### 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?

### 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?

### Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

# Snakes

## Snakes

Explore the different snakes that can be made using five cubes.

### Why do this problem?

This is a good investigation for even the youngest children because all children will be able to find more than one snake. Interlocking cubes are suggested because they set the limitations of working with right angles and only joining whole faces to whole faces. You might want to set the further limitation of keeping the snakes flat on the table, not rearing up.
It is an excellent opportunity to get the children to record the different snakes that they make, either by freehand drawing or colouring boxes on grid paper. This adds to the spatial thinking required as it not only develops the idea of a plan view, but can also lead to a discussion about rotations and mirror images. If snakes that rear up from the table are part of the investigation, the children will have to think of a way to show this third dimension in their drawings.

### Possible approach

It would be helpful to do an introductory activity with carpet tiles or large squares of cardboard, so that the children understand the idea of making a snake from squares, and have the opportunity to start using relevant language. Words such as up, down, across, left, right, same and different are likely to be used to describe and compare the snakes.

Make the most of the children's recorded arrangements by having them cut up their paper so that the drawings can by grouped and sequenced in various ways. This will prompt further discussion as they explain their groupings, and perhaps uncover some patterns. It might also prompt the discovery of more possibilities.

### Key questions

Are any of your shapes the same?
How will you draw your shape?

### Possible extension

Collectively, the whole class may establish that they have found all the arrangements, or more some children might pursue this goal individually. An obvious extension is to investigate snakes made from six or more cubes, though this would require a systematic approach if all possibilities were being sought.

### Possible support

Reassurance for the most insecure pupils may be necessary because of the openness of this activity.