### Course 4 Unit 8 - Space Geometry 1st Edition

In previous courses of the Contemporary Mathematics in Context program, students have developed the ability to model and solve problems involving data, change, shape, and chance. They have also developed important mathematical habits of mind such as visual thinking. Students intending to pursue college majors in the mathematical, physical, and biological sciences, or engineering should study this unit. (See the descriptions of Course 4 Units.)

#### Unit Overview

Unit 8, Space Geometry, extends studeet ability to visualize and represent three-dimensional surfaces using contours, cross sections, and reliefs and to visualize and sketch surfaces and conic sections defined by algebraic equations.

 Unit Objectives To represent shapes in space with contour lines or horizontal and vertical cross sections To interpret and describe shapes or surfaces in space represented with contour lines To use a three-dimensional coordinate system to locate points and represent shapes and surfaces in space To identify and sketch graphs of conic sections represented algebraically and write equations matching graphs of conics To use information inherent in an equation of a shape or surface to visualize, characterize, and sketch the shape or surface To identify and sketch surfaces of revolution and cylindrical surfaces

#### Sample Overview

The sample material from Unit 8 is the final lesson of the unit, called the "Looking Back" lesson. Each unit in the Contemporary Mathematics in Context program ends with a "Looking Back" lesson. This lesson is intended to provide students with tasks that encourage them to look back at the unit as a whole. Students have the opportunity to pull together, apply, and communicate the mathematical concepts and methods they have developed while studying the particular unit. Reading the final unit Checkpoint of Space Geometry (on page 576) gives one a synopsis of the mathematical ideas covered in this unit.

#### Instructional Design

Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.

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