Area and Measurement

Area and Measurement

Math Alliance

November 2, 2010

Chris Guthrie

Melissa Hedges

Kevin McLeod

Beth Schefelker

Judy Winn

Session Goals

• Review the meaning of area

• Understand the moving and combining principles for finding areas

• Understand how area formulas arise from composing and decomposing figures

What is area?

Write your answer on an index card.

Discuss your table’s answers and come to consensus.

What does the student work tell you about their understanding about area?

3rd Grade Measurement CABS

Janelle and her family want to go canoeing. They are looking for a 25-acre lake. Estimate the number of acre units needed to cover the lake.

= 1 acre

My estimate: ______

Is this lake big enough for Janelle and her family to go canoeing on? Why or why not?

Student Area Task

Name: ______Date: ______

School: ______Grade:______

Part I.

When a teacher asks you to find the area of a shape, what are they asking you to find?

What is area?

Part II.

Draw a shape. Show and explain how you would find its area.

Part III.

What is the area of this shape?

1 square unit

How do you know?

Area of a Triangle

What is the area of this triangle?

Answer this question in at least 2 different ways.

Dot Paper

The Moving and Combining Principles for Area

When a shape is moved without stretching it in any way (a rigid motion), its area does not change.

When a shape is composed of (a finite number of) non-overlapping shapes, the area of the composed shape is the sum of the areas of the individual shapes.

Determine the area of shape h

Determine the area of shape i

Determine the area of shape j

Determine the area of shape k

Determine the area of shape l

Area of a Triangle

Use your area techniques to find a formula for the area of a triangle.

Area of a Parallelogram

Use your area techniques to find a formula for the area of a parallelogram.

Area of a Trapezoid

Use your area techniques to find a formula for the area of a trapezoid.

Big Ideas for Measuring Area

·  Area is defined by covering.

·  (The Moving Principle) The area of a shape does not depend on its position or orientation.

·  (The Combining Principle) Area is additive.

·  Students can derive and make sense of area formulas by using the moving and combining principles

Prepared for the Milwaukee Mathematics Partnership (MMP). This material is based upon
work supported by the National Science Foundation under Grant No. 0314898.