![](https://wild.maths.org/sites/wild.maths.org/files/media/photos/section_photos/Visual_Proofs/counting%20stick%20challenge%2031.jpg)
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...