Common Core Geometry. Chapter 12. Surface Area and Volume

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So, this is the year when you have to switch over to the new Common Core Standards for high school geometry, but you don't quite know what that means. Or perhaps you know the new standards but haven't had time to re-align your course. I have your answer. I've created a set of PowerPoints and Word worksheets, aligned to the Common Core, that will take you from the first day of the course to the last.

This is Chapter 12 of my Common Core-aligned course in geometry. The topic is surface area and volume. Below is a description of the chapter's seven sections.

12.1 Solids. The core concepts - solid, prism, face, edge, vertex, etc. - are defined and illustrated. The worksheet is an exploration of the Platonic solids. Students are led through the proof that the number of Platonic solids can be at most five.

12.2 Surface Area of Prisms and Pyramids. The formulae are obvious (find the surface area of each face and then add), and thus the emphasis is on application.

12.3 Surface Area of Cylinders and Cones. The cylinder and cone surface area formulae are derived (the second in two ways) and then applied.

12.4 Volumes of Prisms and Cylinders. Volume is defined as the number of unit cubes necessary to fill a solid without gap or overlap. The volume formulae of prisms and cylinders are then derived and applied.

12.5 Volumes of Pyramids and Cones. Students are shown how to decompose a prism into three pyramids of equal volume. The key here is Cavalieri's Principle. The pyramid and cone volume formulae then quickly follow.

12.6 Archimedes and the Volume of a Sphere. Archimedes's ingenious derivation of the sphere volume formula is given. Applications follows.

12.7 Surface Area of Sphere. The surface area formula for a sphere is derived by use of the sphere and pyramid volume formula. Applications follow.


For each section, there is both a PowerPoint and a Word worksheet. The worksheets give ample practice in the day's topic.

The worksheets are appropriate for both Honors and non-Honors classes. Questions marked H are intended for Honors only. The chapter includes a Challenge problem set. It is intended for Honors students. Worksheets include answers to selected questions.

A description of the course can be found among my downloads. The title is "Course Contents with Commentary".
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3 Weeks

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Common Core Geometry. Chapter 12. Surface Area and Volume
Common Core Geometry. Chapter 12. Surface Area and Volume
Common Core Geometry. Chapter 12. Surface Area and Volume