G5 U8 Constructed Response Rubric
Grade 5 Unit 8 Constructed Response Polygons and Volume Description Task
1. Categorizing Polygons
Common Core State Standard for Mathematical Content (MC) 5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
2. Volume of Rectangular Prisms
3. Volume of 3Dimensional Complex Figures
5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical Copyright © Swun Math Grade 5 Unit 8 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP) MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8
MP.1 MP.2 MP.3 MP.6 MP.7 MP.8
MP.1 MP.2 MP.3 MP.6 MP.7 MP.8
problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world 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 5 Unit 8 Constructed Response Rubric, Page 2
Scoring Rubric Question 1. a. Student gives the correct answer and an accurate explanation: No, this polygon is not a right equilateral because there is no such thing. A triangle cannot have three congruent sides if one angle is right. This is an acute equilateral triangle. All of the angles are acute because they are congruent 60o angles. b. Student gives the correct answer and an accurate explanation: Yes, this is a rhombus because opposite sides are parallel and all four sides are congruent. A square is a special kind of rhombus. c. Student gives the correct answer and an accurate explanation: This polygon can be called a quadrilateral and trapezoid. d. Student gives the correct answer and an accurate explanation: This polygon is a right scalene triangle. 2. a. Student gives the correct answer and an accurate explanation: No, Maria did not classify all of the polygons correctly. It is true that the polygons in the left circle are all right triangles. However, not all of the triangles in the right circle are isosceles. One triangle is scalene and should be outside of the Venn diagram. Then the polygons outside the Venn diagram would include any non-right, non-isosceles triangle and any other polygon.
Copyright © Swun Math Grade 5 Unit 8 Constructed Response Rubric, Page 3
Points 1
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1 1
2
Total
3. a. Student correctly names each shape and draws each shape in its place in the Hierarchy of Quadrilaterals.
3
b. Student gives an accurate answer. Responses and wording may vary. Sample response: All quadrilaterals are closed-sided polygons with four sides and four angles. c. Student gives an accurate response. Responses and wording may vary. Sample response: All squares are parallelograms because both pairs of opposite sides are parallel and the opposite angles are congruent. However, not all parallelograms are squares. Squares are defined by four congruent sides and four 90o angles. Those are not defining attributes of all parallelograms. A parallelogram has those features in a special case called a square, but other parallelograms do not fall into those categories. 4. a. Student gives the correct answer and shows accuate work. Cyrus’s Tank has the greatest volume (100 cubic units) b. Student gives the correct answer. 242 cubic units (242 units3) 5. a. Student gives the correct answer and shows accuate work. 192 in3 b. Student gives the correct answer and shows accuate work. 24 cubes
1
6. a. Student gives an accurate explanation. Marquesh’s error was that he did not use the formula correctly. Instead of solving for length, he solved for volume. Volume was already given in the problem. b. Student gives the correct answer and shows accuate work. 9 yd
2
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7. a. Student gives the correct answer and an accurate explanation: Yes, Mr. Hartzog has enough dirt to fill the planter boxes. The total volume of the planter box is 135 ft3, which is a little less than the amount of dirt he bought. b. Student gives the correct answer: The volume of both planters will be 225 ft3. 8. a. Student gives the correct answer and shows accurate work: 30 cm3 b. Student an accurate explanation. Responses may vary. Sample response: I found the volume of the entire rectangular prism (4 × 6 × 2 = 48 cm3). Then I subtracted the volume of the two missing pieces (2 × 2 × 3 = 12 cm3) and (1 × 3 × 2) = 6 cm3). 48 cm3 – 18 cm3 = 30 cm3. 9. a. Student gives the correct answer and an accurate explanation: Yes, Marlin found the correct volume of Figure A. He used the correct dimensions for the whole rectangular prism and the missing rectangular prism. His calculations are correct. b. Student gives the correct answer and shows accurate work: 84 m2 c. Student gives an accurate explanation: To find the volume of Figure B, I decomposed the figure into three smaller prisms, found their volumes, then added them together. The volume of the base is (6 × 3 × 1) = 18 m2. The volume of the tall pillar on the left is (6 × 1 × 1) = 6 m2. The volume of larger rectangular prism in the back is (6 × 5 × 2) = 60 m2. 18 m2 + 6 m2 + 60 m2 = 84 m2. Total
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1. Categorizing Polygons
Common Core State Standard for Mathematical Content (MC) 5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
2. Volume of Rectangular Prisms
3. Volume of 3Dimensional Complex Figures
5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical Copyright © Swun Math Grade 5 Unit 8 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP) MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8
MP.1 MP.2 MP.3 MP.6 MP.7 MP.8
MP.1 MP.2 MP.3 MP.6 MP.7 MP.8
problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world 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 5 Unit 8 Constructed Response Rubric, Page 2
Scoring Rubric Question 1. a. Student gives the correct answer and an accurate explanation: No, this polygon is not a right equilateral because there is no such thing. A triangle cannot have three congruent sides if one angle is right. This is an acute equilateral triangle. All of the angles are acute because they are congruent 60o angles. b. Student gives the correct answer and an accurate explanation: Yes, this is a rhombus because opposite sides are parallel and all four sides are congruent. A square is a special kind of rhombus. c. Student gives the correct answer and an accurate explanation: This polygon can be called a quadrilateral and trapezoid. d. Student gives the correct answer and an accurate explanation: This polygon is a right scalene triangle. 2. a. Student gives the correct answer and an accurate explanation: No, Maria did not classify all of the polygons correctly. It is true that the polygons in the left circle are all right triangles. However, not all of the triangles in the right circle are isosceles. One triangle is scalene and should be outside of the Venn diagram. Then the polygons outside the Venn diagram would include any non-right, non-isosceles triangle and any other polygon.
Copyright © Swun Math Grade 5 Unit 8 Constructed Response Rubric, Page 3
Points 1
1
1 1
2
Total
3. a. Student correctly names each shape and draws each shape in its place in the Hierarchy of Quadrilaterals.
3
b. Student gives an accurate answer. Responses and wording may vary. Sample response: All quadrilaterals are closed-sided polygons with four sides and four angles. c. Student gives an accurate response. Responses and wording may vary. Sample response: All squares are parallelograms because both pairs of opposite sides are parallel and the opposite angles are congruent. However, not all parallelograms are squares. Squares are defined by four congruent sides and four 90o angles. Those are not defining attributes of all parallelograms. A parallelogram has those features in a special case called a square, but other parallelograms do not fall into those categories. 4. a. Student gives the correct answer and shows accuate work. Cyrus’s Tank has the greatest volume (100 cubic units) b. Student gives the correct answer. 242 cubic units (242 units3) 5. a. Student gives the correct answer and shows accuate work. 192 in3 b. Student gives the correct answer and shows accuate work. 24 cubes
1
6. a. Student gives an accurate explanation. Marquesh’s error was that he did not use the formula correctly. Instead of solving for length, he solved for volume. Volume was already given in the problem. b. Student gives the correct answer and shows accuate work. 9 yd
2
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7. a. Student gives the correct answer and an accurate explanation: Yes, Mr. Hartzog has enough dirt to fill the planter boxes. The total volume of the planter box is 135 ft3, which is a little less than the amount of dirt he bought. b. Student gives the correct answer: The volume of both planters will be 225 ft3. 8. a. Student gives the correct answer and shows accurate work: 30 cm3 b. Student an accurate explanation. Responses may vary. Sample response: I found the volume of the entire rectangular prism (4 × 6 × 2 = 48 cm3). Then I subtracted the volume of the two missing pieces (2 × 2 × 3 = 12 cm3) and (1 × 3 × 2) = 6 cm3). 48 cm3 – 18 cm3 = 30 cm3. 9. a. Student gives the correct answer and an accurate explanation: Yes, Marlin found the correct volume of Figure A. He used the correct dimensions for the whole rectangular prism and the missing rectangular prism. His calculations are correct. b. Student gives the correct answer and shows accurate work: 84 m2 c. Student gives an accurate explanation: To find the volume of Figure B, I decomposed the figure into three smaller prisms, found their volumes, then added them together. The volume of the base is (6 × 3 × 1) = 18 m2. The volume of the tall pillar on the left is (6 × 1 × 1) = 6 m2. The volume of larger rectangular prism in the back is (6 × 5 × 2) = 60 m2. 18 m2 + 6 m2 + 60 m2 = 84 m2. Total
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