Math Curiosity: Odds & Squares

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Students will try to explain why the first X odds add up to the same number as X2.

Here's a math curiosity that turns out to always be true (but don't tell students up front!):

  • Take the first few odds and sum them.
  • If we choose 3, we'd get 1 + 3 + 5 = 9
  • Then, square the number of odds you chose: 32 also equals 9.

Try it for the first 5 odds:

  • 1 + 3 + 5 + 7 + 9 = 25
  • 52 = 25

Let students explore! Does it always work? Can they break it? Can they explain the pattern? A visual explanation is included in the video.

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