## Reflection: Discourse and Questioning CORNERSTONE: Circumference Formula - Section 1: Lesson Notes + Examples

Students begin the lesson knowing the PI is the ratio of Circumference to Diameter or PI = C/d.  Getting students to derive the circumference formula using triangles was not as straightforward for them as I had expected.

I presented an image similar to the one here.  I then asked students to complete the fact triangles.  By convention, the product goes in the top vertex of the fact triangle and the factors go in the bottom left and bottom right vertices; they all knew this and had no problem with 3,4, and 12.

Students were not quite sure what to do with the symbols PI, C, and d.  We looked back at the division factors to see where the dividend would be.  They noticed it was in the same place as the product.  Then I asked, what is the division problem implied by the ratio PI.  We then concluded that circumference belongs in the top vertex.  See that here.

That left the bottom left and bottom right vertices for PI and the diameter.  See that here.  Students then were able to write the fact families and see that C = PI * d was the circumference formula.

Deriving the Circumference Formula Using Fact Triangles
Discourse and Questioning: Deriving the Circumference Formula Using Fact Triangles

# CORNERSTONE: Circumference Formula

Unit 6: Geometry
Lesson 7 of 37

## Big Idea: Students apply the circumference formula and use fact families to see how it is derived from the ratio PI.

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Standards:
Subject(s):
Math, areas, circumference (Determining Measurements), Geometry, 7th Grade M, Circumference Formula, circles, perimeter, Diameter, pi
50 minutes

### Grant Harris

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