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There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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Train Carriages

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Cuisenaire Counting

Stage: 1 Challenge Level: Challenge Level:1

Jack, Alice, Phoebe, Eva and Holly from Georgeham C of E School explained their findings:

We did all the 1s.
Then we did one 2 block on the right filling in the spaces with 1s.
We moved the 2 block over a square, filled that with 1s.
Then we moved the 2 block over again and filled the space with 1s.
We moved the 2 block for the last time with 1s in the spaces.

The pattern for two 2 blocks is... there's a single white square on the left with two 2 blocks on the right.
There's another with the single white square in between the two 2 blocks.
The third is the single white square on the right with the two 2 blocks on the left.

So, I think that makes eight ways in total.  I love the way you have done this in a careful order.  As Chelsea from Templars Primary said:

... the trick is to work systematically ...

Laura sent in her solution as pictures copied from the interactivity, which is very helpful - thank you, Laura.

Here is her solution to the first challenge which we can compare with the solution from Georgeham:

partitioning 5

Laura's pictures are in a slightly different order to the children from Georgeham's.  I wonder which you think is more systematic?  

Here Laura shows the thirteen different ways to make the green rod using reds and whites:

partitioning 6

Would you have done them in the same order?  Why or why not?