progress check 12 - everyday math - login check 12 the end-of-year ... 1 4 5–9 find the prime...

Lesson 12�9 957

�

Objective To assess students’ progress on mathematical

content through the end of Unit 12.

Oc

Progress Check 12

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�8

� Assessment Handbook, pp. 142–149, 210–215, 227, and 280–283

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

� slate

Find the greatest common factor of two numbers. [Number and Numeration Goal 3]

12�1 3 4

Find least common multiple of two numbers. [Number and Numeration Goal 3]

12�1 4 5–9

Find the prime factorization of numbers. [Number and Numeration Goal 3]

12�1 2 1–3

Find the factors of numbers. [Number and Numeration Goal 3]

12�1 1 1, 3 1, 2

Use least common multiples to find common denominators. [Number and Numeration Goal 5]

6 – 8

Multiply and divide fractions. [Operations and Computation Goal 5]

14, 15

Understand and use tree diagrams to solve problems. [Data and Chance Goal 4]

12�2 7 4 16

Use the Multiplication Counting Principle to find the total number of possible outcomes of a sequence of choices. [Data and Chance Goal 4]

12�2 6 2 16

Compute the probability of outcomes when choices are equally likely. [Data and Chance Goal 4]

12�2 17

Solve ratio and rate problems. [Operations and Computation Goal 7]

12�3, 12�6, 12�8

5 10–13 18–22�

ASSESSMENT ITEMSSELF ORAL/SLA OPEN

RESPONSETE WRITTEN

CONTENT ASSESSED LESSON(S)

PART BPART A

Math Boxes 12�9

Study Link 12�9: End-of-Year Family Letter

Materials � Math Journal 2, p. 427

� Math Masters, pp. 368–371

Looking Back: Cumulative AssessmentL

Looking Ahead: Preparing for Grade 6L

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LESSON

12 � 9

Name Date Time

Self Assessment Progress Check 12

1. Find all the factors

of a number.

2. Find the prime

factorization of a

number.

3. Find the greatest

common factor of

two numbers.

4. Find the least

common multiple of

two numbers.

5. Solve rate and ratio

number stories.

6. Use the

Multiplication

Counting Principle

to solve problems.

7. Use tree diagrams

to solve problems.

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

explain how to at an example.do it.

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

the most appropriate box.

Assessment Handbook, p. 210

Assessment Master

958 Unit 12 Progress Check 12

Getting Started

1 Looking Back: Cumulative Assessment

▶ Math Message Follow-Up

INDEPENDENT ACTIVITY

(Self Assessment, Assessment Handbook, p. 210)

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

▶ Oral and Slate Assessments

WHOLE-CLASS ACTIVITY

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

Oral Assessment 1. Show thumbs up if the first number is a factor of the second

and thumbs down if it is not.

● 8; 64 up ● 6; 303 down

● 4; 256 up ● 5; 8,045 up

2. Show thumbs up if the statement is true and thumbs down if it is false.

● If there are 4 flavors of ice cream and 2 types of cones, there are 6 possible ice cream cone choices. down

● If there are 8 notebook covers and 3 different colored pencils, there are 12 possible combinations of notebooks and pencils. down

● If there are 2 styles of team uniforms and 4 colors of athletic shoes, there are 8 possible combinations of uniforms and shoes. up

● If there are 6 pasta choices and 5 sauce choices, there are 30 possible combinations of sauce and pasta. up

Slate Assessment 3. Name all the factors of each number.

● 12 1, 2, 3, 4, 6, 12 ● 16 1, 2, 4, 8, 16

● 36 1, 2, 3, 4, 6, 9, 12, 18, 36 ● 47 1, 47

Math Message • Self AssessmentComplete the Self Assessment (Assessment Handbook, page 210).

Study Link 12�8 Follow-UpBriefly review students’ answers.

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Written Assessment continued LESSON

12�9

9. Sven bought a large pizza. He wants to cut the pizza so that it

can be shared equally by 2 people, 3 people, 4 people, 6 people,

or 8 people. Into how many slices should Sven cut the pizza? (unit)

10. There are 30 students in Linda’s class. Two-thirds of her class

rides to school on the school bus. The other students walk to

school. How many students walk to school? (unit)

11. Matt was playing Name That Number. Of the 5 cards he turned

over, 60% were black. How many black cards were there? (unit)

12. Three out of 7 cars parked on one street were red. If there were

28 cars, how many cars were red? (unit)

13. What is the ratio of cars that were not red to total cars in Problem 12?

Explain how you found your answer.

Solve each number story. Record the number model and the solution.

14. Susan rode her bike 4 4

__

5 miles on Thursday. She rode her bike 2

1

__

2 times that

far on Friday. How far did she ride her bike on Friday?

a. Open number model:

b. Solution:

15. At a bank, Maggie exchanged a $5 bill for $5 in quarters. How many quarters

did she get?


b. Solution:

Since 12 out of 28 cars were red, and 28 - 12 = 16, then 16 cars were not red.

24 slices

10 students

3 cards

12 cars

16

__ 28 or 4 _

7

4 4 _ 5 ∗ 2 1 _

2 = m

12 miles

5 ÷ 1 _ 4 = q

20 quarters

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Assessment Master

LESSON

12 � 9 Written Assessment

Name Date Time

Progress Check 12

Part A

For each number below, draw a factor tree and write the prime factorization.

1. 60 2. 84

60 � 84 �

3. What prime factors do 60 and 84 have in common?

4. What is the greatest common factor of 60 and 84?

Explain how you found it.

5. What is the least common multiple of 60 and 84?

Explain how you found it.

Rewrite each fraction pair with a common denominator.

6. �38

� and �152� and 7. �

67

� and �150� and

8. Explain how you found the answer to Problem 6.

I multiplied the common primefactors: 2 º 2 º 3 � 12.

2 º 2 º 3 º 52 º 2 º 3 º 72 º 2 º 3 º 5 º 7 � 420

2 º 2 º 3 º 7

2, 2, and 3

12

420

2 º 2 º 3 º 5

�294� �1

204� �6

700� �3

750�

Answers vary.

º ºº

º2

2

30

2 ºº2

3 52

15º4

I found the least common multiple of 8 and 12,which is 24. Then I multiplied �

38

ºº

33

� and �152

ºº

22

� tofind fractions with denominators equal to 24.

21

º ºº 22 3 7


Assessment Master

Lesson 12�9 959

4. Make a tree diagram to show the possible choices.

● There are 4 flavors of ice cream and 2 types of cones.

Ice cream C V S N

Cones C S C S C S C S

● There are 8 notebook covers and 3 different colored pencils.

Notebookcovers I II III IV V VI VII VIII

Pencils BRG BRG BRG BRG BRG BRG BRG BRG

▶ Written Assessment


(Assessment Handbook, pp. 211–214)

Part A Recognizing Student AchievementProblems 1–13 provide summative information and may be used for grading purposes.

Problem(s) Description

1, 2 Find the factors of numbers.

1–3 Find the prime factorizations of numbers.

4 Find the greatest common factor of two numbers.

5–9 Find the least common multiple of two numbers.

10–13 Solve ratio and rate number stories.

14 Solve a fraction multiplication number story.

15 Solve a fraction division number story.

Part B Informing InstructionProblems 14–20 provide formative information that can be useful in planning future instruction.

Problem(s) Description

16 Understand and use tree diagrams.

17 Compute the probability of outcomes.

18–22 Solve ratio and rate number stories.

Use the checklists on pages 281 and 283 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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Name Date Time


12�9

16. Darin rolls a 6-sided die and then flips a coin.

How many different ways can the die roll and coin toss turn out?

a. Use the Multiplication Counting Principle to answer. different ways

b. Draw a tree diagram to show all the possible ways.

Suggestion: Use the letters H and T to represent HEADS and TAILS.

c. Which method do you think is easier for finding the number of

possible results?

d. Explain your answer.

17. In Problem 16, what is the probability that Darin…

a. rolls a 5 and the coin lands on HEADS?

b. rolls an even number and the coin lands on TAILS?

c. rolls a prime number?

d. tosses the coin so that it lands on HEADS?

Part B

12

Answers vary.

1 __ 12

3 __ 12 , or

1

_ 4

6 __ 12 ,

3

_ 6 , or

1

_ 2

6 __ 12 , or

1

_ 2

1

H T

2

H T

3

H T

4

H T

5

H T

6

H T

Answers vary.

die:

coin:

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Assessment Master

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Name Date Time


12 �9

Write a number model for each problem. Then solve the problem.

18. Rosalyn’s family was driving from home to her aunt’s house. After going

48 miles, they were 3

__

4 of the way there. How far from home was her

aunt’s house?

Number model: Answer: miles

19. In Doreen’s first basketball game, she made a basket 9 times out of

15 attempts. She made the same ratio of baskets out of 25 attempts in

the second game. How many baskets did she make in her 25 attempts?

Number model: Answer: baskets

20. Explain how you found your answer to Problem 19.

21. Marcus’s heart beats 11 times in 10 seconds. At this rate,

about how many times would it beat in 1 minute? times

22. Carlo was buying tickets for his family at the school fair.

He got 7 tickets for each dollar. He received a total of

224 tickets. How much did he spend on tickets?

3

_ 4 = 48

__

□

9

__ 15 = □

__ 25

64

15

So the number model can be written as 3 _

5 = □ __

25 ∑ 3 ∗ 5

____ 5 ∗ 5 = 15

__

25 . 9 out of 15 is the same ratio as 15 out of 25. She made 15 baskets.

9

__ 15 = 3 _

5 .

$32

66

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Assessment Master Assessment MasterName Date Time

Progress Check 12

Counting Cars

Use the statements below to figure out how many trips the Rock Island Ferry made.

� The Rock Island Ferry took 64 cars and trucks across the Rock Island River

one Saturday.

� The total ratio of cars to trucks for the day was 5 to 3.

� The ferry carries 6 cars and 4 trucks when it is full.

� It was full on every trip except for the last trip of the day.

How many trips did the ferry make?

Show all of your work and describe, in words, the steps you followed to solve

the problem.

Open ResponseLESSON

12 � 9


960 Unit 12 Progress Check 12

▶ Open Response


(Assessment Handbook, p. 215)

Counting CarsThe open-response item requires students to apply skills and concepts 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


(Assessment Handbook, pp. 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 Fifth Grade Everyday Mathematics. It should be used along with ongoing and periodic assessments. Please see the Assessment Handbook for further information.

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XXXXXXXXX, p. XXX

Student Page

XXXXXXXXX, p. XXX

Student Page

Math Boxes LESSON

12�9

Date Time

5. The water in Leroy’s fish tank had

evaporated so that it was about �5

8� inch

below the level it should be. He added

water and the water level went up about

�3

4� inch. Did the water level end up above

or below where it should be? How much

above or below?

Number model:

Answer:

6. Insert parentheses to make each

expression true.

a. �28 � 43 � 2 � 30

b. �19 � 12 / 2 � 6 � (�20)

c. 16 � 12 / 2 � 6 � (�20)

d. 24 / 6 � (�2) � 5 � 8

e. 24 / 6 � (�2) � 5 � 11

1. One square

weighs as much as ounces.

23 ounces3 + 14 ounces

3

3. Write a fraction or a mixed number for

each of the following.

a. 5 minutes � hour

b. 20 minutes � hour

c. 35 minutes � hour

d. 10 minutes � hour

e. 55 minutes � hour

�172�

�112�

4. Multiply.

a. �7

8� � �

8

9� �

b. � 1�1

3� � 2�

1

5�

c. � 4�1

6� � 3 �

1

3�

d. � �2

6

5� � �

8

9�

e. � 5 � 2�5

7�

�79

�

189

76–78

228 229

397

66 67243 222

2. The area of the cover of the dictionary is

about .(unit)

Dictionaryof

AmericanEnglish

58

9 in.

34

7 in.

74�1392� in2

�142�, or �

13

�2�

1145�

13�89

�

3�1297�

13�47

�

�122�, or �

16

�

�11

12�

�58

� � �34

�, or �58

� � �68

�

Above by �18

� inch

( )

( )

( )

( )

( )

Math Journal 2, p. 427

Student Page

Study Link Masters

STUDY LINK

12�9 End-of-Year Family Letter

Name Date Time

Congratulations!

By completing Fifth Grade Everyday Mathematics, your child has accomplished a greatdeal. Thank you for your support!

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

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

1. Review multiplication facts. For example, include basic facts such as 7 º 8 � 56, andextended facts, such as 70 º 8 � 560 and 70 º 80� 5,600.

2. Create opportunities to work with rulers,yardsticks, metersticks, tape measures, and scales.Have your child measure items using metric andU.S. customary units.

3. Ask your child to solve multiplication and divisionproblems that are based on real-life situations. Varythe problems so that some are suitable for mentalcomputation, some require paper-and-pencilcalculation, and some require the use of acalculator.

4. Practice using percents by asking your child to cal-culate sales tax, percent discounts, sports statistics,and so on.

5. Continue the American Tour by reading aboutimportant people, events, inventions, explorations,and other topics in American history. Focus ondata displays such as bar, line, and circle graphs,and on color-coded maps.

Math Masters, pp. 368–371

Lesson 12�9 961

2 Looking Ahead: Preparing for Grade 6

▶ Math Boxes 12�9


(Math Journal 2, p. 427)

Mixed Practice This Math Boxes page previews Grade 6 content.

▶ Study Link 12�9:


End-of-Year Family Letter(Math Masters, pp. 368–371)

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

can be done at home during vacation, and provides a preview of Sixth Grade Everyday Mathematics.

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212 Assessment Handbook

Name Date Time


12�9

9. Sven bought a large pizza. He wants to cut the pizza so that it

can be shared equally by 2 people, 3 people, 4 people, 6 people,

or 8 people. Into how many slices should Sven cut the pizza? (unit)

10. There are 30 students in Linda’s class. Two-thirds of her class

rides to school on the school bus. The other students walk to

school. How many students walk to school? (unit)

11. Matt was playing Name That Number. Of the 5 cards he turned

over, 60% were black. How many black cards were there? (unit)

12. Three out of 7 cars parked on one street were red. If there were

28 cars, how many cars were red? (unit)

13. What is the ratio of cars that were not red to total cars in Problem 12?

Explain how you found your answer.

Solve each number story. Record the number model and the solution.

14. Susan rode her bike 4 4

__

5 miles on Thursday. She rode her bike 2

1

__

2 times that

far on Friday. How far did she ride her bike on Friday?


b. Solution:

15. At a bank, Maggie exchanged a $5 bill for $5 in quarters. How many quarters

did she get?


b. Solution:

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Assessment Masters 213

Name Date Time


12�9

16. Darin rolls a 6-sided die and then flips a coin.

How many different ways can the die roll and coin toss turn out?

a. Use the Multiplication Counting Principle to answer. different ways

b. Draw a tree diagram to show all the possible ways.

Suggestion: Use the letters H and T to represent HEADS and TAILS.

c. Which method do you think is easier for finding the number of

possible results?

d. Explain your answer.

17. In Problem 16, what is the probability that Darin…

a. rolls a 5 and the coin lands on HEADS?

b. rolls an even number and the coin lands on TAILS?

c. rolls a prime number?

d. tosses the coin so that it lands on HEADS?

Part B

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214 Assessment Handbook

Name Date Time


12 �9

Write a number model for each problem. Then solve the problem.

18. Rosalyn’s family was driving from home to her aunt’s house. After going

48 miles, they were 3

__

4 of the way there. How far from home was her

aunt’s house?

Number model: Answer: miles

19. In Doreen’s first basketball game, she made a basket 9 times out of

15 attempts. She made the same ratio of baskets out of 25 attempts in

the second game. How many baskets did she make in her 25 attempts?

Number model: Answer: baskets

20. Explain how you found your answer to Problem 19.

21. Marcus’s heart beats 11 times in 10 seconds. At this rate,

about how many times would it beat in 1 minute? times

22. Carlo was buying tickets for his family at the school fair.

He got 7 tickets for each dollar. He received a total of

224 tickets. How much did he spend on tickets?

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progress check 12 - everyday math - login check 12 the end-of-year ... 1 4 5–9 find the prime...

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