M A T H

N A V I G A T O R®

ASSESSMENT RESOURCES

Ratios and Rates

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ISBN: 1 2 3 4 5 6 7 8 9 10

978-1-40261-352-4 16 15 14 13 12

Contents

Teacher Materials Pre-Test/Post-Test Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Checkpoint Test Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Student Materials Lesson 5: Checkpoint 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Checkpoint 1A Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12



Checkpoint 1 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Lesson 10: Checkpoint 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Checkpoint 2A Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23



Checkpoint 2 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Lesson 15: Checkpoint 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Checkpoint 3A Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33



Checkpoint 3 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Image Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

iii

Pre-Test/Post-Test Administration

➲

test administration Pre-test: Let students know that this test will help you determine what they already know. Explain that the module will help students learn how to solve problems on the test that seem difficult now. Post-test: Explain that this test will help you determine what students have learned about ration and rates. Online Testing

Once your testing window has started, you can begin testing. • Seat students individually in front of a computer. • Give each student a piece of scratch paper. • Make sure that students have pencils. • Have students use their access codes to log in to the pre-test. • Before each student begins the test, confirm that he or she is taking the correct test. Tell students that: • Each question will be displayed on the computer screen. Students should select the answer they think is best by clicking on the option choice and then clicking to confirm the choice. • After students answer a question, the next question will appear on the computer screen. • Students may opt to skip a question and flag it to come back to before ending the test. During the test: • Observe students as they work to make sure that they are actively engaged in the testing process. • Support any students who seem to find the material challenging. Encourage them to make a good estimate for any problem they find difficult. • You may wish to provide manipulatives. Once students have answered all the questions, they should follow the online prompts to conclude the test. Pre-test: If any students finish the test early, group them into pairs. Give each of the students a Student Book. Tell them to read the instructions on page 1 and start working with their partners.

RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

1

Pre-Test/Post-Test Administration

Paper-and-Pencil Test

• Print copies of the test and answer sheet from ARO for each student. • Seat students individually. • Distribute tests, answer sheets, and scratch paper. • Make sure that students have #2 pencils. • Instruct students to fill in the answers on their answer sheets. During the test: • Observe students as they work to make sure that they are actively engaged in the testing process. • Support any students who seem to find the material challenging. Encourage them to make a good estimate for any problem they find difficult. • You may wish to provide manipulatives. After students finish, collect their tests, answer sheets, and scratch paper. You will need to upload students’ answers to the ARO system so you can analyze the results. Pre-test: If any students finish the test early, group them into pairs. Give each of the students a Student Book. Tell them to read the instructions on page 1 and start working with their partners.

➲

analyzing results Irrespective of the method (online or paper-and-pencil) that you chose to administer the test, your students must be enrolled in the ARO system in order for you to obtain computer-generated reports. These reports: • Offer rich, instructionally-relevant information to teachers and administrators at the individual student, class, grade, school, and district levels • Include total test score performance information and item-level analysis for each student and for all students combined • Are important references in helping you assess the misconceptions your students are struggling with and decide what concepts to focus on during the module For results: • Online Testing: ARO will automatically generate performance reports. • Paper-and-Pencil Test: Upload students’ data to ARO. Once you have uploaded the data, ARO will generate performance reports. Additional information about the online test reporting can be found on ARO. Remember to give a copy of the reports to students’ regular mathematics teachers to help them plan subsequent instruction.

RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

2

Pre-Test/Post-Test Administration

➲

reflection When students finish working on the test, ask them to open the Student Book and continue with the work time or reflection task that follows.

RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

3

Checkpoint Test Administration

➲

preparation • Make a copy of the appropriate checkpoint lesson, answer sheet, and answer key for each student. • Hand out the checkpoint lesson to each student.

➲

setting the direction Lessons 5, 10, and 15 of this module are checkpoint lessons. In checkpoint lessons, students practice skills by answering multiple‑choice and free‑response questions in a test‑like atmosphere, and then work in groups to “debug” their procedural knowledge. Each checkpoint lesson is structured as follows: 1. Students work independently on Checkpoint A. 2. Students work in groups to debug their work, concentrating on procedural knowledge. 3. Students work independently on either Checkpoint B or C, based on their success with Checkpoint A. Checkpoint C is easier than Checkpoint B. 4. Students meet in groups to debug their work. The problems in the checkpoints follow up on the week’s work. When students have completed Checkpoint A, collect their answer sheets before the debug group. Enter the data from Checkpoints 1A, 2A, and 3A into ARO. The report generated by ARO will help you assess whether students are on track and making sufficient progress.

➲

checkpoint A A. Work on Checkpoint A

Have students work individually to answer the multiple‑choice and free‑response problems found in Checkpoint A. Have students show their work in the checkpoint lesson and then transfer their answers to the answer sheet. Give students about 10–15 minutes to complete the checkpoint. Observe students as they work in order to identify students who are struggling. You will use this information to decide how to organize the debug groups, and to determine which students will work on Checkpoint B versus Checkpoint C later in the lesson. B. Model Debug Groups in Lesson 5

The debug groups are an important step of the checkpoint lesson because it gives students further mathematical practice in constructing viable arguments and critiquing the reasoning of others (MP3). Many of the problems in Checkpoint 1A ask students to reason abstractly and qualitatively (MP2) and to attend to precision (MP6). The debug discussions give students a chance to refine their understanding of the content while engaging in these mathematical practices. RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

4

Checkpoint Test Administration

In Lesson 5 during Checkpoint 1A, you will deviate slightly from the typical checkpoint lesson structure by first modeling the debug group routine. Spend about 5 minutes modeling this routine in front of the class. Create a model group to help you. Choose students who have been willing to share their mistakes during the first four lessons. Participate as a member of the group in order to model how students should debug their work. Model the following debug group routine, which students will use in all checkpoint lessons: • Hand out the answer key for Checkpoint 1A. • First, group members check their answers against the answer key. Students can check their own work or they can exchange work with a partner and check each other’s work. You can determine the rules for the process, or you can decide as a group. • Next, members of the group should each choose a problem that they got wrong, show their work for the problem, and ask the group, “What am I doing wrong?” As resources, group members can use their own work, information they have from earlier lessons, the procedural help in the back of the Student Book, and the Concept Book. • As a member of the model debug group, model for students how you would present an incorrect answer. Tell them that you answered D for question 3. What did you do wrong? Listen to their advice. Hopefully, some of the students will point out the ratio is boys to girls, not girls to boys, thus the 1 represents the boys and there are twice as many girls. If there are 4 girls that means there are 1 as 2 many boys or 2 boys: 2 : 4 is the same as 1 : 2. Ask them where they might get more help. Hopefully some of the students might answer “page 69 of the procedural help page”, which describes equivalent ratios. You might not want to take the time to have all the students in the model group present their work. However, emphasize to students that in their own groups, all students should present their work. Be sure to spend the time required for your students to understand the purpose and routines of the debug process. In subsequent checkpoint lessons, you may skip Part B—Model Debug Groups in Lesson 5. C. Debug Groups

Divide students into groups of three or four students each and have the groups follow the debug routine. Try to balance the groups with regard to strong and weak students, based on your earlier observations. In Lesson 5, integrate students from your model group into the other groups. RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

5

Checkpoint Test Administration

Make sure all students have a copy of the answer key for the appropriate checkpoint. Some groups may need more help than others. Spend extra time with groups that need more help, but be sure to take time to monitor all of the groups.

➲

checkpoints B and C A. Work on Checkpoint B or C

Give the debug groups about 15 minutes to finish. Then assign students to work on either Checkpoint B or Checkpoint C. Checkpoint C is easier than Checkpoint B, so assign Checkpoint C to any students who had difficulty with Checkpoint A. Allow 7–10 minutes for the second checkpoint. Observe students as they work to assess whether they still need help with the material—either individually or as a class. B. Debug Groups

Hand out the answer key for the appropriate checkpoint. If you have time, form debug groups again and have them follow the debug routine. If you run short of time, just have students check their answers using the answer keys. Spend time with students who are struggling.

➲

reflection When you have about 2 minutes left, stop the debug groups, even if they are not finished. Have students respond to the reflection prompt in the Student Book.

RATIOS AND RATES

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6

5

Checkpoint 1

➲ setting the direction

For each problem, circle the correct answer or write your solution. Show your work. Copy your answers to the Checkpoint 1A answer sheet. Turn in your answer sheet to your teacher and get an answer key. Check your answers against the answer key. Then have each person in your group share one problem with the group. • If you got one or more problems wrong, select one and ask the group, “What did I do wrong in this problem?” • If you answered all the problems correctly, share with the group something that you did to solve a problem that you think was interesting or unusual. To help you and the members of your group, use the procedural help on pages 69–72 at the end of the Student Book or use the Concept Book pages 291–303. Then complete either Checkpoint 1B or Checkpoint 1C as instructed by your teacher. When completed, check your answers against the answer key. Have one person in your group share a problem using the routine described above.

➲ checkpoint 1A 1. Which fraction represents the ratio 4 : 3? A 

3 4



B 

3 12



C 

4



D 

10 : 12

D 

3

12 4

2. The ratio 10 : 2 can also be written as: A 

5 : 1

B 

10 : 8

C 

20 : 2

3. The ratio of boys to girls in a group is 1 : 2. There are 4 girls in the group. How many boys are in the group? A 

RATIOS AND RATES

1

B 

2

C 

6

D 

8

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

7

Checkpoint 1

4. What is the ratio of Jill’s juice to Kate’s juice? A 

1 : 4

B 

1 : 5

C 

1 : 3

D 

1 : 2

Jill’s juice

Kate’s juice

50 mL

150 mL

5

5. The ratio of Joe’s stamps to Max’s stamps is 3 : 2. Which figure shows this ratio? A 

C 

Joe

Max



B 

Joe

Max



D 

Joe

Max

Joe

Max

6. Write the correct value in the denominator. 20% = 

20

7. Guests at a party eat a total of 10 pizzas and drink a total of 45 sodas. What is the ratio of pizzas to sodas?

8. A cruise ship has a crew of 750 and carries 2,250 passengers. What is the passenger to crew ratio expressed in simplest form?

RATIOS AND RATES

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8

Checkpoint 1

5

9. A cruise ship has a crew of 750 and carries 2,250 passengers. What is the part-whole ratio of crew to all persons on the ship?

10. Sketch a tape diagram divided into equal parts where the ratio between the shaded and unshaded parts is 1 : 3.

Check your answers using the Checkpoint 1A Answer Key. Then share one problem with the group. RATIOS AND RATES

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9

Checkpoint 1

5

➲ checkpoint 1B 1. Which fraction represents the ratio 7 : 6? A 

12 14



B 

17 16



C 

16 14



D 

28 24

2. The ratio of lions to tigers at the city zoo is 2 : 3. There are 30 tigers at the zoo. How many lions are at the zoo? A 

2

B 

30

C 

20

D 

40

3. Which of the following shapes do not show the ratio 2 : 3? A 



B 



C 



D 

4. Express the ratio 1.5 : 1 as a fraction.

5. Dan made lemonade by mixing 2 parts of lemon concentrate to 4 parts of water. How much concentrate should Dan use with 2 parts of water?

Check your answers using the Checkpoint 1B Answer Key. Then share one problem with the group. RATIOS AND RATES

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10

Checkpoint 1

5

➲ checkpoint 1C 3 1. Which ratio represents the fraction  ? 4 A 

3 : 7

B 

4 : 7

C 

4 : 3

D 

3 : 4

2. Which of these shows 30% ? A 

30 300



B 

30 200



C 

30 100



D 

30 10

3. In which of the following figures is 20% of the shape shaded? A 



B 

C 



D 

4. At Martindale Elementary school, the ratio of boys to girls is 6 : 5. There are 60 boys in the school. How many girls are there at Martindale Elementary school?

5. 6 eggs are used to make an omelet. 3 eggs are used to make a chocolate cake. What is the ratio of the eggs in the omelet to the eggs in the chocolate cake?

Check your answers using the Checkpoint 1C Answer Key. Then share one problem with the group. RATIOS AND RATES

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11

Checkpoint 1A Answer Sheet

Class Information

School _____________________________________________________________________________ City ______________________________________________________  State ___________________ Teacher (mathematics class) __________________________________________________________

Student Information

Grade __________ First name _________________________________________________________________________ Last name _ ________________________________________________________________________ Date of birth  ______ (month)  ______ (day)  ______(year) Male  o    Female  o How many years have you been at this school?  _______ years Do you usually speak English at home?  Yes  o    No  o Does anyone in your home usually speak a language other than English? Yes  o    No  o

RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

12

Checkpoint 1A Answer Sheet

Name _______________________________________

A

B

C

D

1.

m

m

m

m

2.

m

m

m

m

3.

m

m

m

m

4.

m

m

m

m

5.

m

m

m

m

6. 7. 8. 9. 10. RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

13

Checkpoint 1 Answer Key

Checkpoint 1A

1. C  

4 3

2. A   5 : 1 3. B   2 4. C   1 : 3 5. D  

Joe

Max

6. 100 7. 2 : 9 8. 3 : 1 9. 1 : 4  or  1 to 4 10.

RATIOS AND RATES

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14

Checkpoint 1 Answer Key

Checkpoint 1B

1. D  

28 24

2. C   20 3. D  

4.

3 2

5. 1 part

Checkpoint 1C

1. D   3 : 4 2. C  

30 100

3. B  

4. 50 girls 5. 2 : 1

RATIOS AND RATES

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15

Checkpoint 2

➲ setting the direction

10

For each problem, circle the correct answer or write your solution. Show your work. Copy your answers to the Checkpoint 2A answer sheet. Turn in your answer sheet to your teacher and get an answer key. Check your answers against the answer key. Then have each person in your group share one problem with the group. • If you got one or more problems wrong, select one and ask the group, “What did I do wrong in this problem?” • If you answered all the problems correctly, share with the group something that you did to solve a problem that you think was interesting or unusual. To help you and the members of your group, use the procedural help on pages 69–72 at the end of the Student Book or use the Concept Book pages 291–303. Then complete either Checkpoint 2B or Checkpoint 2C as instructed by your teacher. When completed, check your answers against the answer key. Have one person in your group share a problem using the routine described above.

➲ checkpoint 2A 1. Steve is making cookies using this recipe.  He wants to make 3 times as many cookies as the amount this recipe makes. How many cups of chocolate chips will he need?

RATIOS AND RATES

A 

3 cups

B 

2 cups

C 

2  cup 3

D 

2

Chocolate Chip Cookies 140 g butter 1 egg 1 cup sugar 1 12 cups flour 2 3 cup chocolate chips

1  cups 3

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16

Checkpoint 2

10

2. Flavored milk is made by adding flavoring to milk in the ratio of 1 to 15. Which of these tables shows this situation? A 

Milk (cup)

1

2

3

4

5

Flavoring (cup)

15

25

35

45

55

Milk (cup)

30

45

60

75

90

Flavoring (cup)

2

3

4

5

6

Milk (cup)

1

2

3

4

5

Flavoring (cup)

15

30

45

60

75

Milk (cup)

10

20

30

40

50

Flavoring (cup)

1

2

3

4

5

B 

C 

D 

3. Jane’s dog weights 10 kg and her rabbit weights 2,000 g. What is the ratio of her dog’s weight to her rabbit’s weight? (Remember: 1 kg = 1,000 g) A 

5 : 1

B 

10 : 1

C 

10 : 2,000

D 

1 : 10

4. A new measure of length is the zeetle. The conversion rate between zeetles and meters is: 5 zeetles = 1 meter Jim’s apartment is 15 zeetles high and Jim is 2 meters tall. What is the ratio of the height of Jim’s apartment to the height of Jim? A 

RATIOS AND RATES

5 : 1

B 

3 : 2

C 

5 : 2

D 

15 : 2

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17

Checkpoint 2

10

5. This table shows how much Leanne is paid for the hours she works. Hours Worked

1

2

3

4

Pay Rate

$6

$12

$18

$24

At this rate, how much will Leanne be paid for working 7 hours? A 

$30

B 

$42

C 

$48

D 

$70

6. Complete this ratio table. A

5

6

B

1

1.2

11

17

7. Using the table in problem 6, write the ratio A : B as a percent.

8. Complete this ratio table for oranges priced at 5 oranges for a dollar. Oranges Cost ($)

RATIOS AND RATES

1

2

3

4

5 1

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18

Checkpoint 2

10

9. At one animal shelter, the ratio of cats to dogs was 2 : 3. Dogs Cats If the shelter had 75 dogs, how many cats were at the shelter?

10. Sketch a tape diagram to show how many tickets are purchased with $25 if there is a ratio of 6 raffle tickets purchased for every 5 dollars spent.

Check your answers using the Checkpoint 2A Answer Key. Then share one problem with the group.

RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

19

Checkpoint 2

10

➲ checkpoint 2B 1. Tim measured his arm and leg in 4th grade and 6th grade. Both times, the length of his arm was two-thirds the length of his leg. Which table shows this? A 

4th

6th

Length of Arm

50 cm

52 cm

Length of Leg

75 cm

81 cm

4th

6th

Length of Arm

54 cm

57 cm

Length of Leg

81 cm

84 cm

C 





B 

4th

6th

Length of Arm

60 cm

62 cm

Length of Leg

90 cm

93 cm

4th

6th

Length of Arm

52 cm

62 cm

Length of Leg

78 cm

84 cm

D 

2. This double number line shows equivalent values for dollars and yen. 1

0

2

3

4

dollars yen

0

20

40

60

80 100 120 140 160 180 200 220 240 260 280 300 320

a. How much is 140 yen approximately equal to in dollars?

b. What would be an approximate unit rate for converting dollars to yen?

RATIOS AND RATES

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20

Checkpoint 2

10

3. Is the following a ratio table? Explain why or why not. x

b

4b

16b

y

a

4a

16a

4. Carla, John, and Jorge work in a family restaurant. They share tips according to a ratio of 10 : 3 : 8, respectively. One night, John made $22.50 in tips. a. How much money did Carla make in tips that night?

b. How much money did Jorge make in tips that night?

Check your answers using the Checkpoint 2B Answer Key. Then share one problem with the group. RATIOS AND RATES

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21

Checkpoint 2

10

➲ checkpoint 2C 1. Jim is 2 meters tall. The ceiling is 3 meters high. What is the ratio of Jim’s height to the ceiling’s height? A 

1 : 1

B 

3 : 2

C 

23 : 1

D 

2 : 3

2. A certain cake is made by adding 1 teaspoon of sugar for every 12 ounces of flour (a ratio of 1 to 12). Howard is using 4 teaspoons of sugar. How many ounces of flour should he use? A 

16 ounces

B 

17 ounces

C 

48 ounces

D 

8 ounces

C 

1 : 5

D 

5 : 1

3. What is the ratio of 50 cents to $2.50? A 

50 : 2.5

B 

2.5 : 50

4. Complete this ratio table for tickets priced at $8 a piece. Tickets

2

3

Cost ($)

16

24

5

10

5. Is the following a ratio table? Explain why or why not. x

12

30

58

y

6

8

16

Check your answers using the Checkpoint 2C Answer Key. Then share one problem with the group.

RATIOS AND RATES

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22

Checkpoint 2A Answer Sheet

Class Information

School _____________________________________________________________________________ City ______________________________________________________  State ___________________ Teacher (mathematics class) __________________________________________________________

Student Information

Grade __________ First name _________________________________________________________________________ Last name _ ________________________________________________________________________ Date of birth  ______ (month)  ______ (day)  ______(year) Male  o    Female  o How many years have you been at this school?  _______ years Do you usually speak English at home?  Yes  o    No  o Does anyone in your home usually speak a language other than English? Yes  o    No  o

RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

23

Checkpoint 2A Answer Sheet

Name _______________________________________

A

B

C

D

1.

m

m

m

m

2.

m

m

m

m

3.

m

m

m

m

4.

m

m

m

m

5.

m

m

m

m

6. 7. 8. 9. 10. RATIOS AND RATES

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.

24

Checkpoint 2 Answer Key

Checkpoint 2A

1. B   2 cups 2. B   Milk (cup)

30

45

60

75

90

2

3

4

5

6

Flavoring (cup) 3. A   5 : 1 4. B   3 : 2 5. B   $42 6.

A

5

6

11

17

B

1

1.2

2.2

3.4

Oranges

1

2

3

4

5

Cost ($)

0.2

0.4

0.6

0.8

1

7. 500% 8.

9. 50 cats

30

10.

Tickets Dollars 25

RATIOS AND RATES

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25

Checkpoint 2 Answer Key

Checkpoint 2B

1. B  

4th

6th

Length of Arm

60 cm

62 cm

Length of Leg

90 cm

93 cm

2. a. $1.70 b. 1 : 0.012 3. It is a ratio table because there is a common ratio between quantities. 4. a. $75.00 b. $60.00

Checkpoint 2C

1. D   2 : 3 2. C   48 ounces 3. C   1 : 5 4.

Tickets

2

3

5

10

Cost ($)

16

24

40

80

5. It is not a ratio table because there is not a constant ratio between quantities.

RATIOS AND RATES

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26

Checkpoint 3

➲ setting the direction

15

For each problem, circle the correct answer or write your solution. Show your work. Copy your answers to the Checkpoint 3A answer sheet. Turn in your answer sheet to your teacher and get an answer key. Check your answers against the answer key. Then have each person in your group share one problem with the group. • If you got one or more problems wrong, select one and ask the group, “What did I do wrong in this problem?” • If you answered all the problems correctly, share with the group something that you did to solve a problem that you think was interesting or unusual. To help you and the members of your group, use the procedural help on page 72 at the end of the Student Book or use the Concept Book pages 305–308. Then complete either Checkpoint 3B or Checkpoint 3C as instructed by your teacher. When completed, check your answers against the answer key. Have one person in your group share a problem using the routine described above.

➲ checkpoint 3A 1. Suppose a bank will exchange 10 euros for 15 dollars. How many dollars would you get if you exchanged 25 euros? A 

$6.00

B 

$16.67

C 

$25.00

D 

$37.50

D 

$4.80

2. Flour costs $1.20 per kg. What is the cost of 4 kg of flour? A 

$1.20

B 

$2.40

C 

$3.60

3. Andrew rides his bike at a speed of 28 km per hour. He rides for one and one quarter hours at this speed without stopping. How far does he ride? A 

RATIOS AND RATES

32 km

B 

35 km

C 

36 km

D 

42 km

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27

Checkpoint 3

15

4. The cost of packs of baseball cards at a local sports store is shown in the table below. If the cost of packs always increases at the same rate, how much will 7 packs cost? 1

2

3

4

5

$1.50

$3.00

$4.50

$6.00

$7.50

Number of Packs Cost of Packs A 

$10.50

B 

$9.50

C 

6

$7.50

D 

7

$10.00

5. The cost of pencils at the student store is shown in the table below. If the cost of 3 pencils always increases at the same rate, how much will 9 pencils cost? Number of Pencils Cost of Pencils A 

$1.50

B 

3

6

9

12

15

$0.50

$1.00

?

$2.00

$2.50

$4.50

C 

$2.00

D 

$1.75

6. Joshua can read 40 pages in an hour. If he reads for an hour each day, how many pages will he read in 7 days? Which table can be used to solve this problem? A 

Pages 40

33

26

19

12

5

0

Pages

1

2

3

4

5

6

7

1

2

3

4

5

6

7

Days

40

40

40

40

40

40

40

Pages 40

47

54

61

68

75

82

1

2

3

4

5

6

7

Days C 

RATIOS AND RATES

B 

Pages

1

2

3

4

5

6

7

Days

40

80 120 160 200 240 280

D 

Days

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28

Checkpoint 3

15

7. Joan travels by car an average of 100 kilometers per hour. How many hours will it take her to drive 9,500 kilometers? A 

95 hours

B 

9,600 hours

C 

9,400 hours

D 

9.5 hours

Use this table for problems 8–10. City Chicago San Francisco

Population

Area

(2000 Census)

(square kilometers)

2,896,016

227.13

776,733

46.69

Population Density

8. What is the population density of Chicago (people per square kilometer)

9. What is the population density of San Francisco (people per square kilometer)

10. Which city is more crowded? How do you know?

Check your answers using the Checkpoint 3A Answer Key. Then share one problem with the group. RATIOS AND RATES

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29

Checkpoint 3

15

➲ checkpoint 3B 1. Which calculation gives the correct answer to the following problem? Mr. Okawa has an empty tank that holds 240 gallons. He can fill it at a rate of 36 gallons per 2 hours. How long does it take him to fill the tank? A 

240 ÷ 36

B 

240 × 36 ÷ 2

C 

240 ÷ 36 ÷ 2

D 

240 ÷ 36 × 2

2. Rosa can type words on her keyboard at 60 words per minute. Which table represents this situation? A 



B 

Minutes  m

60

120

300

Minutes  m

500

200

100

Words   w

1

2

5

Words   w

5

2

1

Minutes  m

90

60

30

6,000

3,000

C 

Minutes  m

10

30

60

Words   w

600

1,800

3,600

D 

Words   w 9,000

3. Water flows over Niagra Falls at a rate of 2,832 cubic meters per second. What is this rate in cubic meters per day?

RATIOS AND RATES

A 

2,832 × 60 × 24

C 

2,832 × 

60 24





B 

2,832 × 60 × 60 × 24

D 

2,832 × 

60 × 60 24

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30

Checkpoint 3

15

Use this table for problems 4 and 5. State

Population

(2000 Census)

Area

(square miles)

California

37,593,222

163.695

Georgia

8,186,453

59,425

Montana

902,195

147,042

8,414,350

8,722

New Jersey

Population Density

4. Which state is most crowded? How do you know?

5. Which state is least crowded? How do you know?

Check your answers using the Checkpoint 3B Answer Key. Then share one problem with the group. RATIOS AND RATES

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31

Checkpoint 3

15

➲ checkpoint 3C 1. Mrs. Chi’s new car gets an average of 24 miles per gallon of gasoline. Last week she used 10 gallons of gasoline. About how many miles did she travel? A 

34 miles

B 

240 miles

C 

2,040 miles

D 

204 miles

C 

$5.00

D 

$6.25

2. Peaches cost $1.25 per pound. What will 4 pounds of peaches cost? A 

about $0.32

B 

$1.25

3. Suppose a bank will exchange 20 dollars for 268 pesos. How many pesos would you get if you exchanged 10 dollars? A 

13.4 pesos

B 

200 pesos

C 

134 pesos

D 

2,680 pesos.

4. Brittany bought 2 pounds of peas for $5.00. What is the price of peas per one pound?

5. If Brittany changes her mind and buys 6 pounds of peas, what will she pay?

Check your answers using the Checkpoint 3C Answer Key. Then share one problem with the group. RATIOS AND RATES

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32

Checkpoint 3A Answer Sheet

Class Information

School _____________________________________________________________________________ City ______________________________________________________  State ___________________ Teacher (mathematics class) __________________________________________________________

Student Information

Grade __________ First name _________________________________________________________________________ Last name _ ________________________________________________________________________ Date of birth  ______ (month)  ______ (day)  ______(year) Male  o    Female  o How many years have you been at this school?  _______ years Do you usually speak English at home?  Yes  o    No  o Does anyone in your home usually speak a language other than English? Yes  o    No  o

RATIOS AND RATES

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33

Checkpoint 3A Answer Sheet

Name _______________________________________

A

B

C

D

1.

m

m

m

m

2.

m

m

m

m

3.

m

m

m

m

4.

m

m

m

m

5.

m

m

m

m

6.

m

m

m

m

7.

m

m

m

m

8. 9. 10. RATIOS AND RATES

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34

Checkpoint 3 Answer Key

Checkpoint 3A

1. D   $37.50 2. D   $4.80 3. B   35 km 4. A   $10.50 5. A   $1.50 6. C  

Pages

1

2

3

4

5

6

7

Days

40

80 120 160 200 240 280

7. A   95 hours 8. 12,750 people / km 2 9. 16,636 people / km 2 10. San Francisco

RATIOS AND RATES

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35

Checkpoint 3 Answer Key

Checkpoint 3B

1. D   240 ÷ 36 × 2 2. C   Minutes  m

10

30

60

Words   w

600

1,800

3,600

3. B   2,832 × 60 × 60 × 24 4. New Jersey 5. Montana

Checkpoint 3C

1. B   240 miles 2. C   $5.00 3. C   134 pesos 4. $2.50 per pound 5. $15

RATIOS AND RATES

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Image Credits

Grateful acknowledgement is made to the following for copyrighted material: 8 m. ©Pearson 10 t.l. ©iStockphoto.com/Eric Isselée 10 t.r. ©iStockphoto.com/Eric Isselée 10 b. ©iStockphoto.com/Danny Smythe 11 b. ©iStockphoto.com 16 b. ©iStockphoto.com/Uyen Le 17 m. ©iStockphoto.com/Palle Christensen 18 b. ©iStockphoto.com/Amanda Rohde 19 t.l. ©iStockphoto.com 19 t.r. ©iStockphoto.com/Eric Isselée 19 m. ©iStockphoto.com/Scott Rothstein 29 b. ©iStockphoto.com/ René Mansi 32 t.r. ©iStockphoto.com/Joanna Pecha 32 m.r. ©iStockphoto.com Note: Every effort has been made to locate the copyright owner of material reproduced in this component. Omissions brought to our attention will be corrected in subsequent editions.

RATIOS AND RATES

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