### 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?

# Three Ball Line Up

## Three Ball Line Up

Two children are playing with three balls, one blue, one red and one green.

They toss up the balls, which run down a slope so that they land in a row of three.

How many different ways could the balls land?

You might like to use the interactivity below to explore the problem.

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### Why do this problem?

This problem is a good context for encouraging learners to work systematically. Then they will be able to convince someone else that they have found all the possibilities.

### Possible approach

The interactivity will help children to get a feel for the problem.

### Key questions

If red landed in the middle, how could the blue and green fall?
Where else could red land if it wasn't in the middle?
Can you use this idea to find all the ways?
How will you remember the ways you have found so far?

### Possible extension

Encourage children to use four balls/counters.

### Possible support

Pupils would benefit from having three differently-coloured counters to use while tackling this problem.