3.MD.D.8

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

4.MD.A.3

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. *For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.*

Students will learn how to find the perimeter of composite rectangles (rectilinear figures) by adding. They'll also learn how to solve missing number addition problems involving perimeter. Next, students will be given unit squares, as wooden blocks, or otherwise, which they'll use throughout the remainder of this lesson. Students will first use the blocks to find rectangles that have the same perimeter, but different area, and vice-versa. Next, students will use the blocks to learn how to find the dimensions of the rectangle with the smallest/largest perimeter, given its area. By doing several such problems, students should see that perimeter increases as the rectangle flattens. That's because as the rectangle flattens, the number of unit squares whose edges are on the boundary of the rectangle increases. After that, students will use the blocks to find the dimensions of a rectangle given both its area and perimeter, as seen here.