Working systematically

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

How could you put eight bean bags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Can you go through this maze so that the numbers you pass add to exactly 100?