G3 U10 Constructed Response Rubric
Grade 3 Unit 10 Constructed Response Measurement Description Task
1. Finding the Area of Rectangles
2. Find the Area of Rectangles using the Distributive Property and Decomposition
Common Core State Standard for Mathematical Content (MC) 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7 Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. 3.MD.7 Relate area to the operations of multiplication and addition. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP)
MP.1 MP.3 MP.4 MP.6 MP.7 MP.8
MP.1 MP.2 MP.3 MP.4 MP.6 MP.7 MP.8
3. Area and Perimeter of Rectangles and Complex Figures
3.MD.7 Relate area to the operations of multiplication and addition. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
MP.1 MP.2 MP.4 MP.6 MP.7 MP.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.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 2
Scoring Rubric Points 1 1 1
1 1
Wall = 5 yards
Question 1. a. Student gives the correct answer: 81 square feet (81 ft2) b. Student gives the correct answer: 9 square yards (9 yd2) c. Student draws in the lines of another playing square, and gives the correct equation and solution: 6 yards × 3 yards = 18 square yards OR 3 yards × 6 yards = 18 square yards d. Student gives the correct equation and solution: 6 yards × 6 yards = 36 square yards 2. a. Student accurately sketches the area of the handball court.
b. Student gives an accurate equation. Equations may vary. Sample equations: 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35; 5 × 7 = 35 c. Student gives the correct answer and an accurate explanation. Wording may vary. Sample explanation: Yes, the drawing I made in Part A matches the solution I found in Part B. The drawing I made is like an array. I knew there were 5 rows. In order to have a total of 35 squares, I needed to draw 7 columns. 5 × 7 = 35 or 35 ÷ 5 = 7.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 3
1 1
Total
3. a. Student gives the correct answer. 1 square foot (1 ft2) b. Student gives the correct answer and proves it with a drawing. 3 square feet (3 ft2) c. Student gives an accurate explanation. Wording may vary. Sample explanation: The painter is correct. No matter how he arranges them, as long as there are no gaps or overlaps, the area of the shape formed with the ten stencils will always be 10 square feet. Each stencil is 1 square foot. Ten of them is 10 square feet because 1 × 10 = 10. d. Student draws at least 2 sketches, each with an area of 10 ft2. Shapes will vary. Sample responses:
4. a. Student fills in the formula correctly and gives the correct answer. (30 × 10) + (30 × 20) = 900 ft2 b. Student fills in the formula correctly and gives the correct answer. (9 × 7) + (9 × 6) = 117 yd2 c. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: No, Grandpa did not find the area of the half-court correctly. He did not use the distributive property correctly. He used the 5 in both parts of the expression instead of the 7. He should have found the area like this: (7 × 5) + (7 × 2) = 35 + 14 = 49 yd2 5. a. Student gives the correct answer and shows accurate work: 13 m2 b. Student gives the correct answer and shows accurate work: 12 m2 c. Student gives the correct answer and shows accurate work: 21 m2 d. Student gives the correct answer and shows accurate work: 13 m2
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 4
1 1 1
2
1 1 1
1 1 1 1
6. a. Student gives correct answer and shows accurate work. Student must use either the Distributive Property or decomposition: (9 × 4) + (9 × 3) + (9 × 5) = 108 ft2 OR 36 ft2 + 27 ft2 + 45 ft2 = 108 ft2. b. Student gives an accurate explanation related to the solution modeled in Part A. Wording may vary. Sample explanation: I decomposed the larger rectangle into three smaller rectangles. I found the area of each smaller rectangle and added them together. 7. a. Student gives the correct answer and shows accurate work: 66 ft b. Student gives the correct answer and shows accurate work: 90 ft2 c. Student gives an accurate explanation. Wording may vary. Sample explanation: Perimeter and area are related because they both describe a polygon. The perimeter is the measure of the distance around the polygon, and the area is the measure of the space within the polygon. 8. a. Student gives the correct answer and shows accurate work: 10 in b. Student gives the correct answer and shows accurate work: 120 in2 9. a. Student gives the correct answer and shows accurate work: 44 ft b. Student gives the correct answer and shows accurate work: 40 ft2 c. Student draws a polygon with an area of 40 square feet. Shapes will vary. Sample responses:
1
1
1 1 1
1 1 1 1 1
perimeter = 44 ft
perimeter = 28 ft
perimeter = 44 ft
perimeter = 32 ft
d. Student finds the correct area for the polygon in Part C. Answers will vary. See sample responses listed in Part C. Total
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 5
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1. Finding the Area of Rectangles
2. Find the Area of Rectangles using the Distributive Property and Decomposition
Common Core State Standard for Mathematical Content (MC) 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7 Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. 3.MD.7 Relate area to the operations of multiplication and addition. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP)
MP.1 MP.3 MP.4 MP.6 MP.7 MP.8
MP.1 MP.2 MP.3 MP.4 MP.6 MP.7 MP.8
3. Area and Perimeter of Rectangles and Complex Figures
3.MD.7 Relate area to the operations of multiplication and addition. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
MP.1 MP.2 MP.4 MP.6 MP.7 MP.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.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 2
Scoring Rubric Points 1 1 1
1 1
Wall = 5 yards
Question 1. a. Student gives the correct answer: 81 square feet (81 ft2) b. Student gives the correct answer: 9 square yards (9 yd2) c. Student draws in the lines of another playing square, and gives the correct equation and solution: 6 yards × 3 yards = 18 square yards OR 3 yards × 6 yards = 18 square yards d. Student gives the correct equation and solution: 6 yards × 6 yards = 36 square yards 2. a. Student accurately sketches the area of the handball court.
b. Student gives an accurate equation. Equations may vary. Sample equations: 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35; 5 × 7 = 35 c. Student gives the correct answer and an accurate explanation. Wording may vary. Sample explanation: Yes, the drawing I made in Part A matches the solution I found in Part B. The drawing I made is like an array. I knew there were 5 rows. In order to have a total of 35 squares, I needed to draw 7 columns. 5 × 7 = 35 or 35 ÷ 5 = 7.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 3
1 1
Total
3. a. Student gives the correct answer. 1 square foot (1 ft2) b. Student gives the correct answer and proves it with a drawing. 3 square feet (3 ft2) c. Student gives an accurate explanation. Wording may vary. Sample explanation: The painter is correct. No matter how he arranges them, as long as there are no gaps or overlaps, the area of the shape formed with the ten stencils will always be 10 square feet. Each stencil is 1 square foot. Ten of them is 10 square feet because 1 × 10 = 10. d. Student draws at least 2 sketches, each with an area of 10 ft2. Shapes will vary. Sample responses:
4. a. Student fills in the formula correctly and gives the correct answer. (30 × 10) + (30 × 20) = 900 ft2 b. Student fills in the formula correctly and gives the correct answer. (9 × 7) + (9 × 6) = 117 yd2 c. Student gives the correct answer and an accurate explanation. Wording may vary. Sample response: No, Grandpa did not find the area of the half-court correctly. He did not use the distributive property correctly. He used the 5 in both parts of the expression instead of the 7. He should have found the area like this: (7 × 5) + (7 × 2) = 35 + 14 = 49 yd2 5. a. Student gives the correct answer and shows accurate work: 13 m2 b. Student gives the correct answer and shows accurate work: 12 m2 c. Student gives the correct answer and shows accurate work: 21 m2 d. Student gives the correct answer and shows accurate work: 13 m2
Copyright © Swun Math Grade 3 Unit 10 Constructed Response Rubric, Page 4
1 1 1
2
1 1 1
1 1 1 1
6. a. Student gives correct answer and shows accurate work. Student must use either the Distributive Property or decomposition: (9 × 4) + (9 × 3) + (9 × 5) = 108 ft2 OR 36 ft2 + 27 ft2 + 45 ft2 = 108 ft2. b. Student gives an accurate explanation related to the solution modeled in Part A. Wording may vary. Sample explanation: I decomposed the larger rectangle into three smaller rectangles. I found the area of each smaller rectangle and added them together. 7. a. Student gives the correct answer and shows accurate work: 66 ft b. Student gives the correct answer and shows accurate work: 90 ft2 c. Student gives an accurate explanation. Wording may vary. Sample explanation: Perimeter and area are related because they both describe a polygon. The perimeter is the measure of the distance around the polygon, and the area is the measure of the space within the polygon. 8. a. Student gives the correct answer and shows accurate work: 10 in b. Student gives the correct answer and shows accurate work: 120 in2 9. a. Student gives the correct answer and shows accurate work: 44 ft b. Student gives the correct answer and shows accurate work: 40 ft2 c. Student draws a polygon with an area of 40 square feet. Shapes will vary. Sample responses:
1
1
1 1 1
1 1 1 1 1
perimeter = 44 ft
perimeter = 28 ft
perimeter = 44 ft
perimeter = 32 ft
d. Student finds the correct area for the polygon in Part C. Answers will vary. See sample responses listed in Part C. Total
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