##
* *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

Lesson 7 of 37

## Objective: SWBAT solve problems involving the circumference of a circle using the circumference formula

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

*50 minutes*

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- LESSON 1: Explore Perimeter and Area of Composite Shapes
- LESSON 2: Perimeter of Irregular Rectilinear Shapes
- LESSON 3: Area of Composite Shapes Using a Grid
- LESSON 4: Area of Composite Shapes
- LESSON 5: Area of Regions Formed by Inscribed Shapes
- LESSON 6: CORNERSTONE:Circle Ratios: Diameter to Radius; Circumference to Diameter
- LESSON 7: CORNERSTONE: Circumference Formula
- LESSON 8: Area of a Circle
- LESSON 9: Circumference & Area Fluency Practice
- LESSON 10: Finding the Radius From a Given Circumference or Area
- LESSON 11: Circumference from Area / Area from Circumference
- LESSON 12: Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments
- LESSON 13: Assessment_Area and Perimeter (Circumference) of Composite Shapes and Circles
- LESSON 14: Drawing Prisms & Pyramids
- LESSON 15: Describe Prisms and Pyramids Using Algebra
- LESSON 16: Using Nets to Find the Surface Area of Prisms
- LESSON 17: Using a Formula to Find the Surface Area of Prisms
- LESSON 18: Finding the surface area of triangular prisms using a net
- LESSON 19: Finding the Surface Area of a Triangular Prism Using A Formula
- LESSON 20: Discovering the Formula for the Surface Area of A Cylinder
- LESSON 21: Finding the Surface Area of Cylinders Using a Formula
- LESSON 22: Practice Day: Surface Area of Prisms & Cylinders
- LESSON 23: Surface Area of Prisms and Cylinders Assessment
- LESSON 24: Finding the Surface Area of Pyramids Using Nets
- LESSON 25: Finding the Surface Area of Pyramids Using a Formula
- LESSON 26: Surface Area of Composite Shapes
- LESSON 27: Surface Area of Composite Shapes With Holes
- LESSON 28: Surface Area Assessment
- LESSON 29: 3-D Models from 2-D Views
- LESSON 30: Exploring Volume and Surface Area with Unifix Cubes
- LESSON 31: Explore Volume of Rectangular Prisms
- LESSON 32: Find the Volume of Prisms Using a Formula
- LESSON 33: Volume Of Cylinders Using a Formula
- LESSON 34: Volume of Composite Shapes
- LESSON 35: Volume and Surface Area - Accelerated Math Fluency Day
- LESSON 36: Volume of Pyramids
- LESSON 37: Surface Area and Volume Final Assessment