All Tasks

How Many Squares on a Checkerboard?

How many Squares are there on a Checkerboard?

We may see this problem as somewhat easy, counting just the 64 small (1x1) squares.

However, the board also has 2 x 2 squares, 3 x 3 squares, and so on. Watch this video to see one way to think about the other sized squares:

Use this canvas to explore the number of squares in a checkerboard:

A systematic way of counting the squares can be helpful:

  • What did you realize?
  • How many 3 x3 Squares are there on a Checkerboard?
  • What is the total number of squares are there on a Checkerboard?

Extension

How many cubes are there in an 8x8x8 cube such as this?