### Cubes

Investigate the number of faces you can see when you arrange three cubes in different ways.

### Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

### Colouring Triangles

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

# Break it Up!

##### Stage: 1 and 2 Challenge Level:

You have a stick of $7$ interlocking cubes. You cannot change the order of the cubes.

You break off a bit of it leaving it in two pieces.

Here are $3$ of the ways in which you can do it:

In how many different ways can it be done?

Now try with a stick of $8$ cubes and a stick of $6$ cubes:

Make a table of your results like this:

 Number of cubes Number of ways $6$ cubes ? $7$ cubes ? $8$ cubes ?

Now predict how many ways there will be with $5$ cubes.

Were you right?

How many ways with $20$ cubes? $50$ cubes? $100$ cubes?

ANY number of cubes?

* * * * * * * * * * * * * * * * * * * *

If all the cubes are the same colour, a split of $4$ and $2$ will look the same as a split of $2$ and $4$.

How many ways are there of splitting $6$ cubes now?

Can you predict how may ways there will be with any number of cubes?