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

Surface Area and Volume of Similar Solids

Objective

The student will be able to determine and apply the relationship between surface area and/or volume 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 corresponding dimensions using surface area ratios of similar figures.
    Worksheet: Surface Area of Similar Solids

    Development of Ideas

    Activity:
     
    Investigate the relationship between scale factor and corresponding dimensions using volume ratios of similar figures.
    Worksheet: Volume of Similar Solids
     
    Activity:
     
    Apply surface area and volume ratios of similar figures.
    Worksheet: Using Similar Solids

    Closure

    Summary questions
     
    Draw two spheres such that the ratio of their volumes is 1:64.
     
    Answer: The radii of the spheres should have a ratio of 1:4
     
    Justify why all cubes are similar to each other.
     
    Answer: The dimensions of a cube are all equal. The ratio of any corresponding dimensions of any 2 cubes will be the same ratio of the other corresponding dimensions.

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