### 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?

# Late Again

## Late Again

Here is a picture of Moira's school which has a paved playground at the front:

If Moira was sitting on the bench nearest the school gate, to get to the climbing frame she could:
Go forward $2$ squares to the pond.
Turn to the right and go $1$ square forward.
Turn to the left and go $2$ squares forward.

This morning, Moira is late for school.
What is the shortest route she can take from the school gate to the school door?
Is there more than one way she could go?

### Why do this problem?

This problem introduces children to the language involved in describing position and direction. It could be done in a practical context and adapted to suit your playground.

It would be useful to project the plan onto a screen for the children to see and you could give pairs a copy of it on paper.  This sheet contains two plans.

### Key questions

Which direction might you go in first?
Try and describe any route.
Can you make it shorter?
How will you know which routes you have tried?

### Possible extension

Children could be encouraged to make a plan of their own playground and set each other challenges.

### Possible support

Having a paper copy of the plan will help children get started. Encourage them to work with a partner.