In this lesson, students will explore the area of irregular shapes to find multiple different
methods for calculating area.

Objectives

Upon completion of this lesson, students will:

have practiced finding area of irregular shapes with right angles.

understand that area can be found in multiple ways.

Standards Addressed:

Grade 10

Geometry

The student solves problems (including real-world situations).

Grade 3

Geometry

The student demonstrates an understanding of geometric relationships.

The student solves problems using perimeter or area.

Grade 4

Geometry

The student demonstrates an understanding of geometric relationships.

The student solves problems using perimeter or area.

Grade 5

Geometry

The student demonstrates an understanding of geometric relationships.

The student solves problems (including real-world situations) using perimeter or area.

Grade 6

Geometry

The student solves problems (including real-world situations) using perimeter, area, or volume.

Grade 7

Geometry

The student solves problems (including real-world situations).

Grade 8

Geometry

The student solves problems (including real-world situations).

Grade 9

Geometry

The student solves problems (including real-world situations).

Seventh Grade

Geometry

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Sixth Grade

Geometry

Solve real-world and mathematical problems involving area, surface area, and volume.

Third Grade

Geometry

Reason with shapes and their attributes.

Measurement and Data

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Student Prerequisites

Technological: Students must be able to:

perform basic mouse manipulations such as point, click and drag

use a browser for experimenting with the activities

Teacher Preparation

access to a browser

computer connected to projector

dry erase markers

markers or crayons (three different colors for each group)

record sheets and pencils

Key Terms

area

The number of square units needed to cover a surface

Lesson Outline

Focus and Review

Using the
Shape Explorer applet, draw a rectangular shape for the students to see. Activate prior knowledge using these
guiding questions:

How would you find the area of this shape?

Are there other ways to find the area?

How do you know that these methods work?

Objectives

Let the students know what they will be doing and learning today. Say something like this:

Today, we will be learning about finding the area of irregular shapes.

We will be looking for several methods to solve each problem.

Teacher Input

Project an irregular shape on the board.

Discuss with students different ways to find the area of the shape.

Include counting the squares individually as well as breaking the shape into smaller
rectangular shapes as methods for finding the area.

Guided Practice

Project an irregular shape on the board using the Shape Explorer applet.

Have students volunteer to draw outlines of the smaller shapes that compose the bigger shape.

Look for at least 3 methods for finding the area for each shape.

For each method, compose a number sentence.

Use the following chart as a guideline:

Picture

Number sentence

Area

(1x4)+(2x7)+(1x3)

21 square units

(3x4)+(2x3)+(1x3)

21 square units

(3x1)+(4x3)+(2x3)

21 square units

Independent Practice

Break the students into groups of three and give them the following instructions:

For each shape that is projected on the board, your group is to come up with three different
ways of finding its area.

Using the
record sheet, write down number sentences for those three methods.

For each shape, give the students a set amount of time to develop methods. Then have the each
group share their methods to see how many methods the whole class used.

Closure

Lead the class in a discussion about how they found the area for a given shape. Ask the students
how the developed new methods of finding the area each time.

Suggested Follow-Up

Students who have mastered the skills necessary to find the area of irregular shapes may be ready
to learn about finding
triangle area or
surface area and volume.