Reflection: Student Ownership The Defining Pi Project, Day 3 - Section 2: Work Time: Completing Construction #1

 

The conversation about our next step is fun, and I encourage you to think about ways to orchestrate it.  The goal is get students to come up with the idea that an octagon or decagon or 12-gon or 15-gon would "fill" more of the circle than our hexagon, and its perimeter would come closer to the circumference of the circle.  One instructive way to illustrate this is to take one side of the hexagon and split it in half.  

Students pretty quickly get the gist of what they're going to do on their next two constructions: inscribe polygons with more that six sides.  As they get started on construction #2, I tell them to use the same radius as their first one.  If they need ideas for which polygons to try (or even better, if they're arguing about which polygons are possible) I might ask them to list all the factors of 360.

Once they get going, students will notice that their new polygons no longer consist of equilateral triangles, but that they are made up of isosceles triangles.  This is why we've been practicing with isosceles triangles in previous lessons, and hopefully students can now see the payoff.

  When students work with anticipation...
  Student Ownership: When students work with anticipation...
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The Defining Pi Project, Day 3

Unit 6: Trigonometry: Circles
Lesson 7 of 17

Objective: SWBAT complete the first construction of the Defining Pi Project, and begin to learn that successively more-sided n-gons will allow us better approximate the circumference of a circle.

Big Idea: Students experience firsthand a famous method for approximating pi to successively greater levels of precision.

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