Area Explorations

Abstract

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 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).

Grade 10

  • Geometry

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

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.

Sixth Grade

  • Geometry

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

Seventh Grade

  • Geometry

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

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

  1. 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?

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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.