As the World Terns: Reason Abstractly and Quantitatively

Making use of structure to make sense of mathematics

Kevin McLeod

Connie Laughlin

Hank Kepner

Beth Schefelker

Mary Mooney

Math Teacher Leader Meeting, April 5th and 7th

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

 Explore examples that look for andmake use of structure.

To understand CCSS Math Practice #7:Look for and Make Use of Structure

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA),is supported with funding by the National Science Foundation.

Structure

What does structure mean…

•of a building?

•of a classroom?

•in mathematics?

Launch

19 x 8

Find the product in two different way

Do not use the standard algorithm.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA),is supported with funding by the National Science Foundation.

What is Area?

Write your answer on an index card.

Discuss your table’s answers and come toconsensus.

Mathematical Practice Standard #7Look for and Make Use of Structure

Mathematically proficient students look closely to

discern a pattern or structure….students will see that

7 x8 equals the well remembered 7x5 + 7x3, in

preparation for learning about the distributive property.

But how does structure help us make connectionswithin and between math strands?

Success Criteria

We will know we were successful whenwe are able to use structure to explainand justify area formulas for selectedquadrilaterals.

Explore: Area formula forparallelograms

Follow the steps below to write a formula for the area of aparallelogram.

Step 1: Use two different width straight edges toconstruct a large parallelogram on large patty paper.

Step 2: Show how you can split the parallelogram andrearrange the pieces to form a rectangle.

Compare your results with your table partners. Come toconsensus as to a formula that could be used.

Explore: Area formula fortriangles

Follow the steps below to write a formula for the area of atriangle.

Step 1: Each person at the table should construct adifferent large triangle on patty paper.

Step 2: Place a 2nd patty paper over the first and copythe triangle. Form a parallelogram from the twotriangles.

Compare your results with your table partners. Come toconsensus as to a formula that could be used to findthe area of a triangle.

Explore: Area formula fortrapezoid

Step 1: Draw a large trapezoid on your patty paper.

Step 2: Place a second patty paper over the first and copythe trapezoid. Form a parallelogram from the twotrapezoids.

Compare your results with your table partners. Come toconsensus as to a formula that could be used.

Explore: Area formula fortrapezoid

Step 1: Draw a large trapezoid on your patty paper byfolding or drawing.

Step 2: Explore finding the area of a trapezoid usingtriangles.

Experiment to find as many different ways as you can toarrive at a formula for a trapezoid.

What have you found?

Turn and Talk at your table:

How does structure of the polygons help make sense ofthe area formulas?

Success Criteria

We will know we were successfulwhen we are able to use structureto explain and justify areaformulas for selectedquadrilaterals.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA),is supported with funding by the National Science Foundation.

Standard for Mathematical Practice

Walk Away Question

When you engage your teachers in the contentsessions, how are you (1) using the sessions to connectthe Mathematical Practices to classrooms? or (2) usingthe sessions to assist you in clarifying the LESA lessonstructure?