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Number line inquiry Describe the procedures used in the prompt. What do you notice about the results?

If the four numbers are consecutive, the difference between the products is …………. If the four numbers go up in twos, the difference between the products is …………. If the four numbers go up in threes, the difference between the products is …………. Fill in this table of your results The numbers go up in … 1

The difference between the products is …

Can you see a pattern in the differences column?

2

2 3

Can you make a prediction if the numbers go up in 8, 9 or 10?

4 5 6 7 Change the prompt in one way and explore further  

Join up the four numbers in different ways. Use five, six or more consecutive numbers.

Use symbols to prove the difference is always the same Why does the number line start with n? Explain why the number line continues with the expressions n+1, n+2 and n+3? Multiply n by n+3 and n+1 by n+2. What do you notice? Can you use this approach to prove any of your other results?