Math Released Item Grade 6. Volume of the Box VH122131

Transcription

1 Math Released Item 2017 Grade 6 Volume of the Box VH122131

2 Anchor Set A1 A10 With Annotations

3 Prompt

4 M06_VH Rubric Part A Score Description 2 Student response includes the following 2 elements. Computation component = 1 point o The student provides that Diego is incorrect and gives the correct volume of one box, 390 cubic inches. Reasoning component = 1 point o The student provides valid work or explanation for calculating the volume of one box. Sample Student Response: Note: Diego is incorrect. To find the volume of one box, find the value of , which is 390 cubic inches. The student may receive a total of 1 point if the reasoning process is correct but the student makes a computational error resulting in an incorrect answer. 1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant. Score Description M06_VH Rubric Part B 2 Student response includes the following 2 elements. Computation component = 1 point o The student correctly selects the carton that will completely contain 8 boxes with the least amount of packing material, Carton C. Reasoning component = 1 point o The student provides valid work or explanation for determining which carton meets the conditions. Sample Student Response: I found the volume of each carton. Carton A has a volume of ,640 cubic inches. Carton B has a volume of ,080 cubic inches. Carton C has a volume of ,432 cubic inches. The boxes can be put into Carton C so that there are 4 boxes on the bottom layer and 2 layers that each have a height of 13 inches. Carton C can hold 8 boxes with the least amount of packing material.

5 Note: The student may receive a combined total of 2 points if the reasoning processes are correct but the student makes one or more computational errors resulting in incorrect answers. The student may receive a total of 2 points if he or she computes the correct answers but show no work or insufficient work to indicate a correct reasoning process. 1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant.

6 A1 Part A: Score Point 2 Part B: Score Point 2

7 Annotation Anchor Paper 1 Part A: Score Point 2 This response receives full credit. It includes each of the two required elements: Determines that Diego is incorrect and provides the volume of one box equal to 390 cubic inches (390). Correctly shows the steps for calculating the volume of one box (To find volume, you multiply length by width by height: 13 x 5 x 6). Part B: Score Point 2 This response receives full credit. It includes each of the two required elements: Selection of the carton that will completely contain 8 boxes with the least amount of packing material (Carton C). Correctly shows the steps for determining which carton meets the conditions (volume of 8 boxes: 390 x 8 = 3120, Carton A: 10 x 13 x 28 = 3640, = 520, Carton B: 10 x 14 x 22 = 3080, = -40, Carton C: 11 x 12 x 26 = 3432, = 312, Diego would choose Carton C. It fits all 8 boxes and leaves the least amount of space).

8 A2 Part A: Score Point 2 Part B: Score Point 2

9 Annotation Anchor Paper 2 Part A: Score Point 2 This response receives full credit. It includes each of the two required elements: Determines that Diego is incorrect and provides the volume of one box equal to 390 cubic inches (390). Correctly shows the steps for calculating the volume of one box [(13 x 5) x 6]. Part B: Score Point 2 This response receives full credit. It includes each of the two required elements: Selection of the carton that will completely contain 8 boxes with the least amount of packing material (cartoon C). Correctly shows the steps for determining which carton meets the conditions (for all 8 boxes its 3120 and catoon C can 3432 and cartoon A can hold 3640 and Cartoon B holds only Thats why I think cartoon C is the best because its got enough room for all 8 boxes and a little bit more room. Cartoon B doesnt have enough. Cartoon A has too much space).

10 A3 Part A: Score Point 2 Part B: Score Point 1

11 Annotation Anchor Paper 3 Part A: Score Point 2 This response receives full credit. It includes each of the two required elements: Determines that Diego is incorrect and provides the volume of one box equal to 390 cubic inches (390). Correctly shows the steps for calculating the volume of one box (13 5 x 6). Part B: Score Point 1 This response receives partial credit. It includes one of the two required elements: Selection of the carton that will completely contain 8 boxes with the least amount of packing material (carton c). The response only addresses the volume of Carton C and the total volume of 8 boxes. The response does not address the volume of Carton A or Carton B.

12 A4 Part A: Score Point 2 Part B: Score Point 1

13 Annotation Anchor Paper 4 Part A: Score Point 2 This response receives full credit. It includes each of the two required elements: Determines that Diego is incorrect and provides the volume of one box equal to 390 cubic inches (390). Correctly shows the steps for calculating the volume of one box (13 5 6). Part B: Score Point 1 This response receives partial credit. It includes one of the two required elements: Selection of the carton that will completely contain 8 boxes with the least amount of packing material (carton c). Providing only the calculations, for the volume of 8 boxes (3120) and the volumes of each carton (a=3640, b=3080, c=3432), is insufficient to earn credit for this element. This response does not provide sufficient explanation or steps to determine that Carton C will hold all 8 boxes completely AND use the least amount of packing material.

14 A5 Part A: Score Point 2 Part B: Score Point 0

15 Annotation Anchor Paper 5 Part A: Score Point 2 This response receives full credit. It includes each of the two required elements: Determines that Diego is incorrect and provides the volume of one box equal to 390 cubic inches (390). Correctly shows the steps for calculating the volume of one box (13 5 x 6). Part B: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not select the carton that will completely contain the 8 boxes. The response correctly finds the volume of all three cartons ( = 3640 is A, = 3080 is B, = 3432 is C) and correctly finds the volume of 8 boxes ( = = 3120), but incorrectly attempts to support the choice of carton B with this information. Box B has the smallest volume but will not contain all 8 boxes completely.

16 A6a Part A: Score Point 0 Part B: Score Point 2

17 A6b Part A: Score Point 0 Part B: Score Point 2

18 Annotation Anchor Paper 6 Part A: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not determine that Diego is incorrect and does not provide the volume of one box equal to 390 cubic inches. The response only finds the area of one face of the box (13 5 = 65). Part B: Score Point 2 This response receives full credit. It includes each of the two required elements: Selection of the carton that will completely contain 8 boxes with the least amount of packing material (Carton C). Correctly shows the steps for determining which carton meets the conditions ( = 390, = 3,120, = 3640, = 3,080, = 3,432 which is enough for all 8 boxes and packing material).

19 A7 Part A: Score Point 1 Part B: Score Point 0

20 Annotation Anchor Paper 7 Part A: Score Point 1 This response receives partial credit. It includes one of the two required elements: Correctly shows the steps for calculating the volume of one box (V = ). The response does not determine that Diego is incorrect and provide the volume of one box equal to 390 cubic inches. The response incorrectly calculates the volume as 690. Part B: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not select the carton that will completely contain the 8 boxes. The response only shows the correct volume and equation for determining the volume for Carton B (V = , V = 3080).

21 A8 Part A: Score Point 1 Part B: Score Point 0

22 Annotation Anchor Paper 8 Part A: Score Point 1 This response receives partial credit. It includes one of the two required elements: Determines that Diego is incorrect and provides the volume of one box equal to 390 cubic inches (If I add it all it equals 216, the right answer should be 390). The response does not correctly show the steps for calculating the volume of one box. Part B: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not select the carton that will completely contain the 8 boxes. The response does not correctly show the steps for determining which carton meets the conditions. The response only shows the selection of the incorrect carton (carton a).

23 A9 Part A: Score Point 0 Part B: Score Point 0

24 Annotation Anchor Paper 9 Part A: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not determine that Diego is incorrect and provide the volume of one box equal to 390 cubic inches [Diegio is incorrect the correct answer is (13 + 5) 6]. The response does not correctly show the steps for calculating the volume of one box. Part B: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not select the carton that will completely contain the 8 boxes. The response does not correctly show the steps for determining which carton meets the conditions. The response only shows incorrect volumes for the cartons (carton A 644, carton B 528, carton C - 598).

25 A10 Part A: Score Point 0 Part B: Score Point 0

26 Annotation Anchor Paper 10 Part A: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not determine that Diego is incorrect (Diego s answer was correct) and provide the volume of one box equal to 390 cubic inches. The response does not correctly show the steps for calculating the volume of one box [when you add ( ) 6 you get a reasonable answer and the answer i was to get to check his was 156 and thats how i got the volume of one rectangular box]. Part B: Score Point 0 This response receives no credit. It includes none of the required elements: The response does not select the carton that will completely contain the 8 boxes (the good carton to get would be carton A). The response does not correctly show the steps for determining which carton meets the conditions (because carton A s total was 51 while both carton B and Carton C was 46 and 49 so that why a good carton to chhose would be Carton A).

27 Practice Set P101 - P105 No Annotations Included

28 P101

29 P102

30 P103

31 P104a

32 P104b

33 P105a

34 P105b

35 Practice Set Paper Score P101 2,0 P102 2,2 P103 1,0 P104 2,1 P105 2,2