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
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
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.

 
Favorites (2)
 
Resources (27)
 
Reflections (2)
trapezoid area image resized
   

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

Geometry » Unit: Geometric Measurement and Dimension
Geometry » Unit: Geometric Measurement and Dimension
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
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.

 
Favorites (1)
 
Resources (28)
 
Reflections (3)
candy bar lesson image
   

Exploring Circumference, Area and Cavalieri's principle

Geometry » Unit: 3-D Shapes and Volume
Geometry » Unit: 3-D Shapes and Volume
Stephanie Conklin
Saratoga Springs, NY
Environment: Suburban
 
Big Idea:

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

 
Favorites (6)
 
Resources (19)
 
Reflections (1)
image for circumference area of circles and cavalieri s principle
   

Volume of Cylinders, Cones, and Spheres

Geometry » Unit: The Third Dimension
Geometry » Unit: The Third Dimension
Marisa Laks
New York, NY
Environment: Urban
 
Big Idea:

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

 
Favorites (4)
 
Resources (14)
volume of cylinders cones and spheres image
   

Pyramids and Spheres Exploration

Geometry » Unit: 3-D Shapes and Volume
Geometry » Unit: 3-D Shapes and Volume
Stephanie Conklin
Saratoga Springs, NY
Environment: Suburban
 
Big Idea:

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

 
Favorites (8)
 
Resources (36)
 
Reflections (2)
playdough image for pyramids and spheres exploration
   

Step Into the 3rd Dimension

Geometry » Unit: 3-D Shapes and Volume
Geometry » Unit: 3-D Shapes and Volume
Stephanie Conklin
Saratoga Springs, NY
Environment: Suburban
 
Big Idea:

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

 
Favorites (4)
 
Resources (32)
 
Reflections (4)
walking image step into the third dimension image
   

Choose Your Loot

Geometry » Unit: Volume of Cones, Pyramids, and Spheres
Geometry » Unit: Volume of Cones, Pyramids, and Spheres
Tom Chandler
Ault, CO
Environment: Rural
 
Big Idea:

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

 
Favorites (1)
 
Resources (18)
treasureroomb
   

Circles, Circumference and Area

Geometry » Unit: The Third Dimension
Geometry » Unit: The Third Dimension
Marisa Laks
New York, NY
Environment: Urban
 
Big Idea:

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

 
Favorites (2)
 
Resources (14)
area and circumference image resized
   

End of Year Assessment

Geometry » Unit: Final Assessment
Geometry » Unit: Final Assessment
Marisa Laks
New York, NY
Environment: Urban
   

The Pyramid Stack (Part 1)

Geometry » Unit: Volume of Cones, Pyramids, and Spheres
Geometry » Unit: Volume of Cones, Pyramids, and Spheres
Tom Chandler
Ault, CO
Environment: Rural
 
Big Idea:

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

 
Resources (22)
thepyramidstack image
   

The Pyramid Stack (Part 2)

Geometry » Unit: Volume of Cones, Pyramids, and Spheres
Geometry » Unit: Volume of Cones, Pyramids, and Spheres
Tom Chandler
Ault, CO
Environment: Rural
 
Big Idea:

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

 
Resources (22)
thepyramidstack2 image
   

Old and New Knowledge of Circles

12th Grade Math » Unit: Trigonometry: Circles
12th Grade Math » Unit: Trigonometry: Circles
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

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

 
Resources (13)
definingpi
   

Constructing an Argument for the Circumference Formula

Geometry » Unit: Measurement and Dimension
Geometry » Unit: Measurement and Dimension
Anthony Carruthers
Pasadena, CA
Environment: Suburban
 
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.

 
Favorites (1)
 
Resources (14)
 
Reflections (3)
circumference formula
   

Arguments for Volume Formulas for Pyramids and Cones

Geometry » Unit: Measurement and Dimension
Geometry » Unit: Measurement and Dimension
Anthony Carruthers
Pasadena, CA
Environment: Suburban
 
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.

 
Resources (20)
 
Reflections (3)
great pyramid
   

Argument for the Volume Formula of a Cylinder

Geometry » Unit: Measurement and Dimension
Geometry » Unit: Measurement and Dimension
Anthony Carruthers
Pasadena, CA
Environment: Suburban
 
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)
prisms to cylinder
Common Core Math
 
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