rectangular Prism Base = ___________ Height = 4 feet Volume = 36 cu. ft.

Shape: Cube Length = ___________ Width = ___________ Height = ___________ Volume = 125 cu. in.

Princess Purr Cat Food Show your work.

Fur Favorite Cat Food Show your work.

Fish Stew Cat Food Show your work.

Reﬂ ect What can you do if you need to ﬁnd missing dimensions of a rectangular prism? _____________________________________________________________________ _____________________________________________________________________ When might it be useful to use both volume formulas on the same problem? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Volume | 235

Graph in the First Quadrant

237

Graph in the First Quadrant

Explore 1

Name: _______________________ Date: __________

The Coordinate Plane Part I: Plotting Points What role did you have? ____________________________ Write the ordered pair for your location, and describe the process of how you located that point on the coordinate plane. _____________________________________________________________________ _____________________________________________________________________ Choose 3 ship locations, and record the ordered pairs below. Graph the points, and label each point on the graph with the letter it represents. A: (___, ___) B: (___, ___)

C: (___, ___) Label the following attributes on the graph: • x-axis x • y-axis y • Origin • Point Choose one ordered pair above, and label the following: • x-coordinate x • y-coordinate y

9 8 7 6 5 4 3 2 1 0

x 1

9 10

Graph in the First Quadrant | 239

Graph in the First Quadrant

Explore 1 Part II: Missing Ships Plot the missing ships on the coordinate grid below. y 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Reﬂ ect

x 1

10 11 12 13 14 15

What is the purpose of ordered pairs? _____________________________________________________________________ _____________________________________________________________________ What process did you use to graph ordered pairs? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How can your prior knowledge of number lines help you navigate a coordinate plane? _____________________________________________________________________ _____________________________________________________________________ 240 | Graph in the First Quadrant

Explore 2

Graph in the First Quadrant

Name: _______________________ Date: __________

Plot Shapes Cut out the Furniture Shapes, and place them on the Blueprint using the following coordinates. Sofa: (4, 1), (4, 5), (16, 1), (16, 5) TV table: Coffee table:

(7, 17), (7, 20), (11, 17), (11, 20) (6, 7), (13, 7), (7, 10), (12, 10)

Plant stand: (20, 11), (16, 14), (20, 17) Draw the locations of the furniture, and record the coordinates of each corner on the blueprint below. y 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Graph in the First Quadrant | 241

Explore 2

Graph in the First Quadrant

Michaela decided to move a small square end table from her dining room into her living room. Three of the corners of the table are at (17, 2), (19, 2), and (19, 4). Using a marker, draw and label the square on the blueprint. What are the coordinates of the fourth corner? ___________ Next, she bought a rug that is shaped like a parallelogram to put in the room. Three of its vertices are at (6, 11), (7, 15), and (12, 15). Using a different-colored marker, draw and label the rug on the blueprint. What are the coordinates of the fourth vertex? ___________ She’s hoping to also fit a hexagonal desk inside the room. The vertices of the desk would be at (1, 16), (0, 18), (1, 20), (4, 20), and (5, 18). Using a different-colored marker, draw and label the desk on the blueprint. What are the sixth coordinates of the desk? ___________ Refl ect How did you find the missing vertices in the shapes? _____________________________________________________________________ _____________________________________________________________________ How would your blueprint change if the given points had their xx- and y-coordinates y switched? _____________________________________________________________________ _____________________________________________________________________

242 | Graph in the First Quadrant

Graph in the First Quadrant

Explore 3

Name: _______________________ Date: __________

Graph Real-World Problems Plot your points for each scenario on your Business Scenario Cards, and then complete each corresponding table and the questions below. T-Shirt Titan

x-axis

y-axis

Ordered Pair

Which ordered pair represents how much money you earned after selling 5 shirts?

x-axis

y-axis

Ordered Pair

Using your ordered pairs, how much money did you earn from selling 7 shirts?

Graph in the First Quadrant | 243

Graph in the First Quadrant

Explore 3 Budgeting for Success

x-axis

y-axis

Ordered Pair

Which ordered pair represents how much money is left in the budget after buying products for 9 shirts?

x-axis

y-axis

Ordered Pair

Using your ordered pairs, how much money is left in the budget after buying products for 3 shirts?

Made to Order

x-axis

y-axis

Ordered Pair

Which ordered pair represents how many shirts you made in 8 hours? 244 | Graph in the First Quadrant

x-axis

y-axis

Ordered Pair

Graph in the First Quadrant

Explore 3 Shipping Out

x-axis

y-axis

Ordered Pair

Which ordered pair represents how many shirts were in 6 full boxes?

x-axis

y-axis

Ordered Pair

Using your ordered pairs, how many shirts were in 3 full boxes?

Supplying Shirts

x-axis

y-axis

Ordered Pair

x-axis

y-axis

Ordered Pair

Using your ordered pairs, how many miles did you travel after all 7 trips? Graph in the First Quadrant | 245

Graph in the First Quadrant

Explore 3 Reﬂ ect What process did you use to create your ordered pairs?

246 | Graph in the First Quadrant

Generate and Graph Numerical Patterns

247

Generate and Graph Numerical Patterns

Explore 1

Name: _______________________ Date: __________

Generate and Graph One Numerical Pattern Complete the sections below about each scenario. Use the materials provided to model each scenario. Scenario 1 Draw your model.

What is the rule? _________________________________ List what each variable stands for. x: ____________________________ y: ____________________________ Describe the rule in your own words. ________________________________ ________________________________

Table:

Ordered Pair

0 1

(Paste the graph here.)

2 3 If you continue the pattern, what is the corresponding term of y if x is 25? ___________ What does that value mean? _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Generate and Graph Numerical Patterns | 249

Generate and Graph Numerical Patterns

Explore 1 Scenario 2 Draw your model.

Table:

6 (Paste the graph here.)

Ordered Pair

If you continue the pattern, what is the corresponding term of y when x is 13? _________________ What does that value mean? _____________________________________________________________________ What could you do if you knew the value of y and needed to ﬁnd the corresponding term of x? _____________________________________________________________ 250 | Generate and Graph Numerical Patterns

Generate and Graph Numerical Patterns

Explore 1 Scenario 3 Draw your model.

Table:

Ordered Pair

0 25

(Paste the graph here.)

32 84 If you continue the pattern, what is the corresponding term of y when x is 418? ________________ What does that value mean? _____________________________________________________________________ What would be the corresponding term of x if y were 44? _________________

Generate and Graph Numerical Patterns | 251

Generate and Graph Numerical Patterns

Explore 1 Scenario 4 Draw your model.

Table:

9 (Paste the graph here.)

Ordered Pair

If you continue the pattern, what is the corresponding term of y when x is 21? ________________ What does that value mean? _____________________________________________________________________ What could you do if you knew the value of y and needed to ﬁnd the corresponding term of x? _____________________________________________________________ 252 | Generate and Graph Numerical Patterns

Generate and Graph Numerical Patterns

Explore 1

Graphing Templates Use the tables you created, and graph the values on the templates below. Be sure to include a title for your graph, and label the xx-axis and the yy-axis. Decide on a scale for each axis, and label them.

Title ____________________________

yy-axis: __________________________

When you ﬁnish, cut out each graph, and glue it next to the table it represents.

Title ____________________________

Title ____________________________ yy-axis: __________________________

xx-axis: _____________________________

yy-axis: __________________________

x-axis: _____________________________ x

xx-axis: _____________________________

Generate and Graph Numerical Patterns | 253

Generate and Graph Numerical Patterns

Explore 2

Name: _______________________ Date: __________

Generate and Graph Two Numerical Patterns Complete the sections below about each scenario. Use the materials provided to model each scenario.

Footlongs What is the rule for Sam?

What is the rule for Hank?

________________________________

List what each variable stands for.

x: ___________________________

y: ___________________________

Describe the rule in your own words.

________________________________

Sam

Hank

y (Paste the graph here.)

How do the two rules relate to each other? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Generate and Graph Numerical Patterns | 255

Generate and Graph Numerical Patterns

Explore 2 Free Fish What rule represents the Fish Cup game?

What rule represents the Fish Pond game?

________________________________

List what each variable stands for.

x: ___________________________

y: ___________________________

y: ___________________________ Describe the rule in your own words.

________________________________

Fish Cup

Describe the rule in your own words.

Fish Pond

(Paste the graph here.)

Generate and Graph Numerical Patterns

Explore 2 Power Bell What rule represents ages 3–10?

What rule represents ages 11–16?

________________________________

List what each variable stands for.

x: ___________________________

y: ___________________________

Describe the rule in your own words.

________________________________

Ages 3–10

Ages 11–16

y (Paste the graph here.)

Generate and Graph Numerical Patterns | 257

Generate and Graph Numerical Patterns

Explore 2 Milk Bottles What rule represents Mickey’s?

What rule represents Matt’s?

________________________________

List what each variable stands for.

x: ___________________________

y: ___________________________

y: ___________________________ Describe the rule in your own words.

________________________________

Mickey

Describe the rule in your own words.

Matt

(Paste the graph here.)

Generate and Graph Numerical Patterns

Explore 2

Graphing Templates

Title ____________________________

yy-axis: __________________________

Use the tables you created, and graph the values on the templates below. Be sure to include a title for your graph and label the xx-axis and yy-axis. Decide on a scale for each axis, and label them. Be sure to graph both lines. When you ﬁnish, cut out each graph on the dotted lines, and glue it next to the table it represents.

Title ____________________________

Title ____________________________ yy-axis: __________________________

xx-axis: _____________________________

yy-axis: __________________________

xx-axis: _____________________________

Generate and Graph Numerical Patterns | 259

Explore 2

Generate and Graph Numerical Patterns

Reﬂ ect Why do you think we should know how to graph something like this? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What connections did you make while doing this Explore activity? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ How does your graph compare to the table? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What observations did you make with the two patterns in the same contest? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 260 | Generate and Graph Numerical Patterns

Represent and Interpret Data

261

Explore 1

Represent and Interpret Data

Name: _______________________ Date: __________

Line Plots Part I: Flip It Copy the class data onto the table, and then use an appropriate scale to plot it on the number line below. Class Data Table

Title: ___________________________________________

1. How many people participated in Flip It? __________________________________ 2. What is the difference between the greatest and least number of times the bottle got ﬂipped and landed upright? _____________________________________________ 3. What Flip It number(s) occurred the most times? ____________________________ 4. Circle the nearest fraction that shows how many students got the water bottle to 1 2 1 3 stand up 4 or more times. 4

5. How is this line plot useful? ___________________________________________________________________ ___________________________________________________________________

Represent and Interpret Data | 263

Explore 1

Represent and Interpret Data

Part II: Blow It Off See how many seconds it takes your group to move a 1 cm cube from one side of the desk off the other end of the desk using only a straw. Each person in the group gets a try, and the group picks the fastest time. Record each group’s best result on the data table and then on the line plot. Group Data Table

Title: ___________________________________________

1. How many groups participated in Blow It Off? ______________________________ 2. What is the difference between the fastest and slowest times required to move a cube? _____________________________________________________________ 3. What Blow It Off number(s) occurred the most times? ________________________ 4. How many groups blew a cube off the end of a desk in less than 1.5 seconds? _______________ 5. Is it easier to understand the data in the data table or in the line plot? Why? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 264 | Represent and Interpret Data

Represent and Interpret Data

Explore 1 Part III: Grab It

Record each student’s reaction measurement on the table and then on the line plot below. Class Data Table

Title: ___________________________________________

1. How many people participated in this activity? ______________________________ 2. What is the difference between the longest and shortest reaction measurement? ___________________________________________________________________ 3. What reaction measurement(s) occurred the most times? _____________________ 4. What fraction of students had a reaction measurement of greater than 5 inches? 3 2 1 Circle the nearest fraction. 4

5. What is the total length of inches from students who have a reaction measurement of less than 5 inches? ___________________________________________________________________

Represent and Interpret Data | 265

Represent and Interpret Data

Explore 2

Name: _______________________ Date: __________

Bar Graphs Part I: Collecting and Representing Data on a Bar Graph Create a business idea, and determine ﬁve services for your business to offer. Collect fellow classmate responses on their favorite services, and represent them using a bar graph. What is the name of your business? ________________________________________ What are the ﬁve services your business will offer? • _______________________________________ • _______________________________________ • _______________________________________ • _______________________________________ • _______________________________________ After collecting classmate responses, display the data from your business chart paper on the bar graph below.

Number of votes

Title:

Represent and Interpret Data | 267

Represent and Interpret Data

Explore 2 Part II: Interpreting Data on a Bar Graph

Using each group’s business bar graph, interpret the data represented to determine which services had the greatest number of votes and which had the least number of votes and what their values were. Outdoor Care

Indoor Care

Which service had the most votes? _______________________________

What was the value? __________

Which service had the least votes?

_______________________________

What was the value? __________

Athletics

Arts and Crafts

Which service had the most votes? _______________________________

What was the value? __________

Which service had the least votes?

_______________________________

What was the value? __________

Technology

Tutoring

Which service had the most votes? _______________________________

What was the value? __________

Which service had the least votes?

_______________________________

What was the value? __________

268 | Represent and Interpret Data

Represent and Interpret Data

Explore 2

Create a bar graph using the service with the most votes from each business. Then, write two questions, and answer them using the information represented on the bar graph.

Number of votes

Title:

Business services

Question and answer 1: _____________________________________________________________________ _____________________________________________________________________ Question and answer 2: _____________________________________________________________________ _____________________________________________________________________ Reﬂ ect How are bar graphs useful? _____________________________________________________________________ _____________________________________________________________________ In what situations might you want to use a bar graph? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Interpret Data | 269

Represent and Interpret Data

Explore 3

Name: _______________________ Date: __________

Interpret Mean Part I: Mean as Balance Point For each scenario, order the data from least to greatest. Plot the data on the line plot given, and then circle the balance point. Data points for scenario 1: ____, ____, ____, ____, ____

Cookies eaten

What do you notice about the distance between the points? __________________________________________________________________ How could you keep the balance point if Mrs. Martinez ate one cookie? __________________________________________________________________ Data points for scenario 2: ____, ____, ____, ____, ____, ____, ____

Minutes read

What does the balance point for this data represent? __________________________________________________________________ __________________________________________________________________ What is the balance point? How can you ﬁnd the balance point in a set of data? _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Interpret Data | 271

Explore 3

Represent and Interpret Data

Part II: Mean as Equal Shares Each Scenario Card shows how a different type of candy is currently distributed in the ﬁve party favor bags. In the workspace below, use centimeter cubes to model each candy type, and then equally share the candy among the ﬁve bags to determine the mean. Record the mean for each candy type in the table.

Candy Type

Mean

Sugar Snaps Sweet Twists Sour Swirls 1. What strategy did you use to split the candy equally among the ﬁve bags? ___________________________________________________________________ ___________________________________________________________________ 2. How many more sugar snaps would Anna need to buy if she wanted each bag to have 5 sugar snaps inside? ___________________________________________________________________ ___________________________________________________________________ 3. How can you use the idea of equal shares to ﬁnd the mean of the following data set? 5, 5, 5, 6, 4 ___________________________________________________________________ ___________________________________________________________________ 272 | Represent and Interpret Data

Explore 3

Represent and Interpret Data

Part III: Mean as Leveling Out Each Scenario Card shows a different collection of towers Marco and Candace pulled out of the linking cube box. Use your own linking cubes to model each collection, and then redistribute the cubes until all towers contain the same number of cubes to level them out. Record the mean for each collection in the table below. Collection

Mean

Collection 1 Collection 2 Collection 3 Describe your process for redistributing your cubes to level out the towers. What do the leveled out towers represent? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Refl ect Define the term mean in your own words. How can you find the mean in a set of data? _____________________________________________________________________ What similarities and differences did you see between balance point, equal share, and leveling out? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ What operation(s) are you modeling as you find the mean of a data set? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ © Accelerate Learning Inc. – All Rights Reserved

Represent and Interpret Data | 273

Represent and Interpret Data

Explore 4

Name: _______________________ Date: __________

Mean, Mode, Median, and Range Gather the data from each basketball team’s Data Card by listing the numbers in order from least to greatest. Then, ﬁnd the mean, median, mode, and range of the given data to report back to the head coach so the team can prepare for their upcoming opponents.

Houston Heroes List data in order from least to greatest. ____ , ____ , ____ , ____ , ____ Mean When we equally shared the values of the given data, the mean for the points scored was ___________ .

Mode Circle the correct response. ( Yes, No ) there ( is, isn’t ) a mode. Mode = _____________ Median The median for our data was _________ points. Range The range for our data was ________ because _______ – ______ = ______.

Represent and Interpret Data | 275

Represent and Interpret Data

Explore 4 Los Angeles Laserbeams List data in order.

____ , ____ , ____ , ____ , ____ , ____ Mean

Mode

When we equally shared the values

Circle the correct response. ( Yes, No ) there ( is, isn’t ) a mode.

of the given data, the mean for the

Mode = _____________

rebounds was ___________ .

Median The median for our data was _________ rebounds. Range The range for our data was ________ because _______ – ______ = ______.

Orlando Warriors List data in order. ____ , ____ , ____ , ____ , ____ , ____ , ____ , ____ , ____ , ____ Mean I found the mean by ﬁnding the balance

Mode Circle the correct response. ( Yes, No ) there ( is, isn’t ) a mode.

point of the line plot.

Mode = _____________

The mean for the minutes played is

Median

___________ .

The median for our data was _________ minutes. Range The range for our data was ________ because _______ – ______ = ______.

276 | Represent and Interpret Data

Represent and Interpret Data

Explore 4 Utah Hawks List data in order.

____ , ____ , ____ , ____ , ____ , ____ , ____ Mean

Mode

I found the mean by ﬁnding the balance

Circle the correct response. ( Yes, No ) there ( is, isn’t ) a mode.

point or equal share of the line plot.

Mode = _____________

The mean for the points scored is

Median

___________.

The median for our data was _________ points. Range The range for our data was ________ because _______ – ______ = ______.

Georgia Terriers List data in order.

____ , ____ , ____ , ____ , ____ , ____ , ____ Mean

When we equally shared the values of

Mode Circle the correct response. ( Yes, No ) there ( is, isn’t ) a mode.

the given data, the mean for the minutes

Mode = _____________

played was ___________ .

Median The median for our data was _________ minutes. Range The range for our data was ________ because _______ – ______ = ______.

Represent and Interpret Data | 277

Represent and Interpret Data

Explore 4 Chicago Longhorns List data in order.

____ , ____ , ____ , ____ , ____ , ____ , ____ , ____ Mean

When we equally shared the values

Mode Circle the correct response. ( Yes, No ) there ( is, isn’t ) a mode.

of the given data, the mean for the

Mode = _____________

rebounds was ___________ .

Median The median for our data was _________ rebounds. Range The range for our data was ________ because _______ – ______ = ______.

Reﬂ ect What do you notice about the value of the mean and the value of the median for each basketball team? _____________________________________________________________________ _____________________________________________________________________ Why do you think the mean, median, mode, and range are important when analyzing data? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 278 | Represent and Interpret Data

Skills Quizzes

279

Skills Quiz

Place Value Relationships

Name: _______________________ Date: __________

Place Value Relationships Write the number that has the place value position that is 10 times the value of the underlined digit. 1.

304,879.267 ______________________________________________________

482,273.596 ______________________________________________________

98,253.174 _______________________________________________________ 1

Write the number that has the place value position that is 10 of the value of the underlined digit. 4.

987,654.321 ______________________________________________________

123,456.789 ______________________________________________________

678,543.107 ______________________________________________________

Use multiplication or division to ﬁnd the answer that ﬁlls in the blank. 7.

________ × 10 = 9,292

79,110 ÷ 100 = ________

________ × 1,000 = 151,370

10.

563.9 × 100 = ________

11.

3,456.789 × 10 = ________

Apply your knowledge of exponents to ﬁnd the answer in standard form. 12.

653 × 102 = __________

13.

52 ÷ 101 = __________

14.

5,732 × 103 = __________

Place Value Relationships | 281

Read and Write Decimals

Skills Quiz

Name: _______________________ Date: __________

Read and Write Decimals Use the place value chart to answer questions 1–3. Thousands Hundreds

Tens

Ones Decimal Tenths Hundredths Thousandths

Write the number nine thousand three hundred four and ﬁfty-six hundredths in the place value chart.

Write the number using base-ten numerals. _____________________________

Write the number using expanded form. ________________________________________________________________

Use the place value chart to answer questions 4–6. Thousands Hundreds

Tens

Ones Decimal Tenths Hundredths Thousandths

Write the number ﬁve hundred thirty-six and one hundred forty-nine thousandths in the place value chart.

Write the base-ten numerals of the number. _____________________________

Write the expanded form. ________________________________________________________________

Read and Write Decimals | 283

Read and Write Decimals

Skills Quiz Use the place value chart to answer questions 7–9. Hundred Ten Thousands Thousands Thousands

Hundreds

Tens Ones Decimal Tenths Hundredths Thousandths

Write the number twenty-ﬁve thousand six hundred twenty and seven hundredths in the place value chart.

Write the base-ten numeral of the number. ______________________________

Write the expanded form. ________________________________________________________________

284 | Read and Write Decimals

Skills Quiz

Compare and Order Decimals

Name: _______________________ Date: __________

Compare and Order Decimals Use the appropriate symbol (>, <, or =) to make each statement true. Then, write the meaning of the symbol you used to the right of each statement. 1.

0.017 __________ 0.018

_______________________

44.063 __________ 44.603

_______________________

23,067.8 __________ 23,607.9

_______________________

711.445 __________ 711.435

_______________________

1.111 __________ 1.110

_______________________

1,224.07 __________ 1,224.70

_______________________

0.090 __________ 0.09

_______________________

Compare and Order Decimals | 285

Compare and Order Decimals

Skills Quiz Write two comparisons for each pair of numbers. 8.

6.354

6.35

____________________

26.263

_______________________

26.257

____________________

10.

31.004

_______________________

31.04

____________________

_______________________

Write the following sets of numbers in order from least to greatest. Use the appropriate symbol (> or <) between the values. 11.

7.38

7.315

7.05

7.405

7.5

________________________________________________________________

12.

2.605

2.6

2.56

2.065

2.06

________________________________________________________________

286 | Compare and Order Decimals

Compare and Order Decimals

Skills Quiz

Write the following sets of numbers in order from greatest to least. Use the appropriate symbol (> or <) between the values. 13.

619.018

617.97

617.309

618.537

618.63

________________________________________________________________

14.

0.005

0.05

0.009

0.9

0.50

________________________________________________________________

15.

45.67 2

45.65 3

46.751

45.056

46.875

________________________________________________________________

Compare and Order Decimals | 287

Round Decimals

Skills Quiz

Name: _______________________ Date: __________

Round Decimals Round the numbers to the nearest tenth. 1.

32.456 = _____

95.65 = _____

123.78 = _____

34.34 = _____

444.453 = _____

Round the numbers to the nearest hundredth. 6.

868.488 = _____

34.654 = _____

960.954 = _____

44.459 = _____

10.

808.987 = _____

Round the numbers to the nearest whole number. 11.

904.43 = _____

12.

989.06 = _____

13.

87.098 = _____

14.

324.78 = _____

15.

23.990 = _____

Round Decimals | 289

Skills Quiz

Add and Subtract Decimals

Name: _______________________ Date: __________

Add and Subtract Decimals Add the decimals to ﬁnd the sum. 1.

19.9 + 8.2 =

0.51 + 0.78 =

22.3 + 2.04 =

3.94 + 0.78 =

47.05 + 3.8 =

Subtract the decimals to ﬁnd the difference. 6.

0.6 – 0.03 =

5.72 – 1.2 =

5.53 – 2.9 =

0.34 – 0.12 =

10.

27.8 – 3.19 =

Add and Subtract Decimals | 291

Skills Quiz

Add and Subtract Decimals

Add or subtract to ﬁnd the sum or difference. 11.

5.09 + 3.4 =

12.

35 – 30.35 =

13.

9.27 + 12.55 =

14.

0.31 – 0.06 =

15.

0.87 + 9.1 =

292 | Add and Subtract Decimals

Skills Quiz

Multiply Multi-Digit Whole Numbers

Name: _______________________ Date: __________

Multiply Multi-Digit Whole Numbers Use any strategy to solve the examples below. 1.

100 × 59 = _____________

What is the product of 576 and 87?

789 × 35 = _____________

What is the product of 234 and 32?

909 × 73 = ______________

What is the product of 565 and 43?

Multiply Multi-Digit Whole Numbers | 293

Skills Quiz 7.

67 × 76 = _________________

What is the product of 654 and 23?

760 × 89 = __________________

10.

What is the product of 22 and 777?

11.

708 × 90 = _________________

12.

What is the product of 32 and 45?

13.

234 × 58 = ________________

294 | Multiply Multi-Digit Whole Numbers

Multiply Multi-Digit Whole Numbers

Skills Quiz

Divide Multi-Digit Whole Numbers

Name: _______________________ Date: __________

Divide Multi-Digit Whole Numbers Solve for the quotients in the division equations below. Try not to use the same strategy twice in a row. 1.

5,040 ÷ 20 = ______

1,875 ÷ 25 = ______

7,650 ÷ 18 = ______

Divide Multi-Digit Whole Numbers | 295

Skills Quiz 4.

1,050 ÷ 21 = ______

1,254 ÷ 19 = ______

1,184 ÷ 16 = ______

296 | Divide Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers

Skills Quiz 7.

1,577 ÷ 19 = ______

2,156 ÷ 14 = ______

1,173 ÷ 23 = ______

10.

2,091 ÷ 17 = ______

Divide Multi-Digit Whole Numbers

Divide Multi-Digit Whole Numbers | 297

Skills Quiz

Numerical Expressions

Name: _______________________ Date: __________

Numerical Expressions Draw a model for each scenario. Then, write and evaluate an expression to solve. 1.

Reginald earned $32 walking dogs, $18 washing cars, and $15 mowing the lawn. He then spent $12 on a new toy. How much money does Reginald have left?

Model:

Expression:

Value:

Violet is a cupcake designer who needs to make 500 cupcakes for her local farmers’ market. She’s already made 40 dozen cupcakes. How many more cupcakes does Violet need to make to be ready for the farmers’ market?

Model:

Expression:

Value:

Numerical Expressions | 299

Numerical Expressions

Skills Quiz 3.

Kevin was getting ready to build an entertainment center for his house. He purchased 4 sheets of plywood that each cost $63 and 8 pieces of lumber that cost $7 each. How much money did Kevin spend on materials for the entertainment center?

Model:

Expression:

Value:

Evaluate each given expression. 4.

15 × (5 – 3) = _____________________________________________________

15 × 5 – 3 = ______________________________________________________

1,050 ÷ (5 × 10) = _________________________________________________

Interpret each statement into a numerical expression. 7.

Find 4 more than the quotient of 49 divided by 7.

Find 8 less than the product of 4 and 7.

Find 6 times the sum of 8 plus 8.

10.

Find the quotient of 81 and 9, and then subtract 12.

300 | Numerical Expressions

Compare and Order Fractions and Mixed Numbers

Skills Quiz

Name: _______________________ Date: __________

Compare and Order Fractions and Mixed Numbers Use <, >, or = to solve each problem. Show your work on the number lines by using labels. 1.

13 5

3 6

2 3

___

6 10

1 2

8 10

Compare and Order Fractions and Mixed Numbers | 301

Compare and Order Fractions and Mixed Numbers

Skills Quiz

Use the number lines below to represent each fraction. Circle the fraction that is closest to 0. Put a square around the fraction that is closest to 2. 4.

9 12

14 6

13 4

7 8

11 2

4 4

Use <, >, or = to solve each problem. 6.

302 | Compare and Order Fractions and Mixed Numbers

Compare and Order Fractions and Mixed Numbers

Skills Quiz 9.

Plot each fraction and mixed number on the given number line. Then, write them in order from greatest to least.

1 >

Greatest to least:

10.

16 7

1 2

1 14

2 >

Plot each fraction and mixed number on the given number line. Then, write them in order from least to greatest.

8 9

0 Least to greatest:

11 3

3 3

1 <

2 <

Compare and Order Fractions and Mixed Numbers | 303

Skills Quiz

Add and Subtract Fractions

Name: _______________________ Date: __________

Add and Subtract Fractions Use the models to solve the fraction addition and subtraction problems. 1.

2 3

–

2 6

3 4

–

2 3

1 2

–

3 10

2 3

–

1 2

Add and Subtract Fractions | 305

Skills Quiz 5.

2 3

5 8

3 5

–

3 6

3 4

5 6

2 4

–

1 8

6 8

2 3

306 | Add and Subtract Fractions

Add and Subtract Fractions

Multiply Fractions

Skills Quiz

Name: _______________________ Date: __________

Multiply Fractions Use the model to ﬁnd the product. 1.

7 5

2 ×

= _____________

1 1 5

1 5

3 4

1 5

× 3 = _____________

Write an equation that is represented by the model. 3.

__________________

1 1 2

1 2

1 1 2

1 2

Multiply Fractions | 307

Skills Quiz

Multiply Fractions

Create a model for each of the following to represent and solve for the product.

3 8

9 ×

5 6

5 ×

4 9

35 ×

× 4 =

1 7

308 | Multiply Fractions

Multiply Fractions

Skills Quiz

Compare the fractions below. Write the word greater or the word less for each comparison. 9.

2 3

× 4

Will the product be greater than or less than 23 ? __________

10.

5 9

× 3

Will the product be greater than or less than 3? __________

11.

3 4

× 5

Will the product be greater than or less than 4 ? __________

12.

5 8

× 2

Will the product be greater than or less than 2? __________

Multiply Fractions | 309

Fractions as Division

Skills Quiz

Name: _______________________ Date: __________

Fractions as Division Read the word problems, and solve. 1.

There are 3 siblings who want to equally share 5 cookies. How many cookies does each sibling get?

The Lowells have some land that they want to divide among their 4 grandchildren. If the grandparents have 13 acres, how much land does each grandchild get?

13 ? 3.

Ten teachers are sharing 3 boxes of dry-erase markers. How much of a box does each teacher get, once the boxes are divided?

Luis was making 8 wood fence pieces. If he had 14 feet of wood, how long would each fence piece be?

Fractions as Division | 311

Fractions as Division

Skills Quiz 5.

Rhonda was making scarves. She had 23 feet of fabric and needed to make 10 scarves. How much fabric could Rhonda have used for each scarf?

Marcus is mowing lawns to earn money. He is asked to mow 21 lawns over the course of 4 days. How many lawns does Marcus need to mow each day to be done on time?

21 ? 7.

Cheryl is creating hairbows for her business. She has 52 feet of ribbon and plans on making 16 bows. How many feet of ribbon can she use per bow?

Lola wants to run 7 miles in 8 days. How many miles must she run per day?

7 ? 312 | Fractions as Division

Divide Fractions

Skills Quiz

Name: _______________________ Date: __________

Divide Fractions Solve the word problems below by using a model of your choosing. 1.

Mary is making 5 cakes. Each cake will be divided into fourths. How many pieces of cake will there be when Mary cuts all of the cakes?

A seamstress is using 2 of a yard of fabric to make dresses for 3 girls. How much fabric will the seamstress use on each dress?

Ms. Davis is reﬁlling her glue bottles for her art classes. She has 3 of a gallon of glue to reﬁll 6 glue bottles. How much glue from the gallon will go into the glue bottles?

George is making peanut butter and jelly sandwiches for himself and 4 siblings. George cuts each sandwich into halves. How many sandwich pieces will there be when all the sandwiches are cut?

Divide Fractions | 313

Skills Quiz

Divide Fractions

A sandwich shop sells sub sandwiches that are 16 of a foot long. If the shop cuts the sandwiches into 2 pieces, what fraction of a foot would each section be?

A candy store owner has 5 pounds of fudge left over from the day’s sales. She decided to divide the leftover fudge into ﬁfths and put them out as samples for the customers on the following day. How many pieces of fudge will be available to sample?

Rodney has 2 of a package of canned dog food. He plans on feeding his dog Spot with this canned dog food over the next four days. How much of the package of dog food will Rodney feed Spot during the next four days?

Julie has 13 of a loaf of bread to make toast for herself and her 2 friends. How much toast will each person get?

Mark is making paintings for his room. He has 3 canvases, and he plans on dividing each canvas into thirds to have a different color for each piece. How many colors can he use for his paintings?

314 | Divide Fractions

Classify Two-Dimensional Figures

Skills Quiz

Name: _______________________ Date: __________

Classify Two-Dimensional Figures Use the classiﬁcation chart to classify the two-dimensional ﬁgures by shape and/or description. Two-Dimensional Figure

Numbers of Sides and Angles

Type of Angles

Quadrilateral

4 sides of any length

Angles can be acute, right, or obtuse.

Trapezoid

4 sides of any length, at Angles can be acute, right, or least 1 pair of parallel sides obtuse.

Parallelogram

4 sides, opposite sides are equal and parallel.

Opposite angles are the same type of angle.

Rhombus

4 sides of equal length, opposite sides are parallel.

Opposite angles are the same type of angle.

Square

4 sides of equal length, opposite sides are parallel.

All angles are right angles.

Rectangle

4 sides, opposites sides are equal in length, opposite sides are parallel.

All angles are right angles.

Classify the ﬁgure with the category or categories it belongs to based on its properties.

Classify Two-Dimensional Figures | 315

Skills Quiz

Classify Two-Dimensional Figures

Classify the ﬁgure with the category or categories it belongs to based on its properties.

316 | Classify Two-Dimensional Figures

Classify Two-Dimensional Figures

Skills Quiz

Investigate the side lengths and angles of each triangle shown. Use the categories to determine the classiﬁcation of each triangle. Write the number of each triangle in its classiﬁed box under the correct category. Then, write the name of each triangle in the space below each triangle image. Triangle Equilateral

Scalene

Acute

Right

Obtuse

Acute

Right

Obtuse

_____

Isosceles

Acute

Right

Obtuse

_____

10.

Classify Two-Dimensional Figures | 317

Unit Conversions

Skills Quiz

Name: _______________________ Date: __________

Unit Conversions Convert the following measurements. 1.

16 cups = ________ ounces

2 liters = ________ milliliters

10 meters = ________ centimeters

4 pints = ________ quarts

2 gallons = ________ quarts

18 minutes = ________ seconds

12.5 grams = ________ milligrams

48 feet = ________ yards

2 hours and 24 minutes = ________ minutes

10.

128 ounces = ________ gallon(s)

Unit Conversions | 319

Skills Quiz

Volume

Name: _______________________ Date: __________

Volume 1.

The area of the base of this prism is 30 cubic inches. What do you need to know in order to determine its volume?

Write the expression needed to determine its volume if the height of the prism is 7 inches. Solve the expression.

This ﬁgure was built by stacking centimeter cubes. Label the three dimensions of the prism.

What is the area of the base of the cube?

Write the expression needed to determine its volume. Solve the expression.

Volume | 321

Volume

Skills Quiz 6.

What is the area of the base of the rectangular prism?

6 units

10 units

8 units

How many of the cubic units will it take to ﬁll the entire prism?

The cube below has a side length of 6 cm. What is the area of the base?

Write an expression to determine the volume of the cube. Solve the expression.

322 | Volume

Skills Quiz 10.

Label the three dimensions of the rectangular prism below.

11.

What is the area of the base layer?

12.

Write an expression to determine the volume. Solve the expression.

Volume

Volume | 323

Volume

Skills Quiz 13.

Label the three dimensions of the rectangular prism below.

14.

What is the area of the base layer?

15.

Write an expression to determine the volume. Solve the expression.

324 | Volume

Graph in the First Quadrant

Skills Quiz

Name: _______________________ Date: __________

Graph in the First Quadrant Plot the points on the coordinate grids below. 1.

(8, 2)

y 10 9 8 7 6 5 4 3 2 1

(2, 6)

y 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

(10, 5)

1 2 3 4 5 6 7 8 9 10

y 10 9 8 7 6 5 4 3 2 1

(3, 3)

y 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

(4, 10)

1 2 3 4 5 6 7 8 9 10

y 10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

(7, 8)

y 10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

Graph in the First Quadrant | 325

Graph in the First Quadrant

Skills Quiz Write the coordinates of the points below. 7.

______

10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

______

10.

y 10 9 8 7 6 5 4 3 2 1

11.

10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

326 | Graph in the First Quadrant

y 10 9 8 7 6 5 4 3 2 1

12.

x 1 2 3 4 5 6 7 8 9 10

______

x 1 2 3 4 5 6 7 8 9 10

______

10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

______

y 10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

Generate and Graph Numerical Patterns

Skills Quiz

Name: _______________________ Date: __________

Generate and Graph Numerical Patterns Complete each table based on the given rule, and plot the data points. 1.

Complete the table below with the rule y = x + 5, and plot the data points on the graph.

y x-axis

y-axis

1 3 5

10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

Generate and Graph Numerical Patterns | 327

Generate and Graph Numerical Patterns

Skills Quiz 2.

Complete the table below with the rule y = x + 2, and plot the data points on the graph. y

x-axis

y-axis

0 1 2

10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 Complete the table below with the rule y = 3x, and plot the data points.

x-axis

y-axis

0 1 2

10 9 8 7 6 5 4 3 2 1

x 1 2 3 4 5 6 7 8 9 10

328 | Generate and Graph Numerical Patterns

Generate and Graph Numerical Patterns

Skills Quiz 4.

Twin siblings work at different restaurants and get paid different hourly wages. Timothy gets paid $7 for every hour he works. Anthony gets paid $9 for every hour he works. Create a table and a graph for each rule below. Be sure to create a scale, and label the xx-axis and yy-axis for your graph. Anthony’s rule: y = 9x

Timothy’s rule: y = 7x

1 2 3 4

What is the relationship between the two patterns? _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________

Generate and Graph Numerical Patterns | 329

Represent and Interpret Data

Skills Quiz

Name: _______________________ Date: __________

Represent and Interpret Data 1.

Rachel kept track of her math grades. They are listed below. Use the data to complete the table that follows by ﬁnding the median, mode, and range of Rachel’s grades. 81, 79, 79, 95, 85, 82, 96, 75, 40, 70, 89, 71, 96, 90, and 85 Median

Mode

Range

The amount of snowfall in inches recorded last week in Minneapolis, Minnesota, is shown in the table below. Snowfall in Inches Mon.

Tues.

Wed.

Thurs.

Fri.

Sat.

Sun.

2 in.

3 in.

1 in.

2 in.

0 in.

3 in.

Using the equal shares or leveling out strategy, what was the mean for the amount of snowfall in Minneapolis last week?

What was the median in the data above?

Represent and Interpret Data | 331

Represent and Interpret Data

Skills Quiz 4.

Use the data below to complete the line plot. 51 4

63 4

71 2

63 4

51 2

What is the mode for the data displayed on the line plot?

What is the range of the data set above?

332 | Represent and Interpret Data

63 4

51 2

Represent and Interpret Data

Skills Quiz

Steve was studying the wildlife at his local pond. As he analyzed the pond, he decided to record the number of wildlife he saw in the time he was there. Steve recorded the information on the bar graph below. Use Steve’s bar graph to answer questions 7–9.

Wildlife Seen at a Pond

Number of wildlife

10 9 8 7 6 5 4 3 2 1 0

Ducks

Frogs

Turtles

Fish

Snakes

Wildlife

What is the range for wildlife seen at the pond?

What is the mode for the amount of wildlife seen at the pond?

Using the leveling out or equal shares strategy, what is the mean for the amount of wildlife seen at the pond?

Represent and Interpret Data | 333

Represent and Interpret Data

Skills Quiz 10.

Rita just opened up a food truck and is documenting the number of food orders she received for each food item she had on opening day. She is hoping that by keeping track of the most popular food items, she can make sure she has enough ingredients to complete all of the orders she receives each day. Fish Tacos

Bacon Burger

Alfredo Pasta

Pepperoni Pizza

BBQ Sandwich

7 orders

15 orders

9 orders

13 orders

10 orders

Use the data from the table above to complete the bar graph below. Make sure to come up with a title, create a scale for the yy-axis, label each food item on the x-axis, x and accurately represent each bar on the bar graph.

Number of food orders

Title:

Food items

334 | Represent and Interpret Data

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.

335

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

336

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

337

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 338

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

339

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

340

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 341

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 342

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

343

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 344

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

345

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

346

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

347

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 348

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 349

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 351

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) 352

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 353

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 354

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 356

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 358

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 359

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. 360

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 362

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 363

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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