Reflection: Connection to Prior Knowledge Making Sense of Area Formulas for Regular Polygons and Circles - Section 3: Whole-Class Discussion: Area of Circles


For me, there is almost nothing better than seeing my students build on their prior knowledge to make meaning out of a previously nonsensical idea.  Today was the day we rearranged our circle into a parallelogram-like figure, which helped many students to visually see why the area of a circle is given by pr2.   Students seemed to be able to grasp the notion that the “base” of our “parallelogram” was equal to half the circle’s circumference and that the “height” of our “parallelogram” was equal to the radius of the circle.  I was happy to have called on several students who were able to summarize the strategy and explain their understanding to the class. 


While facilitating this discussion, I decided to ask the class, “what questions might a skeptic ask us?”  This question provoked all kinds of responses, like “how do we know this is a parallelogram?” or “why can we think of this as a parallelogram when the base is curvy and not straight?”  or even, “if you really drew the height of the ‘parallelogram,’ which must be perpendicular to the base, wouldn’t it be less than the radius?”  I responded to this last question with another question, “what could we change to make our circle even more like a parallelogram?” which set the stage for students to consider slicing the circle into more and more sectors until the number of sectors approached a million or even infinity; this was a great moment in that students began to develop in their heads the idea of a limit.           

  Circles are Sort of Like Parallelograms
  Connection to Prior Knowledge: Circles are Sort of Like Parallelograms
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Making Sense of Area Formulas for Regular Polygons and Circles

Unit 10: Geometric Measurement and Dimension
Lesson 3 of 14

Objective: Students will be able to make sense of and explain area formulas for regular polygons and circles.

Big Idea: Students will use dissection strategies to connect circle area to the area of a parallelogram in addition to watching a YouTube video to connect circle area to triangle area.

  Print Lesson
Math, Geometry, coordinate geometry, Measurement, modeling, area of polygons, space, shapes
  75 minutes
regular polygon area
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