Chessboard Squares

No 3 in a series of posts based on Thinking Mathematically (1985) by Mason, Burton, Stacey

This is a classic task for working systematically:

```It was once claimed that there are 204 squares on an ordinary chessboard.
Can you justify this claim?```

I like this way of stating the problem, rather than just “how many squares on a chessboard?” because it gets straight to the nub of the issue – we are looking at different sized squares, some of which overlap.

Do you understand reciprocals?

These questions test a lot of things so use them carefully.

Firstly there is what do we understand about reciprocals, namely:

These are tricky concepts to grasp. This is the order in which I teach them, but I don’t think the “flow” through these 4 concepts is particularly obvious and students need to be carefully led with lots of examples using Mini Whiteboards.

Other understanding required includes:

• Finding equivalent fractions
• Finding common denominators and using them to find the right equivalent fractions