G6 U3 Constructed Response Rubric
Grade 6 Unit 3 Constructed Response Graphing Scoring Rubric Task
Common Core State Standard
1. Ordered Points on a Plane
2. Symmetry, Rational Numbers and the Coordinate Plane
3. Absolute Value and Polygons on the Coordinate Plane
6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.G.3: Draw polygons in the coordinate plane given coordinates for the vertices;
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 1
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.4, SMP.6
SMP.1, SMP.2, SMP.4, SMP.6
SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.7
Grade 6 Unit 3 Constructed Response Graphing use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical 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.
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 2
Grade 6 Unit 3 Constructed Response Graphing Scoring Rubric Question 1. a. Student graphs and labels point S at (–8, –4)
Points 0.5
b. Student graphs and labels point T at (5, –1) c. Student names ordered pair: (5, 6) d. Student names ordered pair: (–4, –2) e. Student gives explanation: In order to plot an ordered pair on a coordinate grid, start at the origin of the grid which is (0, 0). Second, identify the x value, which is the first number in the ordered pair. Move that many units either to the right (for positive values) or the left (for negative values) along the horizontal xaxis. Third, identify the y-value, which is the second number in the ordered pair. From the point you moved to along the x-axis you need to move up (for positive values) or down (for negative values) on the y-axis and mark the position with a point.
2. a. Student creates coordinate grid:
0.5
1.5
10 9 8 7
E
6
F
5 4
B A
3 2 1 -100 -90 -80 −70 −60 −50 −40 −30 −20 −10 −1
10 20 30 40 50 60 70 80 90 100
−2
C
−3 −4 −5 −6 −7 −8
D
−9 −10
b. Student completes table with correct answers: Point A B C D E F
Quadrant I I IV III II II Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 3
0.5
Total
Grade 6 Unit 3 Constructed Response Graphing 3. a. Student gives explanation: In order to find the range and scale of the x and y-axes, I first had to look at the range of values used for the x coordinates. The lowest value is −20 and the highest value is 90. So, the scale on the x-axis I chose included the range of −100 to 100. The scale I used for this axis was 10 units. The next thing I looked at was the range of values used for the y coordinates. The lowest value was −8 and the highest value was 7. The scale I chose for the y-axis included the range of −10 to 10. The scale I used for this axis was of 1 unit. b. Student gives explanation: A mathematical concept or tool that I learned about that connected to these two questions was the use of a number line. This tool connected to these two problems because as in number lines positive numbers are to the right of and above zero, and negative numbers are to the left of and below zero. 4. a. Student creates coordinate grid:
1
1
1
7 6 5 4 3
S
2 1
-−7 −6 −5 −4 −3
−2 −1
1
2
3
4
5
6
7
−1 −2 −3
T
−4 −5 −6 −7
V
U
b. Student gives explanation: For the first group of ordered pairs, I found that point S was located in the in Quadrant II and point T was located in Quadrant IV. After analyzing their locations I was able to conclude that points S and T were reflected over both the y-axis and the x-axis. For the second group of ordered pairs, I found that point U was located in Quadrant IV and point V was located in Quadrant III. After analyzing their locations I was able to conclude that points S and T were reflected over both The y-axis.
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 4
1
Grade 6 Unit 3 Constructed Response Graphing 5. a. Student creates coordinate grid:
1
7 6 5
F
4 3
B
2 1
A -−7 −6 −5 −4 −3
−2 −1
1 −1
C
2
3
4
5
6
7
E
−2 −3 −4 −5 −6
D
−7
6. A. Student gives correct answer and explanation: The types of numbers in this question are rational numbers. A rational number is any number that can be written in fraction form where the denominator is a non-zero number. This included integers, terminating decimals, and repeating decimals. b. Student gives explanation: The process for placing these points on the grid was the same as when I worked with integers. The only difference here was that I was working with decimals instead of just whole numbers, so I had to figure out where the decimal had to be placed on the grid between the whole numbers. 7. a. Student gives correct answer and explanation: After analyzing the coordinate grid and Stan’s work, I was able to determine that his process for finding the distance between the two points was incorrect. The error he made was that he added the x coordinates without taking the absolute value of each number. Just by looking at the position of the points of the grid you can tell that his answer of 3 for the distance between the points does not make sense. To find the correct answer he should have set up the absolute equation |−2| + |3| =?, and solved for the missing distance. b. Students gives correct answer and shows work: 7
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 5
1
1
0.75
0.25
Grade 6 Unit 3 Constructed Response Graphing 8. a. Student creates coordinate grid and gives correct answer: S ( −4, −3.5)
0.5
10 9 8 7
P
Q
6 5 4 3 2 1
-10 -9
-8 −7 −6 −5 −4 −3
−2 −1
1
2
3
4
5
6
7
8
9 10
−1 −2 −3
S
−4
R
−5 −6 −7 −8 −9 −10
b. Student gives correct answers and shows work: Perimeter: 42 units; Area: 110 units2 c. Student gives explanation: In order to find the perimeter and the area of the rectangle PQRS I first had to find the distance between the points that made up a side of the shape. Since I was told this shape is a rectangle and my coordinate grid confirmed it, I proceeded to find the length and width of two sides. The first two points I looked at were P and S. Since they shared an x coordinate I wrote an absolute value equation using the y coordinates. The equation was: |7.5| + |−3.5| = 11. The next two points I looked at were S and R. Since they shared a y coordinate I wrote an absolute value equation using the x coordinates. The equation was: |−4| + |6| = 10. Since I knew the length of PS I also knew the length of segment QR, and with the length of SR I also knew the length of PQ. With this information I could now move on to finding the perimeter and area. To find the perimeter I had to add up all the sides so 10 + 10 + 11 + 11= 42 units. To find the area I had to use to use the equation A= l × w, so 10 × 11= 110 units2. 9. a, b, c. Student creates coordinate grid: Check student’s grid for accuracy; points should be plotted and labeled correctly. See example below:
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 6
0.5 1
1.25
Grade 6 Unit 3 Constructed Response Graphing Family Restaurant (−1.5, 7 1/2)
10 9 8 7 6 5 4
Charlene’s Home (−7, 3)
3
-10 -9
-8 −7 −6 −5 −4 −3
Antique Stop (5, 3)
2
(−1.5, 3)
1
−2 −1
1
2
3
4
5
6
7
8
9 10
−1 −2 −3 −4 −5
Gina’s Home
−6 −7 −8 −9 −10
d. Student gives correct answer and shows work: |−7| + |5| = 12 e. Student gives correct answer and shows work: 20 miles f. Student completes coordinate grid: Check Student’s grid for accuracy; points should be plotted and labelled correctly. See example above. g. Student gives correct answer and shows work: 14.63 mi2 Test Total
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 7
0.25 0.25
0.25 15
Common Core State Standard
1. Ordered Points on a Plane
2. Symmetry, Rational Numbers and the Coordinate Plane
3. Absolute Value and Polygons on the Coordinate Plane
6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.NS.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.G.3: Draw polygons in the coordinate plane given coordinates for the vertices;
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 1
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.4, SMP.6
SMP.1, SMP.2, SMP.4, SMP.6
SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.7
Grade 6 Unit 3 Constructed Response Graphing use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical 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.
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 2
Grade 6 Unit 3 Constructed Response Graphing Scoring Rubric Question 1. a. Student graphs and labels point S at (–8, –4)
Points 0.5
b. Student graphs and labels point T at (5, –1) c. Student names ordered pair: (5, 6) d. Student names ordered pair: (–4, –2) e. Student gives explanation: In order to plot an ordered pair on a coordinate grid, start at the origin of the grid which is (0, 0). Second, identify the x value, which is the first number in the ordered pair. Move that many units either to the right (for positive values) or the left (for negative values) along the horizontal xaxis. Third, identify the y-value, which is the second number in the ordered pair. From the point you moved to along the x-axis you need to move up (for positive values) or down (for negative values) on the y-axis and mark the position with a point.
2. a. Student creates coordinate grid:
0.5
1.5
10 9 8 7
E
6
F
5 4
B A
3 2 1 -100 -90 -80 −70 −60 −50 −40 −30 −20 −10 −1
10 20 30 40 50 60 70 80 90 100
−2
C
−3 −4 −5 −6 −7 −8
D
−9 −10
b. Student completes table with correct answers: Point A B C D E F
Quadrant I I IV III II II Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 3
0.5
Total
Grade 6 Unit 3 Constructed Response Graphing 3. a. Student gives explanation: In order to find the range and scale of the x and y-axes, I first had to look at the range of values used for the x coordinates. The lowest value is −20 and the highest value is 90. So, the scale on the x-axis I chose included the range of −100 to 100. The scale I used for this axis was 10 units. The next thing I looked at was the range of values used for the y coordinates. The lowest value was −8 and the highest value was 7. The scale I chose for the y-axis included the range of −10 to 10. The scale I used for this axis was of 1 unit. b. Student gives explanation: A mathematical concept or tool that I learned about that connected to these two questions was the use of a number line. This tool connected to these two problems because as in number lines positive numbers are to the right of and above zero, and negative numbers are to the left of and below zero. 4. a. Student creates coordinate grid:
1
1
1
7 6 5 4 3
S
2 1
-−7 −6 −5 −4 −3
−2 −1
1
2
3
4
5
6
7
−1 −2 −3
T
−4 −5 −6 −7
V
U
b. Student gives explanation: For the first group of ordered pairs, I found that point S was located in the in Quadrant II and point T was located in Quadrant IV. After analyzing their locations I was able to conclude that points S and T were reflected over both the y-axis and the x-axis. For the second group of ordered pairs, I found that point U was located in Quadrant IV and point V was located in Quadrant III. After analyzing their locations I was able to conclude that points S and T were reflected over both The y-axis.
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 4
1
Grade 6 Unit 3 Constructed Response Graphing 5. a. Student creates coordinate grid:
1
7 6 5
F
4 3
B
2 1
A -−7 −6 −5 −4 −3
−2 −1
1 −1
C
2
3
4
5
6
7
E
−2 −3 −4 −5 −6
D
−7
6. A. Student gives correct answer and explanation: The types of numbers in this question are rational numbers. A rational number is any number that can be written in fraction form where the denominator is a non-zero number. This included integers, terminating decimals, and repeating decimals. b. Student gives explanation: The process for placing these points on the grid was the same as when I worked with integers. The only difference here was that I was working with decimals instead of just whole numbers, so I had to figure out where the decimal had to be placed on the grid between the whole numbers. 7. a. Student gives correct answer and explanation: After analyzing the coordinate grid and Stan’s work, I was able to determine that his process for finding the distance between the two points was incorrect. The error he made was that he added the x coordinates without taking the absolute value of each number. Just by looking at the position of the points of the grid you can tell that his answer of 3 for the distance between the points does not make sense. To find the correct answer he should have set up the absolute equation |−2| + |3| =?, and solved for the missing distance. b. Students gives correct answer and shows work: 7
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 5
1
1
0.75
0.25
Grade 6 Unit 3 Constructed Response Graphing 8. a. Student creates coordinate grid and gives correct answer: S ( −4, −3.5)
0.5
10 9 8 7
P
Q
6 5 4 3 2 1
-10 -9
-8 −7 −6 −5 −4 −3
−2 −1
1
2
3
4
5
6
7
8
9 10
−1 −2 −3
S
−4
R
−5 −6 −7 −8 −9 −10
b. Student gives correct answers and shows work: Perimeter: 42 units; Area: 110 units2 c. Student gives explanation: In order to find the perimeter and the area of the rectangle PQRS I first had to find the distance between the points that made up a side of the shape. Since I was told this shape is a rectangle and my coordinate grid confirmed it, I proceeded to find the length and width of two sides. The first two points I looked at were P and S. Since they shared an x coordinate I wrote an absolute value equation using the y coordinates. The equation was: |7.5| + |−3.5| = 11. The next two points I looked at were S and R. Since they shared a y coordinate I wrote an absolute value equation using the x coordinates. The equation was: |−4| + |6| = 10. Since I knew the length of PS I also knew the length of segment QR, and with the length of SR I also knew the length of PQ. With this information I could now move on to finding the perimeter and area. To find the perimeter I had to add up all the sides so 10 + 10 + 11 + 11= 42 units. To find the area I had to use to use the equation A= l × w, so 10 × 11= 110 units2. 9. a, b, c. Student creates coordinate grid: Check student’s grid for accuracy; points should be plotted and labeled correctly. See example below:
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 6
0.5 1
1.25
Grade 6 Unit 3 Constructed Response Graphing Family Restaurant (−1.5, 7 1/2)
10 9 8 7 6 5 4
Charlene’s Home (−7, 3)
3
-10 -9
-8 −7 −6 −5 −4 −3
Antique Stop (5, 3)
2
(−1.5, 3)
1
−2 −1
1
2
3
4
5
6
7
8
9 10
−1 −2 −3 −4 −5
Gina’s Home
−6 −7 −8 −9 −10
d. Student gives correct answer and shows work: |−7| + |5| = 12 e. Student gives correct answer and shows work: 20 miles f. Student completes coordinate grid: Check Student’s grid for accuracy; points should be plotted and labelled correctly. See example above. g. Student gives correct answer and shows work: 14.63 mi2 Test Total
Copyright © Swun Math Grade 6 Unit 3 Constructed Response Rubric, Page 7
0.25 0.25
0.25 15
