Last updated: 7/14/2016

## Mat230 Geometry CCLS - Module 3 - Extending to Three Dimensions (10 days - 2 weeks)

Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
 (1) G-GMD.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.
 (2) 7.G.3 Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. (2) 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Lessons 1-13

11-3 Area of Circles and Sectors

12-4 Volume of Prisms and Cylinders

12-5 Give an informal argument for the formulas for circumference, area of circle, volume of cylinder, pyramid, cone.

12-6 Surface Areas and Volumes of Spheres

Tangent to a circle, Inscribed Polygon, Cavalieri's Principle, Sphere, Solid Sphere (Ball), Disc, Lateral Edges and Faces of Prisms, General Cylinder, Right Rectangular Prism, Cone, Regular Pyramid

[1a,1b,1c]

 (1) G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
 (1) 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Lessons 5-13

1-7 Volume of Cylinder, Pyramid, Cones, Spheres

12-4 Use volume for cylinders, pyramids, cones, spheres to solve problems.

12-5 Give an informal argument for the formulas for circumference, area of circle, volume of cylinder, pyramid, cone.

General Cylinder, Right Rectangular Prism, Cone, Rectangular Pyramid, Sphere, Solid Sphere (Ball)

[2a,2b,2c,2d]

 (1) G-GMD.4 Identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
 (2) 7.G.3 Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. (2) 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. (1) 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Lessons 5-13

9-3 Rotations

12-1 Representations of three-dimensional figures

Cavilieri's Principle

[3a,3b,3c,3d,3e,3f,3g,4a,4b,4c,4d]