mathematics work sample assessment - oregon...mathematics work sample assessment flagpole spotlight....

Use the information provided to solve the problem listed below. Be sure to who your work at all phases of problem solving. Refer to the Mathematics Problem Solving Official Scoring Guide to receive the highest score in each of the five process dimensions.

The base of a ten foot ladder is 6 feet from a building. The top of the leaning ladder reaches and makes contact with the building’s roof. On the corner of the building, a 4 foot flag pole is erected on the roof. A spot light with a fixed angle of elevation of 57 degrees is to be permanently secured to the ground and aimed to shine on the top of the flagpole. Determine how many feet from the corner of the building to place the spotlight.

Mathematics Work Sample Assessment Flagpole Spotlight

Mathematics Work Sample Assessment

Flagpole Spotlight


Flagpole Spotlight

Scores and Commentary: Flagpole Spotlight, Paper #E-28

Making Sense of the Task

(MS)

Representing and Solving

the Task (RS)

Communicating Reasoning

(CR)

Accuracy

(AC)

Reflecting and Evaluating

(RE)

2

3

4

2

2

MS 2: The student uses inappropriate concepts. The spotlight is aimed at the roof and the student assumes that the spotlight is 6 feet from the building.

RS 3: The strategy is only partially effective. It could work with an appropriate interpretation of the task.

CR 4: With the exception of the diagram, the reasoning is clearly communicated and the work leads to a clearly identified solution. This is an example of a weak 4.

AC 2: The solution is incorrect.

RE 2: The review is underdeveloped. The student checks a calculation and describes part of the strategy, but does not review the task situation, concepts, the remainder of the calculations, or reasonableness.



(MS)


the Task (RS)


(CR)

Accuracy

(AC)


(RE)

4

4

4

4

3

MS 4: The interpretation and translation are adequately developed. The student addresses the key concepts and translates them appropriately.

RS 4: The strategy is both effective and complete. The student uses the Pythagorean Theorem and right triangle trigonometry effectively.

CR 4: The work follows a clear and coherent path and leads to a clearly identified solution. The narrative on the second page supports the mathematics used on page 1.

AC 4: The solution is correct and supported by the work.

RE 3: The reflection only partially justifies the solution by providing a guide to the

solution but it does not review the calculations or reasonableness.



(MS)


the Task (RS)


(CR)

Accuracy

(AC)


(RE)

5

4

5

4

3

MS 5: The translation is thoroughly developed. The student rephrases the task situation and breaks it into parts that guide the interpretation of the task into mathematics.

RS 4: The strategy selected and mathematics used is effective and complete.

CR 5: the communication of the reasoning is enhanced (labels, graphics and explanations throughout) allowing the reader to move easily from one thought to another. The work is tutorial in nature.

AC 4: The solution is correct and both supported and justified by the work.

RE 3: The reflection only reviews the task situation. The “proof” is circular in nature verifying only the existence of a right triangle. There is an error in the calculation of the hypotenuse, which is used to verify the solution. The student finds the error and incorrectly attributes it to a rounding issue.



(MS)


the Task (RS)


(CR)

Accuracy

(AC)


(RE)

2

3

3

2

3

MS 2: The student uses inappropriate concepts. Aside from the placement of the 57 degree angle and the drawing of a right triangle, the information is jumbled.

RS 3: The strategy used is only partially effective. Had the interpretation been less confused, the strategy could have worked.

CR 3: The communication of the reasoning is only partially displayed. It is not clear why the flag is horizontal and why the student solves for the hypotenuse.

AC 2: The solution is incorrect.

RE 3: The student reviews strategy and calculations, but not the task situation as it relates to the drawing. This is an example of a strong 3.



(MS)


the Task (RS)


(CR)

Accuracy

(AC)


(RE)

4

4

5

4

4

MS 4: The interpretation and translation are adequately developed. The student addresses the key concepts appropriately.

RS 4: The strategy selected using both right triangle trigonometry and the Pythagorean Theorem is effective and complete.

CR 5: The communication of the reasoning is enhanced through the drawing of multiple triangles in order to focus on each calculation. Carefully showing every step also allows the reader to move easily from one thought to another.

AC 4: The solution of 7.8 feet is correct and supported by the work.

RE 4: The student justifies both the calculations and the reasonableness through the use of the Pythagorean Theorem. Review of the task situation is embedded through multiple drawings.

mathematics work sample assessment - oregon...mathematics work sample assessment flagpole spotlight....

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