Grade 5

Write the following story on the board. You might suggest that students think about the similarities and differences between the two lists.

Begin with 1 and keep doubling it (1, 2, 4, 8…), writing down each number until you have a list of at least 10 numbers (including 1). Now make a list of the first 10 or so square numbers beginning with 1. What can you say about the patterns in both lists?

- Except for 1, all the numbers in the first list are even because once you start doubling, all the numbers will have 2 as factor.
- The list of differences between neighbors in the list of doubles is the same as the list itself!
- Square numbers alternate odd, even, odd, even, and so on.
- The list of differences between neighboring square number is the list of odd numbers in order, beginning with 3.
- The numbers in the first list grow faster.

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