Here are two tasks where having good ways to sort and organize can be very helpful. Young children often find working in a systematic way very difficult.  These problems provide a real context and an opportunity to record thinking, which  leads to the very beginnings of a proof.




Max has a shirt with 4 different buttons:  blue, red, purple and yellow

 Sometimes, Max buttons them up starting with the top button.  Sometimes, he starts somewhere else.

How many ways can you find to button up  Max’s shirt?

Draw a diagram to show how many ways you find.

Do you think you found all the ways?  How do you know?






Max has a piece of four by four dotty grid paper.
He wants to figure out how many triangles he can draw with one dot in the middle of each triangles.


He has joined three dots on the grid to make a triangle which has one dot inside it…

How many different triangles with one dot in the middle can Max draw?

Help Max find all the triangles.


How do you know have found them all?

You may want to make your own 4 x 4 Dotty Grid, or you could print a copy of a dotty grid to work on.