progress check 6 - everyday math · pdf fileinput student data from progress check 6 and the...

434 Unit 6 Progress Check 6

The Mid-Year Assessment in the Assessment Handbook is a written assessment that you may use to determine how students are progressing toward a range of Grade-Level Goals.

Input student data from Progress Check 6 and the Mid-Year Assessment into the Assessment Management Spreadsheets.

Materials � Study Link 6�10

� Assessment Handbook, pp. 92–99, 180–184, 221, and 266–269

� Mid-Year Assessment (Assessment Handbook, pp. 228–233, 242, and 243)

� slate

Identify place value in numbers to billions. [Number and Numeration Goal 1]

2

Solve problems involving percent. [Number and Numeration Goal 2]

6�5 20b–20d

Convert among fractions, decimals, and percents. [Number and Numeration Goal 5]

6�5, 6�6 7 3, 4 22

Find common denominators. [Number and Numeration Goal 5]

6�9, 6�10 4 14, 15 21

Use paper-and-pencil algorithms to solve problems involving whole numbers. [Operations and Computation Goals 1 and 3]

�

Add and subtract fractions with like denominators. [Operations and Computation Goal 4]

6�8–6�10 5 6, 8 19c

Add and subtract fractions with unlike denominators. [Operations and Computation Goal 4]

6�8–6�10 6 7, 9–13 19b

Use benchmarks to estimate sums and differences. [Operations and Computation Goal 6]

6�8–6�10 1

Construct stem-and-leaf plots. [Data and Chance Goal 1]

6�3, 6�4, 6�6 1, 2 18

Identify and use data landmarks; interpret data. [Data and Chance Goal 2]

6�1–6�3, 6�5–6�7

1–5a, 16 17, 20a�

Understand how sample size affects results. [Data and Chance Goal 2]

6�5, 6�6 3 5b, 5c 20e

Measure to the nearest 1

_ 8 of an inch.

[Measurement and Reference Frames Goal 1]

6�2, 6�3 19a

ASSESSMENT ITEMSSELF ORAL/SLA OPEN

RESPONSETE WRITTEN

CONTENT ASSESSED LESSON(S)

PART BPART A

Math Boxes 6�11

Study Link 6�11: Unit 7 Family Letter

Materials � Math Journal 1, p. 204

� Math Masters, pp. 183–186

Looking Back: Cumulative AssessmentL

Looking Ahead: Preparing for Unit 7L

Objective To assess students’ progress on mathematical

content through the end of Unit 6.

Oc

Progress Check 6��

434_EMCS_T_TLG1_G5_U06_L11_576825.indd 434434_EMCS_T_TLG1_G5_U06_L11_576825.indd 434 2/14/11 1:36 PM2/14/11 1:36 PM

Name Date Time

LESSON

6�11 Self Assessment Progress Check 6

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

the most appropriate box.

1. Read stem-

and-leaf plots.

2. Make stem-

and-leaf plots.

3. Explain how

sample size

affects results.

4. Find common

denominators.

5. Add and subtract

fractions with like

denominators.

6. Add and subtract

fractions with unlike

denominators.

7. Convert between

fractions, decimals,

and percents.

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

how to do it. at an example.

Assessment Handbook, p. 180

Assessment Master

Lesson 6�11 435

Getting Started

1 Looking Back: Cumulative Assessment

▶ Math Message Follow-Up

INDEPENDENT ACTIVITY

(Self Assessment, Assessment Handbook, p. 180)

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

▶ Oral and Slate Assessments SMALL-GROUP

ACTIVITY

Problems 1 and 2 provide summative information and can be used for grading purposes. Problems 3 and 4 provide formative information that can be useful in planning future instruction.

Oral Assessment 1. Decide if the sum or difference for each fraction expression

is closest to 0, 1 _ 2 , or 1.

● 3 _ 8 + 2 _ 8 1 _ 2 ● 3 _ 19 + 8 _ 9 1

● 1 _ 5 + 1 _ 4 1 _ 2 ● 1 _ 12 + 1 _ 9 0

● 8 _ 8 - 1 _ 9 1 ● 3 _ 4 - 1 _ 5 1 _ 2

2. Round the following numbers to the indicated place value:

● 489 to the nearest ten 490

● 608 to the nearest ten 610

● 23,605 to the nearest hundred 23,600

● 18.27 to the nearest tenth 18.3

● 200.73 to the nearest whole number 201

Slate Assessment 3. Write the decimal and percent for each fraction:

● 2 _ 3 0. ⎯ 6 ; 66 2 _ 3 % ● 3 _ 10 0.3; 30% ● 7 _ 25 0.28; 28%

4. Rename as improper fractions:

● 2 3 _ 7 17 _ 7 ● 3 8 _ 6 26 _ 6 , or 13 _ 3 ● 4 1 _ 2 9 _ 2

Study Link 6�10 Follow-UpBriefly review students’ answers.

Math Message • Self AssessmentComplete the Self Assessment (Assessment Handbook, p. 180).

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Name Date Time

LESSON

6�11 Written Assessment Progress Check 6

Part A

Fill in the ovals to match the words to their definitions.

5. Sonia asked seven girls in her fifth-grade class how many CDs they own. Here are the

results of her survey: 2 0 6 5 7 5 1

a. What was the median number of CDs owned?

b. Sonia concluded: The typical fifth grader owns about 5 CDs.

Do you agree with her conclusion? Explain.

c. Describe two ways Sonia could improve her survey.

6. �45

� � �25

� � 7. 1 � �34

� � 8. �58

� � �38

� � 9. �196� � �

28

� �

10. 11. 12. 13. �23

�

� �34

�

�56

�

� �38

�

�23

�

� �25

�

�78

�

� �12

�

1. Median

smallest value

largest value

most frequent

value

middle value

2. Maximum

smallest value

largest value

most frequent

value

middle value

3. Mode

smallest value

largest value

most frequent

value

middle value

4. Minimum

smallest value

largest value

most frequent

value

middle value

Answers vary.

Sample answers:Ask more students. Ask boys and girls.

5 CDs

14. Circle the fraction pair represented by the drawing below.

�125� and �

35

� �53

� and �95

� �23

� and �34

� �145� and �

125�

�1165�, or �

1172�, or

�65

�, or 1�15

� �14

� �28

�, or �14

� �1136�

�38

� 1�115� �

1214� 1�

152�


Assessment Master

Written Assessment continuedLESSON

6�11

Name Date Time

15. Write a pair of fractions with common denominators for the

pictures in Problem 14.

16. David was writing a report on sleep and dreams. He gave a survey to the

21 students in his class. The following were three of the questions:

A. About how many hours do you sleep each night?

B. About how many dreams do you remember having in an average week?

C. What time do you usually get up on a school day?

The graphs below show the answers to two of these questions. Match the questions

with their graphs. (Write A, B, or C under each graph.)

17. Circle each stem-and-leaf plot with a median of 24. Put an X through each stem-and-

leaf plot with a mode of 28. (There may be more than one.)

�182� �

192�

7 8 9 10 11

xx xx

xxxxx

xx

x

xx

x

xx

xx

xx

0 1 2 3 4 5 6

xx

xxxx

xx

x

xx

xxxxx

xxxxx

A B

Stems Leaves(10s) (1s)

1 3 4 7

2 0 2 4 4 4 4 8

3 0


1 5 6 7

2 3 3 4 8 8 8 9

3 0


1 8 9

2 3 4 8 8 8 9 9

3 0 1

Part B

Stems Leaves(100s and 10s) (1s)

12 8 6 0

13 5 9 2 0 7 5 514 5 7 515 5 8

19 1

18. Martha’s class made these estimates for the number of jellybeans in a jar:

128, 126, 135, 139, 132, 130, 145, 147, 155, 120,

191, 135, 145, 135, 137, 158

a. Explain the mistake in the stem-and-leaf plot

for the jellybean estimates.

b. Correct the stem-and-leaf plot at the right.

Sample answer: 135 appears only

once, and it should appear 3 times. 145

appears once; it should appear 2 times.


Assessment Master

436 Unit 6 Progress Check 6

▶ Written Assessment


(Assessment Handbook, pp. 181–183)

Part A Recognizing Student AchievementProblems 1–16 provide summative information and may be used for grading purposes.

Problem(s) Description

1–5a, 16 Find and use data landmarks.

6, 8 Add and subtract fractions with like denominators.

7, 9–13 Add and subtract fractions with unlike denominators.

14, 15 Find a common denominator.

5b, 5c Understand how sample size affects results.

Part B Informing InstructionProblems 17–22 provide formative information that can be useful in planning future instruction.

Problem(s) Description

17 Read and interpret stem-and-leaf plots.

18 Construct stem-and-leaf plots.

19a-b Add and subtract fractions with unlike denominators.

19c Add and subtract fractions with common denominators.

21 Find a common denominator.

20a–20d, 22 Convert between fractions, decimals, and percents.

20e Understand how sample size affects results.

Use the checklists on pages 267 and 269 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.

▶ Open Response


(Assessment Handbook, p. 184)

Mean AgeThe open-response item requires students to apply skills and concepts from Unit 6 to solve a multistep problem. See Assessment Handbook, pages 95–99 for rubrics and students’ work samples for this problem.


Name Date Time

Written Assessment continuedLESSON

6�11

19. a. Use your ruler to draw a line segment that is 2�3

8� in. long.

b. If you erased �34

� inch from this line segment, how long would it be?

c. If you drew a line segment twice as long as the

original line segment, how long would it be?

20. One survey reported favorite types of books for fifth graders.

The results of the survey were as follows:

adventure books: 38%

mystery books: 30%

comedies: 22%

other: 10%

a. Circle the bar graph that

best represents the survey results.

b. If 100 students answered the survey, how many of them chose adventures?

c. If 10 students answered the survey, how many of them chose other?

d. If 50 students answered the survey, how many of them chose mysteries?

e. If you were trying to decide what kinds of books to buy for the

library in your town, how many fifth graders would you interview?

Explain why you chose that number.

21. Explain how you would use the multiplication rule to find common denominators for the

fraction pair you circled in Problem 14.

22. Explain one way to rename �35

� as a percent without using a calculator.

1�58

� in.

4 �68

� in., or 4 �34

� in.

Number of Children

Adventure

Mystery

Comedy

Other

0 2 4 6 8 10

0102030405060708090

100

% o

f C

hild

ren

Adven

ture

Mys

tery

Com

edy

Oth

er

38

15

1

Answers vary.

Answers vary.

Sample answer: Multiply the denominators, 3and 4, to get the common denominator of 12.

Sample answer: Rewrite �35

� as �160�, or �

16000

�.�160� or �

16000

� � 60%, so �35

� � 60%.


Assessment Master

Date Time

1 2 _ 3

5 _ 3

5. Write the mixed number

name and fraction name

by each diagram.

a.

Mixed

number

Fraction

b.

Mixednumber

Fraction

4. Complete the

“What’s My Rule?”

table and state

the rule.

1. Use your calculator to rename each of the

following in standard notation.

a. 55 = 3,125

b. 73 = 343

c. 93 = 729

d. 39 = 19,683

2. Continue each pattern.

a. 5, 14, 23, 32

, 41

,50

b. 48, 100

, 152, 204, 256

, 308

c. 12, 72, 132

, 192, 252

, 312

d. 60.5, 111, 161.5

, 212

, 262.5

e. 20.75, 21.50, 22.25,

23, 23.75

3. Write the following numbers in order from

greatest to least.

50,200; 5,200; 52,000; 5,200,002; 500,200

5,200,002

500,200

52,000

50,200

5,200

in out

20 800

3 120

40

50 2,000

8 320

700

Whole

hexagon

6. Make true sentences by inserting

parentheses.

a. 4 ∗ 8 – 5 = 12

b. 2 + 7 ∗ 7 = 51

c. 91 / 4 – 3 = 91

d. 63 / 9 + 11 = 18

e. 72 / 30 + 6 = 2

)(

)

)

)(

(

)(

(

28,000

1,600

6

9 231 232

222 223

230

2 1 _ 2

5 _ 2

62

Math BoxesLESSON

6�11

Ruleout = in ∗ 40

EM3MJ1_G5_U06_164-204.indd 204 1/18/11 6:58 PM

Math Journal 1, p. 204

Student Page

Lesson 6�11 437

▶ Mid-Year Assessment


(Assessment Handbook, pp. 228–233)

The Mid-Year Assessment (Assessment Handbook, pages 228–233) provides an additional assessment opportunity that you may use as part of your balanced assessment plan. This assessment covers some of the important concepts and skills presented in Fifth Grade Everyday Mathematics. They should be used to complement the ongoing and periodic assessments that appear within lessons and at the end of the units. Please see the Assessment Handbook, pages 100 and 101 for further information.

2 Looking Ahead: Preparing for Unit 7

▶ Math Boxes 6�11 INDEPENDENT

ACTIVITY (Math Journal 1, p. 204)

Mixed Practice This Math Boxes page previews Unit 7 content.

▶ Study Link 6�11:


Unit 7 Family Letter(Math Masters, pp. 183–186)

Home Connection The Unit 7 Family Letter provides parents and guardians with information and activities related to Unit 7 topics.


Copyright

© W

right

Gro

up/M

cG

raw

-Hill

STUDY LINK

6�11 Unit 7: Family Letter

183

Name Date Time

Exponents and Negative NumbersIn Unit 7, your child will learn to write exponential and scientific notation for naming very large and very small numbers. These topics become increasingly important later on when your child begins algebra. If you have enjoyed playing math games in the past, you might want to play Exponent Ball during these lessons.

Your child will also review how parentheses make expressions unambiguous and will learn rules that determine the order for performing operations in a mathematical expression.

Finally, your child will learn to work with positive and negative numbers, using a variety of tools. For example, your child will use number lines and red and black “counters” to model addition and subtraction problems.

The counter activities are especially helpful. Students use counters to represent an account balance. The red counters (-$1) represent a debit, and the black counters (+$1) represent a credit. If there are more red counters than black ones, the account is “in the red,” that is, the balance is negative. On the other hand, if there are more black counters than red ones, the account is “in the black,” that is, the balance is positive. By adding or subtracting red and black counters from an account, your child can model addition and subtraction of positive and negative numbers. To assist your child, you might want to explain how a checking or savings account works. Students will practice their new skills in the Credits/Debits Game.

Please keep this Family Letter for reference as your child works through Unit 7.

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VocabularyImportant terms in Unit 7:

account balance An amount of money that you have or that you owe.

exponential notation A way to show repeated multiplication by the same factor. For example, 23 is exponential notation for 2 ∗ 2 ∗ 2.

expression A mathematical phrase made up of numbers, variables, operation symbols, and/or grouping symbols. An expression does not contain symbols such as =, >, and <.

in the black Having a positive balance; having more money than is owed.

in the red Having a negative balance; owing more money than is available.

negative number A number less than zero.

nested parentheses Parentheses within parentheses in an expression. Expressions are evaluated from within the innermost parentheses outward following the order of operations.

Example:

((6 ∗ 4) - 2) / 2 (24 - 2) / 2 22 / 2 = 11

number-and-word notation A way of writing a large number using a combination of numbers and words. For example, 27 billion is number-and-word notation for 27,000,000,000.

opposite of a number A number that is the same distance from 0 on the number line as a given number but on the opposite side of 0. For example, the opposite of +3 is -3; the opposite of -5 is +5.

order of operations Rules that tell the order in which operations in an expression should be carried out. The order of operations is:

1. Do operations inside grouping symbols first. (Use rules 2–4 inside the grouping symbols.)

2. Calculate all the expressions with exponents.

3. Multiply and divide in order from left to right.

4. Add and subtract in order from left to right.

parentheses ( ) Grouping symbols used to indicate which operations in an expression should be done first.

scientific notation A system for writing numbers in which a number is written as the product of a power of 10 and a number that is at least 1 and less than 10. Scientific notation allows you to write big and small numbers with only a few symbols. For example, 4 ∗ 1012 is scientific notation for 4,000,000,000,000.

standard notation Our most common way of representing whole numbers, integers, and decimals. Standard notation is base-ten, place-value numeration. For example, standard notation for three hundred fifty-six is 356.

Unit 7: Family Letter cont. STUDY LINK

6�11

184

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186

Study Link 7�1

2. Should be 63 = 6 ∗ 6 ∗ 6; 216

3. Should be 29 = 2 ∗ 2 ∗ 2 ∗ 2 ∗ 2 ∗ 2 ∗ 2 ∗ 2 ∗ 2; 512

4. Should be 47 = 4 ∗ 4 ∗ 4 ∗ 4 ∗ 4 ∗ 4 ∗ 4; 16,384

5. 14.7 6. 0.48 7. 15 _

7 , or 2 1 _

7

Study Link 7�2

1. billion 2. 103 3. trillion

4. 106 5. thousand; 103 6. million; 106

7. 24 ∗ 3 8. 22 ∗ 3 ∗ 5

9. 3,000 + 200 + 60 + 4

Study Link 7�3

1. 600; 3 2. 6 3. 500 million

4. 260 million 5. 10 million 6. 125

Study Link 7�4

1. 2 = (3 ∗ 2) - (4 / 1) 2. 3 = (4 + 3 - 1) / 2

3. 4 = (3 - 1) + (4 / 2) 5. 1 = ((4 + 1) - 3) / 2

6. 6 = (1 + (4 ∗ 2)) - 3

7. (42 – ((3 ∗ 3)) + 1((2 + 1)4 ÷ 9) –1

8. a = 1 4 _ 12

, or 1 1 _ 3 9. p = 1 1 _

2

10. d = 2 2 _ 8 , or 2 1 _

4 11. y = 0

Study Link 7�5

1. 34 2. 25 3. 28 4. 30

5. 21 6. 28 7. false 8. true

9. true 10. true 11. false 12. true

13. false 14. true 15. z = 9,204

16. r = 78,002 17. s = 1.25

Study Link 7�6

1. Sales were at their highest in 1930. Sales dropped by 60 million from 1940 to 1970.

3. Before TV sets were common, more people went to the movies.

Study Link 7�7

1. 2.6 2. 1.58 3. -5.5

4. -9.8 5. -1.2, -1, 3.8, 5 1 _ 4 , 5 3 _

8

7. F 8. F 9. T

10. T 11. -1 < 1; T 13. f = 12.53

15. n = 3 _ 4

Study Link 7�8

1. < 2. > 3. > 4. >

5. 2 debt 6. 5 cash 7. -9 9. -88

11. 3 15. a = 30 17. p = 5

Study Link 7�9

1. -41 2. 43 3. 0 4. -8

5. 40 6. 20 7. -85 8. -0.5

9. 2 10. (-10) 12. u = 65, 664

13. e = 3 14. w = 30.841 15. m = 5.46

Study Link 7�10

1. 1 _ 8 2. 1 1 _

4 3. 1 1 _

8 4. 1 _

8 5. 1 _

4

Study Link 7�11

1. -5 - (-58) = 53 3. 104

7. 20,000 13. 7 ∗ 109 19. b = 0.46

21. a = 1,571 23. 137 4 _ 7 , or 137 R4

As You Help Your Child with Homework As your child brings assignments home, you might want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through this unit’s Study Links.

Unit 7: Family Letter cont. STUDY LINK

6�11

Numberof

Insects

X XXX

XXX

X

XXXX

XXXXXXXX

Insect Lengths

Average Length (in.)

0 114

38

18

114

11212

34

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