G6 U6 Constructed Response Rubric
Grade 6 Unit 6 Constructed Response Rate and Ratio Description Task
Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Word Problems using Unit Rates
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. b. Solve unit rate problems including those involving unit pricing and constant speed.
MP.1 MP.2 MP.3 MP.4 MP.6 MP.7 MP.8
2. Word Problems using Equivalent Ratios
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MP.1 MP.2 MP.4 MP.6 MP.7 MP.8
3. Word Problems with Percentage and Measurement Ratios
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
MP.1 MP.2 MP.4 MP.6 MP.7 MP.8
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 1
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 2
Scoring Rubric Question 1. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Tangerines have the lowest cost per pound. I know because I found the unit rate for all of the fruits as follows: apples are 60¢ per pound, tangerines are 20¢ per pound, pears are 75¢ per pound, grapes are 80¢ per pound, and watermelon is 25¢ per pound. The price for tangerines is the least per pound. b. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: If I spent $1.00 on each kind of fruit, I would 1 buy 13 4 lb of fruit. I found this by finding out how many pounds of each kind of fruit I could buy for $1.00, then adding the weights. For $1, I could 2 1 1 buy 1 3 lb of apples, 5 lb of tangerines, 1 3 lb of pears, 1 4 lb of grapes, and 4
Points 2
2
1
lb of watermelon. This adds up to 13 4 lb of fruit. c. Student gives the correct answer and shows work. $5.55 2. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Mom got the best gas mileage because her car went more miles than anyone else’s car on one gallon of gas. I found my answer by finding the unit rate (miles per one gallon) for each family member. Great Uncle Emory got 18 mpg, Aunt Kathy got 21 mpg, Uncle Robert got 12 mpg, Mom got 31 mpg, and Grandma Lou got 27 mpg. Mom’s was the most miles per one gallon. b. Student gives the correct answer: $57.62 c. Student gives the correct answer: Great Uncle Emory is correct. His car 2 1 will use 1 3 gallons of gas, and Uncle Robert’s car will use 2 2 gallons of gas. 3. a. Student gives the correct answer and uses ratio language accurately. Wording may vary. Sample response: 5:16 Five of the 16 fruits are bananas. b. Student gives the correct answer and uses ratio language accurately. Wording may vary. Sample response: 4:7 For every 4 oranges there are 7 apples. c. Student gives the correct answer and uses ratio language accurately. Wording may vary. Sample response:7:9 For every 7 apples there are 9 non-apples. d. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Yes, the ratios would be equivalent since the Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 3
1 2
1 2
1
1
1
2
Total
quantities of each fruit simply doubled. For example, the ratio of bananas was 5:16, and is now 10:32. The ratio of oranges to apples was 4:7 and is now 8:14 The ratio of apples to other fruits was 7:9, and is now 14:18. 4. a. Student accurately completes the table and gives the correct answer: 8 drops of green and 20 drops of blue. Green
2
4
6
8
Blue
5
10
15
20
b. Student draws an accurate double number line and gives the correct answer: 70 drops of red and 30 drops of blue. Sample double number line: Red
14
28
42
56
70
Blue
6
12
18
24
30
5. a. Student draws an accurate tape diagram and gives the correct answer: 40 eggs 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan)
1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan)
1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1
1
1
3:5 6:10 9:15 12:20 15:25
b. Student gives an accurate explanation: To solve this problem, I had to pay attention to how many more eggs Brian painted than Ethan at each equivalent ratio. For example, when Ethan had painted 3 and Brian had painted 5, Brian had 2 more than Ethan. When Ethan had painted 9 and Brian had painted 15, Brian had 6 more than Ethan. When Ethan had painted 15 and Brian had painted 25, Brian finally had 10 more than Ethan. The question asks me how many eggs they painted altogether, so I added Ethan’s and Brian’s eggs (15 + 25) and got 40 eggs total.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 4
2
c. Student makes an accurate table and accurately graphs the ratios on a coordinate grid (including scale labels and title): Brian’s Eggs 5 10 15 20 25
Painted Eggs Number of Eggs Brian Painted
Ethan’s Eggs 3 6 9 12 15
2
35 30 25 20 15 10 5 0 0 3 6 9 12 15 18 Number of Eggs Ethan Painted
6. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Both the broccoli and tomato seeds have the greatest percentage of sprouted seeds. I know because I found the percentage of each type of seed that has sprouted: 75% of the broccoli seeds, 70% of the cauliflower seeds, 25% of the pumpkin seeds, 50% of the radish seeds, and 75% of the tomato seeds. The percentage of broccoli and tomato seeds is the greatest. b. Student gives the correct answer. 65% 7. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: The khakis have a greater dollar discount than the jeans. 15% off of $49 is a $7.35 savings, and 30% off of $23 is a $6.90 savings. Felipe would have a 45¢ greater discount if he bought the khakis. b. Student draws an accurate percentage bar and gives the correct answer: $18.00 Price
0
$6
$12
$18
$24
% Discount
0
25%
50%
75%
100%
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 5
2
1 2
1
8. a. Student gives the correct answer and shows accurate work: A liter is about 1 quart. (1.05669 quarts) b. Student gives the correct answer and shows accurate work: 380 km is about 236 miles (236.12 miles) Total
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Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Word Problems using Unit Rates
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. b. Solve unit rate problems including those involving unit pricing and constant speed.
MP.1 MP.2 MP.3 MP.4 MP.6 MP.7 MP.8
2. Word Problems using Equivalent Ratios
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MP.1 MP.2 MP.4 MP.6 MP.7 MP.8
3. Word Problems with Percentage and Measurement Ratios
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
MP.1 MP.2 MP.4 MP.6 MP.7 MP.8
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 1
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 2
Scoring Rubric Question 1. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Tangerines have the lowest cost per pound. I know because I found the unit rate for all of the fruits as follows: apples are 60¢ per pound, tangerines are 20¢ per pound, pears are 75¢ per pound, grapes are 80¢ per pound, and watermelon is 25¢ per pound. The price for tangerines is the least per pound. b. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: If I spent $1.00 on each kind of fruit, I would 1 buy 13 4 lb of fruit. I found this by finding out how many pounds of each kind of fruit I could buy for $1.00, then adding the weights. For $1, I could 2 1 1 buy 1 3 lb of apples, 5 lb of tangerines, 1 3 lb of pears, 1 4 lb of grapes, and 4
Points 2
2
1
lb of watermelon. This adds up to 13 4 lb of fruit. c. Student gives the correct answer and shows work. $5.55 2. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Mom got the best gas mileage because her car went more miles than anyone else’s car on one gallon of gas. I found my answer by finding the unit rate (miles per one gallon) for each family member. Great Uncle Emory got 18 mpg, Aunt Kathy got 21 mpg, Uncle Robert got 12 mpg, Mom got 31 mpg, and Grandma Lou got 27 mpg. Mom’s was the most miles per one gallon. b. Student gives the correct answer: $57.62 c. Student gives the correct answer: Great Uncle Emory is correct. His car 2 1 will use 1 3 gallons of gas, and Uncle Robert’s car will use 2 2 gallons of gas. 3. a. Student gives the correct answer and uses ratio language accurately. Wording may vary. Sample response: 5:16 Five of the 16 fruits are bananas. b. Student gives the correct answer and uses ratio language accurately. Wording may vary. Sample response: 4:7 For every 4 oranges there are 7 apples. c. Student gives the correct answer and uses ratio language accurately. Wording may vary. Sample response:7:9 For every 7 apples there are 9 non-apples. d. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Yes, the ratios would be equivalent since the Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 3
1 2
1 2
1
1
1
2
Total
quantities of each fruit simply doubled. For example, the ratio of bananas was 5:16, and is now 10:32. The ratio of oranges to apples was 4:7 and is now 8:14 The ratio of apples to other fruits was 7:9, and is now 14:18. 4. a. Student accurately completes the table and gives the correct answer: 8 drops of green and 20 drops of blue. Green
2
4
6
8
Blue
5
10
15
20
b. Student draws an accurate double number line and gives the correct answer: 70 drops of red and 30 drops of blue. Sample double number line: Red
14
28
42
56
70
Blue
6
12
18
24
30
5. a. Student draws an accurate tape diagram and gives the correct answer: 40 eggs 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan)
1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan)
1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan) 1 (Ethan)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian) 1 (Brian)
1
1
1
3:5 6:10 9:15 12:20 15:25
b. Student gives an accurate explanation: To solve this problem, I had to pay attention to how many more eggs Brian painted than Ethan at each equivalent ratio. For example, when Ethan had painted 3 and Brian had painted 5, Brian had 2 more than Ethan. When Ethan had painted 9 and Brian had painted 15, Brian had 6 more than Ethan. When Ethan had painted 15 and Brian had painted 25, Brian finally had 10 more than Ethan. The question asks me how many eggs they painted altogether, so I added Ethan’s and Brian’s eggs (15 + 25) and got 40 eggs total.
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 4
2
c. Student makes an accurate table and accurately graphs the ratios on a coordinate grid (including scale labels and title): Brian’s Eggs 5 10 15 20 25
Painted Eggs Number of Eggs Brian Painted
Ethan’s Eggs 3 6 9 12 15
2
35 30 25 20 15 10 5 0 0 3 6 9 12 15 18 Number of Eggs Ethan Painted
6. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: Both the broccoli and tomato seeds have the greatest percentage of sprouted seeds. I know because I found the percentage of each type of seed that has sprouted: 75% of the broccoli seeds, 70% of the cauliflower seeds, 25% of the pumpkin seeds, 50% of the radish seeds, and 75% of the tomato seeds. The percentage of broccoli and tomato seeds is the greatest. b. Student gives the correct answer. 65% 7. a. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: The khakis have a greater dollar discount than the jeans. 15% off of $49 is a $7.35 savings, and 30% off of $23 is a $6.90 savings. Felipe would have a 45¢ greater discount if he bought the khakis. b. Student draws an accurate percentage bar and gives the correct answer: $18.00 Price
0
$6
$12
$18
$24
% Discount
0
25%
50%
75%
100%
Copyright © Swun Math Grade 6 Unit 6 Constructed Response Rubric, Page 5
2
1 2
1
8. a. Student gives the correct answer and shows accurate work: A liter is about 1 quart. (1.05669 quarts) b. Student gives the correct answer and shows accurate work: 380 km is about 236 miles (236.12 miles) Total
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