HSG-GMD.A.1

Scroll Up

- 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.

Scroll Down

## 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
(2)

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
(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)

### 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
(5)

Resources
(14)

### 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
(8)

Resources
(36)

Reflections
(2)

### 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)

### 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)

### 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)

### 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)

### 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)

Common Core Math

### 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

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