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Age 5 to 7 Challenge Level:

Why not start with the caterpillar's head in one square and find different ways to lay out its body?
What is the same about all the different ways you have found? Why?
What differences do you notice? Can you explain them?
How will you know which ones you have found? How will you know you haven't got the same layout twice?
You could look at sums and differences in the numbers of one of your caterpillars.