HSG-GMD.A.2

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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.

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## 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.

5 Lesson(s)

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

Geometry »
Unit: Geometric Measurement and Dimension

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.

Standards:

Favorites
(1)

Resources
(28)

Reflections
(3)

### Exploring Circumference, Area and Cavalieri's principle

Geometry »
Unit: 3-D Shapes and Volume

Geometry »
Unit: 3-D Shapes and Volume

Big Idea:

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

Standards:

Favorites
(6)

Resources
(19)

Reflections
(1)

### The Sphere and the Cylinder (Part 2)

Geometry »
Unit: Volume of Cones, Pyramids, and Spheres

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!

Standards:

Favorites
(3)

Resources
(29)

### Assessment for 3D Unit

Geometry »
Unit: 3-D Shapes and Volume

Geometry »
Unit: 3-D Shapes and Volume

Big Idea:

#### Students will create a video demonstrating how to derive volume formulas.

Standards:

Favorites
(1)

Resources
(12)

### Volume "Quest"

Geometry »
Unit: Geometric Measurement and Dimension

Geometry »
Unit: Geometric Measurement and Dimension

Big Idea:

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

Standards:

Resources
(3)

Common Core Math

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### Seventh Grade

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### Ninth and Tenth Grade

### Kindergarten

### First grade

### Second grade

### Third Grade

### Fourth grade

### Fifth grade

### Middle School

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

HS Number & Quantity

HS Algebra

HS Functions

HS Geometry

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

Eighth Grade

Ninth and Tenth Grade

Kindergarten

First grade

Second grade

Third Grade

Fourth grade

Fifth grade

Middle School