Square Off: Common Misconceptions

Students often make the mistake of thinking that area and perimeter change proportionally, but that isn’t always the case. For instance, a 3 × 3 square has an area of 9 square units and a perimeter of 12 units, but a 1 × 8 rectangle has an area of 8 square units and a perimeter of 18 units. That is, the area decreased, while the perimeter increased.

This is a concept students will encounter many times during the Square Off game. You can also explore the idea by giving students eight squares and ask them to create various arrangements of rectangles. All of the arrangements will have an area of 8 units, but do all of the figures have the same perimeter? The answer is no, and it can be powerful for kids to discover this on their own.