### 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?

# Jumping Cricket

### Why do this problem?

This problem is a useful context in which to encourage children to work systematically in pairs or small groups.

This sheet, which could be photocopied, has twelve copies of the square patio.

### Key questions

What size jump are you going to try next?
Can all his jumps be the same size?
Can you find another way of doing it?
How will you know which ways you've tried?

### Possible extension

Some children might like to try a bigger grid or differently sized jumps.

### Possible support

Using a counter on a grid may help those that are struggling.