using structure to explore circles

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.

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.

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.

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.

Our Previous Work with Area Formulas

Area of a Rectangle

Area of a Parallelogram

Moving and Combining

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

ExploreWe have a circle divided into for congruent pieces.

Surfacing a RelationshipEach person folds a circle to make

eighthssixteenths

Cut each wedge (sector) apart.

eighths

sixteenths

Putting Structure to Work

•What did you notice about the shape as you moved and combined the sectors from each circle?

A = ½C*r

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

Surfacing Another RelationshipUsing some circular objects, measure the

circumference and diameter.Record these measurements in the table

Object Diameter Circumference

What Relationship Do You See?Diameter Circumferen

ce

π

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???

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.

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.

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

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?