Teach students the Total Turn Theorem to help them reason about drawing regular, closed polygons in Scratch.

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  • The total turn theorem states that: turn degree × number of turns = 360°
  • Have students pretend to be the sprite and "draw shapes" by turning and moving in order to get them to think about why the total turn theorem works.
  • Check out this YouTube video that describes how to use the total turn theorem to draw a shape!
  • Using a turtle as a sprite, Papert provides the following definition for the "Total Turtle Trip Theorem" in Papert's 1980 book Mindstorms: Children, computers, and powerful ideas.
    • "If a Turtle takes a trip around the boundary of any area and ends up in the state in which it started, then the sum of all turns will be 360 degrees" (page 76)
  • This theorem was also presented in Abelson and DiSessa's 1986 paper "Turtle geometry: The computer as a medium for exploring mathematics."

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External Source

Colleen Lewis' CS10K Scratch Webinar.