G7 U1 Constructed Response Rubric
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships Scoring Rubric Task
1. Ratios, Proportions, and Strategies for Testing Proportional Relationships
Common Core State Standard 7.RP.1 [m]: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2a [m]: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Standards for Mathematical Practice SMP.1, SMP. 2, SMP.3, SMP.4, SMP.5
2. Constant of Proportionality and Proportional Relationships as Equations
7.RP.2b [m]: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.2c [m]: Represent proportional relationships by equations.
SMP.1, SMP.3, SMP.4, SMP.5, SMP.6, SMP.8
SMP.1, SMP.3, SMP.6, SMP.8
3. Interpreting Graphs and Applications of Proportional Relationships
7.RP.2d [m]: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.3 [m]: Use proportional relationships to solve multistep ratio and percent problems.
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. [m]: major work for grade level Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 1
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships
[a/s]: additional/supporting standard
Scoring Rubric Question 1. a. Student gives explanation: After analyzing the data I was able to determine that the units being used in this problem are dollars for the money earned and hours for the time worked. The 135 and 120 represent the amount of money Neil earns at each job and the 9 and 6 represent the hours he works at each job. The unit rate in this problem is the dollars earned per hour. b. Student gives correct answer and shows work: Job: Pet Groomers; Rate: $20 per hour c. Student gives explanation: To find the unit rate I had to divide the amount of money he earned by the number of hours he worked, so to check that my answer is correct I would use the inverse operation which is multiplication. I can multiply the unit rate Neil works for at each job by the total number of hours he worked for, if this answer is equal to the amount he earned that is given to me in the problem, then I know my answer is correct. 2. a. Student gives correct answer and completes table: Mathematical process: Student should place data for each day in a ratio in fraction form and simplify each fraction. This should reveal equivalent fractions/ratios for each day. Explanation of Steps: In order to determine if there is a proportional relationship I had to write the data given for the number of laps and the time as ratios in fraction form for each day. Since none of the fractions had a common denominator I had to convert each fraction to one with a common denominator. I did this by simplifying each fraction and this revealed an equivalent fraction for all three days, 4/7. Answer: The number of laps she swam is proportional to the time it took her to complete the laps over the three days. I know this is correct because each day Misty swam had ratios that were equivalent fractions of 4/7. b. Student gives correct answer and explanation: If Misty had swam 12 laps in 14 minutes this would have made the relationship non-proportional. The reason for this is because the ratio in this case is 6/7 which is not proportional to the ratio for Wednesday and Thursday. With this ratio she is actually swimming faster than on the other two days.
Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 2
Points 0.25
0.5 0.25
1.5
0.5
Total
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships
3. a. Student identifies math tool and gives explanation: After analyzing the data in the table, I was able to determine that a good math tool I could use to determine if there is a proportional relationship is a coordinate plane. This tool would be useful because after plotting the coordinate pair created from the data I can determine if there is a proportional relationship based on their position on the coordinate plane. If the points lie on a straight line then I know the relationship is proportional. If a straight line cannot be drawn through the points, then the relationship is not proportional. b. Student creates coordinate plane, table displaying coordinate pairs and gives correct answer with explanation: Kicker
Speed (meters per second)
1 2 3 4 5
Distance (meters) 35 45 68 60 64
Speed (meters per second) 15 19 26 18 22
(x, y) (35, 15) (45, 19) (68, 26) (60, 18) (64, 22)
30 (68, 26) (64, 22) (60, 18)
25 20
(45, 19)
15 (35, 15)
10 5 0 0
20
40
60
80
Distance (meters)
Based on the coordinate plane I created I was able to determine that there is no proportional relationship between the soccer players kicking distance and speed. I know this because after creating my coordinate plane and plotting the ordered pairs I made based on the data for each kicker I was not able to draw a straight line through all five points. In order for there to be a proportional relationship between the quantities all their coordinates must lie on the same straight line. Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 3
0.5
1.5
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships
4. a. Student creates table and gives correct answer: Yes the relationship is proportional. Weight (lbs) 4 8 12
0.25
Price $3.52 $7.04 $10.56
b. Student creates coordinate plane:
c. Student provides correct answer: $0.88 per pound 5. a. Student gives correct answer and explanation: Variables student chooses may vary; Ex. The equation that best represents the relationship between her pay and the total number of hours she works is P = r h. In this equation P represents her total pay, r represents the rate she works for, and h represents the number of hours she works. b. Student gives explanation: Based on the proportional relationship that exists between her pay and the total number of hours she works, I can predict that as the number of hours she works increases her pay will increase as well. This will remain true as long as her hourly rate remains constant. 6. a. Student creates table with correct answers for the number of hours given: P=rh Hours worked Pay Received 3 $14.25 Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 4
0.5
0.25 1
1
1
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 5 7
$23.75 $33.25
b. Student gives explanation: After creating the table I was able to determine that the prediction I made in question 5b was true. I know this because as I plugged in an increasing number of hours that Stella worked I also saw an increase in her pay. For example, working at a constant rate of $4.75 per hour she earned: $14.25 for 3 hours worked, $23.75 for 5 hours worked and $33.25for 7 hours worked. As can be seen in the numbers the number of hours Stella works also increases her pay. 7. a. Student gives correct answer: Each point (x,y), on both graphs represents the y number of miles he drives in x amount of hours throughout each day. b. Student gives correct answer: The (0,0) represents no miles being driven in zero hours. In terms of the scenario given in the problem this could represent the starting point, or location, of each day in his trip before he starts driving. c. Student gives correct answers and shows work: Day 1: 66.25 miles per hour; Day 2: 64.6 miles per hour d. Student gives correct answer: Since Mitch had a unit rate of 66.25 miles per hour on day one, I know that in the point (1, r), the one is equal to one hour and r is going to be equal to 66.25 miles. On day two Mitch had a unit rate of 64.6 miles per hour, so I know that in the point (1, r), the one is equal to one hour and r is going to be equal to 64.6 miles. e. Student gives correct answer and explanation: Mitch drove the most miles on Day one of his trip. I know this because I did a comparison of the units rates for each day he drove. On day one he had a unit rate of 66.25 miles per hour in comparison to a smaller unit rate of 64.6 miles per hour on day two. Since he drove more miles per hour on day one, this means that he covered more miles total in the seven hours he drove that day than in seven hours he drove on day two. 8. a. Student gives correct answers and shows work: Store: Store 2; Price: $18.60. b. Student gives explanation: In order to find my answer I had to first find the total discount being taken off the sweater for each store. This step was the most important because the discount amount was how much I was going to subtract from the original prices of sweaters, which would then allow me to make my comparison between the two prices later. In order to find the amount of discount I had to write each percent as a ratio in which the percent number was placed over 100. I simplified each ratio and set up Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 5
1
0.25
0.25
0.25 0.5
0.5
0.5 1
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships a proportion. In this proportion I had the ratio of the percentage equal to the ratio of the unknown discount over the known price. My next step from there was to solve the proportion for the unknown discount using cross multiplication. Once I found that amount of discount from each store I subtracted it from each price. These new discounted prices I found were $19.13 for Store 1 and $18.60 for Store 2, based on these numbers I was able to determine that Store 2 had the best price. c. Student gives correct answer and shows work: 7.37% 9. a. Student gives correct answer and shows work: $327.53 b. Student gives correct answer and shows work: $229.27 c. Student gives explanation and shows work: I know that my answer is correct because I added $98.26, which is the percent of money he took out, to the remaining balance he had left in the account after the withdrawal and my answer was $327.53. This number is the original amount of money he had in the account before the withdrawal so I know that my answer is correct. Test Total
Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 6
0.25 1 0.25 0.25
15
1. Ratios, Proportions, and Strategies for Testing Proportional Relationships
Common Core State Standard 7.RP.1 [m]: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2a [m]: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Standards for Mathematical Practice SMP.1, SMP. 2, SMP.3, SMP.4, SMP.5
2. Constant of Proportionality and Proportional Relationships as Equations
7.RP.2b [m]: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.2c [m]: Represent proportional relationships by equations.
SMP.1, SMP.3, SMP.4, SMP.5, SMP.6, SMP.8
SMP.1, SMP.3, SMP.6, SMP.8
3. Interpreting Graphs and Applications of Proportional Relationships
7.RP.2d [m]: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.3 [m]: Use proportional relationships to solve multistep ratio and percent problems.
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. [m]: major work for grade level Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 1
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships
[a/s]: additional/supporting standard
Scoring Rubric Question 1. a. Student gives explanation: After analyzing the data I was able to determine that the units being used in this problem are dollars for the money earned and hours for the time worked. The 135 and 120 represent the amount of money Neil earns at each job and the 9 and 6 represent the hours he works at each job. The unit rate in this problem is the dollars earned per hour. b. Student gives correct answer and shows work: Job: Pet Groomers; Rate: $20 per hour c. Student gives explanation: To find the unit rate I had to divide the amount of money he earned by the number of hours he worked, so to check that my answer is correct I would use the inverse operation which is multiplication. I can multiply the unit rate Neil works for at each job by the total number of hours he worked for, if this answer is equal to the amount he earned that is given to me in the problem, then I know my answer is correct. 2. a. Student gives correct answer and completes table: Mathematical process: Student should place data for each day in a ratio in fraction form and simplify each fraction. This should reveal equivalent fractions/ratios for each day. Explanation of Steps: In order to determine if there is a proportional relationship I had to write the data given for the number of laps and the time as ratios in fraction form for each day. Since none of the fractions had a common denominator I had to convert each fraction to one with a common denominator. I did this by simplifying each fraction and this revealed an equivalent fraction for all three days, 4/7. Answer: The number of laps she swam is proportional to the time it took her to complete the laps over the three days. I know this is correct because each day Misty swam had ratios that were equivalent fractions of 4/7. b. Student gives correct answer and explanation: If Misty had swam 12 laps in 14 minutes this would have made the relationship non-proportional. The reason for this is because the ratio in this case is 6/7 which is not proportional to the ratio for Wednesday and Thursday. With this ratio she is actually swimming faster than on the other two days.
Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 2
Points 0.25
0.5 0.25
1.5
0.5
Total
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships
3. a. Student identifies math tool and gives explanation: After analyzing the data in the table, I was able to determine that a good math tool I could use to determine if there is a proportional relationship is a coordinate plane. This tool would be useful because after plotting the coordinate pair created from the data I can determine if there is a proportional relationship based on their position on the coordinate plane. If the points lie on a straight line then I know the relationship is proportional. If a straight line cannot be drawn through the points, then the relationship is not proportional. b. Student creates coordinate plane, table displaying coordinate pairs and gives correct answer with explanation: Kicker
Speed (meters per second)
1 2 3 4 5
Distance (meters) 35 45 68 60 64
Speed (meters per second) 15 19 26 18 22
(x, y) (35, 15) (45, 19) (68, 26) (60, 18) (64, 22)
30 (68, 26) (64, 22) (60, 18)
25 20
(45, 19)
15 (35, 15)
10 5 0 0
20
40
60
80
Distance (meters)
Based on the coordinate plane I created I was able to determine that there is no proportional relationship between the soccer players kicking distance and speed. I know this because after creating my coordinate plane and plotting the ordered pairs I made based on the data for each kicker I was not able to draw a straight line through all five points. In order for there to be a proportional relationship between the quantities all their coordinates must lie on the same straight line. Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 3
0.5
1.5
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships
4. a. Student creates table and gives correct answer: Yes the relationship is proportional. Weight (lbs) 4 8 12
0.25
Price $3.52 $7.04 $10.56
b. Student creates coordinate plane:
c. Student provides correct answer: $0.88 per pound 5. a. Student gives correct answer and explanation: Variables student chooses may vary; Ex. The equation that best represents the relationship between her pay and the total number of hours she works is P = r h. In this equation P represents her total pay, r represents the rate she works for, and h represents the number of hours she works. b. Student gives explanation: Based on the proportional relationship that exists between her pay and the total number of hours she works, I can predict that as the number of hours she works increases her pay will increase as well. This will remain true as long as her hourly rate remains constant. 6. a. Student creates table with correct answers for the number of hours given: P=rh Hours worked Pay Received 3 $14.25 Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 4
0.5
0.25 1
1
1
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 5 7
$23.75 $33.25
b. Student gives explanation: After creating the table I was able to determine that the prediction I made in question 5b was true. I know this because as I plugged in an increasing number of hours that Stella worked I also saw an increase in her pay. For example, working at a constant rate of $4.75 per hour she earned: $14.25 for 3 hours worked, $23.75 for 5 hours worked and $33.25for 7 hours worked. As can be seen in the numbers the number of hours Stella works also increases her pay. 7. a. Student gives correct answer: Each point (x,y), on both graphs represents the y number of miles he drives in x amount of hours throughout each day. b. Student gives correct answer: The (0,0) represents no miles being driven in zero hours. In terms of the scenario given in the problem this could represent the starting point, or location, of each day in his trip before he starts driving. c. Student gives correct answers and shows work: Day 1: 66.25 miles per hour; Day 2: 64.6 miles per hour d. Student gives correct answer: Since Mitch had a unit rate of 66.25 miles per hour on day one, I know that in the point (1, r), the one is equal to one hour and r is going to be equal to 66.25 miles. On day two Mitch had a unit rate of 64.6 miles per hour, so I know that in the point (1, r), the one is equal to one hour and r is going to be equal to 64.6 miles. e. Student gives correct answer and explanation: Mitch drove the most miles on Day one of his trip. I know this because I did a comparison of the units rates for each day he drove. On day one he had a unit rate of 66.25 miles per hour in comparison to a smaller unit rate of 64.6 miles per hour on day two. Since he drove more miles per hour on day one, this means that he covered more miles total in the seven hours he drove that day than in seven hours he drove on day two. 8. a. Student gives correct answers and shows work: Store: Store 2; Price: $18.60. b. Student gives explanation: In order to find my answer I had to first find the total discount being taken off the sweater for each store. This step was the most important because the discount amount was how much I was going to subtract from the original prices of sweaters, which would then allow me to make my comparison between the two prices later. In order to find the amount of discount I had to write each percent as a ratio in which the percent number was placed over 100. I simplified each ratio and set up Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 5
1
0.25
0.25
0.25 0.5
0.5
0.5 1
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships a proportion. In this proportion I had the ratio of the percentage equal to the ratio of the unknown discount over the known price. My next step from there was to solve the proportion for the unknown discount using cross multiplication. Once I found that amount of discount from each store I subtracted it from each price. These new discounted prices I found were $19.13 for Store 1 and $18.60 for Store 2, based on these numbers I was able to determine that Store 2 had the best price. c. Student gives correct answer and shows work: 7.37% 9. a. Student gives correct answer and shows work: $327.53 b. Student gives correct answer and shows work: $229.27 c. Student gives explanation and shows work: I know that my answer is correct because I added $98.26, which is the percent of money he took out, to the remaining balance he had left in the account after the withdrawal and my answer was $327.53. This number is the original amount of money he had in the account before the withdrawal so I know that my answer is correct. Test Total
Copyright © Swun Math Grade 7 Unit 1 Constructed Response Rubric, Page 6
0.25 1 0.25 0.25
15
