It is not as simple as scaling. MIT researchers explain that a micro engine cannot just be a proportional scaling of a working larger engine. The Math at the Core: Ratios resource compares the proportions involved with the surface area and volume when a figure is scaled.

Concepts

proportions, area, surface area, volume, cubes, generating electricity, electricity, heat, real-world applications, scale

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Additional Tags

math

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Instructional Ideas

• Research how an engine generates electricity
• Create a composite three-dimensional figure and have the class determine the surface area and volume of a scaled version of the figure

Classroom Considerations

• Individuals should understand the calculation of surface area and volume of a cube

Pros

• Provides teaching tips
• Includes a diagram to illustrate the comparison of the scale of surface area and the scale of volume

Cons

• None

Common Core

6.RP.A.3.a 6.RP.A.3.b 6.RP.A.3.c 6.RP.A.3.d 7.RP.A.2.a 7.RP.A.2.c 7.RP.A.3 7.G.A.1 7.G.A.2 7.G.A.3 7.G.B.4 7.G.B.5 7.G.B.6