This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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
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?