Students will extend their understanding of volume when working with prisms and pyramids, obtained in 7th grade, to develop and utilize the formulas for finding the volumes of cones, spheres, and cylinders.
Key Concepts:
Prior Knowledge Needed:
 Calculate the area of a circle. (Grade 7, Unit 11; 7.G.B.4)
 Understand that volumes are additive. (Grade 5, Unit 9; 5.MD.C.5.C)
 Understand that the volume of a prism is the product of its height and the area of one of its bases. (Grade 5, Unit 9; 5.MD.C.5.A)
Units on the Horizon:
 Explaining and using volume formulas for cones, cylinders. and spheres in high school geometry.
 Modeling realworld threedimensional figures with cones, cylinders, spheres and the composition of two or more of these shapes in high school geometry.
 Oblique prisms use the same formulas as right prisms and will be studied in high school geometry.
 Rotations of twodimensional figures about an axis also creates threedimensional solids that will be studied in Calculus.
Lessons

Lesson objective: Extend understanding that finding the volume of cylinders, by multiplying the area of their base by their height, is similar to finding the volume of prisms. Students bring prior knowledge of finding the volume of prisms from 5.MD.C.5....

Lesson objective: Fluently find the approximate and exact volumes of cylinders and their component parts. This lesson helps to build procedural skill with finding the volume of cylinders. Threedimensional modeling is used here because it supports the a...

Lesson objective: Apply knowledge of how to use the volume of a cylinder formula to a realworld context. This lesson provides an opportunity for students to apply their knowledge and understanding of finding the volumes of cylinders to a reallife situ...

Lesson objective: Extend understanding that finding the volume of cones is similar to finding the volume of cylinders. Students bring prior knowledge of finding the volume of cylinders from 8.G.9 earlier in this unit. This prior knowledge is extended to...

Lesson objective: Fluently find the exact and approximate volumes of cones. This lesson helps to build fluency with using the formula for finding the volume of cones. Threedimensional modeling is used here because it supports the abstract nature of usi...

Lesson objective: Apply knowledge of how to use the volume of a cone formula to a realworld context. This lesson provides an opportunity for students to apply their knowledge and understanding of finding the volume of cones to a reallife situation. St...

Lesson objective: Extend understanding that finding the volume of spheres is similar to finding the volume of cylinders. Students bring prior knowledge of finding the volume of cylinders from 8.G.9 earlier in this unit. This prior knowledge is extended ...

Lesson objective: Fluently calculate both the exact and approximate volumes of spheres. This lesson helps to build fluency with calculating the volume of a sphere by illustrating its relationship to the volume of a cylinder. A sphere inscribed within a ...

Lesson objective: Apply knowledge of how to use the volume of a sphere formula to a realworld context. This lesson provides an opportunity for students to apply their knowledge and understanding of finding the volume of spheres to a reallife situation...

Lesson objective: Solve problems that involve complex shapes composed of cylinders, cones or spheres. This lesson provides an opportunity for students to apply their knowledge and understanding of finding volumes of cylinders, cones, or spheres to a rea...