The original version of this problem uses only a 4x4 grid, but reducing the size makes this investigation accessible to younger children too.

The learning objectives covered are numerous and cover the entire KS1/KS2 age range:

• Sorting, classifying and organising
• Choosing and using appropriate strategies
• Explaining methods of reasoning
• Understanding and using vocabulary related to position
• Recognising, explaining, generalising and predicting patterns

No matter how old the children, it would be advisable to have objects to represent the teddies and houses as an introduction to the activity. These could be, for example, coloured counters and coloured squares if the real thing weren't to hand. Coloured magnets would be ideal for use on a white board as a demonstration.

It would be worth clarifying the very first instruction. Work out the four different combinations together with the children, using teddies and houses of two different colours:

Yellow teddy in yellow house	Yellow teddy in red house	Red teddy in yellow house	Red teddy in red house

Ask them:

• How can we make sure they are all different?
• Is there a way to go about making the combinations so we don't leave any out?
• Talk about being methodical and systematic i.e. planning and checking

It is vital that the children understand how each of the above is different from the rest and, in addition, that they realise you can put a teddy in a house of the same colour (this has caused confusion in past experience).

Discuss strategies for working out the arrangements of combinations on the streets. Try inviting your pupils to suggest:

• Starting points -- what might we put in the grid first and where?
• Logical approaches to filling in the grid

When a particular grid is complete, look for patterns and find out whether these can be applied to the next grid size up. This can also entail different recording/representation methods and allows you to explore vocabulary of position.

Throughout all of this investigation, encourage the children to explain their thinking orally. This may be to each other, or to the class as a whole. Either way, it is vital in allowing them to clarify their own ideas, reflect critically on their work and so move themselves forward.

To find out about the history and theory of this problem, look at www.cut-the-knot.org/arithmetic/latin3.shtml.