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Using Structure to Explore Circles

Using Structure to Explore Circles. Kevin McLeod Connie Laughlin Hank Kepner Beth Schefelker Mary Mooney Math Teacher Leader Meeting, May 17 th and 19 th.

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Using Structure to Explore Circles

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  1. Using Structure to Explore Circles Kevin McLeod Connie Laughlin Hank Kepner Beth Schefelker Mary Mooney Math Teacher Leader Meeting, May 17th and 19th The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

  2. Learning Intention We are learning to • expand our understanding of structures about area • deepen our understanding of circle measurements • reflect on the Standards of Math Practice The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

  3. Success Criteria • We will know we were successful when we can derive a connection between the area and the circumference of a circle. • We will know we were successful when we can articulate how the standards for math practice work together with the content standards.

  4. Launch What are some structures that supported our previous work in area? The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

  5. Our Previous Work with Area Formulas • Area of a Rectangle • Area of a Parallelogram

  6. Moving and Combining Can the moving and combining principles be used to figure out the area of a circle?

  7. Explore • We have a circle divided into for congruent pieces.

  8. Surfacing a Relationship • Each person folds a circle to make • eighths • sixteenths • Cut each wedge (sector) apart. eighths sixteenths

  9. Putting Structure to Work • What did you notice about the shape as you moved and combined the sectors from each circle?

  10. How can we use this information to find the area of the circle? • A = ½C*r

  11. Have we met our Learning Intention • to expand our understanding of structures about area • to deepen our understanding of circle measurements • reflect on the Standards of Math Practice

  12. Surfacing Another Relationship • Using some circular objects, measure the circumference and diameter. • Record these measurements in the table

  13. What Relationship Do You See? π

  14. Making Connections • Let’s look at our progress. • First we explored area: • We found that…. A = ½C*r • Next we explored relationship between the diameter and circumference • We found that… C = π * diameter Typically we hear this stated as C = 2 π *r Why???

  15. Success Criteria • We will know we were successful when we can derive a connection between the area and the circumference of a circle. • We will know we were successful when we can articulate how the standards for math practice work together with the content standards.

  16. Seventh Grade Cluster Statement and Standard 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 the area of a circle.

  17. In what ways did the standards for math practice work together with the content standard?

  18. Walk Away Question • What are two important things that you have come to understand about the Common Core State Standards over the course of this year?

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