National Council of Teachers of MathematicsAnnual Meeting Philadelphia, PA

Thursday, April 26, 2012Connie Laughlin, UW-Milwaukee, Milwaukee WIBeth Schefelker, Milwaukee Public Schools, WI

Learning Intention

We are learning to

Explore examples that look for and make use of structure.

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

Structure

What does structure mean…• of a building?• of a classroom?• in mathematics?

What is Area?

Write your answer on an index card.

Discuss your table’s answers and come to consensus.

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

Mathematically proficient students look closely todiscern a pattern or structure….students will see

that 7 x8 equals the well remembered 7x5 + 7x3, inpreparation for learning about the distributive

property.

But how does structure help us make connections within and between math strands?

Mathematical Practice Recognize the significance in concepts and

models and use the patterns or structure for solving related problems.

Look for Tool – Howard County Public Schools Office of Secondary Mathematics, May 2011.

Look for and make use of structureStudent Behaviors Teacher ActionsAppreciate and look for

connections in mathRecognize the parts of a

wholeReflect on processes

used and the application of those process as they apply to new but similar situations

Provide multiple examples from which students can draw patterns or rules.

Model of “think aloud” in solving problems

Facilitate discovery activities

Encourage student discourse and provide multiple viewpoints.

Model how problems could be broken down.

Success CriteriaWe will know we were successful when we are able to use structure to explain and justify area formulas for selected quadrilaterals.

Explore: Area formula for parallelogramsFollow the steps below to write a formula for the

area of a parallelogram.Step 1: Use two different width straight edges to

construct a large parallelogram on large patty paper.

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

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

Explore: Area formula for trianglesFollow the steps below to write a formula for the

area of a triangle.Step 1: Each person at the table should

construct a different large triangle on patty paper.

Step 2: Place a 2nd patty paper over the first and copy the triangle. Form a parallelogram from the two triangles.

Compare your results with your table partners. Come to consensus as to a formula that could be used to find the area of a triangle.

Explore: Area formula for trapezoidStep 1: Draw a large trapezoid on your patty

paper.

Step 2: Place a second patty paper over the first and copy the trapezoid. Form a parallelogram from the two trapezoids.

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

Explore: Area formula for trapezoidStep 1: Draw a large trapezoid on your patty

paper by folding or drawing.

Step 2: Explore finding the area of a trapezoid using triangles.

Experiment to find as many different ways as you can to arrive 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 of the area formulas?

Success CriteriaWe will know we were successful when we are able to use structure to explain and justify area formulas for selected quadrilaterals.

Standard for Mathematical Practice

Thank You!The powerpoint can be downloaded from the

Milwaukee Mathematics Partnership website www.mmp.uwm.edu

Beth Schefelker Math Teaching Specialist, MPS schefeba@milwaukee.k12.wi.us

Connie Laughlin, Mathematics Consultant, UW-Milwaukeeconnielaughlinm@gmail.com