Objective To assess students’ progress on mathematical

content through the end of Unit 7.

638 Unit 7 Progress Check 7

Assessing Progress materials

Solve problems involving fractional parts of regions 7�1–7�5, 7�7, 1 4 9–11 24and collections; identify the ONE. 7�9–7�12[Number and Numeration Goal 2]

Rename tenths and hundredths as decimals. 7�8–7�12 3[Number and Numeration Goal 5]

Find equivalent fractions. 7�6–7�10, 7�12 2 1–3, 6[Number and Numeration Goal 5]

Compare and order fractions. 7�8–7�10, 7�12 3 1 4–8 18[Number and Numeration Goal 6]

Solve multidigit multiplication and division problems. 7�1–7�4, 7�6, 4 14 –17[Operations and Computation Goal 4] 7�8–7�12Add and subtract fractions. 7�3–7�6, 7�8, 5 20–24[Operations and Computation Goal 5] 7�9, 7�11Use ordered number pairs on a coordinate grid. 7�1, 7�3, 7�5 13[Measurement and Reference Frames Goal 4] 7�7, 7�9Use basic probability terms. 7�3, 7�6, 7�11, 2[Data and Chance Goal 3] 7�12Calculate expected probability. 7�3, 7�5–7�8, 6 12 19[Data and Chance Goal 4] 7�11, 7�12

Building Background for Unit 8 materials� Math Journal 2, p. 218� Study Link Masters (Math Masters, pp. 243–246)

Math Boxes 7�13 previews and practices skills for Unit 8.The Unit 8 Family Letter introduces families to Unit 8 topics and terms.

2

SELF ORAL/SLATE WRITTENPART A PART B

CONTENT ASSESSED LESSON(S)ASSESSMENT ITEMS

� Study Link 7�12� Assessment Masters (Assessment Handbook,

pp. 184–188)� slate; straightedge � pattern blocks; colored pencils (optional)

Progress Check 7 is a cumulative assessment of concepts and skillstaught in Unit 7 and in previous units.

See the Appendix for a complete list of Grade 4 Goals.

1

Technology Technology Technology Additional InformationSee Assessment Handbook, pages 102–109 for additional assessment information. For assessment checklists, see pages 270–273.

Technology Assessment Management System

Progress Check 7See the iTLG.

� Math Message Follow-Up(Self Assessment, Assessment Handbook, p. 184)

The Self Assessment offers students the opportunity toreflect upon their progress.

� Oral and Slate AssessmentsProblems 2 and 3 provide summative information and can be used for grading purposes. Problems 1 and 4 provide formativeinformation that can be useful in planning future instruction.

Oral Assessment1. Write pairs of fractions on the board. Have students identify

the greater fraction and explain how they know it is greater.Suggestions:● �

25� and �2

20� �

25�; The fractions have like numerators. The smaller

the denominator is, the larger the fraction is.● �1

42� and �1

92� �1

92�; The fractions have like denominators. The

larger the numerator is, the larger the fraction is.

● �152� and �1

96� �1

96�; �1

52� is less than �

12�, and �1

96� is greater than �

12�.

2. Ask students to use probability language to describe the likelihood of the event. Suggestions:● I will flip a coin, and it will land on heads. 50-50 chance● I will flip a coin, and it will land on heads or tails. certain● I will roll a six-sided die, and it will land on a number less

than 6. very likely● I will roll a six-sided die, and it will land on 23. impossible● I will roll a six-sided die, and it will land on a number less

than 2. unlikely

WHOLE-CLASS

ACTIVITY

INDEPENDENT

ACTIVITY

1 Assessing Progress

LESSON

7�13 Written Assessment

Name Date Time

ProgressCheck 7

Part A

For each fraction, write two equivalent fractions.

1. �12� , 2. �

13� , 3. �

68� ,

Write , , or = to make each number sentence true.

4. �16� �

18� 5. �

1112� �1

52� 6. �

23� �1

82�

Write each set of fractions in order from smallest to largest.

7. �120�, �1

90�, �1

70�, �1

10�, �1

50�

smallest largest

8. �17�, �

12�, �

15�, �1

10�, �

13�

smallest largest

Use pattern blocks to help solve Problems 9 and 10.

9. If the red trapezoid is the whole, what fraction of the whole is

a. 1 green triangle? b. 1 blue rhombus?

10. Suppose the green triangle is �12� of the whole. Which pattern block is

a. 1 whole? b. 1�12� wholes?

11. Liam had 9 quarters. He spent �13� of them on video games.

a. How many quarters did he spend? quarters

b. How many quarters does he have left? quarters

c. How much money does he have left? $ .

Sample answers:

�23�

�17� �

12��

13�

�13�

�15�

�120��1

10� �1

50� �1

70� �1

90�

�110�

�

�17050��

34��1

55��

26��

36��

24�

rhombus trapezoid

36

501

Assessment Handbook, p. 185

Assessment Master

Lesson 7�13 639

Getting Started

Study Link 7�12 Follow-Up Have small groups compare the results of thepenny toss experiment. Ask volunteers to sharetheir answers for Problem 5. Have students indicate thumbs-up if they agree.

Math Message • Self Assessment Complete the Self Assessment (Assessment Handbook, page 184).

LESSON

7�13

Name Date Time

Self Assessment ProgressCheck 7

Think about each skill listed below. Assess your own progress by checking the most appropriate box.

1. Solve “fraction-of”problems like these:

�14� of 8

�45� of 30

2. Find equivalentfractions.

3. Compare fractionslike these:

�14� and �1

10�

�25� and �

29�

4. Divide multidigitnumbers like these:492 / 7684 / 5

5. Add fractions likethese:

�16� � �

26�

�13� � �

16�

�12� � �

13�

6. Use a fraction todescribe theprobability of anevent.

Skills I can do this on I can do this on I can do this ifmy own and explain my own. I get help or look

how to do it. at an example.

Assessment Handbook, p. 184

Assessment Master

640 Unit 7 Progress Check 7

Name Date Time

Written Assessment continuedLESSON

7�13

Part B

18. Which fraction is larger: �67� or �1

90�? Explain how you know.

19. Make a spinner.

a. Color it so that the paper clip will land on red about �12� of the time and on blue about �

13� of the time.

Color the rest yellow.

b. About what fraction of the time should you expect the paper clip to land on yellow?

Add or subtract. Use pattern blocks to help you.

20. �16� � �

46� � 21. �

16� � �

13� �

22. �56� � �

36� � 23. �

23� � �

16� �

24. It took Denise �34

� of an hour to drive from Zion to Platt and �12

� hour to drive from Platt to Rome. To figure out her total driving time, Denise wrote thefollowing number model: �

34

� � �12

� � �46

�.

Do you agree that it took her about �46� of an hour? Explain.

�190�

Sample answer: �190� is only �1

10� away from 1, and �

67� is �

17� away

from 1. �110� is a smaller fraction than �

17�, so �1

90� is closer to 1

than �67� is. Also, �

67� is about 0.86 as a decimal, and �1

90� is 0.9.

0.9 is greater than 0.86, so �190� is greater than �

67�.

Sample answer: She added the denominators, which is notcorrect. She should have changed �

12� to �

24�, and then added the

numerators. The correct answer is �34� � �

24� � �

54�, or 1�

14� hours. She

should have noticed that her answer should be greater than 1hour since she drove �

12� hour plus more than �

12� hour ��

34� hour� .

�16�

redblue

yellow

no

Sample answer:

�26�, or �

13�

�36�, or �

12�

�36�, or �

12�

�56�

Assessment Handbook, p. 187

Assessment Master

Name Date Time

Written Assessment continuedLESSON

7�13

12. A bag contains 13. Plot and label each point on thecoordinate grid.

A (4,1)

B (3,4)

C (1,5)

D (2,2)

E (2,5)

Multiply and divide. Use paper-and-pencil algorithms of your choice.

14. 47 º 23 � 15. � 97 º 31

16. 93 � 4 � 17. 7�5�4�2� �

1

2

4

3

5

6

01 2 3 4 5 60

DA

C EB

1,081

77 R3, or 77�37�23 R1, or 23�

14�

3,007

You put your hand in the bagand pull out a block. About whatfraction of the time would youexpect to get a yellow block?

2 blue blocks,3 purple blocks,4 green blocks, and1 yellow block.

�110�

Assessment Handbook, p. 186

Assessment MasterSlate Assessment3. Write fractions with denominators of 10 or 100 on the board,

and have students write the equivalent decimals. Then writedecimals on the board, and ask students to write an equivalentfraction for each. Do not insist that they write fractions in simplest form. Suggestions:

● �180� 0.8 ● �1

3000� 0.30 ● �1

4060� 0.46

● 0.98 �19080� ● 0.7 �1

70� ● 0.20 �1

2000�

4. Pose “fraction-of ” problems. Suggestions:● What is �

14� of 8? 2 �

34� of 8? 6

● What is �15� of 30? 6 �

45� of 30? 24

● What is �13� of 18? 6 �

23� of 18? 12

● What is �16� of 12? 2 �

56� of 12? 10

� Written Assessment(Assessment Handbook, pp. 185–187)

Part A Recognizing Student AchievementProblems 1–17 provide summative information and may be usedfor grading purposes.

Problem(s) Description

1–3 Write equivalent fractions.

4–6 Compare fractions.

7, 8 Order fractions.

9–11 Name fractions of regions or collections; find the ONE.

12 Calculate expected probability of an event.

13 Plot coordinates on a grid.

14, 15 Multiply multidigit numbers.

16, 17 Divide multidigit numbers by one-digit divisors.

Part B Informing InstructionProblems 18–24 provide formative information that can be used in planning future instruction.

Problem(s) Description

18 Explain a strategy to compare fractions.

19 Create a spinner, and predict the probability of an event.

20–23 Add and subtract fractions.

24 Solve a fraction number story.

INDEPENDENT

ACTIVITY

� Open Response(Assessment Handbook, p. 188)

Queen Arlene’s DilemmaThe open response item requires students to applyconcepts and skills from Unit 7 to solve a multistepproblem. See Assessment Handbook, pages 105–109 for rubrics and students’ work samples for this problem.

� Math Boxes 7�13(Math Journal 2, p. 218)

Mixed Practice This Math Boxes page previews Unit 8 content.

� Study Link 7�13:Unit 8 Family Letter(Math Masters, pp. 243–246)

Home Connection The Unit 8 Family Letter providesparents and guardians with information and activitiesrelated to Unit 8 topics.

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

2 Building Background for Unit 8

INDEPENDENT

ACTIVITY

Name Date Time

LESSON

7�13 Open Response ProgressCheck 7

Queen Arlene’s Dilemma

1. Queen Arlene has a problem. She wants to divide her land among her 3 children. She wants her oldest daughter to get �

12� of the land and her younger

daughters to each get �13� of the land. Can she do it? Explain your answer.

2. After thinking about it, Queen Arlene decides to keep �12� of her land and have

her 3 children divide the other �12�. She still wants the oldest daughter to get

more land than her sisters. Think of a way to use fractions to divide the land.Explain your answer.

See the Assessment Handbook for rubrics andstudents’ work samples.

Assessment Handbook, p. 188

Assessment Master

Lesson 7�13 641

218

Math Boxes LESSON

7�13

Date Time

4. Tell if each of these is closest to 1 inch, 1 foot, or 1 yard.

a. the width of a door

b. the width of your ankle

c. the length of your little finger

d. the length of your forearm 1 foot

1 inch

1 inch1 yard

1. Measure the length and width of your deskto the nearest half-inch. Find its perimeter.

a. Length = inches

b. Width = inches

c. Perimeter = inches

3. If 1 centimeter on a map represents 20 kilometers, then

a. 8 cm represent km.

b. 3.5 cm represent km.

c. cm represent 30 km.

d. cm represent 50 km.

e. cm represents 10 km.

70160

2. Find the area of the figure.

� 1 square centimeter

Area = square cm10

5. Complete.

a. 26 in. � ft in.

b. 57 in. � ft in.

c. 9 ft � yd

d. 16 ft � yd ft

e. 8 yd � ft2415

39422

6. Compare.

a. 1 day is times as long as 12 hours.

b. 3 years is times as long as 6 months.

c. 12 cm is times as long as 2 mm.

d. 1 m is times as long as 20 cm.

e. 3 gallons is times as much as 2 cups.

24560

62

Answers vary.131 133

130145

129 315

1.52.50.5

Math Journal 2, p. 218

Student Page

STUDY LINK

7�13 Unit 8: Family Letter

Name Date Time

Perimeter and AreaIn previous grades, your child studied the perimeter (distance around) and the area(amount of surface) of various geometric figures. This next unit will extend your child’sunderstanding of geometry by developing and applying formulas for the areas of figuressuch as rectangles, parallelograms, and triangles.

Area of a Rectangle Area of a Parallelogram

Area � base � height (or length � width) Area � base � height

A � b � h (or l � w) A � b � h

Area of a Triangle

Area � �12

� of (base � height)

A � �12

� � b � h

Students will learn how to make scale drawings and apply their knowledge of perimeter,area, and scale drawing by analyzing the arrangement of the appliances in their kitchensand the furniture in their bedrooms.

Students will also calculate the area of the skin that covers their entire body. A rule ofthumb is that the area of a person’s skin is about 100 times the area of one side of thatperson’s hand. Ask your child to show you how to calculate the area of your own skin.

The World Tour will continue. Students will examine how geographical areas aremeasured and the difficulties in making accurate measurements. They will compare areasfor South American countries by using division to calculate the ratio of areas.

Please keep this Family Letter for reference as your child works through Unit 8.

base (length)

heig

ht (w

idth

)

base

heig

ht

base

heig

ht

Math Masters, pp. 243–246

Study Link Masters