I already knew that students have a hard time with perimeter and area. Mainly, they seem to mix up these two terms. We spent time exploring perimeter and area in many different ways in my classroom. We used geoboards on the iPads to build rectangles with a given perimeter and area, we measured them on "hallway polygons" taped down in the hall, we measured the area of Sao Paolo, Brazil to experiment with irregular figures, and we used base-ten blocks to explore the many ways to make a figure with an area of 5 square centimeters.
This routine extended my thinking because it gave me a window into what misconceptions students still had. It also gave students a way to express in words what math thinking was going on in their minds. Here is a sample of what kids shared:
- I used to think perimeter was by multiplication. Now I think perimeter is by addition and base times height = area.
- I used to think perimeter and area were hard becaus I did not know what was the inside and what was the outside. Now I know that perimeter is the outside of a shape or polygon and area is the inside of a shape or polygon.
- I used to think area and perimeter were the same thing and would add both together. Now I think perimeter is the outside of the area. Area is the squares inside the perimeter.