Whatever you teach (or learn), you should look for the links, the more unexpected, the better. This post is the story of one of them, simple but lovely and strong.

I have a class with a group of adult students who never had a positive experience with mathematics (or as they would say, “they hate mathematics”), have very limited knowledge of mathematics, and yet, likely to work in nurseries and primary schools where they have to teach mathematics somehow or other. My aim is to help them not to hate mathematics (if not like it) and have some positive experience of doing mathematics. They refer to my aim as “great expectation” 🙂 But, last week something changed in them; something that made me so excited that the whole class burst into laughter.

Previously in the class we had worked on the idea of subitizing and the ways we might help children to do so conceptually. We had learned how the “shape” or “structure” of a group of objects could help us (children) to realize “how many they are without counting” (that is the essence of subitizing). For example, children should learn to see the number of dots in the following figure is five without counting.

Also, We had played with Mathlink Cubes to experience different shapes for numbers, and to discover similarities and differences between those shapes. In particular, we learned numbers 3, 6, and 10 can be represented by triangular-looking figures like the following.

So far, it was just the story of what the class knew before facing with this question:

**In how many ways can we represent number two by using the fingers of one hand?**

Here are two of them:

Using just one hand, there was no need to be that much systematics; somehow or the other we could find the answer. However, the problem became more difficult when we were allowed to use the fingers of both hands. Here, the unexpected link of the story appeared. It is amazing and worthy of being discovered if it is the first time that you are counting the twos of your fingers. Please try it before continuing reading.