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Slicing Pi

Slicing Pi. CCSS: 7. G . 4. Common Core Standard. Focus: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

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Slicing Pi

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  1. Slicing Pi CCSS: 7.G.4

  2. Common Core Standard Focus: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

  3. Materials: Scissors Glue Handout—”Slice of Pi” Handout—”Slice of Pi Questionnaire”

  4. Pre-Activity Q&A: What is the area of the circle in terms of triangles? What is the radius of the circle? How can we use the triangles to create a parallelogram? What is the formula for finding area of a rectangle? What is the formula for finding area of a circle?

  5. Directions: Cut apart the slices of the circle and rearrange them to make a parallelogram. Cut half the end piece off and put on the other end to create a rectangle. Glue the pieces to a sheet of paper to make a rectangle. Students should work with a partner to complete the Slice of Pi Questionnaire handout. Prepare to discuss findings and conclusions in class.

  6. Activity Q&A: Did we change the area of the circle when we took it apart and made a parallelogram? Did we change the area when we altered the parallelogram to make a rectangle? Can we give an exact area of the circle or the rectangle? Why do we give the area in terms of Pi? How can you prove that the area of the circle and the area of the rectangle are the same?

  7. Post-Activity Q&A: What is the relationship between the radius and the diameter of a circle? What is the relationship between circumference of a circle and its area? If you know the area of a circle, how can you find the diameter or the radius?

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