Counting stick challenge


Here is a picture of a counting stick:


It is divided into equal rectangular sections.

How many rectangles can you see altogether?

Once you've had a go, here are some questions you might like to consider:

  • Are all your rectangles the same size? (I can see some that are bigger than others...)
  • How many different sizes of rectangle are there?
  • How many rectangles are there of each size?
  • What if my counting stick was longer, or shorter?
  • Is there a quick way to work out how many rectangles there would be, for a counting stick with 100 sections? Or 1000? Or...