Consecutive Numbers
Multiply the smallest and largest of three consecutive numbers, then square the middle one. What do you notice, and why?
First, choose three consecutive numbers – for example:
9, 10, 11
Multiply the smallest number by the largest
9 x 11
Square the other number (multiply it by itself):
10 x 10
What do you notice?
Try this with another three consecutive numbers.
What happens? Why?
Try the whole thing again. This time using numbers which increase by 2 instead of by 1 – for example:
6, 8, 10
Multiply the smallest number by the largest
6 x 10
Square the other number (multiply it by itself):
8 x 8
What do you notice?
Try this with another set of similar numbers.
What happens when you explore different sequences of numbers?
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