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Gopher Security Gopher Security Company has been hired to create a security system for the Portland Museum to guard the famous Hope Diamond. They will be installing a laser bean triggered security system. You will help them determine the distance the beam will travel around the room to protect the diamond. If the beam is broken, the alarm will be triggered. The display box will be placed in the center of the room. The beam travels from the sensor at point A to sensor B to sensor C to sensor D and back to sensor A. What is the total distance the beam will travel around the room? Show all work and reasoning to complete the task.
page 2 of 12 pages
Scores and Commentary: Gopher Security, Paper H.1G.4 #3
Making Sense of the Task
(MS)
Representing and Solving the Task
(RS)
Communicating and Reasoning
(CR)
Accuracy (Acc)
Reflecting and Evaluating
(RS) 5 5 5 4 5
MS 5: The translation and interpretation of the task are thoroughly developed and enhanced through the use of different mathematical ideas (distance formula (Pythagorean theorem) and trigonometric ratios). RS 5: The original strategy in enhanced by another solution using virtually the same strategy and by the second solution using a completely different one. It is further enhanced by the information provided in the margins of the work. CR 5: The Info provided in the left margin, the detailed work in the body and the narrative provided. In the right margin allow the reader to move easily from one thought to another. AC 4: The solution/outcome is correct all three times. It's mathematically justified and supported by the work. RE 5: The solution is justified completely by arriving at the same outcome via different approaches. The student also addresses this fact in the narrative.
page 3 of 12 pages
Gopher Security Gopher Security Company has been hired to create a security system for the Portland Museum to guard the famous Hope Diamond. They will be installing a laser bean triggered security system. You will help them determine the distance the beam will travel around the room to protect the diamond. If the beam is broken, the alarm will be triggered. The display box will be placed in the center of the room. The beam travels from the sensor at point A to sensor B to sensor C to sensor D and back to sensor A. What is the total distance the beam will travel around the room? Show all work and reasoning to complete the task.
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Scores and Commentary: Gopher Security, Paper H.1G.4 #30
Making Sense of the Task
(MS)
Representing and Solving the Task
(RS)
Communicating and Reasoning
(CR)
Accuracy (Acc)
Reflecting and Evaluating
(RS) 4 4 4 4 4
MS 4: The interpretation and translation of the task are adequately displayed and developed.
RS 4: The strategy of using the distance formula followed by the slightly altered Pythagorean theorem is both effective and complete.
CR 4: The work follows a clear and coherent path and leads to a clearly identified solution and is supported by the labeling of the diagram.
AC 4: The solution given is correct and mathematically justified and supported by the work
RE 4: The outcome is stated within the context of the problem. The reflection justifies the interpretation, concepts, strategies, calculations and reasonableness (by obtaining the same result). Because the review is only a slight variation from the first attempt (the distance formula is equivalent to the Pythagorean theorem), it is not a 5.
page 7 of 12 pages
Gopher Security Gopher Security Company has been hired to create a security system for the Portland Museum to guard the famous Hope Diamond. They will be installing a laser bean triggered security system. You will help them determine the distance the beam will travel around the room to protect the diamond. If the beam is broken, the alarm will be triggered. The display box will be placed in the center of the room. The beam travels from the sensor at point A to sensor B to sensor C to sensor D and back to sensor A. What is the total distance the beam will travel around the room? Show all work and reasoning to complete the task.
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Scores and Commentary: Gopher Security, Paper H.1G.4 #24
Making Sense
of the Task (MS)
Representing and Solving the Task
(RS)
Communicating and Reasoning
(CR)
Accuracy (Acc)
Reflecting and Evaluating
(RS) 3 3 3 2 1
MS 3: The interpretation of the task is only partially developed. For each part, the student has used a leg length in the place of the hypotenuse to solve for the very leg used, instead of using the leg length to solve for the hypotenuse.
RS 3: The strategy is only partially effective due to the use of incorrect lengths. It is partially complete in that the sum of the "lengths" is never calculated. CR 3: The solution displayed is only partially displayed and does not lead to an outcome. AC 2: The solution is incomplete and incorrect. The strategy used could have worked, earning a score of 2 instead of I. RE 1: The reflection is not evident
page 11 of 12 pages
Gopher Security Gopher Security Company has been hired to create a security system for the Portland Museum to guard the famous Hope Diamond. They will be installing a laser bean triggered security system. You will help them determine the distance the beam will travel around the room to protect the diamond. If the beam is broken, the alarm will be triggered. The display box will be placed in the center of the room. The beam travels from the sensor at point A to sensor B to sensor C to sensor D and back to sensor A. What is the total distance the beam will travel around the room? Show all work and reasoning to complete the task.
page 12 of 12 pages
