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Comparing Perimeter, Area, and Volume
Resource:
Comparing Perimeter, Area, and Volume

Geometry & Algebra II Archive

Geo U5: Extending to Three Dimensions

Big Idea: Big Idea 1

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.★

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MARS FAL: Evaluating Statements about Length and Area
Resource:
MARS FAL: Evaluating Statements about Length and Area

Geometry & Algebra II Archive

Geo U2: Proofs about Congruence

Big Idea: Big Idea 4

This lesson unit is intended to help you assess how well students can:
Understand the concepts of length and area.
Use the concept of area in proving why two areas are or are not equal.
Construct their own examples and counterexamples to help justify or refute conjectures.

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Type
Geometry: Proofs About Congruence
File
External Link
Tags
area, perimeter, quadrilateral, formative assessment
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