All Lesson Plans

Checkerboard Squares

Puzzle Board

Checkerboard Squares – Polypad – Polypad


How many 1 by 1 squares are there on a checkerboard? 2 by 2? 3 by 3? ..

A systematic way of counting the squares can be helpful. You can use this Polypad to help organize your thoughts.

S_Checkerboard Squares – Polypad – Polypad

To help you count the number of 2 by 2 squares in any given square, create a transparent 2x2 square and drag it over the sides of the main square. Then a 3x3, a 4x4, and so on.

What did you realize?


For the 8 by 8 checkerboard:

The total number of squares is the sum of the first eight square numbers.

More on the Checkerboard problem

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

How many cubes? – Polypad – Polypad


If you like this puzzle, try this one!

Border Tiles of an L Shape Poo – Polypad – Polypad