Chapter 5 Resource Masters - Macmillan/McGraw-Hill

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such materials be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with the California Mathematics program. Any other reproduction, for sale or other use, is expressly prohibited. Send all inquiries to: Macmillan/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-02-106063-4 MHID: 0-02-106063-0 Printed in the United States of America. 4 5 6 7 8 9 10 11 12 13 RHR 19 18 17 16 15 14 13 12 11 10

Grade 5 Chapter 5 Table of Contents Lesson 5 –6

Teacher’s Guide to Using Chapter 5 Resource Masters ............................iv Chapter 5 Graphic Organizer ................................... 1 Student-Built Glossary................................................ 2 Family Letter ................................................................ 4 Family Letter Spanish ................................................. 5 Chapter 5 Anticipation Guide .................................. 6 Chapter 5 Game .......................................................... 7

Problem-Solving Investigation: Choose the Best Strategy Reteach .........................................................................33 Skills Practice ..............................................................35 Homework Practice ..................................................36 Enrich.............................................................................37

Lesson 5 –7

Lesson 5 –1

Adding and Subtracting Mixed Numbers Reteach .........................................................................38 Skills Practice ..............................................................39 Homework Practice ..................................................40 Problem-Solving Practice ........................................41 Enrich.............................................................................42

Rounding Fractions and Mixed Numbers Reteach ........................................................................... 8 Skills Practice ................................................................ 9 Homework Practice ..................................................10 Problem-Solving Practice ........................................11 Enrich.............................................................................12

Lesson 5 –8

Lesson 5 –2

Subtracting Mixed Numbers with Renaming Reteach .........................................................................43 Skills Practice ..............................................................44 Homework Practice ..................................................45 Problem-Solving Practice ........................................46 Enrich.............................................................................47

Estimating Sums and Differences Reteach .........................................................................13 Skills Practice ..............................................................14 Homework Practice ..................................................15 Problem-Solving Practice ........................................16 Enrich.............................................................................17

Lesson 5 –3

Individual Progress Checklist .................................48

Adding and Subtracting Fractions with Like Denominators Reteach .........................................................................18 Skills Practice ..............................................................19 Homework Practice ..................................................20 Problem-Solving Practice ........................................21 Enrich.............................................................................22

Chapter Tests: Chapter Diagnostic Assessment ...........................49 Chapter Pretest ..........................................................50 Quiz 1 ............................................................................51 Quiz 2 ............................................................................52 Quiz 3 ............................................................................53 Mid-Chapter Review .................................................54 Vocabulary Test ..........................................................55 Oral Assessment ........................................................56 Chapter Project Rubric .............................................58 Foldables Rubric ........................................................59 Test Form 1 .................................................................60 Test Form 2A ...............................................................62 Test Form 2B...............................................................64 Test Form 2C...............................................................66 Test Form 2D ..............................................................68 Test Form 3 .................................................................70 Extended-Response Test .........................................72

Lesson 5 –4

Problem-Solving Strategy: Act It Out Reteach .........................................................................23 Skills Practice ..............................................................25 Homework Practice ..................................................26 Enrich.............................................................................27

Lesson 5 –5

Adding and Subtracting Fractions with Unlike Denominators Reteach .........................................................................28 Skills Practice ..............................................................29 Homework Practice ..................................................30 Problem-Solving Practice ........................................31 Enrich.............................................................................32

Student Recording Sheet ....................................73 Cumulative Standardized Test Practice..............................................................74 Answer Pages ...........................................................A1

iii

Teacher’s Guide to Using the Chapter 5 Resource Masters The Chapter 5 Resource Masters includes the core materials needed for Chapter 5. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing on the TeacherWorks PlusTM CD-ROM. but uses a different approach, learning style, or modality than that used in the Student Edition. The Reteach worksheet closes with computational practice of the concept.

Chapter Resources Graphic Organizer (page 1) This master is a tool designed to assist students with comprehension of grade-level concepts. While the content and layout of these tools vary, their goal is to assist students by providing a visual representation from which they can learn new concepts.

Skills Practice The Skills Practice worksheet for each lesson focuses on the computational aspect of the lesson. The Skills Practice worksheet may be helpful in providing additional practice of the skill taught in the lesson.

Student-Built Glossary (page 2) This master is a study tool that presents the key vocabulary terms from the chapter. You may suggest that students highlight or star the terms they do not understand. Give this list to students before beginning Lesson 5–1. Remind them to add these pages to their mathematics study notebooks.

Homework Practice The Homework Practice worksheet provides an opportunity for additional computational practice. The Homework Practice worksheet includes word problems that address the skill taught in the lesson. Problem-Solving Practice The ProblemSolving Practice worksheet presents additional reinforcement in solving word problems that apply both the concepts of the lesson and some review concepts.

Anticipation Guide (page 6) This master is a survey designed for use before beginning the chapter. You can use this survey to highlight what students may or may not know about the concepts in the chapter. If feasible, interview students in small groups, asking them the interview questions in the guide. There is space for recording how well students answer the questions before they complete the chapter. You may find it helpful to interview students a second time, after completing the chapter, to determine their progress.

Enrich The Enrich worksheet presents activities that extend the concepts of the lesson. Some Enrich materials are designed to widen students’ perspectives on the mathematics they are learning. These worksheets are written for use with all levels of students. Resources for Problem-Solving Strategy and Problem-Solving Investigation Lessons In recognition of the importance of problem-solving strategies, worksheets for problem-solving lessons follow a slightly different format. For problem-solving lessons, a two-page Reteach worksheet offers a complete model for choosing a problemsolving strategy. For each Problem-Solving Strategy lesson, Reteach and Homework Practice worksheets offer reinforcement of

Game (page 7) A game is provided to reinforce chapter concepts and may be used at appropriate times throughout the chapter.

Resources for Computational Lessons Reteach Each lesson has an associated Reteach worksheet. In general, the Reteach worksheet focuses on the same lesson content

iv

Chapter Project Rubric This one-page rubric is designed for use in assessing the chapter project. You may want to distribute copies of the rubric when you assign the project and use the rubric to record each student’s chapter project score.

the strategy taught in the Student Edition lesson. In contrast, the Problem-Solving Investigation worksheets include a model strategy on the Reteach worksheets and provide problems requiring several alternate strategies on the Homework Practice and Skills Practice worksheets.

Foldables Rubric This one-page rubric is designed to assess the Foldables graphic organizer. The rubric is written to the students, telling them what you will be looking for as you evaluate their completed Foldables graphic organizer.

Assessment Options The assessment masters in the Chapter 5 Resource Masters offer a wide variety of assessment tools for monitoring progress as well as final assessment. Individual Progress Checklist This checklist explains the chapter’s goals or objectives. Teachers can record whether a student’s mastery of each objective is beginning (B), developing (D), or mastered (M). The checklist includes space to record notes to parents as well as other pertinent observations.

Leveled Chapter Tests • Form 1 assesses basic chapter concepts through multiple-choice questions. • Form 2A is primarily for those who may have missed the Form 1 test. It may be used as a retest for students who received additional instruction following the Form 1 test.

Chapter Diagnostic Assessment This onepage test assesses students’ grasp of skills that are needed for success in the chapter.

• Form 2B is designed for students with a below-level command of the English language.

Chapter Pretest This one-page quick check of the chapter’s concepts is useful for determining pacing. Performance on the pretest can help you determine which concepts can be covered quickly and which specific concepts may need additional time.

• Form 2C is a free-response test. • Form 2D is written for students with a below-level command of the English language. • Form 3 is a free-response test.

Quizzes Three free-response quizzes offer quick assessment opportunities at appropriate intervals in the chapter.

• Extended-Response Test is an extended response test.

Mid-Chapter Review This one-page chapter test provides an option to assess the first half of the chapter. It includes both multiple-choice and free-response questions.

Student Recording Sheet This one-page recording sheet is for the standardized test in the Student Edition. Cumulative Standardized Test Practice This three-page test, aimed at on-level students, offers multiple-choice questions and free-response questions.

Vocabulary Test This one-page test focuses on chapter vocabulary. It is suitable for all students. It includes a list of vocabulary words and questions to assess students’ knowledge of the words.

Answers

Oral Assessment This two-page test consists of one page for teacher directions and questions and a second page for recording responses. Although this assessment is designed to be used with all students, the interview format focuses on assessing chapter content assimilated by ELL students.

The answers for the Anticipation Guide and Lesson Resources are provided as reduced pages with answers appearing in black. Full size line-up answer keys are provided for the Assessment Masters.

5

Date

Name

Chapter Resources

Graphic Organizer Use this graphic organizer to take notes on Chapter 5: Adding and Subtracting Fractions. Fill in the missing information. How do I …

Instructions

Examples

… estimate the sum or difference of fractions?

Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

… estimate the sum or difference of mixed numbers?

… add or subtract fractions with like denominators?

… add or subtract fractions with unlike denominators?

… add or subtract mixed numbers?

Grade 5

1

Chapter 5

5

Name

Date

Student-Built Glossary

This is an alphabetical list of new vocabulary terms you will learn in Chapter 5: Adding and Subtracting Fractions. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term

Found on Page

Definition/Description/Example

denominator

fraction


like fractions

numerator

Grade 5

2

Chapter 5


simplest form

Grade 5

Chapter Resources

5 Name Date

Student-Built Glossary

3

(continued)

unlike fractions

Chapter 5

Dear Family, ractions ubtracting Fractions. nd Subtracting dding and F 5:: Adding Chapter S a started 5 Amy class Today I will be learning to add and subtract fractions. I will also be learning to round fractions and mixed numbers. Here are my vocabulary words and an activity that we can do together. Sincerely, ______________________

Key Vocabulary like fractions Fractions that have the same 1 2 denominator. Example: _ and _ . 5 5 unlike fractions Fractions with different 1 2 denominators. Example: _ and _. 5 3 simplest form A fraction in which the numerator and the denominator have no common factor great than 5 1. Example: _ is in simplest for because 5 and 12 12 have no common factor greater than 1.

denominator The bottom number 5 in a fraction. Example: _, 6 is 6 the denominator.

g to s accordin le b r a g m t Sor tions, usin c a fr te a rs color. Cre arble colo m t n e r the diffe of the ent parts s e r p e r les. to t of marb n u o m a whole e middle th in ie p izza per Draw a p poster pa f o e c ie of a p to the ur pie in o y e id iv and d for each marbles f o r er e b num ing togeth d d a e c ti c color. Pra tions. ts of frac e s t n e r diffe

Books to Read Polar Bear Math, Learning About Fractions by Nagda and Bickel The Doorbell Rang by Pat Hutchins Gator Pie by Louise Mathews

Grade 5

4

Chapter 5


fraction A number that represents part of a whole or 3 1 1 1 part of a set. Example: _, _, _, and _ are fractions. 4 2 3 4 numerator The number above the bar in a fraction; the part of the fraction that tells how many of the 2 equal parts are being used. Example: _, 2 is the 4 numerator.

Activity

Estimada familia:

prenderé a racciones. Aprenderé esta fracciones. uma ay resta A 5:: Suma f el Capítulo r Hoy5 miS clasey comenzó racciones También aprenderé a redondear fracciones y estar fracciones. sumar y a restar números mixtos. A continuación, están mis palabras del vocabulario y una actividad que podemos realizar juntos. Sinceramente, ______________________

Vocabulario clave


fracciones semejantes Fracciones que tienen 1 2 el mismo denominador. Ejemplo: _ y _ 5 5 fracciones con distinto denominador Fracciones con diferentes denominadores. 2 1 Ejemplo: _ y _ 5 3 forma reducida Fracción en que el numerador y el denominador no tienen 5 un factor común mayor que 1. Ejemplo: _ está 12 en forma reducida porque 5 y 12 no tienen un factor común mayor que 1

Actividad

us s según s a ic n a c n e Clasifiqu cciones a a fr n e e r s) colores. C res (parte lo o c s lo partir de nicas ad de ca d ti n a c y de la una pizza n je u ib D una (todo). centro de l e n e a redond según el la n a íd iv yd . cartulina por color s a ic n a c de nnúmero r los disti a m u s a n . Practique acciones fr e d s to n tos conju

fracción Número que representa parte de un todo o parte de un conjunto. 1 1 1 3 Ejemplo: _, _, _ y _ son fracciones 2 3 4 4 numerador Número que está encima de la barra de fracción; la parte de la fracción que indica cuántas partes iguales se están usando. 2 Ejemplo: _, 2 es el numerador 4 denominador El número inferior 5 en una fracción. Ejemplo: _, 6 6 es el denominador

Libros recomendados Polar Bear Math, Learning about Fractions de Nagda and Bickel The Doorbell Rang de Pat Hutchins Gator Pie de Louise Mathews

Grade 5

5

Chapter 5

Name

5

Date

Anticipation Guide Adding and Subtracting Fractions STEP 1

Before you begin Chapter 5

• Read each statement. • Decide whether you agree (A) or disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (not sure). STEP 1 A, D, or NS

Statement

STEP 2 A or D

1. Like fractions have the same numerator. 2. Unlike fractions have different denominators. 1 2 3. _ and _ are like fractions. 5

5

7 4. _ is in simplest form. 12

5. A fraction is a number that represents part of a whole or part of a set. Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

6 3 6. _ and _ are unlike fractions.

4 7 9 7 7. _ and _ are like fractions. 10 10 6 8. In the fraction _, 10 is the denominator. 10 3 9. In the fraction _, 3 is the denominator. 12 3 10. In the fraction _, 3 is the numerator. 4 STEP 2

After you complete Chapter 5

• Reread each statement and complete the last column by entering an A (agree) or a D (disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.

Grade 5

6

Chapter 5

Date

Name

5

Game Chapter Resources

ROLL IT UP!

You will need • a pair of number cubes for each player • paper and pencil

Give each player a pair of number cubes, paper, and pencil.

1. Players toss their pair of number cubes twice and record the 4 numbers.


2. Players form two fractions from their numbers so that the fractions have the greatest sum possible. Players may move their numbers around to increase their sums. 3. The player with the greatest sum wins the first round. The first player to win 3 rounds is the winner of the game.

2 4

Grade 5

5 6

3

3 1

2

6 6

5

2 _

4

7

3

5 _ 6

Chapter 5

Name ____________________________ Date ________________

5–1

Reteach

5MR2.5, 5NS1.1

Rounding Fractions and Mixed Numbers Round Up If the numerator is almost as large as the denominator, round the number up to the next whole number.

9 10

9 _ rounds to 1.

Example:

0

1

10 9 is almost as large as 10.

_1

Round to 2 If the numerator is about half of the 1 denominator, round the fraction to . 2 3 1 _ Example: rounds to _. 5 2 3 is about half of 5.

_

3 5

0

Round Down If the numerator is much smaller than the denominator, round the number down to the previous whole number.

1 5

0


Example:

1

1

1 _ rounds to 0.

5 1 is much smaller than 5.

Round each number to the nearest half. 9 1. 3 _ 10

1 2. 5 _ 10

5 3. 1 _ 8

2 4. 4 _ 7

9 5. 8 _ 16

1 6. 7_ 3

2 7. 6_ 3

5 8. _ 7

4 9. 2_ 9

5 10. 5_ 11

1 11. 9_ 8

7 12. 9_ 8

Grade 5

8

Chapter 5

Name ____________________________ Date ________________

5–1

Skills Practice

5MR2.5, 5NS1.1 Chapter Resources

Rounding Fractions and Mixed Numbers Round each number to the nearest half. 3 1. 6 _ 12

12 2. 8 _ 13

9 3. 3 _ 18

3 4. 6 _ 4

2 5. 6 _ 9

2 6. 5 _ 3

1 7. 2 _ 2

3 8. 6 _ 8

9.

10.

1 _ 8

1 13. 8 _ 4 16.

2 _ 16


2 19. 3 _ 8

7 _ 8

11.

12 _ 15

2 12. 3 _ 9

14.

11 _

15.

17.

1 _

4 18. 2 _ 5

12 3

1 20. 9 _ 5

5 _ 6

2 21. 6_ 3

Solve. 22. Mrs. Jones is putting up blinds to fit in a window opening that 5 5 is 36 _ inches wide. Should she round 36 _ up or down when 8 8 deciding on the size of blinds to purchase?

1 23. Marvin is mailing a copy of a document that is 12 _ inches long 8 1 and 10 _ inches wide. Will the document fit in an envelope that 2

is 12 inches long and 10 _ inches wide or in an envelope that is 2 1 12 _ inches long and 11 inches wide? 2

Grade 5

1

9

Chapter 5

5–1

Name ____________________________ Date ________________

Homework Practice

5MR2.5, 5NS1.1

Rounding Fractions and Mixed Numbers Round each number to the nearest half. 1 1. 2 _ 12 4.

8 _ 12

6 7. 8 _ 16

5 2. 4 _ 11

3 3. 7 _ 10

2 5. 6 _ 9

6.

14 _

7 8. 10 _ 12

9.

3 _

16 8

Solve. 10. Your basement has an 8 _ foot ceiling. To the nearest half foot, 3 12

how tall is the tallest cabinet that can fit in the basement?

11. Alice is giving a book as a gift that is 8 _ inches long and 6 _ 3 8

1 12

1 2

6 _ inches wide or in a box that is 8 inches long and 6 inches wide? 1 2

Graph each ordered pair on the coordinate plane at the right. 1 13. N 1 _, 2 14. P (3, 2.5) 12. M (4, 3) 2 3 15. Q 4 _, 5 4

(

)

( ) 1 16. T (2, 2 _) 4

1 17. V 1, 3 _ 2

(

)

6 y 5 4 3 2 1 O

Grade 5

10

x 1 2 3 4 5 6

Chapter 5


inches wide. Will the book fit in a box that is 8 _ inches long and

5–1

Name ____________________________ Date ________________

Problem-Solving Practice


Rounding Fractions and Mixed Numbers Solve. 3 1. A recipe for cookies calls for _ of a cup of chocolate chips. Should 1 4 you buy a package with _ cup or a package with 1 cup? 2

3 2. The cookie recipe also calls for _ of a cup of walnuts. Should you 8 1 buy a package with 1 cup or a package with _ cup of walnuts? 2


3. To the nearest half foot, what is the tallest refrigerator that can fit in 3 a kitchen with a space that is 6_ feet tall? 4

1 4. Russ is putting his photographs in an album that is 12 _ inches long 8 1 and 10 _ inches wide. Should he trim the edges of the photographs 2 1 to 12 inches long and 10 inches wide or to 12 _ inches long and 4 1 10 _ inches wide? 4

3 5. A farmer is planting squash plants that need 2 _ feet to spread 8 out. Round the amount of space the squash plants need to the 1 nearest _ foot. 2

6. Based on the area of his flowerbed, a gardener calculates that he 8 8 needs 6 _ gallons of fertilizer. Should he round 6 _ up or down 14 14 when deciding on the amount of fertilizer he should purchase?

Grade 5

11

Chapter 5

Name ____________________________ Date ________________

5–1

Enrich

5MR2.5, 5NS1.1

Greatest Possible Error When you measure a quantity, your measurement is more precise when you use a smaller unit of measure. But no measurement is ever exact—there is always some amount of error. The greatest possible error (GPE) of a measurement is one half the unit of measure.

INCHES

1

1 unit of measure: __ inch 8 3 length of line segment: 1 __ inches 8

2

1 1 GPE: half of __ inch, or ___ inch 8 16

3 6 Since 1_ = 1_ , the actual measure of the line segment may range 8 16 _ 5 7 inches to 1_ inches. anywhere from 1 16 16

Use the GPE to give a range for the measure of each line segment. 1.

2. INCHES

1

INCHES

2

2

4. INCHES

1

2

CM 1

5. Using this scale, the weight of a bag

2

3

4

5

6. Using this container, the amount of a

of potatoes is measured as 3 pounds.

liquid is measured as 20 milliliters.

What is the range for the actual

What is the range for the actual amount

weight of the potatoes?

of the liquid?

0 3

pounds

50 mL 40 mL

1

30 mL

2

20 mL 10 mL

Grade 5

12

Chapter 5


3.

1

Name ____________________________ Date ________________

5–2

Reteach


Estimating Sums and Differences You can round mixed numbers to the nearest half to estimate sums and differences of mixed numbers. Use number lines to help you. 5 1 Estimate 5 _ - 2 _ 5 8 55 8

2

2

6

5

1 5

5 1 5 _ is closer to 5 _ than to 5. 2 8 5 1 5_ - 2_ 5 8

3

1 2 _ is closer to 2 than to 3. 5

5 1 1 So, 5 _ - 2 _ is about 3 _. 2 5 8

1 1 5_ - 2 = 3_ 2 2


Show each mixed number on a number line and round it to the nearest half. Then estimate the sum or difference. 9 2 1. 3 _ + 4 _ 5 10 3

49 10

2 5

3 2 3 _ is closer to 5 9 2 3_ + 4_ 5 10 +

5

4

4 than to

9 4 _ is closer to 10

.

than to

.

=

Estimate the sum or difference. You may draw number lines. 9 1 2. 8 _ - 4 _ 6 16 ↓ ↓ Grade 5

9 7 3. 7 _ + 6 _ 10 10 ↓ ↓ =

+

13

3 7 4. 9_ - 1_ 12 8 ↓ ↓ =

-

= Chapter 5

5–2

Name ____________________________ Date ________________

Skills Practice

5MR2.5, 5NS1.1

Estimating Sums and Differences Round to the nearest half. 3 1. 7 _ 4 9 5. 2 _ 16

1 2. 4 _ 6 4 6. 9 _ 5

2 3. 8 _ 5 7 7. 1 _ 8

4 4. 3_ 5 5 8. 5 _ 12

7 1 11. 5 _ - 1 _ 8 8

4 7 12. 9 _ + 3 _ 5 10

3 1 13. 6_ + 7 _ 4 8

3 1 14. 14 _ - 9 _ 5 5

13 5 15. 18_ - 9_ 16 16

5 11 16. 6 _ + 4 _ 12 12

1 7 17. 7_ + 7_ 3 12

3 7 18. 15_ - 7_ 8 16

2 4 19. 9 _ + 6 _ 5 3

11 1 20. 6 _ - 6_ 5 12

2 11 21. 8 _ + 8 _ 5 16

7 1 22. 17_ - 9_ 3 10

3 1 23. 7 _ + 9 _ 3 8

7 1 24. 30_ + 30_ 12 12

4 7 25. 58 _ - 29 _ 5 8

5 1 26. 50_ - 30_ 3 16

Solve. 27. Beth walks 10 _ miles in one week. She walks 2 _ fewer miles the following week. 2 8 About how many miles does she walk the second week? 7

1

28. Jon wants to walk at least 8 miles by the end of the week. He walks 5 _ miles by 4 5 Thursday. If he walks another 2 _ miles on Friday, will he meet his goal? Explain. 3

8

Grade 5

14

Chapter 5


Estimate the sum or difference. 5 7 2 1 9. 3_ + 2_ 10. 8_ - 3_ 3 6 6 8

5–2

Name ____________________________ Date ________________

Homework Practice


Estimating Sums and Differences Estimate the sum or difference. 7 1 2. 7 _ + _ 6 15

8 1 1. 4 _ + _ 3 9 3.

9 2 _ + 3_ 10

6 7 4. 8 _ - 1 _ 8 9

3

2 1 5. 1 _ + 3 _ 10 9

1 1 6. 7 _ + 7 _ 3 8

5 3 7. 3 _ + 6 _ 5 8

8.

4 7 9. 6 _ - _ 7 8

5 7 _ + 2_ 15

9

5 7 10. 10 _ - _ 8 9


Round to the nearest half. (Lesson 5–1) 2 11. 5 _ 3

2 12. 8 _ 13

10 13. 9 _ 10

14.

6 _

1 15. 4 _ 9

16.

14 _

9 17. 7 _ 15

7 18. 11 _ 24

19.

5 _ 6

Grade 5

12 18

1 20. 18 _ 12

15

Chapter 5

5–2

Name ____________________________ Date ________________


5MR2.5, 5NS1.1

Estimating Sums and Differences Solve. 3 1 1. Abdul works _ hour one day and _ 4 3 hour the next day. Estimate the total number of hours he works on both days combined. about

2. Anna is making cookies for the school 1 bake sale. If she uses 1_ pounds of 8 flour per batch, what is the amount of flour she needs for four batches?

hours

pounds

3. Rachel sings in a chorus at a concert. 3 The songs are 4 _ minutes, 10 3 1 7_ minutes, and 10 _ minutes long. 4 12 Estimate the amount of time the chorus spends singing. about

4. Kathy rides her bicycle to her aunt’s 2 house. It takes her 20_ minutes to get 3 there. She is tired when she leaves, 1 and it takes her 24_ minutes to 6 ride home. What is the approximate difference in the two times?

minutes

minutes

about

6. Justin plays football. On one play, he 1 ran the ball 24 _ yards. The following 3 2 play, he was tackled and lost 3 _ yards. 3 1 The next play, he ran for 5_ yards. 4 Estimate how much farther the ball is down the field after the three plays. about

yards

inches

Would this length be the actual amount she should buy? Explain.

Grade 5

16

Chapter 5


5. Carol wants to make a picture frame for an 8 × 10 inch photo. The long 1 pieces of the frame need to be 12_ 8 inches long. The short pieces should 1 be 10_ inches long. Estimate the 4 length of wood Carol must buy to make the frame.

Name ____________________________ Date ________________

5–2

Enrich


Using 1 as a Benchmark When you estimate sums of proper fractions, it often helps to use the number 1 as a benchmark, like this: 1 1 Two halves make a whole, so _ + _ = 1. 2 2 If two fractions are each less than their sum is less than 1.

1 _ ,


Fill in each 1.

5 2 _ +_

4.

27 7 _ +_

3

50

8

5 7 _ +_>1 8

9

9

with < or > to make a true statement.

1 1

10

Fill in each statement.

2

their sum is greater than 1.

3 4 _ +_1

1 _ +

1

1 _ +

1

9 _ +

1

6 _ +

to make a true statement. 5 1 11. 1 _ - 1 _ 2 8 49 14. 1 - _ 99

Grade 5

1 _ 2

1 _ 2

12. 1 -

5 _

1 _

11 3 1 15. 4 _ + _ 7 3

2

5

17

10 13. 1- _ 19 4 16. 3 - _ 7

1 _

2 1 2_ 2

Chapter 5

Name ____________________________ Date ________________

5–3

Reteach

5NS2.3

Adding and Subtracting Fractions with Like Denominators Follow these steps to add or subtract fractions with like denominators. Add

3 1 _ +_ 8

8

Step 1

Step 2

Add the numerators. Use the like denominator. 3 1 4 _ + _= _ 8 8 8 1 3 1 4 So, _ + _ = _ = . 8 8 8 2

Write the sum in simplest form. Divide the numerator and denominator by their greatest common factor.

Step 1

Step 2

Subtract the numerators. Use the like denominator. 6 8 _ 2 _ - =_ 9 9 9 8 6 2 2 So, _ - _ = _ = _. 3 9 9 9

Write the difference in simplest form. Divide the numerator and denominator by their greatest common factor.

_

4÷4 1 4 _ =_=_ 8

8÷4

2

Add or subtract. Write in simplest form. 5 4 1. _ - _ = 7 7

1 1 2. _ + _ = 4 4

3 1 3. _ + _ = 10 10

5 7 4. _ - _ = 8 8

7 11 5. _ - _ = 12 12

3 2 = 6. _ + _ 10 10

Grade 5

18

Chapter 5


6÷3 6 2 _ =_=_ 3 9 9÷3

Name ____________________________ Date ________________

Skills Practice

5NS2.3

Adding and Subtracting Fractions with Like Denominators


Add or subtract. Write in simplest form.

1.

7 1 _ +_=

2.

13 7 _ +_=

3.

4 1 _ +_=

4.

5 7 _ +_=

5.

3 4 _ +_=

6.

5 5 _ +_=

7.

7 2 _ -_=

8.

9 3 _ -_=

9.

3 1 _ -_=

10

12

15

10

12

15

16

5

20

16

5

20

5

6

5

6

8

8

10.

3 1 _ +_=

11.

2 1 _ +_=

12.

5 1 _ -_=

13.

7 3 _ +_=

14.

3 9 _ +_=

15.

7 7 _ +_=

16.

7 11 _ +_=

17.

19 5 _ +_=

18.

11 7 _ -_=

19.

9 _

20.

4 3 _ -_=

21.

7 4 _ -_=

8

16

12

8

16

12

7 -_= 16 16

3

10

20

5

3

10

20

5

6

6

8

20

9

8

20

9

8 22. In Mr. Jane’s homeroom, _ of the students brought a lunch from 25 15 2 home, _ of the students will buy a lunch, and _ of the students 25 25 will go home for lunch. What fraction of the class will eat lunch at school?

Grade 5

19

Chapter 5

Chapter Resources

5–3

Name ____________________________ Date ________________

5–3

Homework Practice

5NS2.3

Adding and Subtracting Fractions with Like Denominators Add or subtract. Write in simplest form. 1.

8 2 _ +_=

2.

5 1 _ -_=

3.

5 6 _ -_=

4.

3 2 _ +_=

5.

3 9 _ +_=

6.

7 2 _ +_=

7.

1 2 _ +_=

8.

3 4 _ -_=

9.

3 12 _ +_=

10.

6 1 _ -_=

5 8 9 2

15

5 8 9 2

15

9 4 8 5 7

9 4 8 5 7

Estimate. (Lesson 5–2) 5 1 11. 2 _ + _ = 2 9 13.

1 2 _ + 6_ = 3

5

4 1 12. 5 _ + _ = 6 2 2 7 14. 3 _ - 1 _ = 8 9

2 1 15. 8 _ + 3 _ = 10 9

6 1 16. 1 _ + 7 _ = 3 7

3 5 17. 8 _ + 6 _ = 5 8

18.

19.

1 7 _ -_= 8

7

5 11 21. _ + _ = 2 8

Grade 5

5 5 _ + 7_ = 15

9

5 1 20. 1 _ - _ = 8 9 6 2 22. 3_ - 1_ = 7 3

20

Chapter 5


5NS2.3

Adding and Subtracting Fractions with Like Denominators Solve. Write your answer in simplest form. 1 2. Laureano worked _ hour one day 4 3 and _ hour the next day. How many 4 hours did he work on the two days?

1. Debbie helped her mother with the 1 laundry. She did _ of it on Monday 3 8 and another _ of it on Tuesday. What 8 fraction of the laundry has she done?

4. John went to a museum to see model 2 trains. He saw _ mile of track on the 5 4 first floor of the museum. He saw _ 5 mile of track on the second floor. How much more track did John see on the second floor than the first?


3. Mindy likes to order fresh meat and vegetable wraps from a local 1 restaurant. One cook can roll _ wraps 3 2 in 5 minutes. Another cook can roll _ 3 wraps in the same amount of time. What is the difference in the number of wraps the two cooks can prepare in 5 minutes?

6. Laura and her sister Katie swim every 3 day. Laura can swim _ mile in 7 2 10 minutes. Katie can swim _ mile 7 in the same amount of time. If they swim for 20 minutes and their speeds stay the same, how much farther does Laura swim than her sister?

5. Sherry was in charge of distributing 250 food items that were donated to the local food pantry. On Monday she distributed 87 items. On Tuesday, she distributed 63 more items. Fifty more items were distributed on Wednesday. What fraction of the food items was distributed by the end of the day on Wednesday?

Grade 5

21

Chapter 5

Chapter Resources

5–3

Name ____________________________ Date ________________

Name ____________________________ Date ________________

5–3

Enrich

5NS2.3

Fraction Puzzles In the puzzles below, the sum of the fractions in each row is the same as the sum of the fractions in each column. Use your knowledge of adding and subtracting fractions to find the missing fractions. Hint: Remember to check the fractions for like denominators before adding.

3 _ 20

9 _ 20

2 _

20

20

25

0 _

20

2 _

7 _

20

25

2 _

7 _

8 _

1 _

1 _

7 _

1 _

16

2 _ 25

2 _

3 _ 25

25

1 _ 25

15

16

8

8

3 _

25

4 _

15

16

6 _

25

15

1 _ 15

11 _

1 _

16

12 _

0 _

25

15

15

15

6 _

2 _

8


25

3 _

4 _

15

15

7 _

20

20

6 _

20

4 _

3 _

3 _

15

2 _

2 _

9 _

8

1 _ 8

2 _ 8

3 _ 8

CHALLENGE Create your own fraction puzzle using a box of 5 rows and 5 columns.

Grade 5

22

Chapter 5

Reteach

5MR2.3, 5NS2.3

Problem-Solving Strategy Use the Act It Out Strategy Akio and Mei began the project of repainting and covering the seats of old dining room 2 chairs. To recover one seat, they need _ of a yard of fabric. How much fabric do they 3 need to buy to recover the seats of 4 chairs? Understand

What facts do you know? 2 There are 4 chairs to recover. _ of a yard of fabric 3 is needed to cover the seat of each chair. What do you need to find? How much fabric is needed to recover the seats of 4 chairs?


Plan

Act out the problem by marking the floor to show 2 a length of _ of a yard. 3 2 Then, continue to mark _ of a yard of fabric until 3 you have done this 4 times.

Solve

8 2 2 2 2 2 _ + _ + _ + _ = _ = 2_ yards of fabric 3 3 3 3 3 3

Check

2 You can estimate by rounding _ to 1. 3 Then, you have each chair needs about 1 yard of fabric. 1 + 1 + 1 + 1 = 4, which is close to your answer 2 of 2_. 3

Grade 5

23

Chapter 5

Chapter Resources

5–4

Name ____________________________ Date ________________

5–4

Name ____________________________ Date ________________

Reteach

5MR2.3, 5NS2.3

Problem-Solving Strategy

(continued)

Solve. Use the act it out strategy. 1 1. The girls need _ can of paint to paint each chair. How many cans of 4 paint will they need to paint all 4 chairs?

2 2. The girls found 6 more chairs that each need _ yard of fabric to 3 cover the seats. How much more fabric do they need to buy?

1 3. Since each of the 6 chairs needs _ can of paint, how much more 4 paint will they need?

1 4. Jean reads _ of her book each day. If she starts reading on Monday, 7 on what day will she complete her book?

3 7 5. Robert lives _ mile from school. Al lives _ mile from school. Who 10 10 lives farther from school? How much farther?

1 6. A puppy eats _ of a can of food at each meal. If he eats two times 3 a day, how long will it take him to eat 4 cans of food?

Grade 5

24

Chapter 5

5–4

Name ____________________________ Date ________________

Skills Practice


Problem-Solving Strategy Solve. Use the act it out strategy. 1. The ceramics class is designing mugs with three colored stripes. The colors are red, yellow, and green. How many different ways can students in the class arrange the three colored stripes?

2. Meg and Matt are painting all 4 walls of a room. Each person is 1 painting 2 walls. After one hour, Meg has painted _ of one wall, 2 and Matt has painted 1 wall. How much longer will it take Meg to paint her 2 walls than it will take Matt to paint his?

3. Twenty-four students are in study hall. Eight more arrive. At the same time, 12 leave. Then, 16 leave and 8 more arrive. How many students are left in study hall?

4. Ellen is decorating a wall with family pictures. She has 2 pictures that are 10 inches, 2 pictures that are 8 inches, and 2 pictures that are 6 inches. If she keeps the same size pictures in rows, how many ways can she arrange the pictures?

5. Dolores has 6 quarters, 5 dimes, 4 nickels, and 10 pennies. How many different combinations of coins can she make to have $0.50?

Grade 5

25

Chapter 5

Name ____________________________ Date ________________

5–4

Homework Practice

5MR2.3, 5NS2.3

Problem-Solving Strategy Solve. Use the act it out strategy. 1. Alberto has 2 quarters, 2 dimes, 2 nickels, and 2 pennies. How many different combinations of coins can he make to have $0.55?

1 2. Carlos is running drills of _ mile. If he runs 5 drills, how many miles 2 did he run?

3. Students are hanging their art projects in the school hallway. Each 7 student wants to hang a project that is _ foot wide. The hallway is 8 16 feet long. If they don’t leave any space between each project, how many projects will fit in the hallway?

4. Hana is wrapping books to give as gifts. She needs pieces of 5 wrapping paper that are _ foot long for each book. She has a total 6 of 6 books. How long a roll of wrapping paper will she need?

Add or subtract. Write in simplest form. (Lesson 5–3) 5.

3 9 _ +_

6.

3 1 _ -_

9.

9 _ _ -3

10.

3 12 _ -_

14.

13.

5 9

15

Grade 5

5

9

15

7 2 _ -_

8.

3 1 _ +_

6 5 _ +_

1 2 11. _ + _ 2 2

12.

6 _ _ -2

6 _ _ -2

5 3 15. _ + _ 8 8

5 3 16. _ - _ 8 8

9 8 8

7.

9 8

8

26

8

8

4 5

4

5

Chapter 5

5–4

Name ____________________________ Date ________________

Enrich


A Fraction of an Inch Fractions are important in measurement. Using fractions allows you to be more exact than when you round to the nearest inch. When you go to the doctor, your height is not measured to the nearest inch. It is measured to fractions of an inch. Scientists use fractions all the time because their measurements need to be very precise. Solve. 7 1. Janelle is cutting a piece of wood that is _ inch long for a 12 miniature picture frame. If she is cutting it from a piece of wood that is 1 inch long, what is the length of wood that will be left over?

3 2. The winning high jump in a track meet was _ inch away from the 78 world record. The second place jump was _ inch away from the 8 world record. What is the difference between the two jumps?

3 3. A carpenter needs to fill a _ inch-wide hole. He has a piece of 4 9 wood that is _ inch wide. How much should he cut off from the 12 piece so that it will fit in the hole?

1 4. Evie is cutting ribbons 8_ feet long for a sewing project. If the 4 3 original ribbon is 36 _ feet long, how long is it after she cuts her 12 first ribbon?

6 5. Fabric is sold by the yard. Derek wants _ yard of a particular kind of 8 1 fabric. There is only _ yard of the fabric left on the bolt. Derek buys 4 what is left. How much more does he need to buy?

Grade 5

27

Chapter 5

Name

5–5

Date

Reteach

5NS2.3

Adding and Subtracting Fractions with Unlike Denominators When adding or subtracting fractions with unlike denominators, it helps to write the problems in vertical form. Step 1

Step 2

Step 3

Find the least common denominator (LCD).

Rename each fraction using the LCD.

Write the problems in vertical form.

7 21 _ =_ 3 24 8 8 Multiples of 3: 16 2 _ =_ 24 3, 6, 9, 12, 15,18, 21, 24, … 3 Multiples of 8: 8, 16, 24, … The LCD is 24. Add

2 7 _ + _.

Subtract

3 1 _ - _.

8

2 +_ 3

3 9 _ =_

Subtract.

4 12 4 1 _ =_ 3 12

2.

=

16 +_

24

24 37 13 _ = 1_ 24 24 9 _ 12

3 11 _ -_

4 12 Multiples of 12: Multiples of 4:

LCD:

LCD:

Grade 5

21 _

12

Multiples of 6:

5 3 _ +_= 8

=

4 - _ 12 5 _

Add or subtract. Write in simplest form. 5 3 1. _ + _ 6 8 Multiples of 8:

So,

7 _

So,

6

28


4 3 3 1 Find the LCD of _ and _. 4 3 Multiples of 4: 4, 8, 12, … Multiples of 3: 3, 6, 9, 12, … 3 1 The LCD of _ and _ is 12. 4 3

Add.

3 11 _ -_= 12

4

Chapter 5

Name

5–5

Date

Skills Practice

5NS2.3 Chapter Resources

Adding and Subtracting Fractions with Unlike Denominators Write the addition or subtraction sentence shown by each model. Write the sum or difference in simplest form. 1.

2.

3. 1 1 1

1 8

16 16 16

1 8

1 8

1 8

1 8

1 1 1 1 1 1 1 1 1 1 1 1 1 16 16 16 16 16 16 16 16 16 16 16 16 16

4.

1 2 1 10

1 10

1 1 1 10 10 10

5.

1 8

1 8

1 8

1 8

1 1 1 1 1 1 12 12 12 12 12 12

6.

1 6

1 6

1 6

1 6

1 6

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24

Add or subtract. Write in simplest form. 1 1 7. _ + _ = 10

5

1 1 8. _ + _ = 12

6

3 5 9. _ + _ = 16

8

3 1 10. _ + _ =

3 1 11. _ + _ =

5 2 12. _ + _ =

1 7 13. _ - _ =

1 1 14. _ - _ =

9 2 15. _ - _ =

5 1 16. _ - _ =

3 11 17. _ - _ =

1 11 18. _ - _ =

4

12 8

Grade 5

12 4

4

2 2

20

8 3

10

29

3

10 12

6

5 3

Chapter 5

Name

5–5

Date

Homework Practice

5NS2.3

Adding and Subtracting Fractions with Unlike Denominators Add or subtract. Write in simplest form. 1.

2 2 _ +_

2.

3 7 _ +_

3.

9 2 _ -_

4.

5 1 _ +_

5.

3 5 _ -_

6.

1 1 _ +_

7.

3 2 _ +_

8.

3 1 _ -_

9.

2 1 _ -_

10.

2 1 _ +_

11.

3 7 _ +_

12.

8 1 _ +_

13.

2 1 _ +_

14.

3 1 _ -_

15.

9 1 _ -_

6 1 16. _ +_

5

10 4 5 3 8

10

8

8 6

10 9 3

6

6 7 6 4 7 9 5

7

8 2 4 2 3

10 8


2

8

2

Solve using the act it out strategy. (Lesson 5–4) 3 17. The Boyd family eats _ of a package of pasta for dinner. How many 4 packages of pasta will they need for 4 pasta dinners?

18. Kayla has 5 quarters, 3 dimes, 2 nickels, and 5 pennies. How many different combinations of coins can she make to have $0.50?

Grade 5

30

Chapter 5

Date


5NS2.3

Adding and Subtracting Fractions with Unlike Denominators


Solve. Write in simplest form. 3 hour on 1. Steve watched television for __ 4 5 __ Monday and 6 hour on Tuesday. How many hours did he watch television on both days?

1 2 cup of flour and __ cup 2. Deanna uses __ 3 4 of shortening in a pie crust recipe. How much more flour than shortening does she use?

3. Marsha and her friend, Tina, are making table decorations for a party. 2 Marsha made __ of a decoration in 9 2 of a half an hour. Tina can make __ 3 decoration in the same amount of time. How much more of a decoration can Tina make in half an hour?

4. Kyle planted flowers in the front of the 11 school. He planted ___ of the plants on 16 1 __ Friday and 4 of the plants on Saturday. What fraction of the total plants did he plant on both days?

6. After school, Laura baby-sits a neighbor’s child for 50 minutes. They rest for 10 minutes, read for 15 minutes, and play for the rest of the time. Write the total baby-sitting time, the resting time, and the reading time, as fractions of an hour.

9 5. Shawn rides his bicycle ___ mile to 10 school. On his way to school, he stops 1 at Mike’s house, which is __ mile from 5 Shawn’s house. Then they both ride 2 to Jose’s house, which is __ mile from 7 Mike’s house. How far is it from Jose’s house to the school?

Use these fractions to find the fraction of an hour they play.

Grade 5

31

Chapter 5

Chapter Resources

5–5

Name

Name

5–5

Date

Enrich

5NS2.3

Unit Fractions A unit fraction is a fraction with a numerator of 1 and a denominator that is any counting number greater than 1. unit fractions:

Did you know?

The Rhind Papyrus indicates that fractions were used in ancient Egypt nearly 4,000 years ago. If a fraction was not a unit fraction, the Egyptians wrote it as a sum of unit fractions. The only exception to this rule seems to be the 2 fraction __ . 3

1 _ 1 _ 1 _ 2 3 10

A curious fact about unit fractions is that each one can be expressed as a sum of two distinct unit fractions. (Distinct means that the two new fractions are different from one another.) 1 1 1 _ =_+_ 3

2

6

1 1 1 _ =_+_ 3

4

12

1 1 1 _ =_+_ 10

11

110

1. The three sums shown above follow a pattern. What is it?

2. Use the pattern you described in Exercise 1. Express each unit fraction as a sum of two distinct unit fractions. 1 _ 4

b.

1 _ 5

c.

1 _ 12

d.

1 _ 100

5 Does it surprise you to know that other fractions, such as __ , can be expressed as 6 sums of unit fractions? One way to do this is by using equivalent fractions. Here’s how. 10 10 6 5 5 1 1 4 1 1 _ _ _ =_ =_+_ → =_ +_=_+_ → 3 6 2 6 2 12 12 12 12 3

3. Express each fraction as a sum of two distinct unit fractions. a.

2 _ 3

b.

4 _ 15

c.

5 _ 9

d.

2 _ 5

4 4. Express __ as the sum of three distinct unit fractions. 5

1 5. CHALLENGE Show two different ways to express __ as the sum of 2 three distinct unit fractions.

Grade 5

32

Chapter 5


a.

Date

Reteach

5MR2.3, 5NS2.3

Problem-Solving Investigation Choose the Best Strategy Fina did a survey of how much time students spend on homework each night. Out of 1 1 16 people interviewed, __ spend about 1 hour on homework and __ spend about 4 2 45 minutes on homework. The rest spend about 30 minutes on homework. How many students spend 30 minutes on homework? Understand

1 __ of 16 students spend 1 hour on homework. 2 1 __ of 16 students spend 45 minutes on homework. 4

You need to know how many people spend 30 minutes on homework. Plan

You can use the act it out strategy. Draw 16 students.


Cross out the students who spend 1 hour and who spend 45 minutes on homework. You will be left with the students who spend 30 minutes on homework. Solve

1 __ of 16 is 8. Cross out 8 students. 2

1 __ of 16 is 4. Cross out 4 more students. 4

Count the students that are left. 4 students spend about 30 minutes on homework. Check

Use math to check your work. 16 – 8 – 4 = 4 Your answer is correct.

Grade 5

33

Chapter 5

Chapter Resources

5–6

Name

5–6

Name

Date

Reteach

5MR2.3, 5NS2.3

Problem-Solving Investigation

(continued)

Use any strategy shown below to solve. • Act it out • Make a table • Use logical reasoning 1. Out of the 200 students at Groves High, 50 spend 2 hours a night on homework, 25 spend 1 hour on homework, and 75 spend 45 minutes on homework. The rest spend 30 minutes on homework. How many students spend 30 minutes on homework?

2. Mrs. Jones told her class of 30 students that 8 people scored 90 on a math test, 7 people scored 80, and 10 people scored 70. How many people scored lower than 70?

3. If square tables are arranged in a restaurant so that only one person can sit on any side of the table, how many tables will it take to seat 40 people?

1 4. If the 40 people in the restaurant spend a total of $600 and __ of 2 1 __ the 40 people spend 2 of what the 20 other people spend, what is the least amount of money a person spends?

5. Alan bought a computer that was on sale for $568. If the computer originally cost $647, how much money did Alan save?

Grade 5

34

Chapter 5

5–6

Name

Date

Skills Practice


Problem-Solving Investigation Use any strategy shown below to solve. • Make a table

• Use logical reasoning

• Act it out

1. In how many ways can 5 people stand in line if one of the people always has to be first in line?

1 of them scored 2. The teacher told the class of 30 students that __ 2 1 __ above an 80 on their math test. An additional 3 of them scored at least a 70. How many of them scored below 70?


3. Alicia bought a CD player for $10 less than the regular price. If she paid $58 for the CD player, what was the regular price?

1 4. Miguel bought boxes of chocolates. The first box weighed 4__ 4 3 1 __ pounds, the second, 2__ , and the third, 1 . What is the total amount 4 3 of chocolate that Miguel bought?

5 5. After Miguel shared the chocolate with his friends, he had 3__ 8 3 pounds left. Then, he gave 2 __ pounds to his mother. Now, how 4 much does he have?

3 1 6. The first __ mile of a __ -mile path through a rose garden is paved 5 4 with bricks. How much of the path is not paved with bricks?

Grade 5

35

Chapter 5

Name

5–6

Date

Homework Practice

5MR2.3, 5NS2.3

Problem-Solving Investigation Use any strategy shown below to solve. • Make a table


• Act it out

1 1. Olivia bought a ring for __ off the regular price. If she paid $50, what 2 was the regular price?

1 of them scored 90 or above on the 2. Mrs. Jones told the class that __ 3 1 __ math test. Another 3 of them had a passing score. What fraction of the class failed?

1 3. At a park, a picnic shelter covers __ of an acre and a playground 4 5 __ covers 8 of an acre. How much area is covered by both the picnic shelter and the playground?


4. Of the 300 students at school, 110 are in the chorus and 150 are in the band. Of these students, 50 are in both chorus and the band. How many students are neither in the chorus nor the band?

Add or subtract. Write in simplest form. (Lesson 5–5) 5.

3 2 _ +_

6.

3 6 _ +_

7.

7 2 _ +_

8.

6 1 _ +_

9.

3 7 _ -_

10.

5 1 _ +_

5

10 8

Grade 5

9

7

5

36

5 7 6

8 2 3

Chapter 5

5–6

Name

Date

Enrich


Choose the Operation Solve. 1 1. A box is _ inch tall. If 5 of the boxes are stacked on top of each 2 other, how tall is the stack of boxes?

3 3 2. Darlene needs _ yard of fabric to cover a chair. She has _ yard of 4 8 fabric. How much more fabric does she need?


3. Mr. Montgomery is a chef. He has created 250 new recipes. He 3 plans to donate _ of them to the school library. How many recipes 5 1 does he plan to donate? Hint: _ of 250 is 50. 5

4. The art department received a shipment of 6 boxes of clay. Each 3 box weighed _ pound. How many pounds of clay were in the 4 shipment?

2 5. A sculptor has a steel tube that is _ foot long. To create a longer 3 5 tube, he attaches it to another steel tube that is _ foot long. How 6 long is the new steel tube?

2 6. Marcel was in a triathalon, a race with 3 events. He ran 4 miles in _ 3 13 hour. He bicycled 5 miles in _ hour, and he swam 880 yards in _ 4 2 hour. What was his total race time?

Grade 5

37

Chapter 5

5–7

Name

Date

Reteach

5NS2.3

Adding and Subtracting Mixed Numbers 7 1 Add 1 _ + 1 _ . 2 8 Rename the addends using their LCD. Multiples of 8: 8, 16, 24, . . . Multiples of 2: 2, 4, 6, 8, . . . 7 1 The LCD of 1 _ and 1 _ is 8. 2 8 1 7 Show 1 _ and 1 _ using eighths as a 2 8 denominator.

7 1_ 8 1 + 1_ 2

7 1_ 8 4 1_ 8 3 3 11 2_ = 2 + 1_ or 3_ 8 8 8

Add the ones. Then count the eighths. 3 5 Subtract 2 _ - 1 _. 4 8 5 3 _ and _. 4

8


Find the LCD of

Multiples of 4: 4, 8, Multiples of 8: 8, . . . 3 5 The LCD of _ and _ is 8. 4 8 3 2_ 4

3 Rename 2 __ so the fraction part is in 4 eighths. Subtract the ones. Then subtract

↓

6 5 1 2_ - 1_ = 1_

the eighths.

8

8

8

Add or subtract. Write in simplest form. 3 5 1. 2 _ + 1 _ = 4 8

3 7 2. 1 _ + 2 _ = 5 10

7 4 3. 6_ - 1 _ = 5 10

3 1 4. 3_ - 1 _ = 4 8

Grade 5

38

Chapter 5

5–7

Name

Date

Skills Practice


Adding and Subtracting Mixed Numbers


Add or subtract. Write in simplest form. 15 11 1. 7 _ - 2 _ = 16 16

3 4 2. 11 _ - 4 _ = 5 10

1 3. 12 + 9 _ = 3

1 5 4. 18 _ - 9 _ = 6 6

1 5. 9 + 5 _ = 12

7 1 6. 16 _ - 7 _ = 3 10

11 7. 34 _ + 15 = 20

3 11 8. 64 _ - 37 _ = 4 12

3 2 9. 51 _ + 25 _ = 5 4

3 10. 46 _ - 27 = 4

4 11. 82 _ + 62 = 5

11 13. 16 _ - 7 = 12 11 16. 6_ 12 5 + 4_ 12

7 1 14. 35 _ + 21 _ = 4 8 7 2 18. 14 _ 17. 11 _ 3 8 2 +5 - 3_ 5

2 1 12. 23 _ - 15 _ = 5 8 4 15. 97 _ - 87 = 5 1 19. 15 _ 4 1 - 6_ 6

5 20. A grocery bag will hold 8 _ pounds of oranges. Kyle puts 3 pounds of oranges in the 8 bag. How many more pounds of oranges can he put in the bag?

7 21. Sara needs 2 _ pounds of grapes for a salad. She buys a bag of grapes that weighs 8 1 only 1 _ pounds. How many more pounds of grapes does she need? 2

3 2 22. Keith is making canvas tent. He needs 12 _ yards of beige canvas for the top and 8_ 4 5 of green canvas for the bottom. How many yards of canvas does he need in all?

Grade 5

39

Chapter 5

5–7

Name

Date

Homework Practice

5NS2.3

Adding and Subtracting Mixed Numbers Add or subtract. Write in simplest form. 3 1 1. 3 _ + 8 _ 4 4

3 1 2. 6 _ + 6 _ 5 5

3 1 3. 11 _ + 1 _ 10 10

5 6 4. 6 _ + 7 _ 8 8

4 1 5. 9 _ - 6 _ 8 8

1 2 6. 8 _ + 9 _ 3 3

3 1 7. 5 _ + 7 _ 5 5

1 8 8. 9 _ - 1 _ 9 9

6 1 9. 7 _ - 5 _ 7 7

4 1 10. 12 _ - 4 _ 8 8

Use any strategy shown below to solve. (Lesson 5–6) • Make a table


• Act it out Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

11. Janice bought 2 pairs of sneakers. The first pair was full price and the second was half price. The original price of the first pair was $32. How much did she spend?

1 pounds, 12. Jill bought five packages of printer paper that weighed 1 __ 2 3 1 1 1 __ __ __ __ 2 8 pounds, 3 4 pounds, 1 8 pounds, and 2 2 pounds. How many pounds of paper did she buy?

13. Chou’s quiz scores are 78, 99, 101, 88, 93, 89, 92, 94, 84, 95. On how many more quizzes did Chou score above 90 than below 90?

Grade 5

40

Chapter 5

Date


5NS2.3

Adding and Subtracting Mixed Numbers Solve. 1 1. Blanca’s children are 6 __ years old and 6 1 ___ 5 12 years old. In simplest form, what are combined ages of her children?

3 2. Rick has a choice of buying 4 __ 4 2 packages of pencils or 2 __ packages 5 of pens. In simplest form, how many more packages of pencils than pens can he buy?


3. Cumberland Valley Coal Company 2 mined 249 __ tons of coal on one day 3 1 __ and 387 7 tons on another day. What is the total number of tons of coal mined on both days?

1 pounds of 5. James recycled 22 __ 2 aluminum in one week. Matt recycled 3 18_ pounds of aluminum the same 7 week. How many more pounds of aluminum did James recycle?

4. One year, Cumberland Valley Coal 1 Company planted 14 __ dozen trees to 6 help prevent erosion. The following 2 dozen trees. year, they planted 20 __ 3 How many more trees did they plant the second year?

1 6. Bethany bought 2 __ pounds of bread, 2 1 1 __ pounds 3 4 pounds of meat, and 3 __ 3 of cheese to make sandwiches for a 1 party. She also bought 2 __ pounds of 3 1 __ tomatoes, 1 6 pounds of onions, and 1 pounds of lettuce. 2 __ 2

What is the total number of pounds of food that she bought?

Grade 5

41

Chapter 5

Chapter Resources

5–7

Name

5–7

Name

Date

Enrich

5NS2.3

A Maze of Mixed Numbers Find your way through the maze to reach the dot. When you come to a letter, solve the problem that matches that letter. Draw your path through the sum or difference in simplest form. Follow the path until you reach the next intersection. Continue finding each sum or difference. 3 1 A. 3 _ + 2 _ 3 5

B.

4 1 E. 2 _ + 5 _ 5 2

1 1 _ + 3_

1 1 C. 4 _ - 1 _ 5 6

3 1 D. 4 _ + 3 _ 4 4

1 1 F. 11 _ - _ 3 6

5 5 G. 3 _ + 2 _ 6 12

3 1 H. 6 _ + 2 _ 5 6

1 1 I. 7 _ - 3 _ 5 4

3 1 J. 8 _ + 6 _ 4 3

2 1 K. 1 _ - 1 _ 3 3

1 7 L. 8 _ - 2 _ 4 8

3 2 M. 1 _ + 9 _ 3 5

5 1 N. 6 _ - 1 _ 3 8

START

10

2

8

D

F

1 72 7— 2 — 3

1 11— 6

3 3— 5

3 810 — 3 710 —

B 1 3 20 —

J 1 1512 —

1 1412 —

E

A

514 — 15 1 6— 5

G I 2 10 — 9 1 420 — 4 10 — 5

C 2 31 511 — — 30

H 4 1115 —

8 11 — 15

8 23 — 30

2 1 — 3

M

5 6— 8

Grade 5

42

L

K

1 10 — 8

Chapter 5


N 1 6 1 5 7 8 23 5— — 30 — 4 — 4 24

5–8

Name

Date

Reteach


Subtracting Mixed Numbers with Renaming To subtract mixed numbers with unlike denominators you need to write equivalent fractions with a common denominator. 3 1 Subtract 6 _ - 2 _. 4 2 Step 1

Write the fractions with a common denominator. 3 1 and __ is 4. Think: The LCD of __ 4 2 1 2 Rename __ as __ . 4 2

Then subtract. Step 2 Subtract the fractions. Regroup if necessary.

Step 3 Subtract the whole numbers.


6 2 6_ 5_ 4 4 3 3 - 2_ → - 2_ 4 4 3 _ 4

6 5_ 4 3 _ -2 4 3 3_ 4

Step 4

Simplify if possible.

3 3 _ is in simplest form. 4

3 3 1 So, 6 _ - 2 _ = 3 _ . 4 4 2 Subtract. Write in simplest form. 1 3 1. 7_ 2. 2 _ 4 16 3 1 _ -3 - 1_ 8 4

1 1 6. 12 _ - 4 _ = 4 8

3.

1 9_ 5 3 _ -4 5

5 2 7. 3 _ - 1 _ = 3 6

4.

4 21 _ 5 1 _ - 11 6

5.

1 15_ 2 1 _ - 11 2

1 1 8. 6 _ - 2 _ = 5 4

7 4 10. 70 _ - 45 _ = 5 10

1 2 11. 10 _ - 3 _ = 5 10

3 3 12. 3 _ - 1 _ = 4 8

5 1 13. 4 _ - 1 _ = 2 12

2 1 14. 6 _ - 2 _ = 5 3

3 2 15. 3 _ - 1 _ = 3 4

1 2 16. 18 _ - 1 _ = 3 2

3 7 17. 4 _ - 1 _ = 8 16

1 1 18. 3 _ - 2 _ = 2 16

1 2 19. 4 _ - 1 _ = 4 3

5 15 20. 25 _ - 17 _ = 8 16

5 1 9. 41_ - 27 _ = 4 6

Grade 5

43

Chapter 5

Name

5–8

Date

Skills Practice

5NS2.3

Subtracting Mixed Numbers with Renaming Subtract. Write in simplest form. 11 1. 10 _ 16 7 - 3_ 8

2.

1 8_ 3 3 _ -2 8

3.

8_

6.

7

7.

5.

1 6

2 - 3_ 5

- 3_ 1 2

9

2 - 3_ 5

1 2_ 8 3 _ -1 4

4.

3 5_ 16 3 - 2_ 8

8.

1 4_ 16 1 - 2_ 8

3 2 10. 10 _ - 7 _ = 3 4

5 1 11. 7 _ - 2 _ = 4 6

1 2 12. 8 _ - 1 _ = 3 2

4 1 13. 10 _ - 2 _ = 5 2

3 2 14. 12 _ - 6 _ = 3 4

3 1 15. 5 _ - 3 _ = 4 2

3 1 16. 15 _ - 7 _ = 4 8

5 1 17. 11 _ - 6 _ = 4 8

3 4 18. 6 _ - 4 _ = 5 10

1 7 19. 15 _ - 8 _ = 3 12

2 7 20. 10 _ - 6 _ = 3 8

Solve. 1 21. Anna has 3 __ yards of fabric. She plans 4 1 __ to use 2 2 yards for curtains. Does she have enough left to make 2 pillows 5 that each use __ yard of fabric? Explain. 8

Grade 5

22. Paula has 2 yards of elastic. One 3 yard piece. Does she project needs a __ 4 have enough for another project that 1 needs 1 __ yards? Explain. 3

44

Chapter 5


1 1 9. 5 _ - 1 _ = 5 4

Name

5–8

Date

Homework Practice


Subtracting Mixed Numbers with Renaming Subtract. Write in simplest form. 1 1. 7 - 4 _ 2

3 2. 9 - 5 _ 5

2 3. 6 - 2 _ 3

1 4. 14 - 5 _ 4

1 5 5. 10 _ - _ 8 8

9 1 6. 12 _ - 6 _ 5 10

1 7. 5 - 4 _ 2

1 1 8. 3 _ - 1 _ 3 3

6 9. 8 - 2 _ 7 11. 9 _ - 3 2 3

1 3 10. 3_ - 1 _ 4 8

5 _ 6


1 1 13. 15 _ - 8 _ 2 12

12.

2 1 2_ - 1_ 10 5

14.

7 7 6_ - 2_ 16 8

Add or subtract. Write in simplest form. (Lesson 5–7) 1 2 15. 2 _ + 7 _ 4 4

3 1 16. 5 _ + 2 _ 5 5

8 3 17. 1 _ + 11 _ 10 10

6 5 18. 6 _ - 4 _ 8 8

4 1 19. 9 _ + 6 _ 8 8

1 2 20. 7 _ - 5 _ 3 3

3 2 21. 5 _ + 4 _ 5 5

1 5 22. 9 _ - 3 _ 9 9

6 1 23. 7 _ + 5 _ 7 7

3 5 24. 11 _ - 4 _ 8 8

Grade 5

45

Chapter 5

5–8

Name

Date


5NS2.3

Subtracting Mixed Numbers with Renaming Solve. 1. When Shane and her family went on vacation, the pilot announced 1 that it would take 4 __ hours to reach their destination. When the 4 3 flight snack was served, they had been in flight 2 __ hours. How 4 much longer was the flight after the snack was served?

3 1 2. Mark bought 5 __ pounds of yellow cheese and 3 __ pounds of white 4 5 cheese. How much more yellow cheese than white cheese did he buy?

3. Stella made 4 quarts of lemon tea for the weekend barbecue. 1 quarts of mint tea for the barbecue. How much Vincent made 3 __ 6 more tea did Stella make than Vincent? Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

4. Taylor’s puppy weighs 9 pounds. Belinda’s kitten weighs 3 3 __ pounds. How much more does Taylor’s puppy weigh than 5 Belinda’s kitten?

1 5. Jillian has a piece of leather cord that is 12 __ inches long. She only 5 9 ___ needs 8 10 inches of cord to make a bracelet. How much leather cord will she trim?

6. The Department of Education prohibits a student from doing more than 50 hours of homework in a 7-day period. Silvio has done 1 hours in the last 5 days. How many more hours homework for 30 __ 4 is he allowed to do homework in the next 2 days?

Grade 5

46

Chapter 5

Name

Enrich

5NS2.3

Equations with Fractions and Decimals 2 = 0.6 m+_

Sometimes an equation involves both fractions and decimals. To solve an equation like this, you probably want to work with numbers in the same form. One method of doing this is to start by expressing the decimals as fractions. The example at the right shows how you might solve the 2 equation m + _ = 0.6.

5

3 2 m+_ =_ 5

← Write 0.6 as a fraction.

5

3 2 m=_ -_ 5

5

1 m=_ 5

5

Name the number that is a solution of the given equation. 1. z =

1 1 3 1 3 _ + 0.375; _, _, _, _

3. c + 0.6 =


5.

2. 0.75 -

8 8 2 4

8

4 _ 1 3 1 2 _ ; , _, 1_, 1_ 5 5 5

5

4

4. 0.6 = j -

5

1 1 1 3 _ + r = 0.75; _, _, _, 1 4

3 1 1 _ = b; 0, _, 1, 1_ 4

1 _ 1 4 2 _ ; , _, 1, 1_

6. d - 0.1 =

4 2 4

4

5 5 5

5

1 3 4 9 7 _ _ ; , _, _, _ 10 2 5 5 10

Solve each equation. If the solution is a fraction or a mixed number, be sure to express it in simplest form. 7.

2 _ + 0.4 = k

8. s =

5

9. 0.6 - n =

2 _

13. 0.8 -

8

10. t + 0.2 =

5

11. 0.375 + g =

7 _ - 0.125

5 _

4 _ 5

12. y - 0.25 =

8

1 _ =x

3 _ 4

14. q + 0.125 =

5

5 _ 8

1 _ - 0.3 = a

15. w =

5 1 _ + 0.375 + _

16. 0.7 +

17. p +

3 1 _ = 0.8 - _

18. k - 0.875 = 0.375 +

Grade 5

8

5

8

5

47

10

1 _ 8

Chapter 5

Chapter Resources

5–8

Date

Name

5

B

Date

Individual Progress Checklist D

M

Goal

Progress

round fractions and mixed numbers estimate sums and differences of fractions and mixed numbers add and subtract mixed numbers solve problems by acting them out add and subtract fractions with like denominators add and subtract fractions with unlike denominators choose the best strategy to solve a problem subtract mixed numbers involving renaming Notes Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Grade 5

48

Chapter 5

5

Name

Date

Chapter Diagnostic Assessment

1. 2.1 + 7.7 =

1.

2. 6.6 + 4.3 =

2.

3. 9.8 - 5.3 =

3.

4. 7.6 - 3.1 =

4.

5. Andrea spent $14.67 on a CD and $5.32 on lunch. About how much did she spend altogether?

5.

Assessment

Estimate using rounding.


Write each fraction in simplest form. 6.

4 _

6.

7.

5 _

7.

8.

14 _

8.

9.

18 _

6

45 21

9.

24

10. Dina read 36 out of 54 pages. Write the fraction, in simplest form, of pages that she read.

10.

Write each improper fraction as a mixed number. 11.

16 _

11.

12.

8 _

12.

13.

16 _

13.

14.

28 _

14.

15 5

5 9

Grade 5

49

Chapter 5

Name

5

Date

Chapter Pretest

Add or subtract. Write in simplest form. 1.

10 _ 12

4 = -_ 12

3 + 3. _ 8 4 + 5. _ 5

2.

6 _ _ -2= 7

7

5 -_ 1 = 4. _ 11 5 2 +_ 1= 6. _ 2 9

7= _

8 2 = _ 10

4 7 7. 2 _ + 5 _ = 5 8

2 1 8. 6_ - 1_ = 7 4

1. 2. 3. 4. 5.

Round each number to the nearest half.

6.

3 9. 3 _ 7 10.

7.

9 _ 11

8.

4 11. 5 _ 9

9.

8 _ _ +1=

11.

3 1 13. 4 _ - 3 _ = 7 5

12.

20 8 +_ 14. _ = 21 21

13.

12.

9


10.

Estimate the sum or difference. 2

14. Solve. Write the answer in simplest form. 15. Terry ate 4 pieces of an apple cut into 8 pieces. Schuyler ate 3 pieces of the apple. How much of the apple did they eat in all?

15.

1 16. Lacey wore a skirt that was 2 _ feet long. Her mother 6 1 hemmed it by _ foot. How long was the skirt after her 4 mother hemmed it?

16.

Grade 5

50

Chapter 5

5

Name

Quiz 1

Date (Lessons 5–1 through 5–3)

Estimate. 5 2 1. 3 _ + _ 3 8 1 7 2. 2 _ + _ 6 8 5 1 3. _ + 3 _ 3 10

1. 2.

Assessment

3.

Round to the nearest half. 1 4. 8 _ 3 1 5. 1 _ 12 5 6. 6 _ 10

4. 5. 6.

Solve. 7 7. Joe is 4 _ feet tall and his younger 8 5 brother is 3 _ feet tall. About how 6 much taller is Joe than his brother?

7.

Add or subtract. 8.

6 7 _ + _

8.

8 8 1 5 _ -_ 9. 10 10 6 1 10. _ + _ 7 7

Grade 5

9. 10.

51

Chapter 5

Name

5

Quiz 2


Solve. 1. Six students are playing basketball. 1 student arrives, and at the same time, 2 students leave. Then, 1 more student leaves and 3 more arrive. Now, how many students are playing basketball? 2. John has 3 quarters, 5 dimes, 2 nickels, and 5 pennies. How many different combinations of coins can he make to have $0.60? 3. Ann is using a roll of shelf paper to line 10 shelves that 1 are all the same size. The roll of paper had 25 _ feet 2 1 on it. She has already used 4 _ feet on 1 shelf. Will she 3 have enough to line the other 9 shelves? 4. Sandra and Janice are painting flowers in a border around two walls of a room. They each are doing one 1 wall. Sandra has _ of her wall painted in 2 hours. How 3 much longer will it take Sandra to finish her wall?

1.

2.

3.

4.


2 2 _ +_

5.

6.

3 7 _ +_

6.

7.

9 2 _ -_

7.

8.

5 1 _ +_

8.

9.

5 7 _ -_

9.

10.

5 1 _ -_

10.

6 4

10 6 9 6

Grade 5

8 8

8

3 8 4

52

Chapter 5

Name

5

Quiz 3


3 2 1. 5 _ + 10 _ 3 7

1.

7 11 2. 7 _ - 2 _ 9 9

2.

3 2 _ - 1_

3.

3. 3

3

10

3 + 25 _ 3 4. 21 _ 4 4

4.

3 8 5. 4_ + 4 _ 6 11

5.

7 - 3 _ 2 6. 5 _ 8 8

6.

1 1 7. 1 _ + 2 _ 4 2

7.

9 1 8. 12_ - 2 _ 5 10

8.

Assessment


Solve. 9. Max is painting clouds on his sister’s bedroom ceiling. 3 1 He needs 5 __ quarts of sky-blue paint and 3 __ quarts of 4 5 white paint. How many more quarts of sky-blue paint does he need than white paint? 10. Brooke worked 10 hours last week as a lifeguard at the 1 local swimming pool. By Friday, she had worked 8 __ 4 hours. How many more hours did she work during the rest of the week?

Grade 5

53

9.

10.

Chapter 5

5

Name

Date

Mid-Chapter Review

(Lessons 5–1 through 5–4)

Read each question carefully. Write your answer on the line provided. 1. 2. 3. 4. 5.

6.

7.


1. When rounding fractions, what do you do if the numerator is almost as large as the denominator? 3 A. round to 1 C. round to _ 4 1 _ D. round to 0 B. round to 2 2. When rounding fractions, what do you do if the numerator is much smaller than the denominator? 3 F. round to 1 H. round to _ 4 1 _ G. round to J. round to 0 2 3. When rounding fractions, what do you do if the numerator is about half of the denominator? 3 A. round to 1 C. round to _ 4 1 B. round to _ D. round to 0 2 1 4. What is 3 _ rounded to the nearest half? 10 F. 3 H. 5 G. 4 J. 6 6 1 5. What is the estimated sum of 3 _ + 2 _ ? 7 9 A. 3 C. 6 B. 5 D. 8

8.

6. How do you estimate sums and differences of fractions? 7. What are like fractions? 8. How do you add fractions with the same denominator?

9.

9. How do you subtract fractions with the same denominator? 10. What is the advantage of using the act it out strategy? 10.

Grade 5

54

Chapter 5

5

Name

Date

Vocabulary Test

Using the word bank below, complete each sentence by writing the correct word or words on the line provided.

unlike fractions numerator renaming

simplest form denominator

1. The is the number above the bar in a fraction; the part of the fraction that tells how many of the equal parts are being used. 2. A

has a whole number part and a fraction part.

3. A fraction in which the numerator and the denominator . have no common factor great than 1 is in 4. The bottom number in a fraction is the

2.

4.

5.

are fractions with different denominators.

7. A number that represents part of a whole or part of a set is a . 8. Fractions that have the same denominator are

1.

3.

.

5. When subtracting mixed numbers, sometimes the fraction part of the larger number is less than the fraction part of the smaller number. When this happens, you must use . 6.

Assessment

like fractions fraction mixed number

.

6. 7. 8.

Grade 5

55

Chapter 5

5

Name

Date

Oral Assessment

Draw pictures of a square and a circle on the board. Divide each shape into 4 equal parts. For the square, shade in 1 section. For the circle, shade in 3 sections. Read each question aloud to the student. Then write the student’s answers on the lines below the question. 1. How many parts are shaded in on the first square?

2. What is the fraction that represents the amount of parts shaded on the first square?

3. How many parts are shaded on the first circle?

4. What is the fraction that represents the amount of parts shaded on the first circle?

5. Tell how you got your answer.

6. If you add the two fractions for the first square and the first circle, what is the sum?

Grade 5

56

Chapter 5

5

Name

Date

Oral Assessment

(continued)

7. Tell how you got your answer.

_

Using a piece of paper or the chalkboard, draw 2 circles. The 2 first circle should be shaded to represent and the second 4 1 circle should be shaded to represent . 4

_

Assessment

8. What is the sum of the shaded area of both circles? 9. Tell how you got your answer.

_

Using a piece of paper or the chalkboard, draw 2 squares. The 4 first square should be shaded to represent and the second 6 2 circle should represent . 6

_

10. What is the sum of the shaded areas of both squares? 11. Tell how you got your answer.

Grade 5

57

Chapter 5

Name

5

Date

Chapter Project Rubric

Score 3

2

1

0

Explanation Student successfully completed the chapter project. Student demonstrated appropriate use of chapter information in completing the chapter project. Student completed the chapter project with partial success. Student partially demonstrated appropriate use of chapter information in completing the chapter project. Student did not complete the chapter project or completed it with little success. Student demonstrated very little appropriate use of chapter information in completing the chapter project. Student did not complete the chapter project. Student demonstrated inappropriate use of chapter information in completing the chapter project.


Grade 5

58

Chapter 5

Name

5

Date

Chapter Foldables Rubric

Adding and Subtracting Fractions Pocket Foldable

Explanation 3

Student properly assembled Foldables graphic organizer according to instructions. Student recorded information related to the chapter in the manner directed by the Foldables graphic organizer. Student used the Foldables graphic organizer as a study guide and organizational tool.

2

Student exhibited partial understanding of proper Foldables graphic organizer assembly. Student recorded most but not all information related to the chapter in the manner directed by the Foldables graphic organizer.


Student demonstrated partial use of the Foldables graphic organizer as a study guide and organizational tool.

1

Student showed little understanding of proper Foldables graphic organizer assembly. Student recorded only some information related to the chapter in the manner directed by the Foldables graphic organizer. Student demonstrated little use of the Foldables graphic organizer as a study guide and organizational tool.

0

Student did not assemble Foldables graphic organizer according to instructions. Student recorded little or no information related to the chapter in the manner directed by the Foldables graphic organizer. Student did not use the Foldables graphic organizer as a study guide and organizational tool.

Grade 5

59

Chapter 5

Assessment

Score

Name

5

Date

Chapter Test, Form 1

Read each question carefully. Write your answer on the line provided. 5 1. Round 5_ to the nearest half. 8 1 1 A. 5 B. 5 _ C. 6 D. 6 _ 2 2 2 5 7 2. Use rounding to order _, _, and _ from least to greatest. 9 8 19 5 2 7 2 5 7 5 7 2 7 5 2 G. _, _, _ H. _, _, _ J. _, _, _ F. _, _, _ 9 8 19 9 19 8 19 9 8 8 9 19

1.

2.

Estimate. 1 4 3. 3 _ + 1 _ 5 10 A. 6

B. 5

C. 4

D. 3

G. 2

H. 3

J. 5

3.

1 9 4. 4 _ - 1 _ 5 10 F. 1

4.


9 2 _ -_ 10

A. 6.

2 _

10

5

5.

15

1 H. 1 _ 10

3 J. 1 _ 10

6.

7 B. 12 _ 8

1 C. 13 _ 4

7 D. 13 _ 24

7.

1 _

G.

10 _

3 7 _ +_

5 4 F. _ 10 5 2 7. 3 _ + 9 _ 3 8 7 A. 12 _ 24 3 13 8. _ - _ 20 10 9 F. _ 10 10

Grade 5

7 _

1 D. 1 _ 10

B.

G.

2

7 _ 10

C.

H.

10

1 _ 2

60

J.

7 _ 20

8.

Chapter 5

Name



1 1 9. 19 _ - 6 _ 6 2 1 A. 12 _ 2 2 4 10. _ + _ 3 5 7 F. 1 _ 15 1 2 11. 42 _ + 16_ 5 10 3 _ A. 58 5 9 1 12. 19 _ - 10 _ 4 10 3 F. 10 _ 20 1 1 13. 31 _ + 9_ 2 6 1 A. 41 _ 3 3 14. 4 - 2 _ 8 5 _ F. 2 8

(continued)

2 B. 12 _ 3

1 C. 13 _ 2

2 D. 13 _ 3

9.

1 G. 1 _ 3

1 H. 1_ 5

3 _

10.

1 B. 58 _ 2

1 C. 57_ 2

3 D. 57 _ 10

11.

7 G. 9 _ 10

13 H. 9 _ 20

1 J. 9 _ 4

12.

2 B. 40 _ 3

1 C. 40 _ 3

2 D. 39 _ 3

13.

3 G. 2 _ 8

5 H. 1 _ 8

3 J. 1 _ 8

14.

J.

4

Solve. 1 15. Janice spent _ of her savings on an outfit. The next week Janice 3_ 1 spent another of her savings on a CD. How much of her total 4 savings did she spend? A.

1 _ 7

B.

5 _ 12

C.

1 _ 2

D.

7 _ 12

15.

1 16. A 20-pound bag of nails has 7_ pounds left. How many pounds of 4 nails have been removed? 1 F. 13 _ lb 4

Grade 5

1 G. 13 _ lb 8

3 H. 12 _ lb 4

61

1 J. 12 _ lb 4

16.

Chapter 5

Assessment

5

Date

Name

5

Date

Chapter Test, Form 2A

Read each question carefully. Write your answer on the line provided. 7 1. Round 4_ to the nearest half. 13 1 1 C. 5 D. 5 _ A. 4 B. 4 _ 2 5 4 4 7 2. Use rounding to order _ , _, and _ from least to greatest. 7 9 21 4 4 7 4 4 7 7 4 4 4 7 4 G. _, _, _ H. _, _, _ J. _, _, _ F. _, _, _ 7 9 21 7 21 9 21 7 9 9 7 21

1.

2.

Estimate. 5 1 3. 2 _ + 1 _ 3 8 A. 6

B. 5

C. 4

D. 3

3.

G. 4

H. 3

J. 2

4.

2 D. 1 _ 3

5.

7 J. 1 _ 8

6.

11 D. 9 _ 12

7.

1 11 4. 6 _ - 1 _ 6 12 F. 5


5 8 _ -_ 9

2 A. _

9

9

6.

B.

3 7 _ +_

4 5 F. _ 8 5 1 7. 2 _ + 7 _ 4 6 1 A. 10 _ 12 5 1 8. _ - _ 8 8 3 F. _ 4 8

Grade 5

1 _ 3

C.

4 _ 9

1 G. 1 _ 2

5 H. 1 _ 8

1 B. 10 _ 4

1 C. 10 _ 6

G.

3 _ 8

H.

1 _ 2

62

J.

1 _ 4

8.

Chapter 5


Date

Chapter Test, Form 2A

3 1 9. 25 _ - 23 _ 4 8 1 A. 2 _ 2 3 1 10. _ + _ 10 8 9 F. _ 10 2 7 11. 8 _ + 6 _ 3 15 1 _ A. 15 15 13 12. 15 _ - 3 16 13 F. 18 _ 16 5 2 13. 21 _ + 5_ 3 6 2 A. 27 _ 3 5 14. 3 - 2 _ 7 2 _ F. 7

1 B. 2 _ 8

G.

19 _ 30

7 C. 1 _ 8

H.

19 _ 40

2 B. 15 _ 15

1 C. 15 _ 5

5 G. 18 _ 8

13 H. 12 _ 16

1 B. 27 _ 2

2 C. 26 _ 3

G.

5 _ 7

2 H. 1 _ 7

(continued)

1 D. 1 _ 2

J.

19 _ 80

1 D. 15 _ 3

3 J. 12 _ 16

9.

10.

11.

12.

1 D. 26 _ 2

13.

5 J. 1 _ 7

14.

Solve. 1 15. A 30-pound bag of dog food has 12_ pounds left. How many 2 pounds of dog food have been removed? A. 17 lb

1 B. 17 _ lb 2

C. 18 lb

1 D. 18_ lb 2

15.

3 16. Paulo cooked 2 _ pounds of chicken for a hiking trip. He also made 4 1 3 _ pounds of meatballs. How many pounds of food did Paulo cook 8 in all? 7 F. 6 _ lb 8

Grade 5

5 G. 6 _ lb 8

7 H. 5 _ lb 8

63

5 J. 5 _ lb 8

16.

Chapter 5

Assessment

5

Name

Name

5

Date

Chapter Test, Form 2B

Read each question carefully. Write your answer on the line provided. 7 to the nearest half. 1. Round 4 ___ 13 1 A. 4 B. 4 _ C. 5 2 4 4 7 2. Order _, _, and _ from least to greatest. Use rounding. 7 9 21 4 4 7 4 4 7 4 7 4 G. _, _, _ H. _, _, _ F. _, _, _ 7 9 21 7 21 9 21 7 9

1.

2.

Estimate. 5 1 3. 2 _ + 1 _ 3 8 A. 3

B. 4

C. 5

3.

G. 4

H. 3

4.

1 11 4. 6 _ - 1 _ 6 12 F. 5


5 8 _ -_ 9

4 A. _

9

9

6.

B.

3 7 _ +_

4 5 F. _ 8 5 1 7. 2 _ + 7 _ 4 6 1 A. 10 _ 12 5 1 8. _ - _ 8 8 3 F. _ 4 8

Grade 5

1 _ 3

C.

2 _ 9

5.

5 G. 1 _ 8

7 H. 1 _ 8

6.

1 B. 10 _ 4

1 C. 10 _ 6

7.

G.

1 _ 2

H.

3 _ 8

64

8.

Chapter 5

9.

10.

11.

12.

13.


14.

Date

Chapter Test, Form 2B

3 1 25 _ - 23 _ 4 8 1 A. 2 _ 8 3 1 _ +_ 10 8 9 F. _ 10 2 7 8_ + 6_ 3 15 1 _ A. 15 15 13 15 _ - 3 16 13 F. 18 _ 16 5 2 21 _ + 5 _ 3 6 2 A. 27 _ 3 5 3 - 2_ 7 2 _ F. 7

1 B. 2 _ 2

(continued)

7 C. 1 _ 8

9.

19 _

10.

2 B. 15 _ 15

1 C. 15 _ 5

11.

5 G. 18 _ 8

13 H. 12 _ 16

12.

1 B. 27 _ 2

1 C. 26 _ 2

13.

2 H. 1 _ 7

14.

G.

G.

19 _ 40

5 _ 7

H.

80

Solve. 15. Find a + b. 3 1 a = 6 _ and b = _ 4 5 19 9 A. 7 _ B. 6 _ 20 10

17 C. 6 _

15.

20

16. Find x - y. 4 1 x = 3 _ and y = 1 _ 3 9 2 1 F. 2 _ G. 2 _ 9 9

Grade 5

1 H. 1 _

16.

9

65

Chapter 5

Assessment

5

Name

5

Name

Date

Chapter Test, Form 2C

Read each question carefully. Fill in the correct answer on the line provided. 7 1. Round 4 _ to the nearest half. 13 4 4 7 2. Use rounding to order _ , _, and _ from least to greatest. 7 9 21

1.

2. 3. 4.

Estimate. 5 1 3. 2 _ + 1 _ 3 8 1 11 4. 6 _ - 1 _ 6 12

5.

6. Add or subtract. Write in simplest form. 5.

8 _ _ -5

7.

9 9 3 7 6. _ + _ 4 8 5 1 7. 2 _ + 7 _ 4 6 5 1 8. _ - _ 8 8 3 1 9. 25 _ - 23 _ 8 4 3 1 10. _ + _ 10 8 2 7 11. 8 _ + 6 _ 3 15 13 12. 15 _ - 3 16 5 2 13. 21 _ + 5 _ 3 6 5 14. 3 - 2 _ 7

8.

9.

10.

11.

12.

13.

14. Grade 5

66

Chapter 5

5

Name

Date

Chapter Test, Form 2C

(continued)

3 1 15. a + b if a = 6 _ and b = _ 4 5

15.

1 4 16. x - y if x = 3 _ and y = 1 _ 3 9

16.

Assessment

Evaluate each expression.

Solve. 1 17. A 30-pound bag of dog food has 12_ pounds left. How many 2 pounds of dog food have been removed? 3 18. Paulo cooked 2_ pounds of chicken for a hiking trip. He also made 4 1 3_ pounds of meatballs. How many pounds of food does Paulo 8 cook in all? 3 1 19. Luisa had 1_ cups of spaghetti sauce in a jar. She used _ cup for 2 4 her dinner. How many cups of sauce are left in the jar? 1 20. In her meatloaf recipe, Ana uses _ cup breadcrumbs, 2 3 1 1_ cups tomato sauce, and _ cup onions. How many cups of 4 4 the ingredients does she use all together?

Grade 5

67

17.

18.

19.

20.

Chapter 5

5

Name

Date

Chapter Test, Form 2D

Read each question carefully. Fill in the correct answer on the line provided. 7 1. Round 4_ to the nearest half. 13 4 4 7 2. Use rounding to order _, _, and _ from least to greatest. 7 9 21 Estimate.

1. 2. 3. 4.

5 1 3. 2 _ + 1 _ 3 8 1 11 4. 6 _ - 1 _ 6 12

5. 6.


7.

5 8 _ -_

9 9 3 7 6. _ + _ 4 8 5 1 7. 2 _ + 7 _ 4 6 5 1 8. _ - _ 8 8 3 1 9. 25 _ - 23 _ 4 8 3 1 10. _ + _ 10 8 7 2 11. 8 _ + 6 _ 3 15 13 12. 15 _ - 3 16 5 2 13. 21 _ + 5 _ 3 6 5 14. 3 - 2 _ 7

Grade 5

8. 9. 10. 11. 12. 13. 14.

68

Chapter 5

5

Name

Date

Chapter Test, Form 2D

(continued)

Solve. 15. Find a + b 1 3 a = 6_ and b = _ 4 5

15.

1 4 x = 3_ and y = 1_ 3 9

16.

1 17. A 30-pound bag of dog food has 12_ pounds left. How many 2 pounds are gone?

17.

3 1 18. Paulo makes 2_ pounds of chicken. Then he makes 3_ pounds of 4 8 meatballs. How many pounds of food does Paulo make in all?

18.

3 1 19. Luisa had 1_ cups of rice in a jar. She uses _ cup. How many cups 4 2 of rice are left in the jar?

19.

3 1 1 20. Ana has _ cup sugar, 1_ cups tomato sauce, and _ cup onions. 4 4 2 How many cups of food does she have in all?

20.

Grade 5

Assessment

16. Find x – y

69

Chapter 5

5

Name

Date


Read each question carefully. Fill in the correct answer on the line provided.

2.

Estimate as directed. 1. Round

3 _ to the nearest half.

3.

25 49 2. Round 1_ to the nearest half. 63

4.

Estimate each sum or difference. 3.

5.

7 1 9_ + 1_

8 9 1 2 4. 6 _ - _ 5 13

6.

Find the sum or difference. Write your response in simplest form.

7. Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

3 1 7 5. 3 _ + 1 _ + 2 _ 4 8 12 3 3 6. _ - _ 4 19 6 1 7. 3 _ + 7 _ 4 7 17 7 8. _ - _ 132 132 3 3 9. 19 _ - 5 _ 4 10 3 7 1 10. _ + 3 _ + 1 _ 4 2 10 3 7 11. _ + _ 8 16 5 12. 14 - 9 _ 7 8 2 13. 22 _ - 1 _ 13 39

Grade 5

1.

8.

9.

10.

11.

12.

13.

70

Chapter 5

5

Name

Date


(continued)

Evaluate each expression. 3 3 1 14. a + b + c if a = 4 _, b = 1 _, and c = _ 4 5 6 4 15. x - y if x = 61 and y = 3_ 11

14. 15.

16.

9 _ 4 _ 4 _ 1 _ , , ,

Assessment

Order from least to greatest. 16.

15 30 10 5


Solve. 1 17. Steve spent _ of his monthly allowance of $24 in May. In June, he 3 1 spent _ of his allowance on repairing his bike. How much more of 2 his allowance did Steve spend in June than in May?

17.

18. Marco buys 4 gallons of cherry stain and 3 gallons of clear stain. He 1 uses 1_ gallons of cherry stain on woodwork. How many gallons of 3 cherry and clear stain does he have left?

18.

5 19. Erica kicks a soccer ball 20_ feet, Maggie kicks a soccer ball 6 7 11 11_ feet, and Marie kicks a soccer ball 11_ feet. Find the 20 12 difference between the farthest and shortest difference.

19.

1 2 20. A triangular fence has sides that measure 5_ feet, 6_ feet, and 3 4 2 2 7_ feet. A rectangular fence has two sides that measure 2_ feet 7 3 1 and two sides that measure 6_ feet. Which fence has the greater 8 perimeter (sum of the measures of the sides)?

20.

Grade 5

71

Chapter 5

5

Name

Date

Chapter Extended-Response Test

Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem. If necessary, record your answer on another piece of paper. 1. a. What is the proper method for rounding fractions and mixed numbers to the nearest half?

b. Describe a situation where it would make sense to round a fraction up to the nearest inch.

1 2. Would you round 3_ to 3 or 4? Explain your reasoning. 4 Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

3. a. Explain in your own words how to subtract fractions with the same denominators. Provide an example.

b. Explain in your own words how to add fractions with different denominators. Provide an example.

4. How do you write a decimal as a fraction? Explain in your own words.

Grade 5

72

Chapter 5

Name

5

Date

Chapter Recording Sheet

Use this recording sheet with pages 278–279 of the Student Edition.


1.

A

B

C

D

2.

F

G

H

J

3.

A

B

C

D

4.

F

G

H

J

5.

A

B

C

D

6.

F

G

H

J

7.

A

B

C

D

8.

F

G

H

J

9.

A

B

C

D

10.

F

G

H

J

Grade 5

Assessment

Read each question. Then fill in the correct answer.

73

Chapter 5

5

Name

Date

Cumulative Standardized Test Practice

Test Example Toni is going to knit three scarves. She will need the following amount of yarn for each scarf. How much yarn does Toni need for all three scarves? Scarf 1

Scarf 2

Scarf 3

1 150 _ yards 2

1 111 _ yards 4

2 120 _ yards 3

5 A. 381 _ yards 12

5 7 B. 381 _ yards C. 382 _ yards 12 12

7 D. 382 _ yards 12

Read the Question You need to find how much yarn Toni needs.

First use the LCD to rename the fractions. Then add. The total amount of 5 yarn needed is 382 ___ yards. 12

1 150 _ 2 1 111_ 4 2 +120 _ 3


Solve the Question

6 150 _ 12 3 111_ 12 8 +120 _ 12 5 17 381_ = 382_ 12 12

So, the answer is C.

Grade 5

74

Chapter 5

Name

5

Date

Cumulative Standardized Test Practice (continued)

Choose the best answer. 2 1. Tina needs to buy wood to create a birdhouse. She needs _ foot 5 7 of oak wood and _ foot of cherry wood. Find the total amount 10 of wood that Tina needs to buy.

F.

1 _ mile 21

G.

2 _ mile

H.

21

9 _ mile 21

J.

10 _ mile 21

1. Assessment

1 1 1 C. 1 _ feet D. _ foot B. 1 _ feet 10 15 10 1 2. Jillian rode her bicycle _ mile to get from her house to the pool. 3 1 Then Jillian rode _ mile from the pool to the post office. What is 7 the total distance that Jillian rode? 1 A. 1 _ feet 5

2.

3 3. Ivette has math and reading homework. It takes Ivette _ hour to 10 1 complete her math homework and _ hour to complete her reading 2 homework. How much time does it take Ivette to complete both her math and reading homework? A.

1 _ hour 5

1 1 4. 2 _ - 1 _ = 4 2 1 F. 1 _ 2

B.

3 _ hour 5

1 G. 1 _ 4

C.

4 _ hour

H.

1 _

5

2

D. 1 hour

J.

1 _ 4

3.

4.

5. Joey cooks two vegetarian pizzas for a class party. The shaded portions of the pizzas below show the pieces that are left. What portion is left altogether?

A.

39 _ of a pizza

C.

6 _ of a pizza

B.

27 _ of a pizza

D

6 _ of a pizza

Grade 5

40 40

13

40

75

5.

Chapter 5

5

Name

Date

Cumulative Standardized Test Practice (continued)

6. Which letter on the number line identifies the location of -3?

A

B

C

–5 F. A

D –1

G. B

H. C

J. D

6.

2 7. Kira read 97 pages of a book last night, which was _ of the book. 5 What decimal represents the fraction of the book that she read? A. 0.2

B. 0.3

C. 0.4

D. 0.5

7.

J. 7

8.

8. If v = 7, what is the value of 4 × v - 11? F. 17

G. 15

9. Paul gives away

H. 11

4 _ of his shirts because they no longer fit. What

9 fraction of his shirts did Paul keep?

11. Lexi reads

10.

5 1 _ of a book in the morning and _ of the book in

8 12 the evening. Find the total fraction of the book that Lexi read.

11.

12. Write the prime factorization of 56.

12.

7 13. 20 - 18 _ = 9

13.

14. Randy and Phil run a 100-meter race. Randy’s time is 16.041 seconds and Phil’s time is 16.149 seconds. Who won the race?

14.

15. A test has 40 questions. Rafael answers

7 _ of the questions

8 correctly. How many questions did Rafael answer correctly?

12 _ 16. Find the value of x to make the fractions equivalent. _ x = 20 3

Grade 5

76


10. Find the least common multiple of 10, 30, and 40.

9.

15. 16.

Chapter 5

Grade 5

Graphic Organizer

Name

Date

A1

Grade 5

… add or subtract mixed numbers?

… add or subtract fractions with unlike denominators?

… add or subtract fractions with like denominators?

… estimate the sum or difference of mixed numbers?

… estimate the sum or difference of fractions?

How do I …

1

Add or subtract the fractions. Add or subtract the whole numbers. Rename and simplify if necessary.

Rename the fractions using LCD. Add or subtract as with like fractions. Simplify the sum or difference if necessary.

Add or subtract the numerators. Use the same denominator in the sum.

Round each mixed number to the nearest half. Then add or subtract.

Round each fraction to the nearest half. Then add or subtract.

Instructions

3 7

4 . 5

9

12

4

3 4

9 1 3 12 5 12

1 8

3 8

3 .

3

1

4 . Add the 8

1 2

and simplify: 4 . Chapter 5

4. Rename

_

whole numbers:

3 8

1 8

Add the fractions:

Add: 1

_ _ _ _ _

4 12

Subtract:

_ _ _ _ _ _

Add:

3 4 11 11 3 4 7 . 11 11

1 or 2.

_ _ _ _

is about 3

3 1 4 rounds to . 7 2 5 3 4 rounds to 1. is 5 7 1 1 about 1 or 1 . 2 2 5 1 Estimate 2 1 . 7 9 5 1 2 rounds to 3. 1 7 9 5 1 rounds to 1. 2 1 7 9

Estimate

Examples

_ _ _ __ _ _ _ _ _ _ _ _ _ _

Use this graphic organizer to take notes on Chapter 5: Adding and Subtracting Fractions. Fill in the missing information.

5

Answers

Answers (Graphic Organizer and Anticipation Guide)

Chapter 5

Chapter Resources

Answers (Lesson 5 –1)

Grade 5

A2

Chapter 5

Grade 5

2

3 12

8.

6

_

2

1 10 7 _ 2 10 12

2 5. 6 _ 9

5 2. 4 _ 11

_1 9.

6.

8

3 _

16

14 _

3 3. 7 _ 10

1 12

A3

_

1

1 2

2

2

Grade 5

(

)

3 15. Q 4 _, 5 4

( ) 1 16. T (2, 2 _) 4

10

( )

1 17. V 1, 3 _ 2 O

Q

P M

2

_1

Chapter 5

x 1 2 3 4 5 6

6 y 5 4 V 3 T 2 N 1

_1 inches long and 6 _1 inches wide

Graph each ordered pair on the coordinate plane at the right. 1 12. M (4, 3) 13. N 1 _, 2 14. P (3, 2.5) 2

8

2

2 1 6 _ inches wide or in a box that is 8 inches long and 6 inches wide?

1

inches wide. Will the book fit in a box that is 8 _ inches long and

3 8

11. Alice is giving a book as a gift that is 8 _ inches long and 6 _

8 feet

how tall is the tallest cabinet that can fit in the basement?

10. Your basement has an 8 _ foot ceiling. To the nearest half foot,

Solve.

6 16

12

2

_1 2 1 8_ _

8 _

7. 8

4.

1 1. 2 _ 12

4

7

5MR2.5, 5NS1.1

Rounding Fractions and Mixed Numbers

Homework Practice

Name ____________________________ Date ________________

Round each number to the nearest half.

5–1


1 cup

2

2

_1 ft


Chapter 5

Answers

Grade 5

up

11

6. Based on the area of his flowerbed, a gardener calculates that he 8 8 needs 6 _ gallons of fertilizer. Should he round 6 _ up or down 14 14 when deciding on the amount of fertilizer he should purchase?

2

3 5. A farmer is planting squash plants that need 2 _ feet to spread 8 out. Round the amount of space the squash plants need to the 1 nearest _ foot.

12 inches long and 10 inches wide

1 4. Russ is putting his photographs in an album that is 12 _ inches long 8 1 and 10 _ inches wide. Should he trim the edges of the photographs 2 1 _ to 12 inches long and 10 inches wide or to 12 inches long and 4 1 10 _ inches wide? 4

6 2 ft

_

3. To the nearest half foot, what is the tallest refrigerator that can fit in 3 a kitchen with a space that is 6_ feet tall? 4 1

_2 cup

3 2. The cookie recipe also calls for _ of a cup of walnuts. Should you 8 1 buy a package with 1 cup or a package with _ cup of walnuts? 2 1

Chapter 5

5MR2.5, 5NS1.1

Rounding Fractions and Mixed Numbers


Name ____________________________ Date ________________

3 1. A recipe for cookies calls for _ of a cup of chocolate chips. Should 1 4 you buy a package with _ cup or a package with 1 cup? 2

Solve.

5–1


Chapter Resources

Grade 5

A4

2

pounds

1

INCHES

3

1

0

1

INCHES

INCHES

1

2

2

2

10 mL

20 mL

30 mL

40 mL

50 mL

CM 1

INCHES

2

3

1

4

5

2

Answers (Lessons 5 –1 and 5 –2)

Chapter 5

Grade 5

2

2

_1

8

6 4 6. 9 _ 5

2.

1 4_

10

4

_2 _21 18 - 10 = 8 _ _ 1 _ _12 15 - 7 = 8 2

A5

2

7 1 30_ + 30_

2

16

2

_1 + 8_1 = 17

8

5

2

7

_2 = 13_12

25.

22.

_2 = 8_12

8

1

59 - 30 = 29

5

13

4 7 58 _ - 29 _

18 - 9

10

2 4 +6 5 3

7 1 17_ - 9_

19. 9

5 11 16. 6 _ + 4 _ 12 1 12

_2 _12 7 + 4 = 11 _ _ _12 _12 10 + 6 = 16

6+7

3 1 13. 6_ + 7 _ 4 18

2

2

_1

2

_2 + 7_12 = 15

8

5 1 26. 50 - 30 3 16

7

3

3 1 7_ + 9_

_21 + 9_12 = 17 _ _ 1 _ _12 50 - 30 = 20 2

7-6=1

11 1 20. 6 _ - 6_ 5 12

1 7 17. 7_ + 7_ 3 1 12

7

2

1 14 - 9_ = 4_

3 1 14. 14 _ - 9 _ 5 51

23.

2

_

4 1 5

5-2=3

1 7 11. 5 _ - 1 _ 8 8

4 4. 3_ 5 5 8. 5 _ 12

5MR2.5, 5NS1.1

2

_1 miles

_1 miles

3

Grade 5

14

yes, he walked about 8

8

2

Chapter 5

28. Jon wants to walk at least 8 miles by the end of the week. He walks 5 _ miles by 4 5 Thursday. If he walks another 2 _ miles on Friday, will he meet his goal? Explain.

about 8

27. Beth walks 10 _ miles in one week. She walks 2 _ fewer miles the following week. 2 8 About how many miles does she walk the second week?

Solve.

24.

12 1 12 1 30_ + 30 = 60_

21.

3 7 -7 8 16

2 11 8_ + 8_

18. 15

13 5 15. 18_ - 9_ 161 16

9

4 7 12. 9 _ + 3 _ 5 110

_2 + 4 = 13_12

4+2=6

8

_12 _12 9-3 =5

Estimate the sum or difference. 5 7 2 1 9. 3_ + 2_ 10. 8_ - 3_ 3 6 6 8

4 9 5. 2 _ 16

1.

3 7_ 2 3. 8 _ 5 7 7. 1 _ 8

Estimating Sums and Differences

Skills Practice

Name ____________________________ Date ________________

Round to the nearest half.

5–2


6

5 _


Chapter 5

1

2

1 7_

10

2

4

5

Answers

Grade 5

19.

9 17. 7 _ 15

1 15. 4 _ 9

10 13. 9 _ 10

2 11. 5 _ 3

_1

6

_1 2

10

Round to the nearest half. (Lesson 5–1)

7 4 9. 6 _ - _ 7 8

5 3 7. 3 _ + 6 _ 5 8

3

4

10

1 2 5. 1 _ + 3 _ 10 9

3.

2

5

9 2 _ + 3_

8 1 1. 4 _ + _ 3 9

_1 2 1 4_

15

9

5 7 _ + 2_

18

14 _

12

6 _

15

1 20. 18 _ 12

7 18. 11 _ 24

16.

14.

2 12. 8 _ 13

18

2

10

2

_1

3

2

Chapter 5

5MR2.5, 5NS1.1

_1 2 1 7_ 2 1 14 _ 7

_1 11

1

2

_1

8

5 7 10. 10 _ - _ 8 9

8.

1 1 6. 7 _ + 7 _ 3 8

6 7 4. 8 _ - 1 _ 8 9

1 7 2. 7 _ + _ 6 15

Estimating Sums and Differences

Homework Practice

Name ____________________________ Date ________________

Estimate the sum or difference.

5–2


Chapter Resources


Grade 5

A6

Chapter 5

Grade 5 5NS2.3


Reteach

Name ____________________________ Date ________________

_

A7

_1

4

5 7 4. _ - _ = 8 8

Grade 5

7

_1

5 4 1. _ - _ = 7 7

18

11 7 5. _ - _ = 12 12

1 1 2. _ + _ = 4 4


3

_1 2 _1 3 2 = 6. _ + _ 10 10

3 1 3. _ + _ = 10 10

6÷3 6 2 _ =_=_ 3 9 9÷3

Chapter 5

2

_2 5 _1

Write the difference in simplest form. Divide the numerator and denominator by their greatest common factor.

Subtract the numerators. Use the like denominator. 6 8 _ 2 _ - =_ 9 9 9 8 6 2 2 So, _ - _ = _ = _. 3 9 9 9

2

Step 2

8÷4

Step 1

8

4÷4 4 1 _ =_=_

Write the sum in simplest form. Divide the numerator and denominator by their greatest common factor.

Add the numerators. Use the like denominator. 3 1 4 _ + _= _ 8 8 8 1 3 1 4 So, _ + _ = _ = . 8 8 8 2

8 Step 2

8

3 1 _ +_

Step 1

Add

Follow these steps to add or subtract fractions with like denominators.

5–3


1 7 11 _ 2 +_=

13.

16.

12

16

8


Chapter 5

Answers

Grade 5

25

8

_1

_1

8

_5

_

7 -_= 16 16

9 _

12

16

8

15

20.

17.

14.

11.

8.

5.

2.

_1

10

5

5

20

4 3 _ -_=

20

19 5 _ +_=

10

3

_1

10

_3

5

_2

1

1

5

_1

1

5

_1

1 3 9 _ 5 +_=

3

20

2 1 _ +_=

20

5

9 3 _ -_=

5

16

3 4 _ +_=

16

1 13 7 _ 4 +_=

21.

18.

15.

12.

9.

6.

3.

9

19

9

20

7 4 _ -_=

20

8

11 7 _ -_=

8

6

3

_1

Chapter 5

_1 5

_3

3

_2

4

3

_2

_1

1

1

1 7 7 _ 4 +_=

6

8

5 1 _ -_=

8

6

3 1 _ -_=

6

5

5 5 _ +_=

5

4 1 _ +_=

8 22. In Mr. Jane’s homeroom, _ of the students brought a lunch from 25 15 2 home, _ of the students will buy a lunch, and _ of the students 25 25 will go home for lunch. What fraction of the class will eat lunch at school? 23

19.

7 3 _ +_=

2

_1

3 1 _ +_=

10.

15

3

_1

7 2 _ -_=

12

7.

12

1

5 7 _ +_=

4.

10

5

_4

1 7 _ +_=

1. 10

5NS2.3


Skills Practice

Name ____________________________ Date ________________


5–3


Chapter Resources

A8

Chapter 5

3 = 9

2 = 2

9 _ +

1 _ +

3 12 _ +_=

5.

7.

9.

1

3

5

2 1 _ + 6_ =

8

7

7 1 _ -_=

Grade 5

5 11 21. _ + _ = 2 8

19.

3 5 17. 8 _ + 6 _ = 5 8

6

1

15

11

2

_

3 1 6

2 1 15. 8 _ + 3 _ = 10 9

13.

5 1 11. 2 _ + _ = 2 9

Estimate. (Lesson 5–2)

15

2

9

15

8

8

2

6 5 _ -_= 8

_1 1 1_ _ 3 1 _ 1 _

2

3.

5

8 2 _ +_=

1.

5

_4 9 1 1_ 4 1 _ 1 _81 5 _5

5NS2.3

7

7

5

6 1 _ -_=

5

8

3 4 _ -_=

8

4

7 2 _ +_=

4

9

3 2 _ +_=

9

5 1 _ -_=

15

9

5 5 _ + 7_ =

20

6 2 22. 3_ - 1_ = 7 3

5 1 20. 1 _ - _ = 8 9

18.

6 1 16. 1 _ + 7 _ = 3 7

7 2 14. 3 _ - 1 _ = 8 9

4 1 12. 5 _ + _ = 6 2

10.

8.

6.

4.

2.

2

_1 2 1 2_

8

9

3

6

7

Chapter 5


Homework Practice

Name ____________________________ Date ________________


Grade 5


5–3

3

Grade 5

5

_4 of the items

5. Sherry was in charge of distributing 250 food items that were donated to the local food pantry. On Monday she distributed 87 items. On Tuesday, she distributed 63 more items. Fifty more items were distributed on Wednesday. What fraction of the food items was distributed by the end of the day on Wednesday?

3. Mindy likes to order fresh meat and vegetable wraps from a local 1 restaurant. One cook can roll _ wraps 3 2 in 5 minutes. Another cook can roll _ 3 wraps in the same amount of time. What is the difference in the number of wraps the two cooks can prepare in 5 minutes? 1

_ wrap

_1 of the laundry

1. Debbie helped her mother with the 1 laundry. She did _ of it on Monday 3 8 and another _ of it on Tuesday. What 8 fraction of the laundry has she done?

2

5NS2.3

21

7

Chapter 5

_2 mile farther

6. Laura and her sister Katie swim every 3 day. Laura can swim _ mile in 7 2 10 minutes. Katie can swim _ mile 7 in the same amount of time. If they swim for 20 minutes and their speeds stay the same, how much farther does Laura swim than her sister?

5

_2 mile

4. John went to a museum to see model 2 trains. He saw _ mile of track on the 5 4 first floor of the museum. He saw _ 5 mile of track on the second floor. How much more track did John see on the second floor than the first?

1 hour

1 2. Laureano worked _ hour one day 4 3 _ and hour the next day. How many 4 hours did he work on the two days?



Name ____________________________ Date ________________

Solve. Write your answer in simplest form.

5–3


Chapter Resources

Grade 5

Fraction Puzzles

Enrich

3 _

6 _

A9

25

4 _

25

25

1 _

25 25

25

8

0 _

3 16

8

1 _

16

7 16

16

1 _

15

2 _

15 4 _ 15

_2 15 _8

8

2 _

16

15

6 _

15

7 _

15

0 _

15

3 _

_1 16 _1 _ _2 16 16 _2 _5 _ 16

8 _

15

1 _

15

2 _

15

4 _

15

9 _

Grade 5

22

CHALLENGE Create your own fraction puzzle using a box of 5 rows and 5 columns.

25

2 25

25

2 _

12 _

25

_0

3 _

25

11 _

20

6 _

25

6 20

7 20

2 20

_1 _5 20 20 _6 _ 20 _5 _ 20 _4 _

_9 _6 _3 25 25 25 _7 _5 _

25

20

20

3 _

20

_5

20

4 _

2 _ 20

20

9 _

2 _

20

_8

20

3 _

8

3 _

8

1 _

8

1 _

8

1 _

15

7 _

15 3 _ 15

4 _

15

2 _

5NS2.3

Chapter 5

Name ____________________________ Date ________________

In the puzzles below, the sum of the fractions in each row is the same as the sum of the fractions in each column. Use your knowledge of adding and subtracting fractions to find the missing fractions. Hint: Remember to check the fractions for like denominators before adding.

5–3



Reteach


Chapter 5

Answers

Grade 5

2 You can estimate by rounding _ to 1. 3 Then, you have each chair needs about 1 yard of fabric.

Check

23

Chapter 5

1 + 1 + 1 + 1 = 4, which is close to your answer 2 of 2_. 3

8 2 2 2 2 2 _ + _ + _ + _ = _ = 2_ yards of fabric 3 3 3 3 3 3

Act out the problem by marking the floor to show 2 a length of _ of a yard. 3 2 Then, continue to mark _ of a yard of fabric until 3 you have done this 4 times.

4 chairs?

How much fabric is needed to recover the seats of

What do you need to find?

2 There are 4 chairs to recover. _ of a yard of fabric 3 is needed to cover the seat of each chair.

What facts do you know?

Solve

Plan

Understand

Akio and Mei began the project of repainting and covering the seats of old dining room 2 chairs. To recover one seat, they need _ of a yard of fabric. How much fabric do they 3 need to buy to recover the seats of 4 chairs?

5MR2.3, 5NS2.3

Name ____________________________ Date ________________

Use the Act It Out Strategy

5–4


Chapter Resources

A10

Chapter 5


Reteach

Al;

_2 mile

Grade 5

24

6 days

1 6. A puppy eats _ of a can of food at each meal. If he eats two times 3 a day, how long will it take him to eat 4 cans of food?

5

3 7 5. Robert lives _ mile from school. Al lives _ mile from school. Who 10 10 lives farther from school? How much farther?

Sunday

1 4. Jean reads _ of her book each day. If she starts reading on Monday, 7 on what day will she complete her book?

2

1 1 _ cans

1 3. Since each of the 6 chairs needs _ can of paint, how much more 4 paint will they need?

4 yards

2 2. The girls found 6 more chairs that each need _ yard of fabric to 3 cover the seats. How much more fabric do they need to buy?

1 can

1 1. The girls need _ can of paint to paint each chair. How many cans of 4 paint will they need to paint all 4 chairs?

(continued)

Chapter 5

5MR2.3, 5NS2.3

Name ____________________________ Date ________________


Grade 5

Solve. Use the act it out strategy.

5–4 Problem-Solving Strategy

Skills Practice

Grade 5

18

25

5. Dolores has 6 quarters, 5 dimes, 4 nickels, and 10 pennies. How many different combinations of coins can she make to have $0.50?

4

4. Ellen is decorating a wall with family pictures. She has 2 pictures that are 10 inches, 2 pictures that are 8 inches, and 2 pictures that are 6 inches. If she keeps the same size pictures in rows, how many ways can she arrange the pictures?

12

3. Twenty-four students are in study hall. Eight more arrive. At the same time, 12 leave. Then, 16 leave and 8 more arrive. How many students are left in study hall?

2 hours

2. Meg and Matt are painting all 4 walls of a room. Each person is 1 painting 2 walls. After one hour, Meg has painted _ of one wall, 2 and Matt has painted 1 wall. How much longer will it take Meg to paint her 2 walls than it will take Matt to paint his?

6

1. The ceramics class is designing mugs with three colored stripes. The colors are red, yellow, and green. How many different ways can students in the class arrange the three colored stripes?

Chapter 5

5MR2.3, 5NS2.3

Name ____________________________ Date ________________

Solve. Use the act it out strategy.

5–4


Chapter Resources

Answers


Grade 5

A11

Chapter 5

A12

Chapter 5

with Unlike Denominators

Adding and Subtracting Fractions

Reteach

Name

Date

5NS2.3

3 1 _ - _.

2 7 _ + _.

_ _ _

24

Grade 5

28

6, 12, 18, 24, . . . .

5 20 29 9 + = = 1_ 3 5 24 24 24 So, _ + _ = 24 8 6

LCD:

Multiples of 6:

Add or subtract. Write in simplest form. 5 3 1. _ + _ 6 8 Multiples of 8: 8, 16, 24, 32, . . .

Subtract

9 3 _ =_ 4 12 4 3 3 1 4 1 _ Find the LCD of _ and _. =_ 4 3 3 12 Multiples of 4: 4, 8, 12, … Multiples of 3: 3, 6, 9, 12, … 3 1 The LCD of _ and _ is 12. 4 3

Add

.

2.

Subtract.

7 _

So, 12

4

12 5 _ 12

Chapter 5

_ _ _ _ 9 1 11 = 2 = 12 12 6 12

4, 8, 12, . . . . .

12

3 11 _ -_=

LCD:

Multiples of 4:

12

4 _

24, 36, . . . . .

-

9 _

21 _ = 24 8 16 2 +_ = +_ 3 24 37 13 _ = 1_ 24 24

Add.

Write the problems in vertical form.

Step 3

4 12 Multiples of 12: 12,

3 11 _ -_

Rename each fraction using the LCD.

Find the least common denominator (LCD).

21 7 _ =_ 3 24 8 8 Multiples of 3: 16 2 _ _ = 24 3, 6, 9, 12, 15,18, 21, 24, … 3 Multiples of 8: 8, 16, 24, … The LCD is 24.

Step 2

Step 1


Grade 5

When adding or subtracting fractions with unlike denominators, it helps to write the problems in vertical form.

5–5 Adding and Subtracting Fractions with Unlike Denominators

Skills Practice

Name

Date

2

1 10

8

1 1 1 10 10 10

1 2

8

10

_3

10

_1 - _2 = _3

1 10

4

_1 + _3 = _5

8

4

Grade 5

5 1 16. _ - _ = 4 8

12

12

1 7 13. _ - _ =

4

5

3 1 10. _ + _ =

10

1 1 7. _ + _ =

8

_1 3 _3

6

_5

10

1 8

10

1 8

10

1 8

12

3

29

3 11 17. _ - _ = 20 10

2

8

1 1 14. _ - _ =

2

6

3 1 11. _ + _ =

12

1 1 8. _ + _ =

6

_1

8

4

_1

_1 4 _7

24

3

1 1 1 1 1 1 12 12 12 12 12 12

1 8

5

_3 + _3 = _9

_4 - _2 = _4 or _1

5.

2.


4.

1.

1 8

1 8

1 8

1 6

8

1 6

1 6

16

1 6

16

5

11 1 18. _ - _ = 3 12

10

6

9 2 15. _ - _ =

3

5 2 12. _ + _ =

8

6

12

24

Chapter 5

_1 2 _7

2

11 _ 16 1_1

24

11 _5 - _9 = _

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24

1 6

16

13 _3 + _5 = _

5 3 9. _ + _ =

6.

1 8

1 1 1 1 1 1 1 1 1 1 1 1 1 16 16 16 16 16 16 16 16 16 16 16 16 16

16 16 16

3. 1 1 1

1 8

5NS2.3

Write the addition or subtraction sentence shown by each model. Write the sum or difference in simplest form.

5–5



Chapter Resources

Answers


Grade 5

A13

Chapter 5

Grade 5


Reteach

Name

5MR2.3, 5NS2.3

Date

A14 Grade 5

Check

Solve

Plan

Understand

8

4

4 Your answer is correct.

16

33

Use math to check your work.

Chapter 5

Count the students that are left. 4 students spend about 30 minutes on homework.

_1_ of 16 is 4. Cross out 4 more students. 4

_1_ of 16 is 8. Cross out 8 students. 2

You will be left with the students who spend 30 minutes on homework.

Cross out the students who spend 1 hour and who spend 45 minutes on homework.

Draw 16 students.

You can use the act it out strategy.

You need to know how many people spend 30 minutes on homework.

_1_ of 16 students spend 45 minutes on homework. 4

_1_ of 16 students spend 1 hour on homework. 2

Fina did a survey of how much time students spend on homework each night. Out of 16 people interviewed, _12_ spend about 1 hour on homework and _14_ spend about 45 minutes on homework. The rest spend about 30 minutes on homework. How many students spend 30 minutes on homework?

Choose the Best Strategy

5–6


Chapter 5

Chapter Resources

Answers


Grade 5

A15

Chapter 5

A16

Chapter 5


Homework Practice

Name


• Act it out

$100

3

_1 failed

3 7 _ -_

9.

Grade 5

8

10

5

7

2 7 _ +_

9

7.

5

3 2 _ +_

5.

40

11 _

70

37 _ 45 69 _

36

10.

8.

6.

6

3

2

5 1 _ +_

7

8

6 1 _ +_

5

3 6 _ +_

Add or subtract. Write in simplest form. (Lesson 5–5)

90 students

6

7 1_ 20 5 1_ 14 1 1_

4. Of the 300 students at school, 110 are in the chorus and 150 are in the band. Of these students, 50 are in both chorus and the band. How many students are neither in the chorus nor the band?

8

_7 acre

1 3. At a park, a picnic shelter covers __ of an acre and a playground 4 5 __ covers 8 of an acre. How much area is covered by both the picnic shelter and the playground?

the class failed?

3

1 2. Mrs. Jones told the class that __ of them scored 90 or above on the 3 1 math test. Another __ of them had a passing score. What fraction of

was the regular price?

1 1. Olivia bought a ring for __ off the regular price. If she paid $50, what 2

• Make a table

Chapter 5

5MR2.3, 5NS2.3

Date


Grade 5

Use any strategy shown below to solve.

5–6

1 2

2_ inches tall

Choose the Operation

Enrich

Name

2

Grade 5

1

12

37

11 _ hour or 1 hour 55 minutes

2 6. Marcel was in a triathalon, a race with 3 events. He ran 4 miles in _ 3 13 _ _ hour. He bicycled 5 miles in hour, and he swam 880 yards in 4 2 hour. What was his total race time?

1

_1 feet long

2

_1 pounds

2 5. A sculptor has a steel tube that is _ foot long. To create a longer 3 5 tube, he attaches it to another steel tube that is _ foot long. How 6 long is the new steel tube?

4

4. The art department received a shipment of 6 boxes of clay. Each 3 box weighed _ pound. How many pounds of clay were in the 4 shipment?

150; 50 X 3 = 150

3. Mr. Montgomery is a chef. He has created 250 new recipes. He 3 plans to donate _ of them to the school library. How many recipes 5 1 does he plan to donate? Hint: _ of 250 is 50. 5

8

3 _ yard

3 3 2. Darlene needs _ yard of fabric to cover a chair. She has _ yard of 4 8 fabric. How much more fabric does she need?

Chapter 5

5MR2.3, 5NS2.3

Date

1 1. A box is _ inch tall. If 5 of the boxes are stacked on top of each 2 other, how tall is the stack of boxes?

Solve.

5–6



Chapter Resources

Grade 5

A17

4

8

3 5 _ and _.

Grade 5

4 7 3. 6_ - 1 _ = 5 10

5 3 1. 2 _ + 1 _ = 4 8

5

10

_1

3 4 8

7 1_ 8 1 + 1_ 2

38

↓

8

3 1 4. 3_ - 1 _ = 4 8

3 7 2. 1 _ + 2 _ = 5 10

8

6 5 1 2_ - 1_ = 1_ 8

8

3 10

_

_1

2

4

Multiples of 8: 8, . . . 3 5 The LCD of _ and _ is 8. 4 8 3 2_ 4

5NS2.3

3 3 11 2_ = 2 + 1_ or 3_ 8 8 8

7 1_ 8 4 1_ 8

Multiples of 4: 4, 8,


_

eighths. Subtract the ones. Then subtract

Rename 2 _34_ so the fraction part is in

Find the LCD of

3 5 Subtract 2 _ - 1 _. 4 8

Then count the eighths.

Add the ones.

Multiples of 2: 2, 4, 6, 8, . . . 1 7 The LCD of 1 _ and 1 _ is 8. 2 8 1 7 Show 1 _ and 1 _ using eighths as a 2 8 denominator.

Multiples of 8: 8, 16, 24, . . .

Rename the addends using their LCD.

the eighths.

Date


Reteach

Name

7 1 Add 1 _ + 1 _ . 2 8

5–7

Chapter 5


_3 11 9_

20

17.

12

_1

7 2

_1 _1

15

4 8_

2 11 _ 3 2 - 3_ 5

14.

_

144

19

+5

8

_7

7 18. 14 _ 8

4

_5 pounds

8

1 57 7 1 8 35 _ + 21 _ =

4 11. 82 _ + 62 = 5

15.

19.

5

8

9

12

_1

1 15 _ 4 1 - 6_ 6

4 97 _ - 87 =

5

3 2 9. 51 _ + 25 _ = 5 4

5

8

11 _ 40 4 10 _

20

_1 3 11 9_ 30 3 77 _ 21 7 1 6. 16 _ - 7 _ = 3 10

1 3. 12 + 9 _ = 3

2 1 5 12. 23 _ - 15 _ =

_4

27 3 11 6 8. 64 _ - 37 _ = 4 12

14 1 12 5. 9 + 5 _ = 12

3 4 2. 11 _ - 4 _ = 5 10

5NS2.3

3 yards 20

_


Chapter 5

Answers

Grade 5

21

39

Chapter 5

3 2 22. Keith is making canvas tent. He needs 12 _ yards of beige canvas for the top and 8_ 4 5 of green canvas for the bottom. How many yards of canvas does he need in all?

8

_3 pounds

1

8

7 21. Sara needs 2 _ pounds of grapes for a salad. She buys a bag of grapes that weighs 8 1 only 1 _ pounds. How many more pounds of grapes does she need? 2

5

5 20. A grocery bag will hold 8 _ pounds of oranges. Kyle puts 3 pounds of oranges in the 8 bag. How many more pounds of oranges can he put in the bag?

3

1 11 _

12 11 16. 6_ 12 5 + 4_ 12

11 16 _ - 7 =

19 3 4 10. 46 _ - 27 = 4

11 7. 34 _ + 15 = 20

5

_1 4 2 _ 9 1 5 3 4. 18 _ - 9 _ = 6 6 11 _ 49

15 11 1. 7 _ - 2 _ = 16 16

13.

Date


Skills Practice

Name


5–7


Chapter Resources

A18

Chapter 5

12

-5

7

7 10. 8


8

• Act it out

8

4 1 12 _ - 4 _

1 8 8. 9 _ - 1 _ 9 9

7 8_ 9 3 8_

18

Grade 5

2 quizzes

40

13. Chou’s quiz scores are 78, 99, 101, 88, 93, 89, 92, 94, 84, 95. On how many more quizzes did Chou score above 90 than below 90?

11 pounds

12. Jill bought five packages of printer paper that weighed 1 _21_ pounds, 2 _18_ pounds, 3 _34_ pounds, 1 _81_ pounds, and 2 _12_ pounds. How many pounds of paper did she buy?

$48

11. Janice bought 2 pairs of sneakers. The first pair was full price and the second was half price. The original price of the first pair was $32. How much did she spend?

• Make a table

8

1 2 6. 8 _ + 9 _ 3 3

8

_ _

4 3 12 5 1 2. 6 _ + 6 _ 5 5 3 5 6 14 8 _ _ 4. 6 + 7

Use any strategy shown below to solve. (Lesson 5–6)

7

_2 3 1 12 5 3. 11 _ + 1 _ 10 10 _3 1 38 4 5. 9 _ - 6 _ 8 8 _4 3 12 5 1 7. 5 _ + 7 _ 5 5 _5 6 1 2 _ _

3 1 1. 3 _ + 8 _ 4 4

9. 7

Date


Homework Practice

Name

5NS2.3

Chapter 5


Grade 5


5–7

11

_1 years old

4

17 _ tons

21

4

1 14

_ pounds

5. James recycled 22 _21_ pounds of aluminum in one week. Matt recycled 3 18_ pounds of aluminum the same 7 week. How many more pounds of aluminum did James recycle?

636

41

3. Cumberland Valley Coal Company mined 249 _23_ tons of coal on one day and 387 _71_ tons on another day. What is the total number of tons of coal mined on both days?

Grade 5

Date

2

15

12

_1 pounds

Chapter 5

What is the total number of pounds of food that she bought?

6. Bethany bought 2 _12_ pounds of bread, 3 _41_ pounds of meat, and 3 _31_ pounds of cheese to make sandwiches for a party. She also bought 2 _31_ pounds of tomatoes, 1 _16_ pounds of onions, and 2 _12_ pounds of lettuce.

6

_1 dozen trees

20

4. One year, Cumberland Valley Coal Company planted 14 _61_ dozen trees to help prevent erosion. The following year, they planted 20 _32_ dozen trees. How many more trees did they plant the second year?

2

_7 packages

5NS2.3

2. Rick has a choice of buying 4 _43_ packages of pencils or 2 _25_ packages of pens. In simplest form, how many more packages of pencils than pens can he buy?



Name

1. Blanca’s children are 6 _16_ years old and 1 5 ___ years old. In simplest form, what 12 are combined ages of her children?

Solve.

5–7



Chapter Resources

Grade 5

A Maze of Mixed Numbers

Enrich

Name

Date

5NS2.3

Grade 5

START

M. 1 _ + 9 _ 3 5

3 1 A. 3 _ + 2 _ 3 5

A19

A

2 31 511 — — 30

C

514 — 15 1 6— 5

8

2 10 — 9

1 420 —

I

8

3

15 N. 6 _ - 1 _

1 72 7— 2 — 3

D

5

42

24

F

M

3 810 — 3 710 —

4 10 — 5

1 11— 6

3 3— 5

H

4 1115 —

E

B 1 3 20 —

8 11 — 15

5 6— 8

8 23 — 30

G

_ _

8

J

N

1 1512 —

8

L

1 10 — 8

1 — 3

2

Chapter 5

K

1 1412 —

4

23 3 18 H. 6 _ + 2 _ 30 5 6 5 6 7 1 L. 8 _ - 2 _ 8

3 1 D. 4 _ + 3 _ 4 4

1 6 1 5 7 8 23 5— — 30 — 4 — 4 24

3 14 _1 _ 3_ 1 1 1 1 3 5 C. 4 _ 15 B. _ + 3_ - 1 _ 30 5 6 _1 _3 10 1 21 11_1 8 5 5 64 4 1 6 G. 3 _ + 2 _ 10 F. 11 _ - _ E. 2 _ + 5 _ 5 3 6 6 12 2 1 1 _ _ _1 15 4 3 1 1 1 2 1 12 K. 1 _ - 1 _ 3 20 J. 8 _ + 6 _ I. 7 _ - 3 _ 5 4 3 3 3 4 4 7 _ _ 11 3 5 2 1 5

Find your way through the maze to reach the dot. When you come to a letter, solve the problem that matches that letter. Draw your path through the sum or difference in simplest form. Follow the path until you reach the next intersection. Continue finding each sum or difference.

5–7


Date

16


Chapter 5

2

Answers

Grade 5

18.

15.

12.

9.

6.

8

_7

15 16

_

_ _ _ _ _

1 8 1 1 8 12 _ - 4 _ = 4 8 5 13 5 1 12 41_ - 27 _ = 4 6 5 1 3 3 _ _ 8 3 -1 = 4 8 11 1 3 2 12 3_ - 1_ = 3 4 9 1 1 16 3_ - 2_ =

3

3.

4

3 5

_

1 9_ 5 3 - 4_ 5

_9

4.

19. 4

16.

4

-1

=

43

3

12

11 _ 5 16 _ 1 2 6 18 _ - 1 _ = 3 2 7 _ 2 1 2 _ _

2 5 1 12 13. 4 _ - 1 _ = 2 12

4

4

20. 25

17.

14.

8

5

- 17

16

=

Chapter 5

16

_ 7 6_ 1 2 10 10 _ - 3 _ = 5 10 8 3_ 1 2 _ _ 15 6 -2 = 5 3 15 2_ 3 7 _ _ 16 4 -1 = 8 16 11 7_ 15 5 _ _ 30

19 _

1 15_ 2 1 - 11 _ 2

19 3 1 1 20 8. 6 _ - 2 _ =

10

5.

3 3 _ is in simplest form. 4

4 21 _ 5 1 - 11 _ 6

24 7 4 10 11. 10. 70 _ - 45 _ = 5 10

5 1 6

_

6 5_ 4 3 - 2_ 4 3 3_ 4

Step 3 Subtract the whole numbers.

5 2 7. 3 _ - 1 _ = 3 6

Subtract. Write in simplest form. 1 3 1. 7_ 2. 2 _ 4 16 3 1 - 3_ - 1_ 8 4

3 3 1 So, 6 _ - 2 _ = 3 _ . 4 4 2

6 2 6_ 5_ 4 4 3 3 - 2_ → - 2_ 4 4 3 _ 4

Step 2 Subtract the fractions. Regroup if necessary.

Then subtract.

Rename _21_ as _24_ .

Think: The LCD of _21_ and _34_ is 4.

Step 1 Write the fractions with a common denominator.

3 1 Subtract 6 _ - 2 _. 4 2

5NS2.3

Step 4 Simplify if possible.

Subtracting Mixed Numbers with Renaming

Reteach

Name

To subtract mixed numbers with unlike denominators you need to write equivalent fractions with a common denominator.

5–8


Chapter Resources

A20

Chapter 5

30

23 4_

2 - 3_ 5

6

1 8_

16

13 _ 6

16 7 - 3_ 8

6

4

_

6 3 7_

3 8

_

3 4

- 1_

8

4

_3

6

8 2 7 20. 10 _ - 6 _ = 3 8

5 1 17. 11 _ - 6 _ = 4 8

3 2 14. 12 _ - 6 _ = 3 4

12

3 24

19 _

_

12

11 _

5 4 8

5

5 4_

16

15 1_

1 8

- 2_

16

16

13 _

1 4_

2

16 3 - 2_ 8

5 1 11. 7 _ - 2 _ = 4 6

8.

4.

3 5_

5NS2.3

44

_ _

1 1 1 1 yd left; 1 < 1 . 3 4 4

_

No; she will have only

Chapter 5

22. Paula has 2 yards of elastic. One project needs a _34_ yard piece. Does she have enough for another project that needs 1 _31_ yards? Explain.

1 7 19. 15 _ - 8 _ = 3 12

_ _ __ _ _ __ _

2

_1

1

3 1 16. 15 _ - 7 _ = 4 8

7 4 1 10 13. 10 _ - 2 _ = 5 2

3 5 5 1 1 No; 3 - 2 = , + = 4 4 8 2 8 10 1 1 3 =1 ,