Comparing Perimeter, Area, and Volume

Resource:

These three parts are intended to support students in making connections between 2 dimensional and 3 dimensional objects, especially how scaling changes these objects and how we can carefully partition objects in order to make relationships between two otherwise different geometric shapes.

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Type

Geometry: Extending to Three Dimensions

File

Google Doc

Tags

cavalieri's principle, perimeter, similarity, surface area, volume

Standards

Common Core: Major Standards ( G-MG.A.1, G-MG.A.3 ) Common Core: Additional Sta…

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Common Core: Major Standards:

G-MG.A.1

Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

G-MG.A.3

Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).^★

Common Core: Additional Standards:

G-GMD.A.1

Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

G-GMD.A.3

Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.^★

Teacher Feedback

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Geo U5
Extending to Three Dimensions