Getting Started 
Misconception/Error The student is unable to reproduce a scale drawing using a different scale. 
Examples of Student Work at this Level The student reproduces the drawing incorrectly. The student:
 Uses the same dimensions as the original drawing.
 Halves each of the original lengths.
 Adds two to the length of each side.
 Changes each side by differing amounts with no clear pattern.
 Interprets the change of scale incorrectly, multiplying each dimension by five.

Questions Eliciting Thinking Can you explain the problem? How will the new scale affect the dimensions?
What length does each square on the original drawing represent? How many squares are needed to represent that same length on the new drawing?
Using the original scale, can you calculate the actual garden dimensions? How would you represent those dimensions if each square on the grid now represents five feet?
Why did you add two to each length in the drawing? What multiplicative relationship exists between the new scale and the old one? 
Instructional Implications Establish that the scale of a scale drawing is a ratio that compares length measurements in the drawing of an object to corresponding actual length measurements. In this case, the scale factor is a ratio that compares a number of centimeters in the drawing to a number of feet in actual length. Have the student use the scale to calculate some actual lengths in the garden. Next assist the student in determining the corresponding lengths in the scale drawing using the new scale. Then guide the student to observe the relationship between lengths in the original scale drawing and lengths in the new scale drawing.
Provide additional experiences with scale drawings. Consider implementing other tasks aligned to this standard. 
Making Progress 
Misconception/Error The student is unable to explain how the new scale changed the dimensions of the drawing. 
Examples of Student Work at this Level The student reproduces the drawing using the new scale but is unable to explain how the two scales are related. The student:
 Says the garden will still be the same size.
 Says five is half of 10 so each side is half the original.
 Does not give a specific comparison, just writes â€śitâ€™s bigger.â€ť

Questions Eliciting Thinking I see you realize the actual dimensions of the garden will not change, however what happened to the dimensions of the scale drawing?
I agree that five is half of 10, but looking at each side of your drawing what is happening to the lengths?
What do you mean by â€śeach side is bigger?â€ť Can you tell me how much bigger? 
Instructional Implications Ask the student to write ratios of corresponding lengths from the two scale drawings (e.g., 2 cm:4 cm and 4 cm:8 cm). Assist the student in describing the relationship between the lengths and in observing why a greater length is now needed given the change in the scale.
Ask the student to solve problems involving proportional reasoning in geometric contexts. For each problem, ask the student to describe the relationship between figures in terms of scale. For example:
 Given a right triangle with a base of five and a height of nine, find the height of a proportionally larger triangle with a base of 12.
 Given a small right triangle with a base of four and a height of seven, use a scale factor of four to find the base and height of a proportionally larger triangle. Consider implementing the MFAS tasks for standard 7.RP.1.2.
Consider administering other MFAS tasks for standard 7.G.1.1.

Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student reproduces the drawing correctly and explains that each dimension in the new drawing is double the length of the original drawing because the scale is half the size.

Questions Eliciting Thinking How would the drawing have been different if the new scale factor had been 1 cm represents 20 feet? 4 feet? 1 foot?
If you were given the actual dimensions and the drawing, how would you determine the scale factor?
How are the perimeters of the two drawings related? How are their areas related? 
Instructional Implications Challenge the student to calculate the perimeters of the figures in the two drawings. Ask the student to find the ratio of these two values and the associated scale factor. Have the student repeat the process using the areas of each figure. Ask the student to determine how these scale factors are related.
Provide additional opportunities to calculate perimeters and areas of figures in scale drawings and perimeters and areas of actual figures. Ask the student to relate the ratio of perimeters and areas to the scale and generalize the result (e.g., explain that the ratio of perimeters is equal to the scale factor and the ratio of areas is the square of the scale factor). Then provide scale factors and ask the student to determine the ratio of areas and vice versa. 