Multiple-Choice Items:
1. A bag of candy has 40 white candies and 30 black candies. What is the ratio of black candies to the total number of candies in the bag?
2. The ratio of boys to girls in Kelly’s class is 3:5. If there are 18 boys in Kelly’s class, how many girls are in Kelly’s class?
3. The ratio of boys to girls in Jason’s class is 2:3. Which of the following could not be the number of girls in Jason’s class?
- A grocery store sells 4 bottles of juice for $9.40. At that rate, what is the cost of one bottle of juice?
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A
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$2.10
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B
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$2.35
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C
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$4.70
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D
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$5.40
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- Mia traveled 5 km in 2 hours. What is her unit rate?
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A
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10 km
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B
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2.5 km per hour
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C
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10 km : 4 hours
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D
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0.4 km per hour
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- Jasmine went to the Bargain Bin Grocery Mart to buy apples to bake a pie. The store had several package sizes. Which of the following is the best buy for her apples?
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A
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4 apples for $3.64
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B
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9 apples for $8.02
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C
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14 apples for $12.43
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D
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24 apples for $21.12
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- What is 32% of 200?
A 32
B 34
C 48
D 64
- What is 16% of 90?
A 14.4
B 17.7
C 144.0
D 562.5
- The number 67.84 is 32% of what number?
A 21.71
B 47.17
C 212.00
D 217.01
Multiple-Choice Answer Key:
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1. B
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2. D
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3. C
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4. B
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5. B
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6. D
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7. D
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8. A
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9. C
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Short-Answer Items:
10. The ratio of boys to girls in Hannah’s class is 6:7. If there are 21 girls in Hannah’s class, find the total number of students in Hannah’s class. Explain the steps you used.
- On his bicycle, Paul can ride 20 miles in 2.5 hours. Find Paul’s unit rate and use it to determine how far he could travel in 3.5 hours. Show or explain your work.
- The Smith family goes out for dinner. The total bill is $48.50. They leave a 14% tip. First, estimate the tip by rounding their dinner bill to the nearest convenient number. Then, determine the actual amount of their tip.
Short-Answer Key and Scoring Rubrics:
10. The ratio of boys to girls in Hannah’s class is 6:7. If there are 21 girls in Hannah’s class, find the total number of students in Hannah’s class. Explain the steps you used.
Sample Answer: Since there are 21 girls, I know the ratio is being changed to 18:21, multiplying both parts by 3. Therefore, there are 18 boys, so there are 18 + 21 = 39 students.
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Points
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Description
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2
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- The student correctly finds the total number of students and accurately explains the steps used.
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1
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- The student correctly finds the total number of students or accurately explains the steps that could be used to do so, but not both.
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0
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- The student does not correctly find the total number of students nor does s/he accurately explain the steps that could be used to do so.
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11. On his bicycle, Paul can ride 20 miles in 2.5 hours. Find Paul’s unit rate and use it to determine how far he could travel in 3.5 hours. Show or explain your work.
Sample Answer: To find the unit rate, I need to divide 20 by 2.5 and get 8 miles per hour. Then, to find out how far he could travel in 3.5 hours, I multiply the unit rate by 3.5 and get 28 miles.
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Points
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Description
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2
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- The student correctly finds the unit rate and uses it to find the distance traveled in 3.5 hours.
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1
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- The student correctly finds either the unit rate or uses it to find the distance traveled in 3.5 hours, but not both.
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0
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- The student does not correctly find the unit rate nor the distance traveled in 3.5 hours.
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12. The Smith family goes out for dinner. The total bill is $48.50. They leave a 14% tip. First, estimate the tip by rounding their dinner bill to the nearest convenient number. Then, determine the actual amount of their tip.
Sample Answer: $50 Ă— 14% = $7 or $50 Ă— 15% = $7.50.
$48.5 Ă— 14% = $6.79
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Points
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Description
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2
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- The student accurately estimates the actual tip using a valid mathematical technique and also finds the exact amount of the tip.
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1
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- The student either accurately estimates the tip using a valid mathematical technique or correctly finds the exact amount of the tip but not both.
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0
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- The student does not estimate the tip using a valid mathematical technique and fails to correctly find the exact amount of the tip.
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Performance Assessment:
Have each student bring in three news articles (from a newspaper, Web site, etc.). The articles should contain data that can be expressed as a ratio, unit rate, or percentage. (The article may not necessarily contain an explicit ratio, but may compare two quantities that can then be compared using a ratio, such as an article that lists the number of states that voted for each of two presidential candidates.)
A poster should be created with three parts, each part pertaining to one of the articles (and one of ratio, unit rate, or percentage). The pertinent information in the article should be highlighted and the ratio, unit rate, or percentage should be displayed on the poster. The poster should use the mathematical information to create a problem related to the article. (For example, “If there was the same ratio of states that voted for each of the two candidates, how many states would have voted for Candidate A if there were 200 states?”)
Students should set up their posters; other students should tour the posters and answer a specific number of questions of each type. (If each student designs his/her own poster, asking students to solve every problem posed is a lot of problems.)
Performance Assessment Scoring Rubric:
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Points
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Description
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4
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- The student correctly finds, displays, and creates a problem about ratios.
- The student correctly finds, displays, and creates a problem about unit rates.
- The student correctly finds, displays, and creates a problem about percentages.
- The student correctly answers a specified number of problems of each type from other students’ displays.
- The student demonstrates an advanced understanding of the concepts of rates, ratios, and percentages.
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3
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- The student correctly completes three of the four tasks detailed above.
- The student demonstrates a strong understanding of the concepts of rates, ratios, and percentages.
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2
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- The student correctly completes two of the four tasks detailed above.
- The student demonstrates a limited understanding of the concepts of rates, ratios, and percentages.
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1
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- The student correctly completes one of the four tasks detailed above.
- The student demonstrates a very limited understanding of the concepts of rates, ratios, and percentages.
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0
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- The student does not complete any of the tasks detailed above.
- The student demonstrates no understanding of the concepts of rates, ratios, and percentages.
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