CHAPTER RESOURCES • Chapter 1elementary.dmschools.org/uploads/1/3/6/0/13604257/5c1.pdf · CHAPTER RESOURCES • Chapter 1 Place Value, ... • Chapter 1 Test • Chapter 1 Performance

CHAPTER RESOURCES • Chapter 1Place Value, Multiplication, & Expressions

INCLUDES • Prerequisite Skills Inventory

• Beginning-of-Year Test

• School-Home Letter

• Vocabulary Game Directions

• Daily Enrichment Activities

• Reteach Intervention for every lesson

• Chapter 1 Test

• Chapter 1 Performance Task • Answer Keys and Individual Record Forms

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Copyright © by Houghton Mifflin Harcourt Publishing Company

All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any

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copying is expressly permitted by federal copyright law.

Only those pages that are specifically enabled by the program and indicated by the presence of the print

icon may be printed and reproduced in classroom quantities by individual teachers using the corresponding

student’s textbook or kit as the major vehicle for regular classroom instruction.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices

and Council of Chief State School Officers. All rights reserved.

This product is not sponsored or endorsed by the Common Core State Standards Initiative of the National

Governors Association Center for Best Practices and the Council of Chief State School Officers.

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Contents Overview & Diagnostic ..................................................................................... v

Formative and Summative Assessment .......................................................... vi

Assessment Technology ................................................................................. vii

Data-Driven Decision Making ........................................................................ viii

Performance Assessment ................................................................................ ix

Portfolio Assessment ........................................................................................ x

Common Core Assessment Formats ............................................................... xi

Test Answer Sheet .......................................................................................... xv

Prerequisite Skills Inventory ........................................................................... 1-1

Beginning-of-Year Test ................................................................................... 1-7

Chapter 1 School-Home Letter (English) ..................................................... 1-17

Chapter 1 School-Home Letter (Spanish) .................................................... 1-18

Vocabulary Game ........................................................................................ 1-19

1.1 Reteach ................................................................................................. 1-21

1.1 Enrich ..................................................................................................... 1-22

1.2 Reteach ................................................................................................. 1-23

1.2 Enrich ..................................................................................................... 1-24

1.3 Reteach ................................................................................................. 1-25

1.3 Enrich ..................................................................................................... 1-26

1.4 Reteach ................................................................................................. 1-27

1.4 Enrich ..................................................................................................... 1-28

Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company

iii

1.5 Reteach ................................................................................................. 1-29

1.5 Enrich ..................................................................................................... 1-30

1.6 Reteach ................................................................................................. 1-31

1.6 Enrich ..................................................................................................... 1-32

1.7 Reteach ................................................................................................. 1-33

1.7 Enrich ..................................................................................................... 1-34

1.8 Reteach ................................................................................................. 1-35

1.8 Enrich ..................................................................................................... 1-36

1.9 Reteach ................................................................................................. 1-37

1.9 Enrich ..................................................................................................... 1-38

1.10 Reteach ............................................................................................... 1-39

1.10 Enrich ................................................................................................... 1-40

1.11 Reteach ............................................................................................... 1-41

1.11 Enrich ................................................................................................... 1-42

1.12 Reteach ............................................................................................... 1-43

1.12 Enrich ................................................................................................... 1-44

Chapter 1 Test ............................................................................................. 1-45

Chapter 1 Performance Task ....................................................................... 1-51

Answer Keys ................................................................................................ 1-56

Individual Record Forms .............................................................................. 1-71

Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company

iv

v OverviewChapter Resources© Houghton Mifflin Harcourt Publishing Company

Overview of Go Math! Assessment

How Assessment Can Help Individualize InstructionThe Chapter Resources contains several types of assessment for use throughout the school year. Assessment pacing can also be found in the Go Math! Teacher Edition. The following pages will explain how these assessments help teachers evaluate students’ understanding of the Common Core standards. These Chapter Resources also contain Individual Record Forms to help guide teachers’ instructional choices and to improve students’ performance.

Diagnostic AssessmentPrerequisite Skills Inventory in the Chapter Resources should be given at the beginning of the school year or when a new student arrives. This short-answer test assesses students’ understanding of prerequisite skills. Test results provide information about the review or intervention that students may need in order to be successful in learning the mathematics related to the standards for this grade level. Suggestions for intervention are provided for this inventory.

Beginning-of-Year Test in the Chapter Resources contains items that are presented in Common Core assessment format. This test should be given early in the year to determine which on-grade level skills that students may already understand. This benchmark test will facilitate customization of instructional content to optimize the time spent teaching specific objectives. Suggestions for intervention are provided for this test.

Show What You Know in the Student Edition is provided for each chapter. It assesses prior knowledge from previous grades as well as content taught earlier in the current grade. Teachers can customize instructional content using the intervention options suggested. The assessment should be scheduled at the beginning of each chapter to determine if students have the prerequisite skills for the chapter.

vi OverviewChapter Resources© Houghton Mifflin Harcourt Publishing Company

Formative AssessmentLesson Quick Check in every lesson of the Teacher Edition monitors students’

understanding of the skills and concepts being presented.

Lesson Practice for every lesson in the Student Edition helps students achieve

fluency, speed, and confidence with grade level skills and concepts.

Mid-Chapter Checkpoint in the Student Edition provides monitoring of students’

progress to permit instructional adjustments, and when required, to facilitate

students’ mastery of the objectives.

Middle-of-Year Test in the Chapter Resources assesses the same standards as

the Beginning-of-Year Test, allowing students’ progress to be tracked and providing

opportunity for instructional adjustments, when required.

Portfolios encourage students to collect work samples throughout the chapter as a

reinforcement of their progress and achievements.

Summative AssessmentChapter Review/Tests in the Student Edition indicate whether additional

instruction or practice is necessary for students to master the concepts and skills

taught in the chapter. These tests include items presented in a variety of Common

Core assessment formats.

Chapter Tests in the Chapter Resources evaluate students’ mastery of concepts

and skills taught in the chapter. These tests assess the mastery of the Common

Core standards taught in a chapter. Item types on these tests are similar to ones a

student would encounter on a test to assess Common Core standards.

Performance Assessment Tasks in the Chapter Resources are provided for each

Chapter and Critical Area. Each assessment contains several tasks to assess

students’ ability to use what they have learned and provides an opportunity for

students to display their thinking strategies. Each set of tasks is accompanied by

teacher support pages, a rubric for scoring, and examples of student work for the

task.

End-of-Year Tests in the Chapter Resources assess the same standards as

the Beginning- and Middle-of-Year Tests. It is the final benchmark test for the

grade level. When students’ performance on the End-of-Year Test is compared

to performance on the Beginning- and Middle-of-Year Tests, teachers are able to

document students’ growth.

vii OverviewChapter Resources© Houghton Mifflin Harcourt Publishing Company

Getting Ready Tests in the Getting Ready Lessons and Resources evaluate the students’ understanding of concepts and skills taught as readiness for the next grade level. These tests are available in a mixed-response format comprised of multiple choice and short answer.

Assessment TechnologyThe Personal Math Trainer offers online homework, assessment, and intervention. There are pre-built tests that lead to intervention and a personal study plan. Algorithmically generated technology-enhanced items have wrong answer feedback and learning aids.

viii Data-Driven Decision MakingChapter Resources© Houghton Mifflin Harcourt Publishing Company

Data-Driven Decision MakingGo Math! allows for quick and accurate data-driven decision making so you can spend more instructional time tailoring to students’ needs. The Data-Driven Decision Making chart with Diagnostic, Formative, and Summative Assessments provides prescribed interventions so students have a greater opportunity for success with the Common Core standards.

Intervention and Review ResourcesFor skills that students have not yet mastered, the Reteach in Chapter Resources, Tier 1 and Tier 2 RtI Activities online, or The Personal Math Trainer provide additional instruction and practice on concepts and skills in the chapter.

Using Individual Record FormsThe Chapter Resources includes Individual Record Forms (IRF) for all tests. On these forms, each test item is correlated to the standard it assesses. There are intervention resources correlated to each item as well. A common error explains why a student may have missed the item. These forms can be used to:

• Follow progress throughout the year.

• Identify strengths, weaknesses, and provide follow-up instruction.

• Make assignments based on the intervention options provided.

ix© Houghton Mifflin Harcourt Publishing Company

Performance AssessmentChapter Resources

Performance AssessmentPerformance Assessment, together with other types of assessment, can supply the missing information not provided by other testing formats. Performance Assessments, in particular, help reveal the thinking strategies students use to work through a problem. Performance Assessments with multiple tasks for each chapter and Critical Area are provided in the Chapter Resources.

Performance Assessment is provided in many places in Go Math!

Each of these assessments has several tasks that target specific math concepts, skills, and strategies. These tasks can help assess students’ ability to use what they have learned to solve everyday problems. Each assessment focuses on a theme. Teachers can plan for students to complete one task at a time or use an extended amount of time to complete the entire assessment.

Teacher support pages introduce each Performance Assessment. A task-specific rubric helps teachers evaluate students’ work. Papers to illustrate actual students’ work are also provided to aid in scoring.

x© Houghton Mifflin Harcourt Publishing Company

Portfolio AssessmentChapter Resources

Portfolio AssessmentA portfolio is a collection of each student’s work gathered over an extended

period of time.

A portfolio illustrates the growth, talents, achievements, and reflections of the

learner and provides a means for you and the student to assess performance

and progress.

Building a PortfolioThere are many opportunities to collect student’s work throughout the year as

you use Go Math! Give students the opportunity to select some work samples

to be included in the portfolio.

• Provide a folder for each student with the student’s name clearly marked.

• Explain to students that throughout the year they will save some of their

work in the folder. Sometimes it will be their individual work; sometimes it

will be group reports and projects or completed checklists.

Evaluating a PortfolioThe following points made with regular portfolio evaluation will encourage

growth in self-evaluation:

• Discuss the contents of the portfolio as you examine it with each student.

• Encourage and reward each student by emphasizing growth, original thinking,

and completion of tasks.

• Reinforce and adjust instruction of the broad goals you want to accomplish

as you evaluate the portfolios.

• Examine each portfolio on the basis of individual growth rather than in

comparison with other portfolios.

• Share the portfolio with family during conferences or send the portfolio,

home with the student.

Common Core Assessment FormatsCommon Core Assessment consortia have developed assessments that contain item types beyond the traditional multiple-choice format. This allows for a more robust assessment of students’ understanding of concepts. Common Core assessments will be administered via computers; and Go Math! presents items in formats similar to what students will see on the tests. The following information is provided to help teachers familiarize students with these different types of items. An example of each item type appears on the following pages. You may want to use the examples to introduce the item types to students. The following explanations are provided to guide students in answering the questions. These pages describe the most common item types. You may find other types on some tests.

Example 1 Tell if a number rounds to a given number.

Yes or No

For this type of item, students respond to a single question with several examples. There are directions similar to, “For numbers 1a–1d, choose Yes or No to tell whether …” Tell students to be sure to answer the question for each part given below the directions. They will fill in the bubble next to “Yes” or “No” to tell whether the example fits the description in the question. They must fill in a bubble for each part.

Example 2 Answer questions about a scenario.

True or False

This type of item is similar to the Yes or No type. For the True or False items, students will see directions similar to, “For numbers 2a–2c, select True or False for each statement.” Each part below the directions must be read as a stand-alone sentence. After reading the sentence, students mark True or False to indicate the answer. They need to fill in a bubble for each sentence.

Example 3 Identify examples of a property.

More Than One Correct Choice

This type of item may confuse students because it looks like a traditional multiple-choice item. Tell students this type of item will ask them to mark all that apply. Younger students may not understand what “mark all that apply” means. Tell them to carefully look at each choice and mark it if it is a correct answer.

Chapter Resources© Houghton Mifflin Harcourt Publishing Company

xi Common Core Assessment Formats

Example 4 Circle the word that completes the sentence.

Choose From a List

Sometimes when students take a test on a computer, they will have to select a word, number, or symbol from a drop-down list. The Go Math! tests show a list and ask students to choose the correct answer. Tell students to make their choice by circling the correct answer. There will only be one choice that is correct.

Example 5 Sort numbers by categories for multiples.

Sorting

Students may be asked to sort something into categories. These items will present numbers, words, or equations on rectangular “tiles.” The directions will ask students to write each of the items in the box that describes it. When the sorting involves more complex equations or drawings, each tile will have a letter next to it. Students will be asked to write the letter for the tile in the box. Tell students that sometimes they may write the same number or word in more than one box. For example, if they need to sort quadrilaterals by category, a square could be in a box labeled rectangle and another box labeled rhombus.

Example 6 Order numbers from least to greatest.

Use Given Numbers in the Answer

Students may also see numbers and symbols on tiles when they are asked to write an equation or answer a question using only numbers. They should use the given numbers to write the answer to the problem. Sometimes there will be extra numbers. They may also need to use each number more than once.

Example 7 Match related facts.

Matching

Some items will ask students to match equivalent values or other related items. The directions will specify what they should match. There will be dots to guide them in drawing lines. The matching may be between columns or rows.

Common Core Assessment FormatsChapter Resources© Houghton Mifflin Harcourt Publishing Company

xii

Example 1

Yes or No

For numbers 1a–1d, choose Yes or No to tell whether

the number is 300,000 when it is rounded to the

nearest hundred thousand.

Fill in a bubble for each part.

1a. 345,235 Yes No

1b. 372,514 Yes No

1c. 350,921 Yes No

1d. 267,847 Yes No

Example 2

True or False

Fill in a bubble for each part.

Max earned 238,450 points in a computer game.

Tristen earned 216,983 points in the same game

For numbers 2a–2c, select True or False for each

statement.

2a. Max earned more points True False

than than Tristen.

2b. The total number of True False

points Max and Tristen

have is an odd number.

2c. Tristen needs 500 more True False

points to have as many as Max.

Example 3

More Than One Correct Choice

Fill in the bubble next to all the correct answers.

Select the equations that show the Commutative

Property of Multiplication. Mark all that apply.

A 35 × 56 = (30 + 5) × (50 + 6)

B 47 × 68 = 68 × 47

C 32 × 54 = 54 × 32

D 12 × 90 = 90 × 12

E 34 × 932 = 34 × (900 + 30 + 2)

F 45 × 167 = (40 + 5) × 167


xiii

Example 4

Choose From a List

Circle the word that completes the sentence.

(25 × 17) × 20 = 25 × (17 × 20)

The equation shows the

factors in a different

Example 5

Sorting

Copy the numbers in the correct box.

Write each number in the box below the word that

describes it.

30

42

72

85

Multiple of 5 Multiple of 6

Example 6

Use Given Numbers in the Answer

Write the given numbers to answer the question.

Write the numbers in order from least to greatest.

18,345

17,467

18,714

16,235

Example 7

Matching

Draw lines to match an item in one column to the related item in the other column.

Match the pairs of related facts.

8 × 7 = 56 • • 8 × 9 = 72

8 × 6 = 48 • • 7 × 8 = 56

72 ÷ 9 = 8 • • 9 × 7 = 63

63 ÷ 7 = 9 • • 48 ÷ 6 = 8

order.

grouping.

operation.


xiv

xv Test Answer SheetChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Date

Test Answer Sheet

1. A B C D 26. A B C D

2. A B C D 27. A B C D

3. A B C D 28. A B C D

4. A B C D 29. A B C D

5. A B C D 30. A B C D

6. A B C D 31. A B C D

7. A B C D 32. A B C D

8. A B C D 33. A B C D

9. A B C D 34. A B C D

10. A B C D 35. A B C D

11. A B C D 36. A B C D

12. A B C D 37. A B C D

13. A B C D 38. A B C D

14. A B C D 39. A B C D

15. A B C D 40. A B C D

16. A B C D 41. A B C D

17. A B C D 42. A B C D

18. A B C D 43. A B C D

19. A B C D 44. A B C D

20. A B C D 45. A B C D

21. A B C D 46. A B C D

22. A B C D 47. A B C D

23. A B C D 48. A B C D

24. A B C D 49. A B C D

25. A B C D 50. A B C D

Go Math!

Name

1-1 Prerequisite Skills Inventory Chapter Resources© Houghton Mifflin Harcourt Publishing Company

5

10 4

Write the correct answer.

1. An office supply store sold 310,409

pencils last year. What is the expanded

form of 310,409?

2. The population of Yuba City, California

is 60,360 people. What is 60,360

rounded to the nearest thousand?

3. Last year, the local animal shelter found

homes for 12,308 dogs and 7,953 cats.

What is the total number of dogs and

cats the animal shelter found homes for

last year?

4. The area of South Dakota is

77,353 square miles. The area of North

Dakota is 70,700 square miles. How

many square miles greater is the area

of South Dakota than the area of North

Dakota?

5. Juan wrote this pattern on his paper.

3 × 6 = 18

3 × 60 = 180

3 × 600 = 1,800

3 × 6,000 =

What is the unknown number in Juan’s

pattern?

6. James uses the Distributive Property to

find how many cans of paint are in the

art supply closet. There are 5 boxes in

the closet. Each box holds 14 cans.

How many cans of paint are in the

closet?

Prerequisite Skills Inventory for Grade 5Page 1

Name


10

6

$10 $2

7. Ling’s parents buy 4 tickets for the

nature museum. Each ticket costs $13.

What is the total cost of the 4 tickets?

8. The theater has 1,678 seats. A

magician performed 3 sold out shows

at the theater. How many people were

able to see the magician’s show?

9. Erin has 4 bags with 19 marbles in

each bag. She also has 7 bags with

14 marbles in each bag. She gives

23 marbles to her brother. She wrote

this expression to find how many

marbles she has left. How many

marbles does Erin have left?

4 × 19 + 7 × 14 − 23

10. Risley’s Restaurant charges $12 for a

spaghetti dinner special. During one

hour 16 people ordered the spaghetti

dinner special.

What is the total amount Risley’s

Restaurant charged during that hour

for the spaghetti dinner specials?

11. Anya used buttons to model a division

problem.

The division problem this model

represents is .

The quotient is and the

remainder is .

12. The Distributive Property can help

you divide. Show how you can break

apart the dividend to find the quotient

for 224 ÷ 7.


Name



13. On Saturday, a total of 1,292 people

went to see a new movie. There were

4 different showings for the new

movie and the same number of people

attended each showing. How many

people attended each showing?

14. A dentist bought 9 bags of prizes for

his patients. Each bag had 12 prizes.

The prizes were divided equally among

3 boxes. How many prizes were in

each box?

15. Rylee is learning about prime numbers

in math class. Her friend asked her to

name all the prime numbers between

10 and 20. What numbers should Rylee

name?

16. Cassie wrote some numbers in a

number pattern.

14, 17, 12, 15, 10, 13, 8, 11

What should be the next number in her

pattern?

17. Mrs. Dalton needs 1 _ 2 cup mixed nuts

for her granola recipe. She only has

a 1 _ 4 cup measuring cup. Write the

equivalent fraction that shows the

amount of mixed nuts she will use for

the recipe.

18. Michael is practicing the piano. He

spends 1 _ 2 hour practicing scales and

1 _ 4 hour practicing the piece for his recital.

What is a common denominator for 1 _ 2

and 1 _ 4 ?

19. Julia and Sam rode their bikes on the

bike path. Julia rode her bike 3 __ 10

of the

path's distance. Sam rode his bike

4 _ 8 of the path's distance. Compare the

distances using <, >, or =.

Name



20. Ali needs 4 __ 10

yard of red ribbon and

5 __ 10

yard of blue ribbon to make a tail

for her kite. How much ribbon does Ali

need in all?

21. Bryan brought 8 __ 10

gallon of water on a

hiking trip. He drank 4 __ 10

gallon of water.

How much water is left?

22. Lily has two kittens. One kitten weighs

15

__ 16

pound. The other kitten weighs 12

__ 16

pound. What is the difference in the

weights of the two kittens?

23. Jamie put 2 3 __ 12

pounds of green apples

into a bag. He then added 3 5 __ 12

pounds

of red apples into the same bag. What

is the total weight of the apples in the

bag?

24. Mrs. Laska buys 4 5 _ 8 yards of blue fabric

and 2 1 _ 8 yards of green fabric. How many

more yards of blue fabric than green

fabric does Mrs. Laska buy?

25. In Crosby’s model collection, 5 __ 16

of the

models are trains and 7 __ 16

of the models

are cars. What part of Crosby’s model

collection is trains and cars?

26. Leo walks his dog 7 _ 8 mile. He walks his

dog 3 times a day. How far does Leo

walk his dog every day? Show how you

can use repeated addition to solve.

Name



27. On Tuesday, Lilly spent 1 _ 4 hour working

on her science fair project. Ben worked

3 times as long on his science fair

project as Lilly did. How much time did

Ben spend on his science fair project?

28. It takes Akio’s family 2 1 _ 2 hours to drive

from their home to the beach. It takes

his family 3 times as long to drive to

the mountains as it takes to drive to

the beach. How long does it take Akio’s

family to drive from their home to the

mountains?

29. The stout infantfish is one of the

world’s smallest fish. It is only about

8 4 __ 10

millimeters long. What is this length

written as a decimal?

30. The distance from Davina’s house to

her school is 2 75

___ 100

miles. What is this

distance written as a decimal?

31. Jill buys a tomato that weighs 0.9 pound.

Write the weight of the tomato as a

fraction with a denominator of 100.

32. Use <, >, or = to compare 0.36

and 0.4.

33. Henry draws an obtuse triangle. How

many obtuse angles does Henry’s

triangle have?

34. What term best describes the lines

shown?

Write perpendicular, parallel, or

intersecting.

Name


10 cm

15 cm

2 3 4 5 6 7 8 9 1610 11 12 13 14 1510

0 1Pounds

Ounces

18

28

38

48

58

68

78

Length of Leaves (in inches)

777 7

77777

7777

777

777

35. Tyler uses craft sticks to make a

quadrilateral like the one shown.

Tell whether she made a trapezoid, parallelogram, rhombus, rectangle, or

square.

36. A puppy weighs 3 pounds.

What is the puppy’s weight in ounces?

37. The line plot shows the lengths of some

leaves Madison collected on a hike.

How many leaves were longer

than 5 _ 8 inch?

38. A piece of ribbon is 86 centimeters long.

Using the information in the chart, find

the length of the ribbon in meters.

39. Mr. Rourke is 5 feet 8 inches tall. How

tall is Mr. Rourke in inches?

40. Greta wants to put ribbon around the

perimeter of her art project. How many

centimeters of ribbon will she need?


Metric Units of Length

1 centimeter (cm) = 10 millimeters (mm)

1 decimeter (dm) = 10 centimeters

1 meter (m) = 10 decimeters

1 meter (m) = 100 centimeters

1 meter (m) = 1,000 millimeters

Name

1-7 Beginning of Year TestChapter Resources© Houghton Mifflin Harcourt Publishing Company

Beginning of Year TestPage 1

Choose the correct answer.

1. Judith has a necklace with a mass of

65.736 grams. What is the mass of her

necklace rounded to the nearest tenth?

A 65.7 grams

B 65.74 grams

C 65.8 grams

D 66.0 grams

2. The post office is 3.56 kilometers from

Maria’s house and 1.38 kilometers from

Simon’s house. How much farther does

Maria live from the library than Simon?

A 4.94 kilometers

B 2.28 kilometers

C 2.18 kilometers

D 1.18 kilometers

3. Crystal’s tomato plant was

32.65 centimeters tall in June. During

July, the plant grew 82.6 centimeters.

How tall was Crystal’s tomato plant at

the end of July?

A 409.1 centimeters

B 115.25 centimeters

C 49.95 centimeters

D 40.91 centimeters

4. Rick and Chad are playing a number

pattern game. Rick wrote the following

pattern.

32.3, 34.5, 36.7, ____, 41.1

What is the unknown number in the

pattern Rick wrote?

A 37.9

B 38.8

C 38.9

D 39.9

5. Yolanda read her book for 1 1 _ 5 hours

Monday evening and for 2 3 _ 5 hours on

Tuesday evening. Which is the best estimate of the time Yolanda read on

Monday and Tuesday?

A about 4 __ 5 hour

B about 3 hours

C about 3 1 __ 2 hours

D about 4 hours

Name



6. Francine has a piece of wood that is

5 5 ___

12 feet long. She uses 3 1 __

4 feet of the

wood for a science project. How much

wood does Francine have left?

A 8 2 __ 3 feet

B 3 2 ___ 12

feet

C 2 4 ___ 12

feet

D 2 2 ___ 12

feet

7. Kevin has 3 bags of apples weighing

a total of 22 1 _ 2 pounds. Two of the bags

weigh 6 3 _ 8 pounds and 3 1

_ 4 pounds. How

much does the third bag weigh?

A 11 7 __ 8 pounds

B 12 4 __ 8 pounds

C 12 7 __ 8 pounds

D 13 5 __

8 pounds

8. Aisha hiked each day for a week. The

first day she hiked 1 _ 6 mile, the second

day she hiked 1 _ 2 mile, and the third day

she hiked 5 _ 6 mile. By how much did she

increase the distance she hiked

each day?

A 9 __

6 miles

B 5 __

6 mile

C 1 __ 2 mile

D 1 __ 3 mile

9. A corn muffin recipe calls for 1 _ 4 cup of

cornmeal and 5 _ 6 cup of flour. What is

the least common denominator of the

fractions?

A 6

B 12

C 18

D 24

10. On a coordinate grid, Carrie’s house

is located 3 blocks to the right and

4 blocks up from (0, 0). Mike’s house

is located 2 blocks to the left and

2 blocks down from Carrie’s house.

What ordered pair describes the

location of Mike’s house?

5432y

axi

s

x axis

x

y

1

0 2 31 4 5

A (1, 5)

B (2, 1)

C (1, 2)

D (5, 2)

Name



11. What is the unknown number in

Sequence 2 in the chart?

A 64

B 80

C 96

D 106

12. The graph shows the relationship

between the number of weeks and

plant growth in inches.

Number of Weeks

Plant Growth (inches)

Num

ber o

f Inc

hes

1

2

3

4

5

6

2 31 4 50

y

x

What rule relates the number of weeks

and plant growth in inches?

A Multiply the number of weeks by 1 1 __ 2 .

B Multiply the number of weeks by 1 1 __ 3 .

C Multiply the number of weeks by 1 1 __ 4 .

D Multiply the number of weeks by 1 __ 2 .

13. A baker is weighing the dough that will

be used to make pastries. The line plot

shows the weight of the dough for each

pastry.

Dough ( in pounds)

✗✗✗✗

✗✗✗✗✗

✗✗✗

14

38

12

How many pastries will be made from

at least 3 _ 8 pound of dough?

A 4

B 7

C 8

D 9

14. Marvin is buying a new computer on

layaway for $302. If he makes a down

payment of $50 and pays $28 each

week, how many weeks will it take

Marvin to pay for the computer?

A 8

B 9

C 10

D 12

Sequence Number 1 2 3 6 8Sequence 1 4 8 12 24 32Sequence 2 12 24 36 72 ?

Name



15. Mary drew a picture of her flower

garden.

What type of quadrilateral is Mary’s

garden?

A rectangle

B rhombus

C square

D trapezoid

16. Dmitri made a box with the dimensions

shown to hold his modeling supplies.

4 ft2 ft

2 ft

What is the volume of the box?

A 8 cubic feet

B 14 cubic feet

C 16 cubic feet

D 18 cubic feet

17. The sidewalk tiles leading to the

town library are shaped like regular

hexagons. Which of the following

describes a regular hexagon?

A a figure with 6 congruent sides and

6 congruent angles

B a figure with 6 sides and angles

that are not congruent

C a figure with 5 sides and 5 angles

that are not congruent

D a figure with 5 congruent sides and

5 congruent angles

18. A toy box in the shape of a rectangular

prism has a volume of 672 cubic

inches. The base area of the toy box is

28 square inches. What is the height of

the toy box?

A 10 inches

B 12 inches

C 22 inches

D 24 inches

19. A pizza parlor uses 42 tomatoes for

each batch of tomato sauce. About how

many batches of sauce can the pizza

parlor make from its last shipment of

1,236 tomatoes?

A 20

B 30

C 35

D 48

Name



20. The art teacher has a list of

134 students who have signed up for

art classes. The art teacher can register

8 students in each class. What is the

least number of classes needed for all

the students to be registered in a class?

A 16

B 17

C 18

D 19

21. The number of roses Mr. Adams

ordered for his store was three times

as many as the number of carnations

ordered. He ordered a total of

56 flowers. How many roses did

Mr. Adams order?

A 14

B 28

C 34

D 42

22. The owner of a clothing store received

a shipment of 1,230 pairs of socks.

The socks came in 36 boxes. The same

number of pairs of socks were in

35 of the boxes. How many pairs of

socks were in the last box?

A 2

B 5

C 15

D 35

23. Jared uses 24 tiles to cover the top of

his desk. Of the 24 tiles, 3 _ 8 are blue.

How many of the tiles are blue?

A 3

B 8

C 9

D 12

24. Tony worked 4 2 _ 3 hours on his science

project. Sonia worked 1 1 _ 4 times as long

on her science project as Tony did. For

how many hours did Sonia work on her

science project?

A 4 5 __

6 hours

B 5 hours

C 5 1 __ 3 hours

D 5 5 __

6 hours

25. Julia had 2 _ 3 quart of cleaning liquid.

She used 1 _ 4 of it to clean the sink

counter. How much cleaning liquid

did Julia use?

A 1 __ 8 quart

B 1 __ 6 quart

C 1 __ 2 quart

D 5 ___

12 quart

Name



26. Carlos had 24 class play tickets to

sell. He sold 3 __

4 of the tickets. How many

tickets did Carlos sell?

A 16

B 18

C 24

D 26

27. Noreen made 8 2 _ 3 cups of snack mix

for a party. Her guests ate 3 _ 4 of the mix.

How much snack mix did her guests

eat?

A 5 1 __ 4 cups

B 5 3 __

4 cups

C 6 5 ___

12 cups

D 6 1 __ 2 cups

28. Ganesh is stacking boxes in a storage

room. There are 12 boxes in all. If each

box weighs 9.6 pounds, how much do

the boxes weigh altogether?

A 11.25 pounds

B 21.6 pounds

C 115.2 pounds

D 1,152 pounds

29. The instruction booklet for a DVD

player says that the player uses about

0.4 kilowatt of electricity per hour. If

electricity costs $0.20 per kilowatt hour,

how much does it cost to run the player

for an hour?

A $0.08

B $0.80

C $8.00

D $80.00

30. Rhianna was doing research for a

report about the highest mountains in

the United States. She read that the

Grand Teton in Wyoming is about

1.37 × 104 feet high. How should

Rhianna write the height of the Grand

Teton in standard form on her report?

A 137 feet

B 1,370 feet

C 13,700 feet

D 137,000 feet

Name



31. Jeremy is training for a race. When he

trains, he runs on a path that is

1.25 miles long. Last week, Jeremy ran

on the path 7 times. How many miles

did Jeremy run on the path last week?

A 0.875 mile

B 8.75 miles

C 87.5 miles

D 875 miles

32. There is 1 _ 3 pound of cake that will be

shared equally among 4 friends. What

fraction of a pound of cake will each

friend get?

A 1 ___ 12

pound

B 1 __ 6 pound

C 1 __ 2 pound

D 3 __

4 pound

33. At lunch, 5 friends share 3 pizzas

equally. What fraction of a pizza does

each friend get?

A 3 __

5

B 2 __ 3

C 3 __

4

D 1 1 __ 5

34. Julie has 3 _ 4 quart of fruit juice. She

pours the same amount into each of

4 glasses. Which equation represents

the fraction of a quart of fruit juice n that is in each glass?

A 3 __

4 ÷ 1 __

4 = n

B 4 ÷ 3 __

4 = n

C 3 __

4 ÷ 4 = n

D 3 ÷ 4 = n

35. Terry evaluates 6 ÷ 1 _ 8 by using a related

multiplication expression.

Which multiplication expression

should he use?

A 6 × 1 __ 8

B 1 __ 6 × 1 __

8

C 1 __ 6 × 8

D 6 × 8

Name



36. Eli made a loaf of bread. He gave equal

portions of 1 _ 2 of the loaf to 3 friends.

What diagram could Eli use to find the

fraction of the whole loaf of bread that

each friend got?

A

B

C

D

37. Lori rode her bicycle 19.5 miles in

3 hours. Which gives the best estimate

of how far Lori rode in 1 hour?

A between 4 and 5 miles

B between 5 and 6 miles

C between 6 and 7 miles

D between 7 and 8 miles

38. Roger is riding in a bike-a-thon to raise

money for his favorite charity. The total

distance of the bike-a-thon is

38.7 miles. So far he has completed

1 __ 10

of the bike-a-thon. How many miles

has Roger biked?

A 387 miles

B 38.7 miles

C 3.87 miles

D 0.387 mile

39. Ellen is making small bags of confetti

from a large bag of confetti that weighs

4.75 pounds. If she puts the same

amount of confetti in each of 5 bags,

how much should each bag weigh?

A 0.09 pound

B 0.9 pound

C 0.95 pound

D 9.1 pounds

40. Trevor bought apples that cost

$0.92 per pound. He paid $5.52 for

the apples. How many pounds of

apples did he buy?

A 60 pounds

B 6 pounds

C 0.6 pound

D 0.06 pound

Name



41. Carly spent a total of $18.20 on Saturday afternoon. She bought a movie ticket for $8.25 and snacks for $3.85. She spent the rest of the money on bus fare to get to the movie and back home. How much was the bus fare each way if each trip cost the same amount?

A $2.20

B $3.05

C $6.10

D $6.20

42. A publisher reports that it sold 1,516,792 travel magazines. What is the value of the digit 5 in 1,516,792 ?

A 5,000

B 50,000

C 500,000

D 5,000,000

43. Martin is buying 400 video games for his entertainment store. Each video game costs $20. Which of the following could he use to find the total amount he will pay for the video games?

A (4 × 2) × 10 2 = 800

B (4 × 2) × 10 3 = 8,000

C (4 × 2) × 10 4 = 80,000

D (4 × 2) × 10 5 = 800,000

44. Jamie’s dad travels 365 miles every week for business. How many miles does he travel in 4 weeks?

A 1,260 miles

B 1,360 miles

C 1,450 miles

D 1,460 miles

45. Amber and her friend Nathan are saving to buy a video game that costs $65. Amber earns $12 per week for babysitting and spends $4 of it. Nathan earns $15 per week for walking dogs and spends $8 of it. Which expression can be used to find how many weeks it will take to save for the video game?

A 65 ÷ [(12 − 4) + (15 − 8)]

B 65 ÷ [(12 + 4) − (15 + 8)]

C 65 ÷ [(12 − 4) + (15 + 8)]

D 65 ÷ [(12 + 4) − (15 − 8)]

Name



46. Chen took 54 photos with his digital

camera. He stored an equal number

of photos in each of 6 folders on

his computer. Which multiplication

sentence could Chen use to find the

number of photos in each folder?

A 54 ÷ 6 = 9

B 5 × 9 = 45

C 6 × 9 = 54

D 6 × 54 = 324

47. Rachel’s home is 5 miles from her

school. How many yards are in

5 miles?

A 1,760 yards

B 7,800 yards

C 8,800 yards

D 26,400 yards

48. Sarah bought 6 pounds of clay for

pottery class. How many ounces of clay

did Sarah buy?

A 48 ounces

B 64 ounces

C 80 ounces

D 96 ounces

49. The basketball game at the high school

started at 7:30 P.M. and ended at

10:38 P.M. How long did the game last?

A 2 hours 8 minutes

B 2 hours 18 minutes

C 3 hours 8 minutes

D 3 hours 18 minutes

50. Kate used 6.15 meters of ribbon to

make bows. How many centimeters of

ribbon did she use?

A 615 centimeters

B 61.5 centimeters

C 6.15 centimeters

D 0.615 centimeter

School-HomeSchool-Home

LetterChapter

1

ActivityYou can write numerical expressions to describe situations around the house. For example, “We bought a case of 24 water bottles and have used 13 bottles. What expression shows how many are left?” can be represented by the expression 24 − 13.

TipsOrder of Operations

To evaluate an expression, first perform the operations in parentheses. Next, multiply and divide from left to right. Finally, add and subtract from left to right.

36 − (2 + 3) × 436 − 5 × 4

36 − 20

16

STEP 1

Perform the operations in parentheses.

STEP 2

Multiply.

STEP 3

Subtract.

36 − (2 + 3) × 4 = 16

This is how we will be evaluating 36 − (2 + 3) × 4.

Evaluate Expressions

Dear Family,

Throughout the next few weeks, our math class will be learning about place value, number properties, and numerical expressions. We will also learn to multiply by 1- and 2-digit whole numbers.

You can expect to see homework that requires students to write and evaluate numerical expressions.

Here is a sample of how your child will be taught to evaluate an expression.

evaluate To find the value of a numerical or algebraic expression

numerical expression A mathematical phrase that has numbers and operation signs but does not have an equal sign

order of operations The process for evaluating expressions

1-17Chapter Resources© Houghton Mifflin Harcourt Publishing Company

para la casaCartaCartaCapítulo

1

ActividadPueden escribir expresiones numéricas para representar cosas que suceden en la casa. Por ejemplo, “Compramos una caja de 24 botellas de agua y usamos 13 botellas. ¿Qué expresión muestra cuántas botellas quedan?”, se puede representar con 24 − 13.

36 − (2 + 3) × 4 36 − 5 × 4

36 − 20

16

PASO 1

Resuelve las operaciones en paréntesis.

PASO 2

Multiplica.

PASO 3

Resta.

36 − (2 + 3) × 4 = 16

Sandra tiene 8 manzanas. Le da algunas manzanas a Josh.

Así es como evaluaremos 36 − (2 + 3) × 4.

Evaluar expresiones

Querida familia,

Durante las próximas semanas, en la clase de matemáticas aprenderemos sobre el valor de posición, las propiedades de los números y las expresiones numéricas.

Llevaré a la casa tareas con actividades para practicar la escritura y evaluación de expresiones numéricas.

Este es un ejemplo de la manera en que evaluaremos expresiones numéricas.

evaluar Hallar el valor de una expresión numérica o algebraica

expresión numérica Una frase matemática que tiene solo números y signos de operaciones.

orden de las operaciones El proceso que se usa para evaluar expresiones

Pistas

Orden de las Operaciones

Para evaluar una expresión, primero resuelve las operaciones en paréntesis. Después multiplica y divide de izquierda a derecha. Finalmente suma y resta de izquierda a derecha.

1-18Chapter Resources© Houghton Mifflin Harcourt Publishing Company

GGGGaaGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGaaaaaaaaaaaaa eeeeemmeeeeeeeeeeeeemmmmmeeeeeeeeeeeeemmmmmmeeemmmmmmeeeeeeeeeeeeGameGame©

Hou

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Word BoxbaseDistributive Propertyevaluate an expression)exponentinverse operationsnumerical expressionorder of operationsperiod

For 2 to 4 players

Materials

Going to London, England

• 3 of 1 color per player: red, blue, green, and yellow

• 1 number cube

How to Play1. Put your 3 connecting cubes in the START circle of the same color.

2. To get a cube out of START, you must roll a 6.

• If you roll a 6, move 1 of your cubes to the same-colored circle on

the path.

• If you do not roll a 6, wait until your next turn.

3. Once you have a cube on the path, toss the number cube to take a turn.

Move the cube that many tan spaces. You must get all three of your cubes

on the path.

4. If you land on a space with a question, answer it. If you are correct, move

ahead 1 space.

5. To reach FINISH move your connecting cubes up the path that is the same

color as your cubes. The first player to get all three cubes on FINISH wins.

Going Places with Words Im

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Cred

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Chapter 1 4A

Chapter 1Vocabulary Game

1-19 Game DirectionsChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

Number10 times as

much as 1

__ 10 of

5. 900

6. 80,000

7. 3,000

8. 40

Number10 times as

much as 1

__ 10 of

1. 200

2. 10

3. 700

4. 5,000

Use place-value patterns to complete the table.

Place Value and Patterns

You can use a place-value chart and patterns to write numbers

that are 10 times as much as or 1 __ 10

of any given number.

Each place to the right is 1 __ 10

of the value of the place to its left.

1 __ 10

of the

hundred

thousands

place

1 __ 10

of the

ten thousands

place

1 __ 10

of the

thousands

place

1 __ 10

of the

hundreds

place

1 __ 10

of the

tens place

Hundred Thousands

Ten Thousands

Thousands Hundreds Tens Ones

10 times

the ten

thousands

place

10 times the

thousands

place

10 times the

hundreds

place

10 times the

tens place

10 times the

ones place

Each place to the left is 10 times the value of the place to its right.

Find 1 __ 10

of 600.

1 __ 10

of 6 hundreds is 6 tens .

So, 1 __ 10

of 600 is 60 .

Find 10 times as much as 600.

10 times as much as 6 hundreds is 6 thousands.

So, 10 times as much as 600 is 6,000 .

Lesson 1.1Reteach

1-21 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

1. 1 ___ 10

of 3,000 is 10 times as much as .

2. 1 ___ 10

of is 10 times as much as 8.

3. 1 ___ 10


4. 1 ___ 10


5. 10 times as much as is 1 ___ 10 of 900.

6. 10 times as much as is 1 ___ 10 of 60,000.

7. 10 times as much as 70 is 1 ___ 10 of .

8. 10 times as much as 2,000 is 1 ___ 10 of .

9. Write Math Explain how you solved Exercise 8.

Place-Value Mystery

Find the number that makes each statement true.

Lesson 1.1Enrich

EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

1-22

Name

Write the number in two other forms.

5. 701,245 6. 40,023,032

Write the value of the underlined digit.

1. 153,732,991 2. 236,143,802

3. 264,807 4. 78,209,146

Place Value of Whole Numbers

You can use a place-value chart to help you understand whole numbers and the value of each digit. A period is a group of three digits within a number separated by a comma.

Millions Period Thousands Period Ones PeriodHundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones

2, 3 6 7, 0 8 9

Standard form: 2,367,089

Expanded Form: Multiply each digit by its place value, and then write an addition expression.

(2 3 1,000,000) 1 (3 3 100,000) 1 (6 3 10,000) 1 (7 3 1,000) 1 (8 3 10) 1 (9 3 1)

Word Form: Write the number in words. Notice that the millions and the thousands periods are followed by the period name and a comma.

two million, three hundred sixty-seven thousand, eighty-nine

To find the value of an underlined digit, multiply the digit by its place value. In 2,367,089, the value of 2 is 2 3 1,000,000, or 2,000,000.

Lesson 1.2Reteach


Name

15. Explain the method you used to match the standard form of a number to either its word form or its expanded form.

Place-Value Match

Match the standard form of the number given in Column A with either the word form or the expanded form of the number in Column B.

Lesson 1.2Enrich

Column A Column B

1. 900,000 thirty million

2. 8,000,000 5 3 1,000,000

3. 30,000,000 six hundred million

4. 2,000,000 eight hundred thousand

5. 100,000 9 3 100,000

6. 5,000,000 three million

7. 60,000,000 sixty million

8. 7,000,000 2 3 1,000,000

9. 800,000 5 3 10,000,000

10. 300,000 3 3 100,000

11. 1,000,000 seven million

12. 50,000,000 one hundred thousand

13. 600,000,000 one million

14. 3,000,000 eight million

1-24 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

Complete the equation, and tell which property you used.

4. (2 3 ) 1 (2 3 2) 5 2 3 (5 1 2) 5. 3 1 5 15

Use properties to find the sum or product.

1. 31 1 27 1 29 2. 41 3 0 3 3 3. 4 1 (6 1 21)

37 1 24 1 43 5 24 1 37 1 43

5 24 1 (37 1 43)

5 24 1 80

5 104

Use properties to find 37 1 24 1 43.

Use the Commutative Property of Addition to reorder the addends.

Use the Associative Property of Addition to group the addends.

Use mental math to add.

Grouping 37 and 43 makes the problem easier to solve because their sum, 80 , is a multiple of 10.

Property Examples

Commutative Property of Addition or Multiplication

Addition: 3 1 4 5 4 1 3Multiplication: 8 3 2 5 2 3 8

Associative Property of Addition or Multiplication

Addition: (1 1 2) 1 3 5 1 1 (2 1 3)Multiplication: 6 3 (7 3 2) 5 (6 3 7) 3 2

Distributive Property 8 3 (2 1 3) 5 (8 3 2) 1 (8 3 3)Identity Property of Addition 9 1 0 5 9 0 1 3 5 3Identity Property of Multiplication 54 3 1 5 54 1 3 16 5 16

Algebra • Properties

Properties of operations are characteristics of the operations that are always true.

Lesson 1.3Reteach


Name

1 3 17 5 _ ___ 3 11 5 13 3 (8 3 11)

9 3 (5 1 3) 5 __ 1 (9 3 3) _ 1 0 5 49

_ 3 29 5 29 3 3 (7 1 6) 1 _ 5 7 1 (6 1 25)

51 1 _ 5 39 1 51

Associative Property of Addition Identity Property of Multiplication

Associative Property of Multiplication Commutative Property of Addition

Commutative Property of Multiplication Distributive Property

Identity Property of Addition

1. Stretch Your Thinking Use the Distributive Property to rewrite and find 4 3 (25 1 4).

2. Explain how the Associative Property of Addition is similar to the Associative Property of Multiplication.

Using Properties of Operations

First, use one of the properties shown below to complete each equation. Then, match each equation to its property by writing the equation on the line below the property.

Lesson 1.3Enrich


Name

exponent

base

Write in exponent form and in word form.

1. 10 3 10 3 10 3 10 3 10 3 10 3 10

exponent form: word form:

2 . 10 3 10 3 10


3. 10 3 10 3 10 3 10 3 10


Find the value.

4. 104

5. 2 3 103

6. 6 3 102

Algebra • Powers of 10 and Exponents

You can represent repeated factors with a base and an exponent.

Write 10 3 10 3 10 3 10 3 10 3 10 in exponent form.

10 is the repeated factor, so 10 is the base.

The base is repeated 6 times, so 6 is the exponent. 106

10 3 10 3 10 3 10 3 10 3 10 5 106

A base with an exponent can be written in words.

Write 106 in words.

The exponent 6 means “the sixth power.”

106 in words is “the sixth power of ten.”

You can read 102 in two ways: “ten squared” or “the second power of ten.”

You can also read 103 in two ways: “ten cubed” or “the third power of ten.”

Lesson 1.4Reteach


Name

1. 70 3 103 5

Word form:

2. 35 3 102 5

Word form:

3. 14 3 103 5

Word form:

4. 60 3 107 5

Word form:

5. 51 3 104 5

Word form:

6. 24 3 105 5

Word form:

7. 86 3 106 5

Word form:

8. 19 3 107 5

Word form:

9. Stretch Your Thinking What is another way to write the number in Exercise 1 using a whole number and a power of 10?

Powers and Words

Find the value. Then write the value in word form.

Lesson 1.4Enrich


Name

Algebra • Multiplication Patterns

You can use basic facts, patterns, and powers of 10 to help you multiply whole numbers by multiples of 10, 100, and 1,000.

Use mental math and a pattern to find 90 3 6,000.

• 9 3 6 is a basic fact. 9 3 6 5 54

• Use basic facts, patterns, and powers of 10 to find 90 3 6,000.

9 3 60 5 (9 3 6) 3 101

5 54 3 101

5 54 3 10 5 540

9 3 600 5 (9 3 6) 3 102 5 54 3 102 5 54 3 100 5 5,400

9 3 6,000 5 (9 3 6) 3 103

5 54 3 103

5 54 3 1,000 5 54,000

90 3 6,000 5 (9 3 6) 3 (10 3 1,000) 5 54 3 104

5 54 3 10,000 5 540,000

So, 90 3 6,000 5 540,000.

Use mental math to complete the pattern.

1. 3 3 1 5 3

3 3 101 5

3 3 102 5

3 3 103 5

2. 8 3 2 5 16

(8 3 2) 3 101 5

(8 3 2) 3 102 5

(8 3 2) 3 103 5

3. 4 3 5 5 20

(4 3 5) 3 5 200

(4 3 5) 3 5 2,000

(4 3 5) 3 5 20,000

4. 7 3 6 5

(7 3 6) 3 5 420

(7 3 6) 3 5 4,200

(7 3 6) 3 5 42,000

Lesson 1.5Reteach


Name

Product Pattern

Look at the pattern of the products below.

11 3 11 5 121

12 3 11 5 132

13 3 11 5 143

14 3 11 5 154

Use the pattern above to find the product.

1. 15 3 11 5 2. 16 3 11 5

3. 17 3 11 5 4. 18 3 11 5

5. 150 3 11 5 6. 120 3 11 5

7. 170 3 11 5 8. 140 3 11 5

9. Stretch Your Thinking How does the product 110 3 n compare to the product 11 3 n? (Hint: n represents any number.)

Lesson 1.5Enrich


Name

511

472 3 7

_

472 3 7

__

472 3 7

_

Estimate. Then find the product.

2. Estimate:

863 3 8

3. Estimate:

809 3 8

4. Estimate:

932 3 7

5. Estimate:

2,767 3 7

Complete to find the product.

1. 7 3 472 Estimate: 7 3 5

Multiply the ones. Multiply the tens. Multiply the hundreds.

Step 1 Multiply the ones.

Step 2 Multiply the tens.

Step 3 Multiply the hundreds.

Thousands

Hundreds

Tens

Ones

Thousands

Hundreds

Tens

Ones

Thousands

Hundreds

Tens

Ones

34

7 84

34

7 84

34

7 8

3 6 3 6 3 6

8 6 8 2, 2 6 8

Multiply by 1-Digit Numbers

You can use place value to help you multiply by 1-digit numbers.

Estimate. Then find the product. 378 3 6

Estimate: 400 3 6 5 2,400

So, 378 3 6 5 2,268.

Lesson 1.6Reteach


1

2

3 4

5

6

7 8

9

10

11 12

13

Name

14. Stretch Your Thinking Write a different clue that has the same product as 1,326 3 9.

Down Across

1. 856 3 9

2. 847 3 6

3. 5,082 3 3

4. 7,028 3 6

5. 24,162 3 8

8. 2,127 3 6

9. 3,289 3 5

12. 601 3 6

5. 12,762 3 9

6. 287 3 6

7. 1,326 3 9

9. 4,027 3 4

10. 4,027 3 6

11. 7,028 3 9

13. 1,722 3 4

Multiplication Number Puzzle

Use the clues to complete the puzzle.

Lesson 1.6Enrich


Name

63 3 29

_

567

1,260

1 1,260 _______ 1,827

63 3 29

_

567

63 3 9 5 ( 60 3 9) 1 ( 3 3 9)

5 540 1 27 , or 567

63 3 29

_

567

2

2

63 3 20 5 ( 60 3 20) 1 ( 3 3 20)

5 1,200 1 60 , or 1,260

122 3 26

_

139 3

139 3

11 1 76 3

76 3

57 3

57 3

139 3 12

_

76 3 45

_

57 3 14

_

Complete to find the product. 1. 2 . 3.

4. Find 26 3 122. Estimate first.

Estimate:

Multiply by Multi-Digit Numbers

You can use place value and regrouping to multiply.

Find 29 3 63.

Step 1 Write the problem vertically. Multiply by the ones.

Step 2 Multiply by the tens.

Step 3 Add the partial products.

So, 63 3 29 5 1,827.

Lesson 1.7Reteach


Name

,,

7. Stretch Your Thinking What two-digit number multiplied by itself has the product 2,025? Explain how you found your answer.

Unknown Digits Multiplication

Find the unknown digits.

1.

3

4

8

1 2 072

5 892,

2.

3

5

7

1 5 054

3 55,

6

55

3.

3 2

1 2 01

0 42,

9

4

8 43

4.

3 6

1 2 0

7 655,

8

8

66

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Lesson 1.7Enrich


Name

Use multiplication and the Distributive Property to find the quotient.

1. 68 4 4 5 _ 2. 75 4 3 5 _ 3. 96 4 6 5 _

4. 80 4 5 5 _ 5. 54 4 3 5 _ 6. 105 4 7 5 _

56 4 4 5

4 3 5 56

(40 1 16) 5 56

(4 3 10) 1 (4 3 4) 5 56

4 3 (10 1 4) 5 56

10 1 4 5 14

4 3 14 5 56

56 4 4 5 14

Relate Multiplication to Division

Use the Distributive Property to find the quotient of 56 4 4.

Step 1 Write a related multiplication sentence for the division problem.

Step 2 Use the Distributive Property to break apart the product into lesser numbers that are multiples of the divisor in the division problem. Use a multiple of 10 for one of the multiples.

Step 3 To find the unknown factor, find the sum of the numbers inside the parentheses.

Step 4 Write the multiplication sentence with the unknown factor you found. Then, use the multiplication sentence to complete the division sentence.

Lesson 1.8Reteach


Name

6. Stretch Your Thinking How can you use inverse operations to write the related multiplication and division sentences?

Number Relationships

Find the unknown number in the group to make related multiplication and division sentences. Write the multiplication and division sentences.

1. 4, ?, 68 2. 5, ?, 65

3. 4, ?, 52 4. 6, ?, 78

5. Describe how the number sentences in each exercise are related.

Lesson 1.8Enrich


Name

128 players 8 teams

how manyplayers are on eachteam in Brett’s town

divide

divide

128 players

1616

1048

?

8048

1. Susan makes clay pots. She sells

125 pots per month to 5 stores. Each

store buys the same number of pots.

How many pots does each store buy?

2. Lou grows 112 rosemary plants. He ships

an equal number of plants to customers in

8 states. How many rosemary plants does

he ship to each customer?

125 4 5 5 (100 1 ) 4 5

5 (100 4 5) 1 ( 4 5)

5 1 5

5

112 4 8 5 (80 1 ) 4 8

5 ( 4 8) 1 ( 4 8)

5 1 4

5

Problem Solving • Multiplication and Division

In Brett’s town, there are 128 baseball players on 8 different teams. Each team has an equal number of players. How many players are on each team?

Read the Problem Solve the Problem

What do I need to find?

I need to find

.

• First, I use the total number of players.

• To find the number of players on each team, I will need to solve this problem. 128 4 8 5

• To find the quotient, I break 128 into two simpler numbers that are easier to divide.

128 4 8 5 (80 1 ) 4 8

5 ( 4 8) 1 ( 4 8)

5 1 6

5

So, there are players on each team.

What information do I need to use?

There are with a

total of .

How will I use the information?

I can the total number of

players by the number of teams. I can use a

simpler problem to .

Lesson 1.9Reteach


Name

7. Stretch Your Thinking When is it helpful to use simpler

numbers to solve a problem?

Simply Put

Solve. You may find it helpful to use the strategy solve a simpler problem.

1. Sal’s Pizza uses 720 pounds of flour in

4 weeks. Sal’s is open 6 days a week

and uses the same amount of flour

each day. How much flour does Sal’s

Pizza use in 1 day?

2. In one 8-hour day, 5 barbers gave a

total of 120 haircuts. The barbers gave

the same number of haircuts per hour.

How many haircuts did each barber

give per hour?

3. Dan runs Freddy’s Deluxe Car Wash.

Nine workers wash a total of 369 cars

in one week. Suppose the workers all

wash the same number of cars. How

many cars does each worker wash

that week?

4. Ali sells tomatoes to 9 restaurants.

Each restaurant buys the same

amount of tomatoes each day. Suppose

Ali sells 162 pounds of tomatoes one

day. How many pounds does she sell

to each restaurant?

5. Dr. Barker and two other dentists work

in the same office. In one day, the three

dentists saw a total of 51 patients.

Suppose each dentist saw the same

number of patients. How many patients

did each dentist see?

6. Micah uses 2 bags of birdseed to fill

up 4 bird feeders. How many bags

will he need to fill up 40 feeders?

Lesson 1.9Enrich


Name

buying 6 of the same item

multiplication and subtraction

Algebra • Numerical Expressions

Write words to match the expression.

6 3 (12 2 4)

Think: Many word problems involve finding the cost of a store purchase.

Step 1 Examine the expression.

• What operations are in the expression?

Step 2 Describe what each part of the expression can represent when finding the cost of a store purchase.

• What can multiplying by 6 represent?

Step 3 Write the words.

• Joe buys 6 DVDs. Each DVD costs $12. If Joe receives a $4 discount on each DVD, what is the total amount of money Joe spends?

1. What is multiplied and what is subtracted?

2. What part of the expression is the price of the item?

3. What can subtracting 4 from 12 represent?

Write words to match the expression.

4. 4 3 (10 2 2) 5. 3 3 (6 2 1)

Lesson 1.10Reteach


Name

Shopping Expressions

The table shows the prices for certain items at a supermarket. Use the information in the table to write problems that match the expressions below.

Supermarket Prices

Item PriceLoaf of bread $3Carton of eggs $2Box of cereal $4Pound of cheese $5Gallon of milk $3Can of tuna fish $2

Write a word problem for each expression. The first word problem has been written for you.

1. 7 2 3 2. (5 3 2) 1 4

3. 5 1 (4 2 1) 4. 20 2 (6 3 2)

Lesson 1.10Enrich

Jerry has $7 to spend at the

supermarket. He buys a loaf of

bread for $3. How much money

does Jerry have now?


Name

640

46

36

Order of Operations1. Parentheses2. Multiply and Divide3. Add and Subtract

46 2 40 5

46 2 4 3 10

46 2 4 3 10 5 46 2

Multiply and divide from left to right.

10 1 6 3 6 5 10 1

Add and subtract from left to right.

10 1 36 5

10 1 6 3 6

Evaluate the numerical expression.

1. 8 2 (7 3 1)

2 . 5 2 2 1 12 4 4

3. 8 3 (16 4 2)

4. 4 3 (28 2 20 4 2)

5. (30 2 9 4 3) 4 9

6. (6 3 6 2 9) 2 9 4 3

7. 11 4 (8 1 9 4 3)

8. 13 3 4 2 65 4 13

9. 9 1 4 3 6 2 65 4 13

Algebra • Evaluate Numerical Expressions

A numerical expression is a mathematical phrase that includes only numbers and operation symbols.

You evaluate the expression when you perform all the computations to find its value.

To evaluate an expression, use the order of operations.

Evaluate the expression (10 1 6 3 6) 2 4 3 10.

Step 1 Start with computations inside the parentheses.

Step 2 Perform the order of operations inside the parentheses.

Step 3 Rewrite the expression with the parentheses evaluated.

Step 4 Multiply and divide from left to right.

Step 5 Add and subtract from left to right.

So, (10 1 6 3 6) 2 4 3 10 5 6.

Lesson 1.11Reteach


FINISH

START

Name

6. Stretch Your Thinking A fourth player joins the game and is

given an expression that moves the game piece directly to the second

black space on the board. The expression has a division, a multiplication,

and a subtraction operation. Write a possible expression.

Player 1 Player 2 Player 3

(50 2 2) 4 4 5 5 1 10 4 5 5 108 4 (27 2 9) 5

(343 2 5 ) 4 26 2 11 5 (7 3 7) 4 (3 1 4) 5 6 1 3 2 7 5

(55 2 1) 4 9 5 (16 3 3) 4 (4 3 6)

5

(64 4 16) 3 (11 2 6)

5

(15 2 36 4 4) 1 (9 3 2)

5

2 3 (3 1 51 4 17)

5

144 2 (10 1 4 3 5 3 5 )

5

(64 1 6) 4 ( 3 5) 5 2 81 4 ( 4 4) 5 9 (4 3 ) 2 (1 1 8 3 2)

5 3

Order of Operations Game

Three players are playing a board game. Complete the exercises below, and move each player’s piece the same number of spaces as the answer for the unknown value. Circle the player who wins the game. Each black space counts as one space.

Lesson 1.11Enrich

1.

2.

3.

4.

5.


Name

Evaluate the numerical expression.

1. 4 3 [(15 2 6) 3 (7 2 3)]

4 3 [9 3 ]

4 3 [ ]

2 . 40 2 [(8 3 7) 2 (5 3 6)]

3. 60 4 [(20 2 6) 1 (14 2 8)]

4. 5 1 [(10 2 2) 1 (4 2 1)]

5. 3 3 [(9 1 4) 2 (2 3 6)]

6. 32 4 [(7 3 2) 2 (2 3 5)]

Algebra • Grouping Symbols

Parentheses ( ), brackets [ ], and braces { }, are different grouping symbols used in expressions. To evaluate an expression with different grouping symbols, perform the operation in the innermost set of grouping symbols first. Then evaluate the expression from the inside out.

Evaluate the expression 2 3 [(9 3 4) 2 (17 2 6)].

Step 1 Perform the operations in the parentheses first.

2 3 [(9 3 4) 2 (17 2 6)]

2 3 [ 36 2 11 ]

Step 2 Next perform the operations in the brackets.

2 3 [ 36 2 11 ]

2 3 25

Step 3 Then multiply.

2 3 25 5 50

So, 2 3 [(9 3 4) 2 (17 2 6)] 5 50

Lesson 1.12Reteach


Name

9. Stretch Your Thinking Two numbers are unknown in the expression below. If the value of the expression is 98, what are the unknown numbers? (Both numbers are greater than 0.)

3 {[(12 2 3) 3 3] 1 ( 3 6) 2 8}

1. 6 3 [(7 1 3) (4 3 2)] 5 108

2. 4 3 [(5 × 3) 1 (24 4)] 5 84

3. 5 3 [(12 3) 2 (15 2 9)] 5 150

4. [(40 1 17) 1 (27 4 9)] 5 5 12

5. [(8 3 7) (4 3 9)] 1 15 5 35

6. 100 4 {[(5 3 5) 2 6] 2 (12 2)} 5 20

7. 4 3{[(8 + 5) 3 4] 2 [(18 9) 3 3]} 5 100

8. {[(21 2 9) 2] 1 [(3 3 7) 2 5 ]} 4 8 5 5

Missing Symbols

Write 1, 2, 3, or 4 in the to make each equation true.

Lesson 1.12Enrich


Chapter 1 TestPage 1

1. Find the property that each equation shows.

Write the equation in the correct box.

11 × (4 × 6) = (11 × 4) × 6 14 + 27 + 18 = 27 + 14 + 18

15 + (12 + 11) = (15 + 12) + 11 18 × 2 = 2 × 18

5 × 1 = 5 72 + 0 = 72

Commutative Property of Multiplication

Associative Property of Addition

Identity Property of Addition

Commutative Property of Addition

Associative Property of Multiplication

Identity Property of Multiplication

2. For numbers 2a–2d, select True or False for each statement.

2a. 50 is 1 __ 10 of 500. True False

2b. 290 is 10 times as much as 2,900. True False

2c. 6,500 is 10 times as much as 65. True False

2d. 700 is 10 times as much as 70. True False


Name

Chapter 1 Test1-45


3. Select other ways to write 304,672. Mark all that apply.

A (3 × 100,000) + (4 × 1,000) + (6 × 100) + (7 × 10) + (2 × 1)

B three hundred forty thousands, six hundred seventy-two

C 300,000 + 4,000 + 600 + 70 + 2

D 30 hundred thousand + 4 thousands + 6 hundreds + 70 tens + 2 ones

4. Erica earned 30,000 bonus points on her computer assignment.

This is 10 times as many bonus points as she earned last week.

How many bonus points did Erica earn last week?

points

5. Rich earns $35 per week mowing lawns in his neighborhood. Which expression

can be used to show how much money he earns in 8 weeks?

A (8 + 30) + (8 + 5) C (8 + 30) × (8 + 5)

B (8 × 30) + (8 × 5) D (8 × 30) × (8 × 5)

6. The table shows the equations Mr. Berger discussed in math

class today.

Equations

4 × 100 = 4

4 × 101 = 40

4 × 102 = 400

4 × 103 = 4,000

Explain the pattern of zeros in the product when multiplying

by powers of 10.


Name

Chapter 1 Test1-46


7. It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon. How many feet does Kinsey walk to school in 5 days?

feet

8. Liam saves $12 of his allowance each week. Complete the table to show the total amount Liam saves.

Liam’s Savings

Number of Weeks Total Amount

4

9

15

9. Kara followed these steps to evaluate the expression 22 + (30 − 4) ÷ 2.

30 − 4 = 26

26 + 22 = 48

48 ÷ 2 = 24

George looks at Kara’s work and says she made a mistake. He says she should have divided by 2 before she added.

Part A

Which student is correct? Explain how you know.

Part B

Evaluate the expression.


Name

Chapter 1 Test1-47


10. Fahed buys 12 stickers for $2 each. He also buys 4 sticker albums. Each album costs twice as much as each sticker. Fahed has a coupon that gives him $2 off the sticker albums. Which numerical expression shows how much he spent?

A (12 × 2) + [(4 × 2) − 2] C (12 × 4) + [(4 × 4) − 2]

B (12 × 2) + [(4 × 4) − 2] D (12 × 4) + [(4 × 2) + 2]

11. Evaluate the numerical expression.

(57 + 4) × 4 − 16 =

12. Paul displays his sports trophies on shelves in his room. He has 5 trophies on each of 3 shelves and 2 trophies on another shelf. Write an expression to represent the number of trophies Paul displays.

13. Veronica is solving this problem in math class.

Janelle buys 4 cases of water. Each case of water contains 12 bottles. Janelle drinks 3 bottles of water.

Veronica writes a numerical expression to represent the situation. Her expression, (12 − 3) × 4, has a mistake.

Part A

Explain Veronica’s mistake.

Part B

Write an expression to find how many bottles of water are left, and then solve it.


Name

Chapter 1 Test1-48


14. Hector has 36 action figures. He separates his action figures into 4 equal groups to share with his friends. How many action figures does each friend get?

Part A

Use the array to show your answer.

Part B

Use the multiplication sentence to complete the division sentence.

4 × = 36 36 ÷ 4 =

15. Marcus is making dinner for 7 people. Marcus opens 6 cans of soup. Each can is 14 ounces. If everyone gets the same amount of soup, how much soup will each person get? Use numbers and words to explain your answer.

16. Megan wants to find the quotient. Use multiplication and the Distributive Property to help Megan find the quotient.

72 ÷ 4 =

Multiplication

Distributive Property


Name

Chapter 1 Test1-49

17. Marlene can type 157 words per minute. If she types at the same

rate, how many words can she type in 25 minutes?

words

18. There are 7 school buses taking students on a field trip.

There are 37 students on each bus. How many students

are going on the field trip?

students

19. Select other ways to write 60,472. Mark all that apply.

A (6 × 10,000) + (4 × 100) + (7 × 10) + (2 × 1)

B 60,000 + 400 + 70 + 2

C sixty thousand, four hundred seventy-two

D six thousand, four hundred seventy-two

20. For numbers 20a–20b, select True or False.

20a. 42 − (9 + 6), value: 27 True False

20b. 18 + (22 − 4) ÷ 6, value: 6 True False

21. Peter ran 3 miles a day for 17 days. On the 18th day, Peter ran 5 miles.

Write an expression that matches the words.

22. Select other ways to express 104. Mark all that apply.

A 10 × 4 D 10,000

B 10 + 4 E 10 + 10 + 10 + 10

C 1,000 F 10 × 10 × 10 × 10



Name

Chapter 1 Test1-50

Name Chapter 1

Talking About Phones

1. The Vega family has a cell phone plan that costs $75 per month including taxes and fees. The plan lets the 5 members of the Vega family share 1,000 minutes of talk time per month and 400 text messages per month. Any minutes over 1,000 cost $1 per minute, and any texts over 400 cost $2 per text.

Because of a family emergency, the family uses 1,050 minutes and 415 texts in March. Write an expression you could use to find the amount of the Vega’s cell phone bill for March. Evaluate the expression. Show your work.

2. Tomás Vega offers to pay $59 of the March cell phone bill. Each of the other 4 members of the family agrees to split the rest of the bill equally among themselves. How much does each of the 4 family members owe? Show your work.

The Vega’s bill for March is __.

Each of the 4 family members owes __.

Chapter 1 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company

1-51

3. The Vega family has a 3-year cell phone contract. Javier Vega says that the family gets a total of 3 3 104 minutes of talk time to share during the 3 years.

Is Javier correct? If yes, write an expression to show how Javier could have found his answer. If no, explain why Javier is incorrect. Write the correct number of minutes as the product of a whole number and a power of 10. Show your work.

4. In April, the Vega family gets 400 text messages included in their plan. Together, Tomás and Marisol use half of the messages. Javier and Sergio use 120 messages. Carmen uses the rest of the messages. Write and evaluate an expression to find the number of messages Carmen uses. Show your work.

Carmen uses messages.


1-52

Place Value, Multiplication, and Expressions

Talking About PhonesCOMMON CORE STANDARDS

5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expression without evaluating them.

MP1 Make sense of problems and persevere in solving them.

Also 5.NBT.A.1, 5.NBT.B.5, 5.NBT.B.6, 5.OA.A.1, MP3, MP6

PURPOSETo assess the ability to use place value, multiplication, and expressions to represent and solve problems

TIME25–30 minutes

GROUPINGIndividuals

MATERIALS• Performance Task, paper, pencil

PREPARATION HINTS• Review multiplication with students before assigning the task.

• Review vocabulary, including evaluate, order of operation, and power.

IMPLEMENTATION NOTES • Read the task aloud to students and make sure that all students have a clear understanding of

the task.

• Students may use manipulatives to complete the task.

• Allow students as much paper as they need to complete the task.

• Allow as much time as students need to complete the task.

• Students must complete the task individually, without collaboration.

• Collect all student work when the task is complete.

TASK SUMMARYStudents write and evaluate expressions with grouping symbols to determine the cost of a family’s cell phone bill and the amounts owed by family members. They critique a mathematical statement and use a multiplication expression using powers of 10 to justify their critique.

Place Value, Multiplication, and ExpressionsChapter 1


1-53

REPRESENTATION In this task, teachers can…

• Use both verbal and visual representations of the order of operations to introduce the task.

ACTION and EXPRESSION In this task, teachers can…

• Provide access to online interactive tools to support multiplication skills before assigning the task.

• Support students in setting explicit goals for completion of the task.

ENGAGEMENT In this task, teachers can…

• Vary the level of social interaction required to discuss the task before it is completed.

• Reduce stress by scheduling a regular time to work on the task.

EXPECTED STUDENT OUTCOMES• Complete the task within the time allowed

• Reflect engagement in a productive struggle

• Write and evaluate expressions with grouping symbols

• Critique a mathematical statement using powers of 10

SCORING Use the associated Rubric to evaluate each student’s work.


1-54

Performance Task Rubric

TALKING ABOUT PHONES

A level 3 response • Indicates that the student has made sense of the task and persevered

• Demonstrates the ability to write and evaluate expressions with grouping symbols to solve word problems

• Demonstrates the ability to write multiples of 10 as products of a whole number and a power of 10

A level 2 response • Indicates that the student has made sense of the task and persevered

• Demonstrates the ability to write and evaluate expressions with grouping symbols to solve word problems

• Demonstrates the ability to write a multiple of 10 as the product of a whole number and a power of 10

• Addresses most or all aspects of the task, using mathematically sound procedures

• May contain an incorrect answer derived from a correct procedure

A level 1 response • Shows that the student has made sense of at least some components of the task

• Shows evidence of uneven ability to write and evaluate expressions with grouping symbols to solve word problems

• May show difficulty with writing a multiple of 10 as the product of a whole number and a power of 10

A level 0 response • Shows little evidence that the student has made sense of the task

• Shows little evidence of ability to write and evaluate expressions with grouping symbols to solve word problems

• Shows an inability to write a multiple of 10 as the product of a whole number and a power of 10

• Shows little evidence of adequately addressing the components of the task

• Shows little evidence of applying mathematics correctly or appropriately to the situation


1-55

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der

is

.

12

. Th

e D

istr

ibu

tive

Pro

pert

y can

help

you

div

ide. S

how

how

you

can

bre

ak

ap

art

th

e d

ivid

en

d t

o f

ind

th

e q

uotien

t

for

22

4 ÷

7.

Prer

equi

site

Ski

lls In

vent

ory

for G

rade

5Pa

ge 2

$52

$192

5,03

4 p

eop

le

15 ÷

2

7

1

Po

ssib

le a

nsw

er:

(210

÷ 7

) +

(14

÷ 7

) =

30 +

2 =

32

151

mar

ble

s

1-56 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company

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e

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13

. O

n S

atu

rday,

a t

ota

l of

1,2

92

peop

le

wen

t to

see a

new

movi

e. Th

ere

were

4 d

iffe

ren

t sh

ow

ing

s fo

r th

e n

ew

movi

e a

nd

th

e s

am

e n

um

ber

of

peop

le

att

en

ded

each

sh

ow

ing

. H

ow

man

y

peop

le a

tten

ded

each

sh

ow

ing

?

14

. A

den

tist

bou

gh

t 9

bag

s of

pri

zes

for

his

patien

ts. Each

bag

had

12

pri

zes.

Th

e p

rize

s w

ere

div

ided

eq

ually

am

on

g

3 b

oxe

s. H

ow

man

y p

rize

s w

ere

in

each

box?

15

. R

ylee is

learn

ing

ab

ou

t p

rim

e n

um

bers

in m

ath

cla

ss. H

er

frie

nd

ask

ed

her

to

nam

e a

ll th

e p

rim

e n

um

bers

betw

een

10

an

d 2

0. W

hat

nu

mb

ers

sh

ou

ld R

ylee

nam

e?

16

. C

ass

ie w

rote

som

e n

um

bers

in

a

nu

mb

er

patt

ern

.

14

, 1

7, 1

2, 1

5, 1

0, 1

3, 8

, 1

1

W

hat

shou

ld b

e t

he n

ext

nu

mb

er

in h

er

patt

ern

?

17

. M

rs. D

alton

need

s 1

_

2 c

up

mix

ed

nu

ts

for

her

gra

nola

recip

e. S

he o

nly

has

a 1

_

4 c

up

measu

rin

g c

up

. W

rite

th

e

eq

uiv

ale

nt

fraction

th

at

show

s th

e

am

ou

nt

of

mix

ed

nu

ts s

he w

ill u

se f

or

the r

ecip

e.

18

. M

ich

ael is

pra

cticin

g t

he p

ian

o. H

e

spen

ds

1

_

2 h

ou

r p

racticin

g s

cale

s an

d

1

_

4 h

our

pra

cticin

g the p

iece for

his

recital.

What

is a

com

mon

den

om

inato

r fo

r 1

_

2

an

d 1

_

4 ?

19

. Ju

lia a

nd

Sam

rod

e t

heir

bik

es

on

th

e

bik

e p

ath

. Ju

lia r

od

e h

er

bik

e

3

__

10 o

f th

e

path

's d

ista

nce. S

am

rod

e h

is b

ike

4

_

8 o

f th

e p

ath

's d

ista

nce. C

om

pare

th

e

dis

tan

ces

usi

ng

<, >

, or =

.

323

peo

ple

11, 1

3, 1

7, 1

9

Po

ssib

le a

nsw

ers:

3 __

10 <

4 _ 8 or 4 _ 8 >

3 __

10

6

2 _ 4 cu

p

Po

ssib

le a

nsw

er: 4

36 p

rize

s

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e

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20

. A

li n

eed

s 4

__

10 y

ard

of

red

rib

bon

an

d

5

__

10 y

ard

of

blu

e r

ibb

on

to m

ake a

tail

for

her

kite. H

ow

mu

ch

rib

bon

does

Ali

need

in

all?

21

. B

ryan

bro

ug

ht

8

__

10 g

allo

n o

f w

ate

r on

a

hik

ing

tri

p. H

e d

ran

k

4

__

10 g

allo

n o

f w

ate

r.

How

mu

ch

wate

r is

left

?

22

. Lily

has

two k

itte

ns.

One k

itte

n w

eig

hs

15

__

16 p

ou

nd

. Th

e o

ther

kitte

n w

eig

hs

12

__

16

pou

nd

. W

hat

is t

he d

iffe

ren

ce in

th

e

weig

hts

of

the t

wo k

itte

ns?

23

. Ja

mie

pu

t 2

3

__

12 p

ou

nds

of

gre

en

ap

ple

s

into

a b

ag

. H

e t

hen

ad

ded

3 5

__

12 p

ou

nd

s

of

red

ap

ple

s in

to t

he s

am

e b

ag

. W

hat

is t

he t

ota

l w

eig

ht

of

the a

pp

les

in t

he

bag

?

24

. M

rs. Lask

a b

uys

4 5

_

8 y

ard

s of

blu

e f

ab

ric

an

d 2

1

_

8 y

ard

s of

gre

en

fab

ric. H

ow

man

y

more

yard

s of

blu

e f

ab

ric t

han

gre

en

fab

ric d

oes

Mrs

. Lask

a b

uy?

25

. In

Cro

sby’

s m

od

el colle

ction

, 5

__

16 o

f th

e

mod

els

are

tra

ins

an

d

7

__

16 o

f th

e m

od

els

are

cars

. W

hat

part

of

Cro

sby’

s m

od

el

colle

ction

is

train

s an

d c

ars

?

26

. Leo w

alk

s h

is d

og

7

_

8 m

ile. H

e w

alk

s h

is

dog

3 t

imes

a d

ay.

How

far

does

Leo

walk

his

dog

eve

ry d

ay?

Sh

ow

how

you

can

use

rep

eate

d a

dd

itio

n t

o s

olv

e.

9 _

10 ya

rd

4 __

10 ga

llon

or 2 _ 5 g

allo

n

3 __

16 po

un

d

Po

ssib

le a

nsw

er: 12

__

16

of t

he

colle

ctio

n

is t

rain

s an

d c

ars

7 _ 8 + 7 _ 8 +

7 _ 8 = 21

__

8 m

iles,

or

2 5 _ 8 mile

s

Po

ssib

le a

nsw

er: 5

8 _ 12 p

ou

nd

s

Po

ssib

le a

nsw

er: 2

4 _ 8 yar

ds


Nam

e

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lin H

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ublis

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Com

pany

10

cm

15

cm

234

56

78

916

101112

1314

151

001

Poun

ds

Oun

ces

1 82 8

3 84 8

5 86 8

7 8

Leng

th o

f Le

aves

(in

inch

es)

777

777777

7777

777

777

35

. Tyl

er

use

s cra

ft s

ticks

to m

ake a

qu

ad

rila

tera

l lik

e t

he o

ne s

how

n.

Tell

wh

eth

er

she m

ad

e a

trap

ezoi

d,

para

llelo

gram

, rho

mbu

s, re

ctan

gle,

or

squa

re.

36

. A

pu

pp

y w

eig

hs

3 p

ou

nd

s.

W

hat

is t

he p

up

py’

s w

eig

ht

in o

un

ces?

37

. Th

e lin

e p

lot

show

s th

e len

gth

s of

som

e

leave

s M

ad

ison

colle

cte

d o

n a

hik

e.

H

ow

man

y le

ave

s w

ere

lon

ger

than

5

_

8 i

nch

?

38

. A

pie

ce o

f ri

bbon is

86

centim

ete

rs long.

U

sin

g t

he in

form

ation

in

th

e c

hart

, fin

d

the len

gth

of

the r

ibb

on

in

mete

rs.

39

. M

r. R

ou

rke is

5 f

eet

8 in

ch

es

tall.

How

tall

is M

r. R

ou

rke in

in

ch

es?

40

. G

reta

wan

ts t

o p

ut

rib

bon

aro

un

d t

he

peri

mete

r of

her

art

pro

ject. H

ow

man

y

cen

tim

ete

rs o

f ri

bb

on

will

sh

e n

eed

?

Prer

equi

site

Ski

lls In

vent

ory

for G

rade

5Pa

ge 6

Me

tric

Un

its

of

Le

ng

th

1 ce

ntim

eter

(cm

) =

10

mill

imet

ers

(mm

)

1 de

cim

eter

(dm

) =

10

cent

imet

ers

1 m

eter

(m

) =

10

deci

met

ers

1 m

eter

(m

) =

100

cen

timet

ers

1 m

eter

(m

) =

1,0

00 m

illim

eter

s

trap

ezo

id

48 o

un

ces

7 le

aves

68 in

ches

50 c

enti

met

ers

Po

ssib

le a

nsw

ers:

86

___

100 m

eter

or

0.86

met

er

Nam

e

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27

. O

n T

uesd

ay,

Lill

y sp

en

t 1

_

4 h

ou

r w

ork

ing

on

her

scie

nce f

air

pro

ject. B

en

work

ed

3 t

imes

as

lon

g o

n h

is s

cie

nce f

air

pro

ject

as

Lill

y d

id. H

ow

mu

ch

tim

e d

id

Ben

sp

en

d o

n h

is s

cie

nce f

air

pro

ject?

28

. It

takes

Akio

’s f

am

ily 2

1

_

2 h

ou

rs t

o d

rive

from

th

eir

hom

e t

o t

he b

each

. It

takes

his

fam

ily 3

tim

es

as

lon

g t

o d

rive

to

the m

ou

nta

ins

as

it t

akes

to d

rive

to

the b

each

. H

ow

lon

g d

oes

it t

ake A

kio

’s

fam

ily t

o d

rive

fro

m t

heir

hom

e t

o t

he

mou

nta

ins?

29

. Th

e s

tou

t in

fan

tfis

h is

on

e o

f th

e

worl

d’s

sm

alle

st f

ish

. It

is

on

ly a

bou

t

8 4

__

10 m

illim

ete

rs lon

g. W

hat

is t

his

len

gth

wri

tten

as

a d

ecim

al?

30

. Th

e d

ista

nce f

rom

Davi

na’s

hou

se t

o

her

sch

ool is

2 7

5

___

10

0 m

iles.

Wh

at

is t

his

dis

tan

ce w

ritt

en

as

a d

ecim

al?

31.

Jill

buys

a tom

ato

that w

eig

hs

0.9

pound.

Wri

te t

he w

eig

ht

of

the t

om

ato

as

a

fraction

with

a d

en

om

inato

r of

10

0.

32

. U

se <

, >

, or =

to c

om

pare

0.3

6

an

d 0

.4.

33

. H

en

ry d

raw

s an

ob

tuse

tri

an

gle

. H

ow

man

y ob

tuse

an

gle

s d

oes

Hen

ry’s

tria

ng

le h

ave

?

34

. W

hat

term

best

desc

rib

es

the lin

es

show

n?

W

rite

per

pend

icul

ar, p

aral

lel,

or

inte

rsec

ting.

7 1 _ 2 ho

urs

8.4

mill

imet

ers

par

alle

l

Po

ssib

le a

nsw

ers:

0.3

6 <

0.4

or

0.4

> 0

.36

1 o

btu

se a

ng

le

2.75

mile

s

90

___

100 p

ou

nd

3 _ 4 ho

ur


Nam

e

1-7

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 1

Ch

oo

se t

he

corr

ect

answ

er.

1

. Ju

dith

has

a n

eckla

ce w

ith

a m

ass

of

65

.73

6 g

ram

s. W

hat

is t

he m

ass

of

her

neckla

ce r

ou

nd

ed

to t

he n

eare

st t

en

th?

A

6

5.7

gra

ms

B

6

5.7

4 g

ram

s

C

6

5.8

gra

ms

D

6

6.0

gra

ms

2

. Th

e p

ost

off

ice is

3.5

6 k

ilom

ete

rs f

rom

Mari

a’s

hou

se a

nd

1.3

8 k

ilom

ete

rs f

rom

Sim

on

’s h

ou

se. H

ow

mu

ch

fart

her

does

Mari

a liv

e f

rom

th

e lib

rary

th

an

Sim

on

?

A

4

.94

kilo

mete

rs

B

2

.28

kilo

mete

rs

C

2

.18

kilo

mete

rs

D

1

.18

kilo

mete

rs

3

. C

ryst

al’s

tom

ato

pla

nt

was

32

.65

cen

tim

ete

rs t

all

in J

un

e. D

uri

ng

July

, th

e p

lan

t g

rew

82

.6 c

en

tim

ete

rs.

How

tall

was

Cry

stal’s

tom

ato

pla

nt

at

the e

nd

of

July

?

A

4

09

.1 c

en

tim

ete

rs

B

1

15

.25

cen

tim

ete

rs

C

4

9.9

5 c

en

tim

ete

rs

D

40

.91

cen

tim

ete

rs

4

. R

ick a

nd

Ch

ad

are

pla

yin

g a

nu

mb

er

patt

ern

gam

e. R

ick w

rote

th

e f

ollo

win

g

patt

ern

.

32

.3, 3

4.5

, 3

6.7

, ____, 4

1.1

W

hat

is t

he u

nkn

ow

n n

um

ber

in t

he

patt

ern

Ric

k w

rote

?

A

3

7.9

B

3

8.8

C

3

8.9

D

3

9.9

5

. Y

ola

nd

a r

ead

her

book f

or

1 1

_

5 h

ou

rs

Mon

day

eve

nin

g a

nd

for

2 3

_

5 h

ou

rs o

n

Tu

esd

ay

eve

nin

g. W

hic

h is

the best

est

imate

of

the t

ime Y

ola

nd

a r

ead

on

Mon

day

an

d T

uesd

ay?

A

ab

ou

t 4

__

5 h

ou

r

B

ab

ou

t 3

hou

rs

C

ab

ou

t 3

1

__

2 h

ou

rs

D

ab

ou

t 4

hou

rs

Nam

e

1-8

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 2

6

. Fra

ncin

e h

as

a p

iece o

f w

ood

th

at

is

5 5

__

_ 1

2 f

eet

lon

g. S

he u

ses

3 1

__

4 f

eet

of

the

wood

for

a s

cie

nce p

roje

ct. H

ow

mu

ch

wood

does

Fra

ncin

e h

ave

left

?

A

8

2

__

3 f

eet

B

3

2

___

12 f

eet

C

2

4

___

12 f

eet

D

2

2

___

12 f

eet

7

. K

evi

n h

as

3 b

ag

s of

ap

ple

s w

eig

hin

g

a t

ota

l of

22

1

_

2 p

ou

nd

s. T

wo o

f th

e b

ag

s

weig

h 6

3

_

8 p

ou

nd

s an

d 3

1

_

4 p

ou

nd

s. H

ow

mu

ch

does

the t

hir

d b

ag

weig

h?

A

1

1 7

__

8 p

ou

nd

s

B

1

2 4

__

8 p

ou

nd

s

C

1

2 7

__

8 p

ou

nd

s

D

1

3 5

__

8 p

ou

nd

s

8

. A

ish

a h

iked

each

day

for

a w

eek. Th

e

firs

t d

ay

she h

iked

1

_

6 m

ile, th

e s

econ

d

day

she h

iked

1

_

2 m

ile, an

d t

he t

hir

d d

ay

she h

iked

5

_

6 m

ile. B

y h

ow

mu

ch

did

sh

e

incre

ase

th

e d

ista

nce s

he h

iked

each

day?

A

9

__

6 m

iles

B

5

__

6 m

ile

C

1

__

2 m

ile

D

1

__

3 m

ile

9

. A

corn

mu

ffin

recip

e c

alls

for

1

_

4 c

up

of

corn

meal an

d 5

_

6 c

up

of

flou

r. W

hat

is

the least

com

mon

den

om

inato

r of

the

fraction

s?

A

6

B

1

2

C

1

8

D

2

4

10

. O

n a

coord

inate

gri

d, C

arr

ie’s

hou

se

is locate

d 3

blo

cks

to t

he r

igh

t an

d

4 b

locks

up

fro

m (

0, 0

). M

ike’s

hou

se

is locate

d 2

blo

cks

to t

he left

an

d

2 b

locks

dow

n f

rom

Carr

ie’s

hou

se.

Wh

at

ord

ere

d p

air

desc

rib

es

the

location

of

Mik

e’s

hou

se?

5 4 3 2

y axis

x ax

is

x

y 1 02

31

45

A

(1

, 5

)

B

(2

, 1

)

C

(1

, 2

)

D

(5

, 2

)


Nam

e

1-10

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 4

15

. M

ary

dre

w a

pic

ture

of

her

flow

er

gard

en

.

W

hat

typ

e o

f q

uad

rila

tera

l is

Mary

’s

gard

en

?

A

re

cta

ng

le

B

rh

om

bu

s

C

sq

uare

D

tr

ap

ezo

id

16

. D

mitri

mad

e a

box

with

th

e d

imen

sion

s

show

n t

o h

old

his

mod

elin

g s

up

plie

s.

4 ft

2 ft2

ft

W

hat

is t

he v

olu

me o

f th

e b

ox?

A

8

cu

bic

feet

B

1

4 c

ub

ic f

eet

C

1

6 c

ub

ic f

eet

D

1

8 c

ub

ic f

eet

17

. Th

e s

idew

alk

tile

s le

ad

ing

to t

he

tow

n lib

rary

are

sh

ap

ed

lik

e r

eg

ula

r

hexa

gon

s. W

hic

h o

f th

e f

ollo

win

g

desc

rib

es

a r

eg

ula

r h

exa

gon

?

A

a f

igu

re w

ith

6 c

on

gru

en

t si

des

an

d

6 c

on

gru

en

t an

gle

s

B

a f

igu

re w

ith

6 s

ides

an

d a

ng

les

that

are

not

con

gru

en

t

C

a f

igu

re w

ith

5 s

ides

an

d 5

an

gle

s

that

are

not

con

gru

en

t

D

a f

igu

re w

ith

5 c

on

gru

en

t si

des

an

d

5 c

on

gru

en

t an

gle

s

18

. A

toy

box

in t

he s

hap

e o

f a r

ecta

ng

ula

r

pri

sm h

as

a v

olu

me o

f 6

72

cu

bic

inch

es.

Th

e b

ase

are

a o

f th

e t

oy

box

is

28

sq

uare

in

ch

es.

Wh

at

is t

he h

eig

ht

of

the t

oy

box?

A

1

0 in

ch

es

B

1

2 in

ch

es

C

2

2 in

ch

es

D

2

4 in

ch

es

19

. A

piz

za p

arl

or

use

s 4

2 t

om

ato

es

for

each

batc

h o

f to

mato

sau

ce. A

bou

t h

ow

man

y b

atc

hes

of

sau

ce c

an

th

e p

izza

parl

or

make f

rom

its

last

sh

ipm

en

t of

1,2

36

tom

ato

es?

A

2

0

B

3

0

C

3

5

D

4

8

Nam

e

1-9

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 3

11

. W

hat

is t

he u

nkn

ow

n n

um

ber

in

Seq

uen

ce 2

in

th

e c

hart

?

A

6

4

B

8

0

C

9

6

D

1

06

12

. Th

e g

rap

h s

how

s th

e r

ela

tion

ship

betw

een

the n

um

ber

of

weeks

an

d

pla

nt

gro

wth

in

in

ch

es.

Num

ber o

f Wee

ks

Plan

t G

row

th (i

nche

s)

Number of Inches

123456

23

14

50y

x

W

hat

rule

rela

tes

the n

um

ber

of

weeks

an

d p

lan

t gro

wth

in

in

ch

es?

A

M

ultip

ly t

he n

um

ber

of

weeks

by

1 1

__

2 .

B

M

ultip

ly t

he n

um

ber

of

weeks

by

1 1

__

3 .

C

M

ultip

ly t

he n

um

ber

of

weeks

by

1 1

__

4 .

D

M

ultip

ly t

he n

um

ber

of

weeks

by

1

__

2 .

13

. A

baker

is w

eig

hin

g t

he d

ou

gh

th

at

will

be u

sed

to m

ake p

ast

ries.

Th

e lin

e p

lot

show

s th

e w

eig

ht

of

the d

ou

gh

for

each

past

ry.

Dou

gh (

in p

ound

s)

✗✗✗✗

✗✗✗✗✗

✗✗✗

1 43 8

1 2

H

ow

man

y p

ast

ries

will

be m

ad

e f

rom

at

least

3

_

8 p

ou

nd

of

dou

gh

?

A

4

B

7

C

8

D

9

14

. M

arv

in is

bu

yin

g a

new

com

pu

ter

on

laya

way

for

$3

02

. If

he m

akes

a d

ow

n

paym

en

t of

$5

0 a

nd

pays

$2

8 e

ach

week, h

ow

man

y w

eeks

will

it

take

Marv

in t

o p

ay

for

the c

om

pu

ter?

A

8

B

9

C

1

0

D

1

2

Sequ

ence

Num

ber

12

36

8Se

quen

ce 1

48

1224

32Se

quen

ce 2

1224

3672

?

1-60 Answer Key© Houghton Mifflin Harcourt Publishing Company

Chapter Resources

Nam

e

1-12

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 6

26

. C

arl

os

had

2

4 c

lass

pla

y tickets

to

sell.

He s

old

3

__

4 o

f th

e t

ickets

. H

ow

man

y

tickets

did

Carl

os

sell?

A

1

6

B

1

8

C

2

4

D

2

6

27

. N

ore

en

mad

e 8

2

_

3 c

up

s of

snack m

ix

for

a p

art

y. H

er

gu

est

s ate

3

_

4 o

f th

e m

ix.

How

mu

ch

sn

ack m

ix d

id h

er

gu

est

s

eat?

A

5

1

__

4 c

up

s

B

5

3

__

4 c

up

s

C

6

5

___

12 c

up

s

D

6

1

__

2 c

up

s

28

. G

an

esh

is

stackin

g b

oxe

s in

a s

tora

ge

room

. Th

ere

are

12

boxe

s in

all.

If

each

box

weig

hs

9.6

pou

nd

s, h

ow

mu

ch

do

the b

oxe

s w

eig

h a

ltog

eth

er?

A

1

1.2

5 p

ou

nd

s

B

2

1.6

pou

nd

s

C

11

5.2

pou

nd

s

D

1

,15

2 p

ou

nd

s

29

. Th

e in

stru

ction

bookle

t fo

r a D

VD

pla

yer

says

th

at

the p

laye

r u

ses

ab

ou

t

0.4

kilo

watt

of

ele

ctr

icity

per

hou

r. If

ele

ctr

icity

cost

s $

0.2

0 p

er

kilo

watt

hou

r,

how

mu

ch

does

it c

ost

to r

un

th

e p

laye

r

for

an

hou

r?

A

$

0.0

8

B

$

0.8

0

C

$

8.0

0

D

$

80

.00

30

. R

hia

nn

a w

as

doin

g r

ese

arc

h f

or

a

rep

ort

ab

ou

t th

e h

igh

est

mou

nta

ins

in

the U

nited

Sta

tes.

Sh

e r

ead

th

at

the

Gra

nd

Teto

n in

Wyo

min

g is

ab

ou

t

1.3

7 ×

10

4 f

eet

hig

h. H

ow

sh

ou

ld

Rh

ian

na w

rite

th

e h

eig

ht

of

the G

ran

d

Teto

n in

sta

nd

ard

form

on

her

rep

ort

?

A

1

37

feet

B

1

,37

0 f

eet

C

1

3,7

00

feet

D

1

37

,00

0 f

eet

Nam

e

1-11

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 5

20

. Th

e a

rt t

each

er

has

a lis

t of

13

4 s

tud

en

ts w

ho h

ave

sig

ned

up

for

art

cla

sses.

Th

e a

rt t

each

er

can

reg

iste

r

8 s

tud

en

ts in

each

cla

ss. W

hat

is t

he

least

nu

mb

er

of

cla

sses

need

ed

for

all

the s

tud

en

ts t

o b

e r

eg

iste

red

in

a c

lass

?

A

1

6

B

1

7

C

1

8

D

1

9

21

. Th

e n

um

ber

of

rose

s M

r. A

dam

s

ord

ere

d f

or

his

sto

re w

as

thre

e t

imes

as

man

y as

the n

um

ber

of

carn

ation

s

ord

ere

d. H

e o

rdere

d a

tota

l of

56

flo

wers

. H

ow

man

y ro

ses

did

Mr. A

dam

s ord

er?

A

1

4

B

2

8

C

3

4

D

4

2

22

. Th

e o

wn

er

of

a c

loth

ing

sto

re r

eceiv

ed

a s

hip

men

t of

1,2

30

pair

s of

socks.

Th

e s

ocks

cam

e in

36

boxe

s. T

he s

am

e

nu

mb

er

of

pair

s of

socks

were

in

35

of

the b

oxe

s. H

ow

man

y p

air

s of

socks

were

in

th

e last

box?

A

2

B

5

C

1

5

D

3

5

23

. Ja

red

use

s 2

4 t

iles

to c

ove

r th

e t

op

of

his

desk

. O

f th

e 2

4 t

iles,

3

_

8 a

re b

lue.

How

man

y of

the t

iles

are

blu

e?

A

3

B

8

C

9

D

1

2

24

. Ton

y w

ork

ed

4 2

_

3 h

ou

rs o

n h

is s

cie

nce

pro

ject. S

on

ia w

ork

ed

1 1

_

4 t

imes

as

lon

g

on

her

scie

nce p

roje

ct

as

Ton

y d

id. For

how

man

y h

ou

rs d

id S

on

ia w

ork

on

her

scie

nce p

roje

ct?

A

4

5

__

6 h

ou

rs

B

5 h

ou

rs

C

5

1

__

3 h

ou

rs

D

5

5

__

6 h

ou

rs

25

. Ju

lia h

ad

2

_

3 q

uart

of

cle

an

ing

liq

uid

.

Sh

e u

sed

1

_

4 o

f it t

o c

lean

th

e s

ink

coun

ter. H

ow

mu

ch

cle

an

ing

liq

uid

did

Ju

lia u

se?

A

1

__

8 q

uart

B

1

__

6 q

uart

C

1

__

2 q

uart

D

5

__

_ 1

2 q

uart


Nam

e

1-14

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 8

36

. Eli

mad

e a

loaf

of

bre

ad

. H

e g

ave

eq

ual

port

ion

s of

1

_

2 o

f th

e loaf

to 3

fri

en

ds.

Wh

at

dia

gra

m c

ou

ld E

li u

se t

o f

ind

th

e

fraction

of

the w

hole

loaf

of

bre

ad

th

at

each

fri

en

d g

ot?

A

B

C

D

37

. Lori

rod

e h

er

bic

ycle

19

.5 m

iles

in

3 h

ou

rs. W

hic

h g

ives

the b

est

est

imate

of

how

far

Lori

rod

e in

1 h

ou

r?

A

b

etw

een

4 a

nd

5 m

iles

B

b

etw

een

5 a

nd

6 m

iles

C

b

etw

een

6 a

nd

7 m

iles

D

b

etw

een

7 a

nd

8 m

iles

38

. R

og

er

is r

idin

g in

a b

ike-a

-th

on

to r

ais

e

mon

ey

for

his

favo

rite

ch

ari

ty. Th

e t

ota

l

dis

tan

ce o

f th

e b

ike-a

-th

on

is

38

.7 m

iles.

So f

ar

he h

as

com

ple

ted

1

__

10 o

f th

e b

ike-a

-th

on

. H

ow

man

y m

iles

has

Rog

er

bik

ed

?

A

3

87

mile

s

B

3

8.7

mile

s

C

3

.87

mile

s

D

0

.38

7 m

ile

39

. Elle

n is

makin

g s

mall

bag

s of

con

fett

i

from

a larg

e b

ag

of

con

fett

i th

at

weig

hs

4.7

5 p

ou

nd

s. If

she p

uts

th

e s

am

e

am

ou

nt

of

con

fett

i in

each

of

5 b

ag

s,

how

mu

ch

sh

ou

ld e

ach

bag

weig

h?

A

0

.09

pou

nd

B

0

.9 p

ou

nd

C

0

.95

pou

nd

D

9

.1 p

ou

nd

s

40

. Tre

vor

bou

gh

t ap

ple

s th

at

cost

$0

.92

per

pou

nd

. H

e p

aid

$5

.52

for

the a

pp

les.

How

man

y p

ou

nd

s of

ap

ple

s d

id h

e b

uy?

A

6

0 p

ou

nd

s

B

6

pou

nd

s

C

0

.6 p

ou

nd

D

0

.06

pou

nd

Nam

e

1-13

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 7

31

. Je

rem

y is

tra

inin

g f

or

a r

ace. W

hen

he

train

s, h

e r

un

s on

a p

ath

th

at

is

1.2

5 m

iles

lon

g. Last

week, Je

rem

y ra

n

on

th

e p

ath

7 t

imes.

How

man

y m

iles

did

Jere

my

run

on

th

e p

ath

last

week?

A

0

.87

5 m

ile

B

8

.75

mile

s

C

8

7.5

mile

s

D

8

75

mile

s

32

. Th

ere

is

1

_

3 p

ou

nd

of

cake t

hat

will

be

share

d e

qu

ally

am

on

g 4

fri

en

ds.

Wh

at

fraction

of

a p

ou

nd

of

cake w

ill e

ach

frie

nd

get?

A

1

__

_ 1

2 p

oun

d

B

1

__

6 p

ou

nd

C

1

__

2 p

ou

nd

D

3

__

4 p

ou

nd

33

. A

t lu

nch

, 5

fri

en

ds

share

3 p

izza

s

eq

ually

. W

hat

fraction

of

a p

izza

does

each

fri

en

d g

et?

A

3

__

5

B

2

__

3

C

3

__

4

D

1

1

__

5

34

. Ju

lie h

as

3

_

4 q

uart

of

fru

it ju

ice. S

he

pours

th

e s

am

e a

mou

nt

into

each

of

4 g

lass

es.

Wh

ich

eq

uation

rep

rese

nts

the f

raction

of

a q

uart

of

fru

it ju

ice n

th

at

is in

each

gla

ss?

A

3

__

4 ÷

1

__

4 =

n

B

4

÷ 3

__

4 =

n

C

3

__

4 ÷

4 =

n

D

3

÷ 4

= n

35

. Terr

y eva

luate

s 6

÷ 1

_

8 b

y u

sin

g a

rela

ted

mu

ltip

lication

exp

ress

ion

.

Wh

ich

mu

ltip

lication

exp

ress

ion

shou

ld h

e u

se?

A

6

× 1

__

8

B

1

__

6 ×

1

__

8

C

1

__

6 ×

8

D

6

× 8


Nam

e

1-15

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 9

41

. C

arly

spe

nt a

tota

l of $

18.2

0 on

Sa

turd

ay a

ftern

oon.

She

bou

ght a

mov

ie

ticke

t for

$8.

25 a

nd s

nack

s fo

r $3

.85.

Sh

e sp

ent t

he r

est o

f the

mon

ey o

n bu

s fa

re to

get

to th

e m

ovie

and

bac

k ho

me.

H

ow m

uch

was

the

bus

fare

eac

h w

ay if

ea

ch tr

ip c

ost t

he s

ame

amou

nt?

A

$2.

20

B

$3.

05

C

$6.

10

D

$6.

20

42

. A

pub

lishe

r re

port

s th

at it

sol

d 1,

516,

792

trav

el m

agaz

ines

. Wha

t is

the

valu

e of

the

digi

t 5 in

1,5

16,7

92 ?

A

5,

000

B

50,

000

C

5

00,0

00

D

5,0

00,0

00

43

. M

artin

is b

uyin

g 40

0 vi

deo

gam

es fo

r hi

s en

tert

ainm

ent s

tore

. Eac

h vi

deo

gam

e co

sts

$20.

Whi

ch o

f the

follo

win

g co

uld

he u

se to

find

the

tota

l am

ount

he

will

pay

for

the

vide

o ga

mes

?

A

(4 ×

2) ×

10

2 = 8

00

B

(4 ×

2) ×

10

3 = 8

,000

C

(4 ×

2) ×

10

4 = 8

0,00

0

D

(4 ×

2) ×

10

5 = 8

00,0

00

44

. Ja

mie

’s d

ad tr

avel

s 36

5 m

iles

ever

y w

eek

for

busi

ness

. How

man

y m

iles

does

he

trav

el in

4 w

eeks

?

A

1,2

60 m

iles

B

1,3

60 m

iles

C

1,4

50 m

iles

D

1,4

60 m

iles

45

. A

mbe

r an

d he

r fr

iend

Nat

han

are

savi

ng to

buy

a v

ideo

gam

e th

at c

osts

$6

5. A

mbe

r ea

rns

$12

per

wee

k fo

r ba

bysi

tting

and

spe

nds

$4 o

f it.

Nat

han

earn

s $1

5 pe

r w

eek

for

wal

king

dog

s an

d sp

ends

$8

of it

. Whi

ch e

xpre

ssio

n ca

n be

use

d to

find

how

man

y w

eeks

it

will

take

to s

ave

for

the

vide

o ga

me?

A

65 ÷

[(1

2 −

4) +

(15

− 8

)]

B

65 ÷

[(1

2 +

4) −

(15

+ 8

)]

C

65 ÷

[(1

2 −

4) +

(15

+ 8

)]

D

65 ÷

[(1

2 +

4) −

(15

− 8

)]

Nam

e

1-16

Begi

nnin

g of

Yea

r Tes

tCh

apte

r Res

ourc

es©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny

Begi

nnin

g of

Yea

r Tes

tPa

ge 1

0

46

. C

hen

took

54

phot

os w

ith h

is d

igita

l ca

mer

a. H

e st

ored

an

equa

l num

ber

of p

hoto

s in

eac

h of

6 fo

lder

s on

hi

s co

mpu

ter.

Whi

ch m

ultip

licat

ion

sent

ence

cou

ld C

hen

use

to fi

nd th

e nu

mbe

r of

pho

tos

in e

ach

fold

er?

A

54 ÷

6 =

9

B

5 ×

9 =

45

C

6 ×

9 =

54

D

6 ×

54 =

324

47

. R

ache

l’s h

ome

is 5

mile

s fr

om h

er

scho

ol. H

ow m

any

yard

s ar

e in

5

mile

s?

A

1

,760

yar

ds

B

7

,800

yar

ds

C

8

,800

yar

ds

D

26,

400

yard

s

48

. Sa

rah

boug

ht 6

pou

nds

of c

lay

for

potte

ry c

lass

. How

man

y ou

nces

of c

lay

did

Sara

h bu

y?

A

48

ounc

es

B

64

ounc

es

C

80

ounc

es

D

96

ounc

es

49

. Th

e ba

sket

ball

gam

e at

the

high

sch

ool

star

ted

at 7

:30

P.M. a

nd e

nded

at

10:3

8 P.M

. How

long

did

the

gam

e la

st?

A

2 h

ours

8 m

inut

es

B

2 h

ours

18

min

utes

C

3 h

ours

8 m

inut

es

D

3 h

ours

18

min

utes

50

. K

ate

used

6.1

5 m

eter

s of

rib

bon

to

mak

e bo

ws.

How

man

y ce

ntim

eter

s of

rib

bon

did

she

use?

A

615

cen

timet

ers

B

61.

5 ce

ntim

eter

s

C

6

.15

cent

imet

ers

D

0

.615

cen

timet

er


Chap

ter 1

Tes

tPa

ge 2

3

. S

ele

ct

oth

er

ways

to w

rite

30

4,6

72

. M

ark

all

that

ap

ply

.

A (

3 ×

10

0,0

00

) +

(4

× 1

,00

0)

+ (

6 ×

10

0)

+ (

7 ×

10

) +

(2

× 1

)

B th

ree h

un

dre

d f

ort

y th

ou

san

ds,

six

hu

nd

red

seve

nty

-tw

o

C 3

00

,00

0 +

4,0

00

+ 6

00

+ 7

0 +

2

D 3

0 h

un

dre

d t

hou

san

d +

4 t

hou

san

ds

+ 6

hu

nd

red

s +

70

ten

s +

2 o

nes

4

. Eri

ca e

arn

ed

30

,00

0 b

on

us

poin

ts o

n h

er

com

pu

ter

ass

ign

men

t.

Th

is is

10

tim

es

as

man

y b

on

us

poin

ts a

s sh

e e

arn

ed

last

week.

How

man

y b

on

us

poin

ts d

id E

rica e

arn

last

week?

poin

ts

5

. R

ich

earn

s $

35

per

week m

ow

ing

law

ns

in h

is n

eig

hb

orh

ood

. W

hic

h e

xpre

ssio

n

can

be u

sed

to s

how

how

mu

ch

mon

ey

he e

arn

s in

8 w

eeks?

A (

8 +

30

) +

(8

+ 5

)

C (8

+ 3

0)

× (

8 +

5)

B (8

× 3

0)

+ (

8 ×

5)

D

(8

× 3

0)

× (

8 ×

5)

6

. Th

e t

ab

le s

how

s th

e e

qu

ation

s M

r. B

erg

er

dis

cu

ssed

in

math

cla

ss t

od

ay.

Equ

atio

ns

4 ×

100

= 4

4 ×

101

= 4

0

4 ×

102

= 4

00

4 ×

103

= 4

,000

Exp

lain

th

e p

att

ern

of

zero

s in

th

e p

rod

uct

wh

en

mu

ltip

lyin

g

by

pow

ers

of

10

.

Po

ssib

le e

xpla

nat

ion

: Fo

r ea

ch p

ow

er o

f te

n, t

he

nu

mb

er

of

zero

s w

ritt

en a

fter

th

e b

ase

is t

he

sam

e as

th

e n

um

ber

in t

he

exp

on

ent.

3,0

00

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

Tes

t1-46

Chap

ter 1

Tes

tPa

ge 1

1.

Fin

d t

he p

rop

ert

y th

at

each

eq

uation

sh

ow

s.

Wri

te t

he e

qu

ation

in

th

e c

orr

ect

box.

11

× (

4 ×

6)

= (

11

× 4

) ×

61

4 +

27

+ 1

8 =

27

+ 1

4 +

18

15

+ (

12

+ 1

1)

= (

15

+ 1

2)

+ 1

11

8 ×

2 =

2 ×

18

5 ×

1 =

57

2 +

0 =

72

Com

mu

tative

Pro

pert

y of

Mu

ltip

lication

Ass

ocia

tive

Pro

pert

y of

Ad

ditio

n

Iden

tity

Pro

pert

y of

Ad

ditio

n

Com

mu

tative

Pro

pert

y

of

Ad

ditio

n

Ass

ocia

tive

Pro

pert

y

of

Mu

ltip

lication

Iden

tity

Pro

pert

y

of

Mu

ltip

lication

2.

For

nu

mb

ers

2a–2

d, se

lect

Tru

e o

r Fals

e f

or

each

sta

tem

en

t.

2a.

50

is

1

__

10 o

f 5

00

.

Tru

e

Fals

e

2b.

29

0 is

10

tim

es

as

mu

ch

as

2,9

00

. T

rue

Fals

e

2c.

6,5

00

is

10

tim

es

as

mu

ch

as

65

.

Tru

e

Fals

e

2d.

70

0 is

10

tim

es

as

mu

ch

as

70

.

Tru

e

Fals

e

18 ×

2 =

2 ×

18

72 +

0 =

72

15 +

(12

+ 1

1) =

(1

5 +

12)

+ 1

1

14 +

27

+ 1

8 =

27

+ 1

4 +

18

11 ×

(4

× 6

) =

(1

1 ×

4)

× 6

5 ×

1 =

5

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

Tes

t1-45


Chap

ter 1

Tes

tPa

ge 4

10

. Fa

hed

buys

12

stic

kers

for

$2 e

ach.

He

also

buy

s 4

stic

ker

albu

ms.

Eac

h al

bum

cos

ts tw

ice

as m

uch

as e

ach

stic

ker.

Fahe

d ha

s a

coup

on th

at g

ives

him

$2

off t

he s

ticke

r al

bum

s. W

hich

nu

mer

ical

exp

ress

ion

show

s ho

w m

uch

he s

pent

?

A (

12 ×

2)

+ [

(4 ×

2)

− 2

]

C (

12 ×

4)

+ [

(4 ×

4)

− 2

]

B (

12 ×

2)

+ [

(4 ×

4)

− 2

]

D (

12 ×

4)

+ [

(4 ×

2)

+ 2

]

11

. Ev

alua

te th

e nu

mer

ical

exp

ress

ion.

(57

+ 4

) ×

4 −

16

=

228

12

. Pa

ul d

ispl

ays

his

spor

ts tr

ophi

es o

n sh

elve

s in

his

roo

m. H

e ha

s 5

trop

hies

on

each

of 3

she

lves

and

2 tr

ophi

es o

n an

othe

r sh

elf.

Writ

e an

exp

ress

ion

to r

epre

sent

the

num

ber

of tr

ophi

es P

aul

disp

lays

.

(5 ×

3)

+ 2

13

. Ve

roni

ca is

sol

ving

this

pro

blem

in m

ath

clas

s.

Jane

lle b

uys

4 ca

ses

of w

ater

. Eac

h ca

se o

f wat

er c

onta

ins

12 b

ottle

s. J

anel

le d

rinks

3 b

ottle

s of

wat

er.

Vero

nica

writ

es a

num

eric

al e

xpre

ssio

n to

rep

rese

nt th

e si

tuat

ion.

Her

exp

ress

ion,

(12

− 3

) ×

4, h

as a

mis

take

.

Par

t A

Expl

ain

Vero

nica

’s m

ista

ke.

Po

ssib

le e

xpla

nat

ion

: Ver

on

ica

sub

trac

ted

3 f

rom

12

wh

en s

he

sho

uld

hav

e m

ult

iplie

d 1

2 ×

4 a

nd

th

en

sub

trac

ted

3 f

rom

th

is a

mo

un

t.

Par

t B

Writ

e an

exp

ress

ion

to fi

nd h

ow m

any

bottl

es o

f wat

er a

re le

ft,

and

then

sol

ve it

.

(12

× 4

) −

3 =

45

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

Tes

t1-48

Chap

ter 1

Tes

tPa

ge 3

7

. It

is 1

,325

feet

from

Kin

sey’

s ho

use

to h

er s

choo

l. K

inse

y w

alks

to

sch

ool e

ach

mor

ning

and

get

s a

ride

hom

e ea

ch a

ftern

oon.

H

ow m

any

feet

doe

s K

inse

y w

alk

to s

choo

l in

5 da

ys?

feet

8

. Li

am s

aves

$12

of h

is a

llow

ance

eac

h w

eek.

Com

plet

e th

e ta

ble

to s

how

th

e to

tal a

mou

nt L

iam

sav

es.

Lia

m’s

Sa

vin

gs

Nu

mb

er o

f Wee

ksTo

tal A

mo

un

t

4$4

8

9$1

08

15$1

80

9

. K

ara

follo

wed

thes

e st

eps

to e

valu

ate

the

expr

essi

on 2

2 +

(30

− 4

) ÷

2.

30 −

4 =

26

26 +

22

= 4

8

48 ÷

2 =

24

Geo

rge

look

s at

Kar

a’s

wor

k an

d sa

ys s

he m

ade

a m

ista

ke. H

e sa

ys

she

shou

ld h

ave

divi

ded

by 2

bef

ore

she

adde

d.

Par

t A

Whi

ch s

tude

nt is

cor

rect

? Ex

plai

n ho

w y

ou k

now

.

Geo

rge;

Po

ssib

le a

nsw

er: A

cco

rdin

g to

th

e o

rder

o

f o

per

atio

ns,

yo

u s

ho

uld

per

form

div

isio

n b

efo

re

add

itio

n.

Par

t B

Eval

uate

the

expr

essi

on.

30 2

4 5

26

26 4

2 5

13

22 1

13

5 3

5

6,62

5

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

Tes

t1-47


17

. M

arl

en

e c

an

typ

e 1

57

word

s p

er

min

ute

. If

sh

e t

ypes

at

the s

am

e

rate

, h

ow

man

y w

ord

s can

sh

e t

ype in

25

min

ute

s?

word

s

18

. Th

ere

are

7 s

ch

ool b

use

s ta

kin

g s

tud

en

ts o

n a

fie

ld t

rip

.

Th

ere

are

37

stu

den

ts o

n e

ach

bu

s. H

ow

man

y st

ud

en

ts

are

goin

g o

n t

he f

ield

tri

p?

stu

dents

19

. S

ele

ct

oth

er

ways

to w

rite

60

,47

2. M

ark

all

that

ap

ply

.

A

(6 ×

10

,00

0)

+ (

4 ×

10

0)

+ (

7 ×

10

) +

(2

× 1

)

B

60

,00

0 +

40

0 +

70

+ 2

C

sixt

y th

ou

san

d, fo

ur

hu

nd

red

seve

nty

-tw

o

D

six

thou

san

d, fo

ur

hu

nd

red

seve

nty

-tw

o

20

. For

nu

mb

ers

20

a–2

0b

, se

lect

Tru

e o

r Fals

e.

20a.

4

2 −

(9

+ 6

), v

alu

e: 2

7

Tru

e

Fals

e

20b.

1

8 +

(2

2 −

4)

÷ 6

, va

lue: 6

Tru

e

Fals

e

21

. P

ete

r ra

n 3

mile

s a d

ay

for

17

days

. O

n t

he 1

8th

day,

Pete

r ra

n 5

mile

s.

Wri

te a

n e

xpre

ssio

n t

hat

matc

hes

the w

ord

s.

(3 ×

17)

+ 5

22

. S

ele

ct

oth

er

ways

to e

xpre

ss 1

04. M

ark

all

that

ap

ply

.

A

10

× 4

D

1

0,0

00

B

10

+ 4

E

1

0 +

10

+ 1

0 +

10

C

1,0

00

F

1

0 ×

10

× 1

0 ×

10

Chap

ter 1

Tes

tPa

ge 6

3,92

5

259

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 1

Tes

t1-50

Chap

ter 1

Tes

tPa

ge 5

14

. H

ecto

r h

as

36

action

fig

ure

s. H

e s

ep

ara

tes

his

action

fig

ure

s

into

4 e

qu

al g

rou

ps

to s

hare

with

his

fri

en

ds.

How

man

y action

fig

ure

s d

oes

each

fri

en

d g

et?

Par

t A

Use

th

e a

rray

to s

how

you

r an

swer.

Par

t B

Use

th

e m

ultip

lication

sen

ten

ce t

o c

om

ple

te t

he d

ivis

ion

sen

ten

ce.

4 ×

9

= 3

6

3

6 ÷

4 =

9

15

. M

arc

us

is m

akin

g d

inn

er

for

7 p

eop

le. M

arc

us

op

en

s 6

can

s of

sou

p. Each

can

is

14

ou

nces.

If

eve

ryon

e g

ets

th

e s

am

e a

mou

nt

of

sou

p, h

ow

mu

ch

sou

p w

ill e

ach

pers

on

get?

Use

nu

mb

ers

an

d w

ord

s to

exp

lain

you

r an

swer.

12 o

un

ces;

Po

ssib

le e

xpla

nat

ion

: Fir

st, I

mu

ltip

ly

6 3

14

5 8

4 to

fin

d t

he

tota

l nu

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Sample Level 3 Response

1-67 Chapter 1 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company







Student’s Name Date

Individual Record Form 1-71© Houghton Mifflin Harcourt Publishing Company

Chapter Resources

Item Standard Content Focus Personal Math Trainer

1 4.NBT.A.2 Write a multi-digit whole number using expanded form. 4.NBT.2

2 4.NBT.A.3 Round a whole number to a given place value. 4.NBT.3

3 4.NBT.B.4 Add multi-digit whole numbers. 4.NBT.4

4 4.NBT.B.4 Subtract multi-digit whole numbers. 4.NBT.4

5 4.NBT.B.5 Use a pattern and a basic fact to find a product. 4.NBT.5

6 4.NBT.B.5 Use a model to find a product. 4.NBT.5

7 4.NBT.B.5 Multiply a two-digit whole number by a one-digit whole number. 4.NBT.5

8 4.NBT.B.5 Multiply a four-digit whole number by a one-digit whole number. 4.NBT.5

9 4.OA.A.3 Use the order of operations to find the value of an expression. 4.OA.3

10 4.NBT.B.5 Use an area model to find a product. 4.NBT.5

11 4.NBT.B.6 Interpret a model of division with a remainder. 4.NBT.6

12 4.NBT.B.6 Apply the Distributive Property to division. 4.NBT.6

13 4.NBT.B.6 Divide a four-digit whole number by a one-digit whole number. 4.NBT.6

14 4.NBT.B.6 Solve a multi-step word problem. 4.NBT.6

15 4.OA.B.4 Identify prime numbers. 4.OA.4

16 4.OA.C.5 Interpret patterns with a two-operation rule. 4.OA.5

17 4.NF.A.1 Find an equivalent fraction. 4.NF.1

18 4.NF.A.1 Find a common denominator of two fractions. 4.NF.1

19 4.NF.A.2 Compare fractions using benchmarks. 4.NF.2

20 4.NF.B.3d Add fractions with like denominators. 4.NF.3d

21 4.NF.B.3d Subtract fractions with like denominators. 4.NF.3d

22 4.NF.B.3d Subtract fractions with like denominators. 4.NF.3d

23 4.NF.B.3c Add two mixed numbers with like denominators. 4.NF.3c

24 4.NF.B.3c Subtract two mixed numbers with like denominators. 4.NF.3c

25 4.NF.B.3d Add fractions with like denominators. 4.NF.3d

26 4.NF.B.4c Add three fractions with like denominators. 4.NF.4c

27 4.NF.B.4c Multiply a fraction by a whole number. 4.NF.4c

28 4.NF.B.4c Solve comparison problems involving multiplication with fractions. 4.NF.4c

29 4.NF.C.6 Write a mixed number as a decimal. 4.NF.6

Prerequisite Skills Inventory



Chapter Resources

Prerequisite Skills Inventory

Item Standard Content Focus Personal Math Trainer

30 4.NF.C.6 Write a mixed number as a decimal. 4.NF.6

31 4.NF.C.5 Write a decimal as a fraction with a denominator of 100. 4.NF.5

32 4.NF.C.7 Compare decimal values. 4.NF.7

33 4.G.A.2 Identify the properties of triangles. 4.G.2

34 4.G.A.1 Identify perpendicular, parallel, and intersecting lines. 4.G.1

35 4.G.A.2 Identify a quadrilateral given a figure. 4.G.2

36 4.MD.A.1 Use a model to convert between customary units of weight. 4.MD.1

37 4.MD.B.4 Interpret a line plot. 4.MD.4

38 4.MD.A.1 Covert metric units of length. 4.MD.1

39 4.MD.A.2 Convert a measurement given in mixed units. 4.MD.2

40 4.MD.A.3 Use a formula to find the perimeter of a rectangle. 4.MD.3



Chapter Resources

Beginning of Year/Middle of Year/End of Year Test

Item Lesson Standard Content Focus Intervene with Personal Math Trainer

1 3.4 5.NBT.A.4 Round a decimal to a given place. R—3.4 5.NBT.4

2 3.9 5.NBT.B.7 Subtract decimals to hundredths. R—3.9 5.NBT.7

3 3.8 5.NBT.B.7 Add decimals to hundredths. R—3.8 5.NBT.7

4 3.10 5.NBT.B.7 Find an unknown number in a decimal number pattern. R—3.10 5.NBT.7

5 6.3 5.NF.A.2 Estimate a sum by rounding fractions. R—6.3 5.NF.2

6 6.7 5.NF.A.1 Subtract mixed numbers. R—6.7 5.NF.1

7 6.9 5.NF.A.2 Solve multi-step word problems involving mixed numbers. R—6.9 5.NF.2

8 6.8 5.NF.A.1 Subtract fractions with different denominators. R—6.8 5.NF.1

9 6.4 5.NF.A.1 Find the least common denominator of two fractions. R—6.4 5.NF.1

10 9.2 5.G.A.1 Find an ordered pair on a coordinate grid. R—9.2 5.G.1

11 9.5 5.OA.B.3 Identify a rule for a number sequence. R—9.5 5.OA.3

12 9.7 5.OA.B.3 Identify a rule using a graph. R—9.7 5.OA.3

13 9.1 5.MD.B.2 Interpret data on a line plot. R—9.1 5.MD.2

14 9.6 5.OA.B.3 Identify and use a rule to solve a word problem. R—9.6 5.OA.3

15 11.3 5.G.B.3,5.G.B.4 Identify a quadrilateral given a figure. R—11.3 5.G.3,

5.G.4

16 11.9 5.MD.C.5a, 5.MD.C.5b Find the volume of a rectangular prism. R—11.9 5.MD.5a,

5.MD.5b

17 11.1 5.G.B.3 Describe a regular polygon. R—11.1 5.G.3

Key: R—Reteach



Chapter Resources


18 11.8 5.MD.C.5a, 5.MD.C.5b

Find a missing dimension given the volume of a rectangular prism. R—11.8 5.MD.5a,

5.MD.5b

19 2.5 5.NBT.B.6 Estimate a quotient. R—2.5 5.NBT.6

20 2.7 5.NF.B.3 Divide whole numbers and interpret the remainder. R—2.7 5.NF.3

21 2.9 5.NBT.B.6 Solve a word problem using division. R—2.9 5.NBT.6

22 2.6 5.NBT.B.6 Divide whole numbers and interpret the remainder. R—2.6 5.NBT.6

23 7.1 5.NF.B.4a Find part of a group by multiplying a fraction and a whole number. R—7.1 5.NF.4a

24 7.9 5.NF.B.6 Multiply two mixed numbers. R—7.9 5.NF.6

25 7.6 5.NF.B.4a, 5.NF.B.5b Multiply two fractions. R—7.6 5.NF.4a,

5.NF.5b

26 7.3 5.NF.B.4a Multiply a fraction and a whole number. R—7.3 5.NF.4a

27 7.9 5.NF.B.6 Multiply a mixed number and a fraction. R—7.9 5.NF.6

28 4.4 5.NBT.B.7 Multiply a whole number and a decimal. R—4.4 5.NBT.7

29 4.8 5.NBT.B.7 Multiply decimals to hundredths. R—4.8 5.NBT.7

30 4.1 5.NBT.A.2 Write the standard form of a number written as a decimal multiplied by a power of 10. R—4.1 5.NBT.2

31 4.3 5.NBT.B.7 Multiply a whole number and a decimal. R—4.3 5.NBT.7

32 8.4 5.NF.B.7c Divide a fraction by a whole number. R—8.4 5.NF.7c

33 8.3 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator. R—8.3 5.NF.3

34 8.5 5.NF.B.7a,5.NF.B.7b Write an equation for a story problem. R—8.5 5.NF.7a,

5.NF.7b

Key: R—Reteach




Chapter Resources


35 8.4 5.NF.B.7c Use a related multiplication expression to divide fractions. R—8.4 5.NF.7c

36 8.2 5.NF.B.7bUse the strategy make a diagram to solve problems involving division of a unit fraction by a whole number.

R—8.2 5.NF.7b

37 5.3 5.NBT.B.7 Estimate a quotient. R—5.3 5.NBT.7

38 5.1 5.NBT.A.2 Use a pattern to place a decimal point in a quotient. R—5.1 5.NBT.2

39 5.4 5.NBT.B.7 Divide a decimal by a whole number. R—5.4 5.NBT.7

40 5.6 5.NBT.B.7 Divide a decimal by a decimal. R—5.6 5.NBT.7

41 5.8 5.NBT.B.7 Use operations to solve problems involving decimals. R—5.8 5.NBT.7

42 1.2 5.NBT.A.1 Identify the value of a digit in a whole number. R—1.2 5.NBT.1

43 1.5 5.NBT.A.2 Use a basic fact and a power of 10 to find a product. R—1.5 5.NBT.2

44 1.6 5.NBT.B.5 Multiply a multi-digit whole number by a one-digit whole number. R—1.6 5.NBT.5

45 1.12 5.OA.A.1 Write a numerical expression with brackets and parentheses. R—1.12 5.OA.1

46 1.8 5.NBT.B.6 Write a related multiplication sentence for a division problem. R—1.8 5.NBT.6

47 10.1 5.MD.A.1 Convert customary units of length. R—10.1 5.MD.1

48 10.3 5.MD.A.1 Convert customary units of weight. R—10.3 5.MD.1

49 10.7 5.MD.A.1 Find elapsed time given a start time and end time. R—10.7 5.MD.1

50 10.5 5.MD.A.1 Convert metric units of length. R—10.5 5.MD.1

Key: R—Reteach




Chapter Resources

Item Lesson Standard Content Focus Intervene With

Personal Math Trainer

1, 5 1.3 5.OA.A.1 Use properties of operations. R—1.3 5.OA.1

2, 4 1.1 5.NBT.A.1 Describe place-value positions. R—1.1 5.NBT.1

3, 19 1.2 5.NBT.A.1 Read, write, and represent whole numbers. R—1.2 5.NBT.1

6 1.5 5.NBT.A.2 Recognize multiplication patterns. R—1.5 5.NBT.2

7, 18 1.6 5.NBT.B.5 Multiply by 1-digit numbers. R—1.6 5.NBT.5

8, 17 1.7 5.NBT.B.5 Multiply by 2-digit numbers. R—1.7 5.NBT.5

9, 11, 13, 20 1.11 5.OA.A.1 Evaluate numerical expressions. R—1.11 5.OA.1

10 1.12 5.OA.A.1 Evaluate with grouping symbols. R—1.12 5.OA.1

12, 21 1.10 5.OA.A.2 Write numerical expressions. R—1.10 5.OA.2

14, 16 1.8 5.NBT.B.6 Relate multiplication to division. R—1.8 5.NBT.6

15 1.9 5.NBT.B.6 Solve multiplication and division problems. R—1.9 5.NBT.6

22 1.4 5.NBT.A.2 Use exponents to show powers of 10. R—1.4 5.NBT.2

Key: R—Reteach

Chapter 1 Test

Documents

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