Using Structure to Explore Circles
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Transcript of Using Structure to Explore Circles
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Kevin McLeodConnie Laughlin
Hank KepnerBeth 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.
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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.
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Success CriteriaWe 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.
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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.
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Our Previous Work with Area Formulas
Area of a Rectangle
Area of a Parallelogram
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Moving and Combining
Can the moving and combining principles be used to figure out the area of a circle?
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ExploreWe have a circle divided into for congruent pieces.
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Surfacing a RelationshipEach person folds a circle to make
eighthssixteenths
Cut each wedge (sector) apart.
eighths
sixteenths
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Putting Structure to Work
•What did you notice about the shape as you moved and combined the sectors from each circle?
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A = ½C*r
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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
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Surfacing Another RelationshipUsing some circular objects, measure the
circumference and diameter.Record these measurements in the table
Object Diameter Circumference
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What Relationship Do You See?Diameter Circumferen
ce
π
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Making ConnectionsLet’s look at our progress. First we explored area:
We found that…. A = ½C*r
Next we explored relationship between the diameter and circumferenceWe found that… C = π * diameter
Typically we hear this stated as C = 2 π *r Why???
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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.
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Seventh Grade Cluster Statement and StandardSolve 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.
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In what ways did the standards for math practice work together with the content standard?
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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?