Grade 7 Geometry Walking Dog

Transcription

1 Grade 7 Geometry Walking Dog A dog walks 32 meters completely around the perimeter of his yard. What are the possible dimensions of his rectangular yard?

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3 3 Geometry Walking dog A dog walks 32 meters completely around the perimeter of his yard. What are all the possible dimensions of his rectangular yard? CU 5 The translation of the key concepts (rectangle, perimeter, and all possible integral dimensions) is thoroughly developed when s/he states that starting with the narrowest x longest rectangle and moving to the square would include all possibilities. PS 5 The process of both listing each of the dimensions starting with the narrowest x longest rectangle with a perimeter of 32 and moving step by step to an 8 x 8 square is thoroughly developed when in the verification s/he shows each has a perimeter of 32. V 4 The review includes showing the perimeter of each of the 8 rectangles is 32 and is complete. [This might have been thoroughly developed if s/he had shown the connection between the numbers used in the verification and the dimensions of the rectangles, instead of requiring the reader make that connection.] C 4 The path connecting the translation of the task to the process of creating a list of all rectangles with a perimeter of 32 and stating how s/he knew the list was complete to the verification, all towards the identified solution is complete. Acc. 5 8 rectangles with a perimeter of 32 meters is a mathematically justifiable solution and is supported by the work.

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5 3 Geometry Walking dog A dog walks 32 meters completely around the perimeter of his yard. What are all the possible dimensions of his rectangular yard? CU 4 The translation of the key concepts (rectangle, perimeter, and all possible integral dimensions) is complete when s/he appears to create the rectangles in random order, but in the verification hints that having short sides from 1 to 8 inclusive means the list is complete. PS 4 The process of creating rectangles and finding each perimeter to be 32 meters and stating if you switch the side lengths.. the answer is double is complete when the verification hints that s/he knows the other 8 would arrive from the switch and would make all possible dimensions. V 3 The review could not stand on its own as a solution to the task. It relies on the work done in the original solution, but provides the hint that the work was complete. This makes the verification partially effective. C 4 The path connecting the explanation of how to find perimeter to the drawings with the dimensions labeled and the perimeters of each rectangle being 32 meters to the explanation of why there are 16 such rectangles and to the verification, all towards the identified solution is complete. Acc rectangles with a perimeter of 32 meters is a mathematically justifiable solution and is supported by the work.

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7 3 Geometry Walking dog A dog walks 32 meters completely around the perimeter of his yard. What are all the possible dimensions of his rectangular yard? CU 3 The translation of the key concepts (rectangle, perimeter, and all possible integral dimensions) is underdeveloped when s/he lacks the understanding of changing rectangles with the same perimeter. The score for CU is raised when s/he recognizes that If two sides are 16 you already have 32 meters, so it would be less than 16 on each side. PS 2 The process of randomly guessing and checking multiples of dimensions that did produce a rectangle with a perimeter of 32 was sketchy when s/he had no method of determining if the two found were all the possible dimensions. V 2 Starting with the perimeter of 32 meters and subtracting the dimensions to end at 0 does verify the two rectangles found fit the requirements of the task --- but fails to help find if there are more, making it a focus only on the reasonableness of the two rectangles found. C 4 The path connecting the translation of the facts about perimeter and that no sides could be 16 to the details of the random guess and check to find 2 rectangles that did fit the requirements to the verification is complete. Acc. 1 Finding 2 rectangles with perimeters of 32 meters is an incomplete solution to the task