### Homes

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?

### Stairs

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.

### 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?

# Whose Sandwich?

### Why do this problem?

This problem requires logical thinking and would be a good context in which to discuss different ways of representing mathematics.

### Key questions

What could you write down or draw to help?
What kind of sandwich did Jane order?

### Possible support

It would help to talk to learners about what they could write or draw as they work on this problem. You could start just by listing all four children's name across the top of a piece of paper, for example, which might help some pupils get started.