Math Released Item 2017 Grade 7 Sum of Perimeters VF801806
Anchor Set A1 A8 With Annotations
Prompt
VF801806 Rubric Part A (This part is machine scored) Score Description 1 Student response includes the following element. Computation component = 1 point o The student provides the correct expression of 3 1 4 x or equivalent. 0 Student response is incorrect or irrelevant. Score Description VF801806 Rubric Part B 3 Student response includes the following 3 elements. Reasoning component = 2 points o o The student provides a correct process for finding the sum of the perimeters of all four smaller rectangles and the perimeter of the larger rectangle. The student provides valid reasoning that indicates a correct comparison between the sum of perimeters of the smaller rectangles and the larger rectangle. Computation component = 1 point o The student provides correct computations, as work or explanation, which is consistent with the reasoning. Sample Student Response: The perimeter of each smaller rectangle is 3 1 4 x. So the perimeter of all 3 4 7 four smaller rectangles is 4 1 x x 7x 4 1 4. The perimeter of the 3 3 2 7 7 larger rectangle is 2 x x 2 1 x x x 4 4 1 4 + 2. Since 7 x is twice 7 x, the sum of the perimeters of all four smaller rectangles is equal to 2 twice the perimeter of the larger rectangle and Rico s conclusion is correct. Notes: 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 or an incorrect conclusion. The student may receive a total of 2 points if they compute the correct answer but shows no work or insufficient work to indicate correct reasoning processes. The response may be more conceptual than computational. For example, the student may reason that the sum of the perimeters of the smaller rectangles is twice the perimeter of the larger by comparing the relative side lengths. The student cannot receive more than 1 point for reasoning if the explanations, while sufficient to indicate that the student had correct reasoning, contain nonsense statements. 2 Student response includes 2 of the 3 elements. 1 Student response includes 1 of the 3 elements. 0 Student response is incorrect or irrelevant.
A1 Part B: Score Point 3
Annotation Anchor Paper 1 Part B: Score Point 3 This response receives full credit. The student includes each of the three required elements: Correct computation is provided that is consistent with the reasoning 1 1 3 [Perimeter of Rectangle ( 1 ) x 2x (3 ) x, One rectangle (1 ) x 2 2 4 3 (7x) Therefore all rectangles (( 1 ) x) 4 4 7x, 7x 2(3.5 x) ]. 4 4 A correct process is provided for finding the sum of all four smaller 3 (7x) rectangles (Therefore all rectangles (( 1 ) x) 4 4 7x) and the 4 4 perimeter of the larger rectangle (Perimeter of Rectangle 1 1 ( 1 ) x 2x (3 ) x ). 2 2 Reasoning is provided that indicates a correct comparison between the perimeters of the rectangles ( 7x 2(3.5 x), therefore rico s conclusion is correct).
A2 Part B: Score Point 3
Annotation Anchor Paper 2 Part B: Score Point 3 This response receives full credit. The student includes each of the three required elements: Correct computation is provided that is consistent with the reasoning 3 [ ( x x) 2 is equal to the perimeter of the big rectangle. Because ther 4 3 are 4 small rectangles, ( x x) 4 would be equal to twice the 4 perimeter of the big rectangle]. The computations receive credit by explaining the expression for the small rectangles is twice the expression for the perimeter of the large rectangle. A correct process is provided for finding the sum of all four smaller 3 rectangles [Because ther are 4 small rectangles, ( x x) 4] and the 4 3 perimeter of the larger rectangle [ ( x x) 2 is equal to the perimeter 4 of the big rectangle]. Reasoning is provided that indicates a correct comparison between the 3 perimeters of the rectangles [ ( x x) 4 would be equal to twice the 4 perimeter of the big rectangle].
A3 Part B: Score Point 2
Annotation Anchor Paper 3 Part B: Score Point 2 This response receives partial credit. The student includes two of the three required elements: A correct process is provided for finding the sum of all four smaller 1 1 3 3 rectangles [ ( x x x x) 4 ] and the perimeter of the larger 2 2 8 8 3 3 rectangle ( x x x x ). 4 4 Reasoning is provided that indicates a correct comparison between the 1 1 perimeters of the rectangles ( 7 3, ( 3 ) 2 7, Rico is correct. The 2 2 perimeter of the four small rectangles added together is equal to 2 times the perimeter of the entire sheett of paper). The computation for both the perimeter of the large rectangle and the sum of the perimeters of the 4 small rectangles is incorrect as the x is dropped in the answer to both equations.
A4 Part B: Score Point 2
Annotation Anchor Paper 4 Part B: Score Point 2 This response receives partial credit. The student includes two of the three required elements: Correct computation is provided that is consistent with the reasoning by finding the perimeter of the large rectangle (3.5x) and the sum of the perimeters of the four smaller rectangles (7x) and correctly comparing them (the sum of the perimeters of all four small rectangles is equal to twice the perimeter of the larger rectangle is correct). Reasoning is provided that indicates a correct comparison between the perimeters of the rectangles (the sum of the perimeters of all four small rectangles is equal to twice the perimeter of the larger rectangle is correct). No process is shown or explained for finding either perimeter.
A5 Part B: Score Point 1
Annotation Anchor Paper 5 Part B: Score Point 1 This response receives partial credit. The student includes one of the three required elements: A correct process is provided for finding the sum of all four smaller 3 rectangles [ ( x x) 4 perimeter of smaller rectangles) and the 4 3 perimeter of the larger rectangle [ 2x ( x) 2 perimeter of bigger 4 rectangle]. While the equations for the perimeters are correct, no computation is made or described to make the comparison of the perimeters. No reasoning is provided that indicates a correct comparison between the perimeters of the rectangles.
A6 Part B: Score Point 1
Annotation Anchor Paper 6 Part B: Score Point 1 This response receives partial credit. The student includes one of the three required elements: Reasoning is provided that indicates a correct comparison between the perimeters of the rectangles (the perimeter of one small rectangle is equal to one half of the perimeter of the larger rectangle. Since 4 small 1 rectangles fit into the one large rectangle, and 4 2, the conclusion 2 that the sum of all 4 small rectangles is equal to the value of 2 large perimeters). While the reasoning provided indicates a correct comparison between the perimeters, there are no computations or explanation to show why the perimeter of one of the small rectangles is half of the perimeter of the large rectangle. No process is shown as to how find the sum of all four smaller rectangles or the perimeter of the larger rectangle.
A7 Part B: Score Point 0
Annotation Anchor Paper 7 Part B: Score Point 0 This response receives no credit. The student includes none of the three required elements: The computations shown are insufficient to explain whether Rico s conclusion is correct. While a correct process is provided for finding the sum of all four smaller 3 3 3 3 rectangles using the incorrect expression for part A ( 1 1 1 1 7 ), no 4 4 4 4 process is shown for finding the perimeter of the large rectangle. Without knowing the perimeter of the large rectangle, the division problem shown ( 7 2 3. 5) is insufficient to show reasoning to indicate a correct comparison between the perimeters of the rectangles.
A8 Part B: Score Point 0
Annotation Anchor Paper 8 Part B: Score Point 0 This response receives no credit. The student includes none of the three required elements: No computations are shown or explained. No process is shown for finding either perimeter. The reasoning shown (there are 4 smaller sides in each of the smaller papers which makes 12 sides) is incorrect as the sides of the smaller rectangles would add up to 16, not 12.
Practice Set P101 - P105 No Annotations Included
P101
P102
P103
P104
P105
Practice Set Paper Score P101 0 P102 3 P103 1 P104 3 P105 0