Math Released Item Geometry. Height of Support VF650053
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1 Math Released Item 2016 Geometry Height of Support VF650053
2 Prompt
3 Task is worth a total of 3 points. Rubric VF Rubric Part A Score Description 2 Student response includes the following 2 elements. Valid explanation or work to calculate the height of the support Correct height of the support at 1.7 feet Sample Student Response: Let x represent the height of the support. A right angle is formed with a 25 angle and a hypotenuse of 4. A possible equation and solution: 1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant. VF Rubric Part B Score Description 1 Student response includes the following element. Valid model and height for Point Q. Sample Student Response: I can draw a line continuation of line segment QS from point Q to the ground creating a right triangle. The distance from point Q to where the hypotenuse of the right triangle touches the ground can be represented as y. Therefore, the hypotenuse from point R to the ground could be represented by 4 + y. I can then find y as follows: From there, I will let the distance from point Q to the ground be represented by z. I can find the length of that segment as follows: Therefore, the distance from point Q to the ground is approximately 1.0 foot.
4 Or: The angle created by the seating board and the left side of the central support is 80. I can draw a perpendicular line from point Q to the central support, RT, creating a right triangle. The distance from point Q to the ground is the same as the distance from the newly drawn line to the ground. Let y represent that distance. Then the distance along the central support from the drawn line to point T can be represented by. Therefore, the distance from point Q to the ground is approximately 1.0 foot. Note: Without support, an answer of 1 foot does not earn any credit. A logical explanation of how to arrive at the height of Point Q from the ground with the correct answer of 1 foot is necessary to earn the point for part B. The modeling of setup and work needs to show understanding of the process, but may contain some vague statements or minor errors. 0 Student response is incorrect or irrelevant.
5 Anchor Set A1 A8 With Annotations
6 A1 Part A: Score Point 2 Part B: Score Point 1
7 Annotation Anchor Paper 1 Part A: Score Point 2 This response receives full credit. It includes each of the two required elements. The correct height of the central support is given (1.7 ft.). The student shows correct modeling using an equation to find the height of the central support (sin 25 = x ; sin 25 4 = x; x = 1.7). 4 Note: A label of feet is not required for credit. Since the prompt asks for the answer rounded to the nearest foot, if a label is used then feet must be used for credit. Part B: Score Point 1 This response receives full credit. It includes the one required element. The response shows the correct height of Point Q (1.0) and correct modeling to find the height of Point Q when the seating board creates an 80 angle with the central support (cos 80 = xx ; cos 80 4 = x; x = 4 approximately 0.7; = 1.0; Point Q is about a foot from the ground).
8 A2 Part A: Score Point 2 Part B: Score Point 1
9 Annotation Anchor Paper 2 Part A: Score Point 2 This response receives full credit. It includes each of the two required elements. The correct height of the central support is given (1.7 ft). The response shows correct modeling using an equation to find the height of the central support ( sin 25 = x ; 4 sin 25 = x; height of the 4 central support is about 1.7 ft tall). Part B: Score Point 1 This response receives full credit. It includes the one required element. The response shows the correct height of Point Q (1.0ft) and correct modeling to find the height of Point Q when the seating board creates an 80 angle with the central support (fin the length of that QR would reach if it went all the way to the ground; find cos 80 = ; xx = ; x = x cos ft; there is 5.8 feet from Q until it meets the ground following the same slope; now find the length from Q to the ground through similar triangles; cos 80 = x ; 5.8 cos 80 = x; Q to the ground is about 1.0ft.). 5.8 Note: This solution is valid and determines the distance from point Q to the ground by first determining the length of the line segment from the central support to the ground if the seating board was extended when the angle (QRT) is 80 degrees. The original 4 ft is subtracted to arrive at the length of that line from point Q to the ground. A line is dropped from point Q to the ground that is parallel to the central support. The distance from Q to the ground is determined using the length of this line segment that was created by extending the seating board past Q to the ground.
10 A3 Part A: Score Point 2 Part B: Score Point 0
11 Annotation Anchor Paper 3 Part A: Score Point 2 This response receives full credit. The student includes each of the two required elements: The correct height of the central support is given (1.7). The student shows correct modeling using an equation to find the height of the central support (sin 25 = xx ; 4 sin 25 = 1.7). 4 Part B: Score Point 0 This response receives no credit. The student does not include the required element: The correct height (1 foot) is provided but modeling of setup or work to determine this amount is missing.
12 A4 Part A: Score Point 2 Part B: Score Point 0
13 Annotation Anchor Paper 4 Part A: Score Point 2 This response receives full credit. The student includes each of the two required elements: The correct height of the central support is given (1.7 ft). The student shows correct modeling using an equation to find the height of the central support (sin 25 = h ; 4 sin 25 = h; H = 1.7). 4 Part B: Score Point 0 This response receives no credit. The student does not include the required element: An incorrect answer of 9.8 ft is given and an incorrect modeling of setup or work is shown for determining the height of Point Q from the ground.
14 A5 Part A: Score Point 1 Part B: Score Point 0
15 Annotation Anchor Paper 5 Part A: Score Point 1 This response receives partial credit. The student includes one of the two required elements: The student shows correct modeling using an equation to find the height of the central support (sin 25 4). This setup is sufficient to show the modeling for this prompt. An incorrect height of the central support is given (.53) which can be found by using radians instead of degrees on the calculator. Using radians the sin 25 is which is then multiplied by 4 giving with the student dropping the minus (negative) sign and making the length be The calculation point is lost but the setup is correct so this receives 1 point for the setup. Part B: Score Point 0 This response receives no credit. The student does not include the required element: An incorrect answer is given (.47) because an incorrect modeling of setup and work provided. The student uses a proportion which is not a method to find the height of Point Q from the ground. Note: If a correct method was used, but the student again used radians instead of degrees, it is possible to receive a score of 1 since the calculation point has already been lost in part A.
16 A6 Part A: Score Point 1 Part B: Score Point 0
17 Annotation Anchor Paper 6 Part A: Score Point 1 This response receives partial credit. The student includes one of the two required elements: The correct height of the central support is given (1.69ft long). The explanation is incomplete and does not receive credit (because since the seating is even the hypotenues would have to be four and I calculated for my answer). The use of a calculator is permitted but the input, operation, and answer need to be shown for credit to be given. Note: The answer is not rounded but not rounding to tenths is considered a precision point and a deduction of one score point taken only if the response is a top score response. Part B: Score Point 0 This response receives no credit. The student does not include the required element: No modeling with setup or work for the height of Point Q is provided and height shown (3.94ft) is incorrect.
18 A7 Part A: Score Point 0 Part B: Score Point 0
19 Annotation Anchor Paper 7 Part A: Score Point 0 This response receives no credit. The student includes none of the two required elements: An incorrect height is shown (height is 2) and an incorrect method provided. Using the Pythagorean theorem does not work because not enough information is given for that method. The properties of the sides of a triangle are used here, but the angles are In a triangle longest leg is x, the hypotenuse is 2x and the shortest leg is 3 x. Part B: Score Point 0 This response receives no credit. The student does not include the required element: The height of Point Q from the ground is missing and the modeling of setup or work is missing. The student wrote only items from the prompt.
20 A8 Part A: Score Point 0 Part B: Score Point 0
21 Annotation Anchor Paper 8 Part A: Score Point 0 This response receives no credit. The student includes none of the two required elements: An incorrect height (2 feet) is provided, and the setup or work is missing. Part B: Score Point 0 This response receives no credit. The student does not include the required element: Modeling with setup or work for the height of Point Q is not provided. The correct answer of 1 foot is given but does not receive credit without setup, work, or explanation how the 1 foot answer was determined.
22 Practice Set P101 - P105 No Annotations Included
23 P101
24 P102
25 P103
26 P104
27 P105
28 Practice Set Paper Score P101 2,0 P102 0,0 P103 2,1 P104 1,0 P105 2,1
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