Lesson 12�7 941

The End-of-Year Assessment in the Assessment Handbook is a written assessment that you may use to assess students’ proficiency with Grade-Level Goals.

Input student data from Progress Check 12 and the End-of-Year Assessment into the Assessment Management Spreadsheets.

Materials � Study Link 12�6

� Assessment Handbook, pp. 142 –149, 211–215, 227, and 290–293

� End-of-Year Assessment (Assessment Handbook, pp. 150, 151, 234–241, and 244–245)

� slate; calculator

Find whole-number factors of numbers. [Number and Numeration Goal 3]

12�1,12�3–12�5

1 4, 5

Compare and order fractions. [Number and Numeration Goal 6]

12�1, 12�5 2 11

Compare and order integers. [Number and Numeration Goal 6]

12�1, 12�3 6, 7

Add and subtract signed numbers. [Operations and Computation Goal 2]

12�2,12�4–12�6

3, 4 1

Add and subtract decimals. [Operations and Computation Goal 2]

12�2, 12�4�

Solve problems involving division. [Operations and Computation Goal 4]

12�2–12�6�

Use scaling to model rate situations. [Operations and Computation Goal 7]

12�2–12�6 5 3, 4 1–3 13, 14�

Analyze and interpret data. [Data and Chance Goal 2]

12�3–12�6 12

Find the volumes of rectangular prisms. [Measurement and Reference Frames Goal 2]

12�1, 12�3,12�5

9

Convert among units of capacity. [Measurement and Reference Frames Goal 3]

12�2,12�4–12�6

6 2 8

Solve open sentences. [Patterns, Functions, and Algebra Goal 2]

12�2, 12�4,12�6

7 10

ASSESSMENT ITEMSSELF ORAL/SLA OPEN

RESPONSETE WRITTEN

CONTENT ASSESSED LESSON(S)

PART BPART A

Math Boxes 12�7

Study Link 12�7: End-of-Year Family Letter

Materials � Math Journal 2, p. 328

� Math Masters, pp. 354–357

Looking Back: Cumulative AssessmentL

Looking Ahead: Preparing for Grade 5L

Objective To assess students’ progress on mathematical

content through the end of Unit 12.

Progress Check 12�

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942 Unit 12 Progress Check 12

LESSON

12�7

Name Date Time

Self Assessment Progress Check 12

Think about each skill listed below. Assess your own progress by checking

the most appropriate box.

Skills I can do this on I can do this on I can do this if my own and explain my own. I get help or look how to do it. at an example.

1. Find factors and

factor pairs.

2. Compare and order

positive and negative

fractions.

3. Add positive and

negative numbers.

4. Subtract positive and

negative numbers.

5. Solve rate problems.

6. Convert among units

of capacity.

7. Solve open

sentences.

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Assessment Handbook, p. 211

Assessment Master

1 Looking Back: Cumulative Assessment

� Math Message Follow-Up INDEPENDENTACTIVITY

(Self Assessment, Assessment Handbook, p. 211)

The Self Assessment offers students the opportunity to reflect upon their progress.

� Oral and Slate Assessments WHOLE-CLASS ACTIVITY

Problems 2, 3, and 4 provide summative information and can be used for grading purposes. Problem 1 provides formative information.

Oral Assessment 1. Pose addition and subtraction problems involving positive

and negative integers. Have students explain their solution strategies. Suggestions:

● 6 + (–8) = –2

● 15 – (–12) = 27

● 20 + (–15) = 5

● –10 – (12) = –22

● –7 – (–9) = 2

● –12 + (–18) = –30

● –20 – (14) = –34

● –16 + 15 = –1

2. Have students show “thumbs-up” if the two quantities are equivalent and “thumbs-down” if they are not. Suggestions:

● 4 quarts and 1 gallon up

● 1 pint and 3 cups down

● 1 liter and 1,000 mL up

● 3 pints and 1 1 _ 2 quarts up

● 3 liters and 300 mL down

● 2 1 _ 2 gallons and 10 quarts up

Getting Started

Study Link 12�6 Follow-Up Briefly review students’ answers.

Math Message • Self AssessmentComplete the Self Assessment (Assessment Handbook, page 211).

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Slate Assessment 3. Pose rate problems. Encourage students to use rate tables if

necessary. Suggestions:

● If 1 pound of apples costs 40 cents, what is the cost of 5 pounds? $2.00

● Roberto earns $3 per hour babysitting. How much does he earn in 4 hours? $12 In 2 1 _ 2 hours? $7.50

● The Hole-in-One shop sells used golf balls for $2.40 per dozen. What is the cost of 1 golf ball? $0.20 Of 4 golf balls? $0.80 Of 1 _ 2 -dozen golf balls? $1.20

● Mitchell walks at the rate of about 3 miles per hour. At that rate, what distance will he walk in 20 minutes? About 1 mile In 1 _ 2 hour? About 1 1 _ 2 miles In 10 minutes? About 1 _ 2 mile In 3 hours? About 9 miles In 1 1 _ 3 hours? About 4 miles

● Caroline reads about 25 pages per hour. About how many pages could she read in 3 hours? 75 pages In 5 hours? 125 pages In 1 1 _ 2 hours? 37 1 _ 2 pages

● Carlos eats about 3 servings of fruit per day. About how many servings is that in 4 days? 12 servings In 1 week? 21 servings In 4 weeks? 84 servings

● Hamburgers cost 70 cents each. What is the cost of 2 hamburgers? $1.40 Of 4 hamburgers? $2.80 Of 1 dozen hamburgers? $8.40

4. Pose problems involving unit prices. Encourage students to use rate tables if necessary. Have them round their answers to the nearest tenth of a cent. Suggestions:

● A 6-pack of cola costs $2.40. What is the price per can? 40 cents

● A box of 8 pieces of chalk costs 64 cents. What is the cost of 1 piece of chalk? 8 cents

● A 46-ounce can of pineapple juice costs $1.75. What is the price per ounce? 3.8 cents

● A 6-ounce can of tomato paste costs 34 cents. What is the price per ounce? 5.7 cents

● An 8-pack of yogurt costs $4.00. What is the cost per container? $0.50

● Twelve bars of soap cost $3.60. What is the price per bar? $0.30

● A 15-ounce can of green beans costs 90 cents. What is the price per ounce? 6 cents

Lesson 12�7 943

1. The Davis family drove 280 miles to visit relatives.

It took 5 hours. At that rate, about how many miles

did the Davises drive in 3 hours? About miles

Fill in the rate table, if needed.

2. Jan earned $19.50 last week for mowing 3 lawns.

At that rate, what would Jan earn for mowing 5 lawns?

Fill in the rate table, if needed.

3. Tina works 7 hours per day, 5 days per week. She earns $56.00 per day.

a. How much does she earn per hour?

b. How much does she earn per week?

4. List the factor pairs of 40.

and and

and and

5. Name all the factors of 64.

LESSON

12�7 Written Assessment

Name Date Time

Progress Check 12

Part A

$32.50

$8

$280

1 4 10

2 5 8

40

20

168

Miles 56 112 168 224 280

Hours 1 2 3 4 5

Dollars 6.50 13 19.50 26 32.50

Lawns 1 2 3 4 5

1, 2, 4, 8, 16, 32, 64

Assessment Handbook, p. 212

Assessment Master

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944 Unit 12 Progress Check 12

Name Date Time

Written Assessment continuedLESSON

12�7

6. Insert �, �, or � to make a true number sentence.

a. �25 22 b. 0 �2

c. �10 �100 d. �82 �64

7. Order the numbers from smallest to largest.

�30, 4, 15, �2, 17, �8

smallest largest

8. Use the diagram to help you solve the problems.

a. c � 2 gal

b. 10 qt � gal qt

c. 22 c � qt pt

d. 13 pt � qt pt

e. 15 qt � c

9. Calculate the volume.

a. b.

Number model: Number model:

Volume � cm3 Volume � cm3

10. Solve the open sentences.

a. 0.930 � 3.59 � y y � b. 51.9 � b � 69.07 b �

c. 1.89 � 0.206 � q q � d. 1.46 � k � 0.028 k �

�

��

�

�30 �8 �2 4 15 17

32

2

(4 � 2) � 5 � 40 (7 � 3) � 2 � 42

2

1

1

5

6

60

40

4.52

1.684 1.488

17.17

42

5 c

m

4 cm 2 cm

2 c

m

7 cm 3 cm

Assessment Handbook, p. 213

Assessment Master

� Written Assessment INDEPENDENTACTIVITY

(Assessment Handbook, pp. 212–214)

Part A Recognizing Student AchievementProblems 1–10 provide summative information and may be used for grading purposes.

Problem(s) Description

1–3 Solve rate problems.

4, 5 Find factors and factor pairs.

6 Compare integers.

7 Order integers.

8 Find equivalent capacities.

9 Calculate volume.

10 Solve open sentences.

Part B Informing InstructionProblems 11–14 provide formative information.

Problem Description

11 Compare and order fractions.

12 Determine the reasonableness of a statistic.

13 Determine which box of cereal is the better buy.

14 Make informed consumer decisions.

Name Date Time

Written Assessment continuedLESSON

12�7

Part B

smallest

smallest

largest

largest

11. Order the fractions from smallest to largest.

a. ��1

7

0�, �

1

7�, ��

7

7�, �

4

7�, ��

5

7�

b. �1

6

2�, ��

1

3�, �

2

9�, �

1

2

5

0�, �

4

4�

12. It was reported that on New Year’s Day in 1907, Theodore Roosevelt shook

hands with 8,513 people. Does this seem reasonable? Explain your answer.

13. A store charges $1.58 for a 20-ounce box of Puff Flakes cereal and

$1.72 for a 24-ounce box of the same cereal. Which is the better buy?

Explain why.

��170� ��

77

� ��57

� �17

� �47

�

��13

� �29

� �162� �

1250� �

44

�

14. Joey goes to Doreen’s Delicious

Doughnuts to buy doughnuts for

the class party. What is the least

amount of money he will have to

pay for 30 doughnuts?

Explain.

$12.10

Sample answer:

Sample answer: Yes. If he shook hands for 18 hours that

day, it would be about 8 hands per minute. That’s a lot of

hands, but it seems like a president might do that.

At Doreen’s the bigger the package, the cheaper the

doughnut. Joey should buy two dozens for $4.80 per

dozen and one half-dozen for $2.50, for a total of

$4.80 � $4.80 � $2.50 � $12.10.

Sample answer: The cereal in the 20-oz box costs 7.9

cents per ounce, while the same cereal in the 24-oz box

costs 7.17 cents per ounce.

the 24-oz box

Assessment Handbook, p. 214

Assessment MasterName Date Time

LESSON

12�7 Open Response Progress Check 12

Buying Cookies

Raheem and India volunteered to buy cookies for the class party. They wanted at least

4 different kinds of cookies, and they wanted to spend as little money as possible. They

decided that 3 pounds of cookies would be enough. When they went to the store, they

saw these prices for packages of cookies:

mint creams . . . . . . . . . . . . . . . .$2.79/lb chocolate chip . . . . . . . . . .$2.39/12 oz

fudge marshmallow . . . . . . . . . . $1.69/12 oz oatmeal . . . . . . . . . . . . . . $2.03/17 oz

sugar wafers . . . . . . . . . . . . . . . $2.99/8 oz windmill . . . . . . . . . . . . . . $2.59/lb

vanilla wafers . . . . . . . . . . . . . . $1.39/11 oz ginger snaps . . . . . . . . . . $0.60/8 oz

1. What 4 packages of cookies would you recommend they buy so that they have a total

of about 3 pounds and they spend as little money as possible? Show all of your work,

and explain how you found your answer. Hint: 1 pound = 16 ounces

2. If they follow your recommendations, how much money will they spend on cookies?

Show your work.

3. About what is the cost per pound of the 3 pounds of cookies you selected?

Show your work.

See the Assessment Handbook for rubricsand students’ work samples.

Assessment Handbook, p. 215

Assessment Master

Use the checklists on pages 291 and

293 of the Assessment Handbook to

record results. Then input the data

into the Assessment Management

Spreadsheets to keep an ongoing

record of students’ progress toward

Grade-Level Goals.

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� Open Response INDEPENDENTACTIVITY

(Assessment Handbook, p. 215)

Buying CookiesThe open-response item requires students to apply concepts and skills from Unit 12 to solve a multistep problem. See Assessment Handbook, pages 145–149 for rubrics and students’ work samples for this problem.

� End-of-Year Assessment INDEPENDENTACTIVITY

(Assessment Handbook, pp. 150, 151, and 234–241)

The End-of-Year Assessment (Assessment Handbook, pages 234–241) provides an additional assessment opportunity that you may use as part of your balanced assessment plan. This assessment covers many of the important concepts and skills presented in Fourth Grade Everyday Mathematics. It should be used along with ongoing and periodic assessments. Please see pages 150 and 151 in the Assessment Handbook for further information.

2 Looking Ahead: Preparing for Grade 5

� Math Boxes 12�7 INDEPENDENTACTIVITY

(Math Journal 2, p. 328)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 12-5.

� Study Link 12�7: INDEPENDENTACTIVITY

End-of-Year Family Letter(Math Masters, pp. 354–357)

Home Connection The End-of-Year Family Letter thanks family members for their participation in Fourth Grade Everyday Mathematics, suggests activities that can be

done at home during the vacation, and provides a preview of Fifth Grade Everyday Mathematics.

STUDY LINK

12�7 Family Letter

py

gg

p

Name Date Time

Congratulations!By completing Fourth Grade Everyday Mathematics, your child has accomplished a great deal. Thank you for all of your support.

This Family Letter is a resource to use throughout your child’s vacation. It includes an extended list of Do-Anytime Activities, directions for games that can be played at home, a list of mathematics-related books to check out over vacation, and a sneak preview of what your child will be learning in Fifth Grade Everyday Mathematics. Enjoy the vacation!

Do-Anytime ActivitiesMathematics means more when it is rooted in real-life situations. To help your child review many of the concepts he or she has learned in fourth grade, we suggest the following activities for you and your child to do together over vacation. These activities will help your child build on the skills he or she has learned this year and help prepare him or her for Fifth Grade Everyday Mathematics.

1. Have your child practice any multiplication and division facts that he or she has not yet mastered. Include some quick drills.

2. Provide items for your child to measure. Have your child use personal references, as well as U.S. customary and metric measuring tools.

3. Use newspapers and magazines as sources of numbers, graphs, and tables that your child may read and discuss.

4. Have your child practice multidigit multiplication and divisionusing the algorithms that he or she is most comfortable with.

5. Ask your child to look at advertisements and find the sale prices of items using the original prices and rates of discount or find rates of discount using original prices and sale prices. Have your child use a calculator and calculate unit prices to determine best or better buys.

6. Continue the World Tour by reading about other countries.

Ever

yd

ay Mathematics

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Math Masters, pp. 354–357

Study Link Masters

Lesson 12�7 945

Math Boxes LESSON

12�7

Date Time

4. Subtract.

a. -$75 - (+$25) =

b. -$45 - (-$30) =

c. -$60 - (+$60) =

d. $55 - (-$25) =

e. $300 - (-$100) =

1. Multiply. Show your work.

79 ∗ 405 =

2. a. Complete the table.

3. It is estimated that in an average

lifetime of 75 years, a person takes

about 50,000 trips in a car.

a. At that rate, about how many times a

day would a person ride in a car?

times

b. Does this number make sense to you?

31,995

b. How many inches are in 11 feet?

inches132

2

yes

-$100-$15-$120

$80

$400

5. Calculate the volume.

Number model:

Volume =

cm3

6. A 10-ounce can of peas costs $0.55.

A 16-ounce can of peas costs $1.19.

a. What is the price per ounce for each

can? (Round to the nearest cent.)

10-oz can:

16-oz can:

b. Which can of peas is the better buy?

5.5 cm

12 cm

3 cm

198

$0.06

$0.07

10-oz can

18 19

47 60

138 47

47

(12 ∗ 5.5) ∗ 3 = 198

10812 24

16 27

Number of Inches 144 192 324

Number of Feet

1 2 9 12

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Math Journal 2, p. 328

Student Page

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Copyright

© W

right

Gro

up/M

cG

raw

-Hill

Assessment Masters 211

LESSON

12�7

Name Date Time

Self Assessment Progress Check 12

Think about each skill listed below. Assess your own progress by checking

the most appropriate box.

Skills I can do this on I can do this on I can do this if my own and explain my own. I get help or look how to do it. at an example.

1. Find factors and

factor pairs.

2. Compare and order

positive and negative

fractions.

3. Add positive and

negative numbers.

4. Subtract positive and

negative numbers.

5. Solve rate problems.

6. Convert among units

of capacity.

7. Solve open

sentences.

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