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- HSG-GMD.A.1Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
- HSG-GMD.A.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
- HSG-GMD.A.2(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Volume Formulas, Cavalieri's Principle, and 2-D Cross-Sections

Geometry

» Unit:

Geometric Measurement and Dimension

Big Idea:In a differentiated lesson based on student choice, students will be able to practice finding the volume of prisms or apply Cavalieri's Principle to determine the volume formula for a sphere.

Exploring Circumference, Area and Cavalieri's principle

Geometry

» Unit:

3-D Shapes and Volume

Big Idea:Students will discover properties of circumference, area and Cavalieri's principle in stations.

The Sphere and the Cylinder (Part 2)

Geometry

» Unit:

Volume of Cones, Pyramids, and Spheres

Big Idea:Using Cavalieri’s Principle to relate the volumes of cylinders, hemispheres, and cones--Hemisphere plus cone equals cylinder!

Assessment for 3D Unit

Geometry

» Unit:

3-D Shapes and Volume

Big Idea:Students will create a video demonstrating how to derive volume formulas.

Volume "Quest"

Geometry

» Unit:

Geometric Measurement and Dimension

Big Idea:On this unit assessment, students will demonstrate their understanding of volume on problems of varying difficulty.

HSG-GMD.A.1

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

HSG-GMD.A.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

HSG-GMD.A.2

(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.