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by Dan Meyer


Act One

  • Dan Meyer

    Dan Meyer

    March 03, 2014

    What's happening here anyway? How are the square and the circle changing? What controls their change?

  • Teacher note
    Host a brief argument. Some students may claim the area is held constant. Some may go for the perimeter. Have students restate each other's ideas. Don't settle the question just yet.

Act Two

  • VideoCircle-Square w/ Numbers
  • 1.

    Guess where the circle and the square have equal area.

  • 2.

    What's a number you know is too high?

  • 3.

    What's a number you know is too low?

  • Teacher note
    Share out.

    Make sure everyone is on the same page. We're talking about the point where the circle is tangent to the square.

    Once everyone has their three numbers guessed. Have everybody share out. Locate the highest answer in the class. Locate the lowest answer.
  • Teacher note

    Now ask them to take their guess and calculate the area of the circle and the square at their guess and find out if they were right.

    If students finish quickly, tell them they should pick a different guess and see if that one is right.
  • Teacher note

    Now have them put an x wherever they previously had their guess and put them in the following Desmos graph.
  • LinkCircle-Square Graph

Act Three


  • 4.

    How would the point change for Circle-Triangle, Circle-Octagon, and Circle-Circle? How do you know?

  • 5.

    Rephrase our original question using words only.

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