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Gauss Summation

Add 1 + 2 + 3 + … + n without adding — two staircases make a rectangle.

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How much is 1 + 2 + 3 + … + 6?

Build the staircase one column at a time.

1 + 2 + … + 6 = 6 × 7 ÷ 2 = 21

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Which picture

How far to count

Up to
6

The rectangle is 6 × 7 = 42 squares.

Build

Speed

0 of 6 columns built

Projector

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Using it in class

  1. Ask for 1 + 2 + … + 10 before showing anything, and time how long the room takes.
  2. Build the staircase a column at a time and read the running total aloud.
  3. Before dropping the copy in, ask what shape two staircases would make.
  4. Switch to the pairing view and ask why an odd n leaves one number over.