Grade 4 – Geometry Marla’s Rectangle Dimensions Marla’s teacher asked her students to find the length and width of all the rectangles with an area of 20 square feet. Show the dimensions (length and width) of all the possible rectangles.

3 – Geometry Marla’s rectangle dimensions Marla’s teacher asked her students to find the length and width of all the rectangles with an area of 20 square feet. Show the dimensions (length and width) of all the possible rectangles. 4 – 3 – 1 CU 5 The translation of the key concepts (rectangle, area, and

dimensions) are thoroughly developed in the verification (where the “cercels” are showing area) and prose around the answer (describing what could happen if flips were considered as additional dimensions).

PS 5 The process of drawing the rectangles and labeling the dimensions

is thoroughly developed in the verification where the flips are displayed and the prose defends why they are not considered additional possible rectangles. [The process/strategy might have been enhanced if s/he had indicated why there were no other possible rectangles with an area of 20.]

V 5 The verification reviews the concepts of area, rectangle, and

dimensions, as well as the process of drawing the rectangles and arriving at 3 different rectangles with an area of 20. The details in the recording and the related prose make this review thoroughly developed.

C 4 The path connects the translation of the task into the key concepts

to the process of drawing and labeling the rectangles to the verification, all towards the identified solution, and is complete.

Acc. 5 3 rectangles (4 x 5; 2 x 10, and 1 x 20) is a mathematically

justifiable solution to the task.

3 – Geometry Marla’s rectangle dimensions Marla’s teacher asked her students to find the length and width of all the rectangles with an area of 20 square feet. Show the dimensions (length and width) of all the possible rectangles. 4 – 3 – 2 CU 5 The translation of the key concepts (rectangle, area, and

dimensions) is thoroughly developed in the drawings of the “squares” with the dimensions labeled and the areas shown in each, and the algorithmic area representation in the verification.

PS 4 The process of drawing each rectangle, labeling the dimensions

and the area, and identifying that there are 3 rectangles meeting the requirements of the task is complete.

V 3 The verification includes the translation of dimensions and area and

the identification that there are 3 rectangles meeting the requirements of the task. It is only partially completed without some review of the thought process that listed 6 sets of dimensions of rectangles (and knew there were no others) but said that the answer is 3.

C 4 The path connecting the translation into rectangles with dimensions

and areas of 20 square feet to the process of drawing and labeling the rectangles to the verification, all towards the identified solution is complete. [The gap of listing 6 sets of dimensions, and stating there are 3 rectangles, is within verification, not between it and another dimension. Also, calling the rectangles squares, should be addressed as a classroom issue not a problem solving issue, so it doesn’t affect any of the scores.]

Acc. 5 3 rectangles (4 x 5; 2 x 10, and 1 x 20) is a mathematically

justifiable solution to the task.

3 – Geometry Marla’s rectangle dimensions Marla’s teacher asked her students to find the length and width of all the rectangles with an area of 20 square feet. Show the dimensions (length and width) of all the possible rectangles. 4 – 3 – 3 CU 2 The translation of the key concept of rectangle is completed. The

concepts of area and dimensions are not evident. Together the conceptual understanding is sketchy.

PS 1 The process of drawing a rectangle composed of 20 rectangles

(with dimension 2 x 4) accompanied by random calculations is ineffective in solving the task.

V 2 The verification is the drawing of the rectangle with the area

indicated by the grid lines and is a review of only the process used to solve the task.

C 1 The path connecting the translation of the key concept to the

process (including the calculations) to the verification (which may be intended to have a different area displayed than the original rectangle) is minimal.

Acc. 1 No actual solution is presented, but if the solution is a 4 x 20

rectangle, it is incorrect.