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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.

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

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.

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.

Volume of Cylinders, Cones, and Spheres

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.

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.

Step Into the 3rd Dimension

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.

Pyramids and Spheres Exploration

Geometry

» Unit:

3-D Shapes and Volume

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

Choose Your Loot

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.

Circles, Circumference and Area

Geometry

» Unit:

The Third Dimension

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

End of Year Assessment

Geometry

» Unit:

Final Assessment

Big Idea:This is a comprehensive assessment of all content learned to date.

The Pyramid Stack (Part 1)

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.

The Pyramid Stack (Part 2)

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.

Old and New Knowledge of 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.

Arguments for Volume Formulas for Pyramids and Cones

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.

Constructing an Argument for the Circumference Formula

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.

Argument for the Volume Formula of a Cylinder

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.

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.