G7 U2 Constructed Response Rubric
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers Scoring Rubric Task
Common Core State Standard
1. Addition and Subtraction of Signed Rational Numbers
7.NS.1c [m]: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7.NS.1d [m]: Apply properties of operations as strategies to add and subtract rational numbers.
2. Combining Opposite Quantities to make Zero
7.NS.1a [m]: Describe situations in which opposite quantities combine to make 0.
3. Absolute Value and Distances
7.NS.1b [m]: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
Standards for Mathematical Practice SMP.1, SMP. 2, SMP.3, SMP.4, SMP.5
SMP.1, SMP.3, SMP.4, SMP.6, SMP.8 SMP.1, SMP.3, SMP.4, SMP.6, SMP.8
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 [a/s]: additional/supporting standard
Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 1
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers Scoring Rubric Question 1. a. Student gives correct answer: 65 + (−15) + 30 b. Student gives explanation: Each value and mathematical symbol in the equation I wrote relates to the situation described in various ways. I am told in the problem that the kite rises to 65ft when Christine releases it so my first number in the equation represents this first height. I am then told that as the wind dies down the kites lowers 15ft in height, so this value is represented by the -15, with the negative representing the decrease in height. The last piece of information I am given is that the kite rises 30ft, so this is represented by the +30 in the equation because of the increase. c. Student gives correct answer and shows work: 80ft 2. a. Student gives correct answer: 4,421.0𝑚 + (−86.0𝑚) b. Student gives correct answer and shows work: 4, 335.0 m c. Student creates diagram: Answers may vary
Points 0.25 0.5
0.25 0.5 0.5 0.5
Mt. Whitney 4,421.0 meters
0 meters Badwater Basin: -86.0 meters
d. Student gives explanation: No it would not make sense for the distance between the two points to be negative because distance cannot be negative. 3. a. Student completes table and gives correct answers: Expression 1= 6; Expression 2= 18 b. Student gives circles correct answer and gives explanation for each scenario: Scenario A: Expression 2 Explanation: Scenario A is best represented by Expression 2 because the problem is asking for the change in temperature. To find the change in temperature you need to subtract the original temperature at midnight from the new temperature at 10 am the next morning, and this set up can be seen in Expression 2. Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 2
0.5 0.5 1.5
Total
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers
Scenario B: Expression 1 Explanation: Scenario B is best represented by Expression 1, because the problem is asking for the final temperature after the temperature fell 6°𝐹. To find the final temperature the two values needed to be added together. However, since there was a drop in temperature, it is represented in the equation by −6°𝐹, which means you need to subtract the two temperatures, and this can be seen in Expression 1. 4. a. Student gives explanation: Since we are told that points s and t are the same distance from zero I know that the expression s + t is equal to zero. I know this because after analyzing the number line I observed that points s and t are on different sides of zero. Point t is on the negative side of zero and s is on the positive side. With this information and the fact that I am told that point s and t are at an equal distance from zero, I know that I am adding opposite positive and negative values, which will equal zero. b. Student gives two correct examples: Answers may vary; Ex. 4 + (−4) = 0, 6 + (−6) = 0 5. a. Student gives correct answer and shows work: 30 ft b. Student creates illustration: 30ft 30ft
0.25
0.5 1 1
22ft
15ft
0ft 6. a. Student gives correct answer and shows work: -$39.43 b. Student creates number line: -$45.12
-$39.43
-$18.26
0 $5.69 $23.95
-$85.00
1 0.75 -$15.00
$109.9
$125
c. Student gives explanation: In order for Pam to have the same balance Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 3
0.5
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers she had before, she needs to deposit $164.43 back into her account. This amount is the total she spent on all the items she purchased. Her balance after all these purchases was brought down to -$39.43, so to get it back to its original amount, she needs to deposit $39.43 to get it back to zero, and then $125 to get it back up to $125. These two amounts are equal to a total deposit of $164.43. 7. a. Student gives correct answer and explanation: After analyzing her answer I was able to conclude that Marlene’s answer was incorrect because distance is not measured in negative units. If I started at the point -10 and counted upwards to 25 my answer would be the absolute value of -35, so the distance between the points will always be positive. b. Student gives correct answers and shows work: |−35| = 35 8. a. Student gives explanation: After analyzing the expressions I predict that the solutions will be different. I can make this prediction because inside the absolute value bar is the absolute value of -12 and +12, which are both equal to 12. The expressions should be identical once this absolute value is taken as well as their answers. b. Student gives explanation: Both expressions will have an answer of 24. 9. a. Student gives explanation: The direction in which they measure the distance between their home and the school will not matter. If they start measuring from their home to the school or from their school to their home, the value of the distance is the same because the absolute value of the distance will always make the value positive. b. Student creates illustration: Home
(South)
0.5
0.5 1
1 1
1
(North)
School
Test Total
Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 4
15
Common Core State Standard
1. Addition and Subtraction of Signed Rational Numbers
7.NS.1c [m]: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7.NS.1d [m]: Apply properties of operations as strategies to add and subtract rational numbers.
2. Combining Opposite Quantities to make Zero
7.NS.1a [m]: Describe situations in which opposite quantities combine to make 0.
3. Absolute Value and Distances
7.NS.1b [m]: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
Standards for Mathematical Practice SMP.1, SMP. 2, SMP.3, SMP.4, SMP.5
SMP.1, SMP.3, SMP.4, SMP.6, SMP.8 SMP.1, SMP.3, SMP.4, SMP.6, SMP.8
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 [a/s]: additional/supporting standard
Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 1
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers Scoring Rubric Question 1. a. Student gives correct answer: 65 + (−15) + 30 b. Student gives explanation: Each value and mathematical symbol in the equation I wrote relates to the situation described in various ways. I am told in the problem that the kite rises to 65ft when Christine releases it so my first number in the equation represents this first height. I am then told that as the wind dies down the kites lowers 15ft in height, so this value is represented by the -15, with the negative representing the decrease in height. The last piece of information I am given is that the kite rises 30ft, so this is represented by the +30 in the equation because of the increase. c. Student gives correct answer and shows work: 80ft 2. a. Student gives correct answer: 4,421.0𝑚 + (−86.0𝑚) b. Student gives correct answer and shows work: 4, 335.0 m c. Student creates diagram: Answers may vary
Points 0.25 0.5
0.25 0.5 0.5 0.5
Mt. Whitney 4,421.0 meters
0 meters Badwater Basin: -86.0 meters
d. Student gives explanation: No it would not make sense for the distance between the two points to be negative because distance cannot be negative. 3. a. Student completes table and gives correct answers: Expression 1= 6; Expression 2= 18 b. Student gives circles correct answer and gives explanation for each scenario: Scenario A: Expression 2 Explanation: Scenario A is best represented by Expression 2 because the problem is asking for the change in temperature. To find the change in temperature you need to subtract the original temperature at midnight from the new temperature at 10 am the next morning, and this set up can be seen in Expression 2. Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 2
0.5 0.5 1.5
Total
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers
Scenario B: Expression 1 Explanation: Scenario B is best represented by Expression 1, because the problem is asking for the final temperature after the temperature fell 6°𝐹. To find the final temperature the two values needed to be added together. However, since there was a drop in temperature, it is represented in the equation by −6°𝐹, which means you need to subtract the two temperatures, and this can be seen in Expression 1. 4. a. Student gives explanation: Since we are told that points s and t are the same distance from zero I know that the expression s + t is equal to zero. I know this because after analyzing the number line I observed that points s and t are on different sides of zero. Point t is on the negative side of zero and s is on the positive side. With this information and the fact that I am told that point s and t are at an equal distance from zero, I know that I am adding opposite positive and negative values, which will equal zero. b. Student gives two correct examples: Answers may vary; Ex. 4 + (−4) = 0, 6 + (−6) = 0 5. a. Student gives correct answer and shows work: 30 ft b. Student creates illustration: 30ft 30ft
0.25
0.5 1 1
22ft
15ft
0ft 6. a. Student gives correct answer and shows work: -$39.43 b. Student creates number line: -$45.12
-$39.43
-$18.26
0 $5.69 $23.95
-$85.00
1 0.75 -$15.00
$109.9
$125
c. Student gives explanation: In order for Pam to have the same balance Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 3
0.5
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers she had before, she needs to deposit $164.43 back into her account. This amount is the total she spent on all the items she purchased. Her balance after all these purchases was brought down to -$39.43, so to get it back to its original amount, she needs to deposit $39.43 to get it back to zero, and then $125 to get it back up to $125. These two amounts are equal to a total deposit of $164.43. 7. a. Student gives correct answer and explanation: After analyzing her answer I was able to conclude that Marlene’s answer was incorrect because distance is not measured in negative units. If I started at the point -10 and counted upwards to 25 my answer would be the absolute value of -35, so the distance between the points will always be positive. b. Student gives correct answers and shows work: |−35| = 35 8. a. Student gives explanation: After analyzing the expressions I predict that the solutions will be different. I can make this prediction because inside the absolute value bar is the absolute value of -12 and +12, which are both equal to 12. The expressions should be identical once this absolute value is taken as well as their answers. b. Student gives explanation: Both expressions will have an answer of 24. 9. a. Student gives explanation: The direction in which they measure the distance between their home and the school will not matter. If they start measuring from their home to the school or from their school to their home, the value of the distance is the same because the absolute value of the distance will always make the value positive. b. Student creates illustration: Home
(South)
0.5
0.5 1
1 1
1
(North)
School
Test Total
Copyright © Swun Math Grade 7 Unit 2 Constructed Response Rubric, Page 4
15
