Math Spring Operational Geometry PBA Item #17 Perimeter of Isosceles Triangle 2221-M41124P
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1 Math Spring Operational 2015 Geometry PBA Item #17 Perimeter of Isosceles Triangle 2221-M41124P
2 Prompt
3 Task is worth a total of 4 points 2221-M41124 Rubric Part A Score Description 1 Student response includes the following element. Computation component = 1 point o Machine Scored: C 0 Student response is incorrect or irrelevant M41124 Rubric Part B Score Description 3 Student response includes the following 3 elements. Reasoning component = 2 points o Correct reasoning to find the length of the legs of isosceles triangle o Correct reasoning to find the length of the base of the isosceles triangle Computation component = 1 point o Correct perimeter Sample Student Response: If A is at the origin and C is at (12, 16), then I can form a right triangle with the base leg being 12 and the height leg being 16. Using the Pythagorean Theorem, I can find the hypotenuse to be 20, which becomes the length of the 2 equal sides of the OR 2 2 isosceles triangle. ( + = = ) I can find the length of the base of ABC by doubling the length of the right triangle I found above. So the length of the base of ABC is 24 ( 2 12 = 24 ). So the perimeter of ABC is 64 units. ( = 64). If A is at the origin and C is at (12, 16), then I can form an isosceles triangle with leg AC and leg AB congruent. Using the Pythagorean Theorem, AC equals 20, ( = = ) , which becomes the length of the 2 congruent legs of the isosceles triangle. This means B is 20 units away from A at (20, 0). Using the Pythagorean Theorem again, BC equals approximately units ( + = ) So the perimeter of ABC is approximately units ( = 57.89).
4 Anchor Set A1 A8
5 A1 Part B: Score Point 3
6 Annotations Anchor Paper 1 Part B: Score Point 3 This response receives full credit. The student includes each of the three required elements: Reasoning to find the length of the legs of the isosceles triangle is correct (I took it s height and half it s base to find one side of the triangle, which is 20 units long; 16²+ 12² = x²). Reasoning to find the length of the base of the isosceles triangle is correct (Therefore, where point C is at now stands as a mid-point on segment AB. So, since it takes 12 units from A to get to C (horizontally), then it will take another 12 to reach B). The perimeter is correct (I get a perimeter of 64 units).
7 A2 Part B: Score Point 3
8 Annotations Anchor Paper 2 Part B: Score Point 3 This response receives full credit. The student includes each of the three required elements: Reasoning to find the length of the legs of the isosceles triangle is correct (half of the triangle becomes a 3, 4, 5 or 12, 16, 20 triangle and so the 2 legs are 20 units). Reasoning to find the length of the base of the isosceles triangle is correct (and the base is 24 because 12 is half of the base). The perimeter is correct ( = 64).
9 A3 Part B: Score Point 2
10 Annotations Anchor Paper 3 Part B: Score Point 2 This response receives partial credit. The student includes two of the three required elements: Reasoning to find the length of the legs of the isosceles triangle is correct 2 2 ( = 20 = AC; AC = CB ). Reasoning to find the length of the base of the isosceles triangle is correct (12 is 1 of 2 the base). The perimeter is missing.
11 A4 Part B: Score Point 2
12 Annotations Anchor Paper 4 Part B: Score Point 2 This response receives partial credit. The student includes two of the three required elements: Reasoning to find the length of the legs of the isosceles triangle is correct (16² + 12² = c²; = ; c = 20). The perimeter is correct (perimeter = 64 inches). Reasoning to find the length of the base of the isosceles triangle is incomplete ( ). Even though the correct length is given, there is no reasoning or work shown for how 24 is found.
13 A5 Part B: Score Point 1
14 Annotations Anchor Paper 5 Part B: Score Point 1 This response receives partial credit. The student includes one of the three required elements. Reasoning to find the length of the base of the isosceles triangle is correct (point C has to be inbetween A and B and since C is 12 away from A on the x axis B has to be 12 away from 12 as well to mak AC to CB). Reasoning to find the length of the legs of the isosceles triangle is missing. The perimeter is missing.
15 A6 Part B: Score Point 1
16 Annotations Anchor Paper 6 Part B: Score Point 1 This response receives partial credit. The student includes one of the three required elements. The perimeter is correct (The new perimeter of ΔABC is 64). Reasoning to find the length of the legs of the isosceles triangle is incomplete (the length of BC is 20, and the length of CA is 20). Even though the correct length is given, there is no reasoning or work shown for how 20 is found. Reasoning to find the length of the base of the isosceles triangle is incomplete (This is because the length of AB is 24). Even though the correct length is given, there is no reasoning or work shown for how 24 is found.
17 A7 Part B: Score Point 0
18 Annotations Anchor Paper 7 Part B: Score Point 0 This response receives no credit. The student includes none of the three required elements. Reasoning to find the length of the legs of the isosceles triangle is missing. Reasoning to find the length of the base of the isosceles triangle is missing. The perimeter is incorrect (The perimeter is 20). The Pythagorean Theorem is used and labeled for finding perimeter, not the lengths of the legs of the triangle.
19 A8 Part B: Score Point 0
20 Annotations Anchor Paper 8 Part B: Score Point 0 This response receives no credit. The student includes none of the three required elements. Reasoning to find the length of the legs of the isosceles triangle is missing. Reasoning to find the length of the base of the isosceles triangle is incomplete. Even though the correct coordinates are given for point B, there is no reasoning or work shown for how they are found. The perimeter is missing.
21 Practice Set P101 - P105
22 P101
23 P102
24 P103
25 P104
26 P105
27 Practice Set Paper Score P101 3 P102 2 P103 1 P104 0 P105 3
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