School Improvement in Maryland

Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.3 The student will apply concepts of measurement using tools and technology when appropriate.

Indicator 2.3.2 The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two-and three-dimensional figures and their parts.

Lesson Content

Perimeter and Area of Similar Figures

Objective

The student will be able to determine and apply the relationship between perimeter, circumference, and/or area of similar figures and their parts.

Approximate Time

One 45 minute lesson.

Prerequisite Concepts Needed

Students will need experience with calculating perimeter, circumference, area and volume, the Pythagorean Theorem, and identifying solid figures.

Materials Needed

Lesson Structure

    Essential Questions

    What is the relationship between perimeter, circumference, area, surface area, and/or volume of similar figures and their parts?

    Warm-Up/Opening Activity

    Recall the relationship between scale factor and perimeter ratios of similar figures.
    Student Guide: Perimeter and Area of Similar Figures (#1-4)

    Development of Ideas

    Activity One
     
    Investigate the relationship between scale factor and area ratios of similar figures.
    Worksheet: Perimeter and Area of Similar Figures (#5-9)
     
    Activity Two
     
    Apply area ratios of similar figures.
    Worksheet: Area Ratios of Similar Figures

    Closure

    Summary question
     
    When a salesperson showed Sam a picture, Sam said, "I need one that is the same shape but twice as big." The salesperson returned with two pictures and said," I wasn't sure what you meant." How do you think the two pictures compared to the original? Discuss why you need to be specific when you say one thing is "twice as big" as another.
     
    Answer: One picture could have the dimensions of the original picture doubled which would mean the area of the larger picture is four times the original picture. The second picture could have twice the area of the original picture.

Additional Resources

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