HSG-GMD.A.1

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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.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.

17 Lesson(s)

### Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites

Geometry »
Unit: Geometric Measurement and Dimension

Geometry »
Unit: Geometric Measurement and Dimension

Big Idea:

#### By critiquing others' written explanations of triangle and trapezoid area formulas, students will develop strategies for determining areas of other 2-D shapes.

Standards:

Favorites
(5)

Resources
(27)

Reflections
(2)

### 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
(3)

Resources
(28)

Reflections
(3)

### Volume of Cylinders, Cones, and Spheres

Geometry »
Unit: The Third Dimension

Geometry »
Unit: The Third Dimension

Big Idea:

#### Students will use manipulative, such as pennies and clay to investigate the volume of cylinders, cones and spheres.

Standards:

Favorites
(7)

Resources
(14)

### 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
(8)

Resources
(19)

Reflections
(1)

### Step Into the 3rd Dimension

Geometry »
Unit: 3-D Shapes and Volume

Geometry »
Unit: 3-D Shapes and Volume

Big Idea:

#### Students will watch a Simpson’s video to introduce the 3rd dimension and will derive formulas for volume of cylinder and cone.

Standards:

Favorites
(4)

Resources
(32)

Reflections
(4)

### Pyramids and Spheres Exploration

Geometry »
Unit: 3-D Shapes and Volume

Geometry »
Unit: 3-D Shapes and Volume

Big Idea:

#### Students will use play dough to discover the volume formulas for pyramids and spheres.

Standards:

Favorites
(9)

Resources
(36)

Reflections
(2)

### Choose Your Loot

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

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

Big Idea:

#### Students are introduced to Cavalieri’s Principle as they compare the volumes of two heaps of treasure—one layer at a time.

Standards:

Favorites
(1)

Resources
(18)

### Circles, Circumference and Area

Geometry »
Unit: The Third Dimension

Geometry »
Unit: The Third Dimension

Big Idea:

#### Students dissect a circle in order to find its circumference and area.

Standards:

Favorites
(2)

Resources
(14)

Big Idea:

#### This is a comprehensive assessment of all content learned to date.

Standards:

Favorites
(1)

Resources
(12)

Reflections
(1)

### The Pyramid Stack (Part 1)

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

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

Big Idea:

#### Students use interactive geometry software to investigate the properties of pyramids and learn how many pyramids it takes to make a prism.

Standards:

Resources
(22)

### The Pyramid Stack (Part 2)

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

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

Big Idea:

#### Students use both algebra and hands-on models to deepen their understanding of the volume of a pyramid.

Standards:

Resources
(22)

### Old and New Knowledge of Circles

12th Grade Math »
Unit: Trigonometry: Circles

12th Grade Math »
Unit: Trigonometry: Circles

Big Idea:

#### Students explore the idea that pi and the trig ratios are really just the same shoes on different feet.

Standards:

Resources
(13)

### Arguments for Volume Formulas for Pyramids and Cones

Geometry »
Unit: Measurement and Dimension

Geometry »
Unit: Measurement and Dimension

Big Idea:

#### Yogi's smarter than the average bear and a cone's like a cylinder with an average base. After this lesson, students will know what this all means.

Standards:

Resources
(20)

Reflections
(3)

### Constructing an Argument for the Circumference Formula

Geometry »
Unit: Measurement and Dimension

Geometry »
Unit: Measurement and Dimension

Big Idea:

#### Circular Argument? In this lesson, students use structural analysis, trigonometry, and limits to show that the circumference of a circle is twice the product of pi and the radius.

Standards:

Favorites
(1)

Resources
(14)

Reflections
(3)

### Argument for the Volume Formula of a Cylinder

Geometry »
Unit: Measurement and Dimension

Geometry »
Unit: Measurement and Dimension

Big Idea:

#### Why don't they just call them circular prisms? In this lesson, students use their knowledge of prisms to reason about the volume formula for cylinders.

Standards:

Resources
(22)

Reflections
(2)

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