In this activity, students use the floor plan of a recreation center to calculate the area of two swimming pools. This helps reinforce the relationship that the area of an actual region is related to its area on a scale drawing by the (scale factor)^2.

Previously, whenever students were asked to use a scale drawing to calculate the area of an actual region, they were able to find the dimensions of the actual region as an intermediate step. Each time, students were prompted to notice the (scale factor)^2 pattern. Some students may have already become comfortable using this relationship to calculate the actual area directly from the scaled area, without needing to calculate the actual dimensions as an intermediate step.

The purpose of this activity is to help all students internalize this more efficient method. The question about the rectangular pool can be solved either way, but for the question about the kidney-shaped pool, students must rely on the relationship between scaled area and actual area. As students apply the (scale factor)^2 pattern they have seen in other activities to determine the scaled area, they are making use of structure (MP7).

As students work, monitor for the different ways that students find the area of the large rectangular pool, such as:

• By first finding the actual side lengths of the pool in meters and then multiplying them.

• By calculating the scaled area in square centimeters and multiplying that area by 25 (or 5^2​​).

This activity uses the Critique, Correct, Clarify math language routine to advance representing and conversing as students critique and revise mathematical arguments.