### Course 2 Unit 6 - Geometric Form and Its Function 1st Edition

Geometric Form and Its Function is the third major unit in the geometry and trigonometry strand of the Contemporary Mathematics in Context program. In the geometry and trigonometry strand, students have developed visualization skills and understanding of properties of two- and three-dimensional shapes including rigidity, symmetry, area, and volume. They also have used coordinate methods for representing and analyzing geometric shapes and relations among shapes and to describe geometric change involving isometric transformations and size transformations. (See the descriptions of Course 2 Units.)

#### Unit Overview

In this unit, students develop ability to model and analyze physical phenomena using triangles, quadrilaterals, and circles. These shapes are used to investigate trigonometric relations, angular velocity, and periodic change.

 Unit Objectives To investigate characteristics of quadrilaterals and the mechanical uses of quadrilateral linkages To investigate ways that triangles are used to maintain rigidity in structures with one side of variable length To explore properties and applications of the sine, cosine, and tangent ratios for right triangles To explore the characteristics of circles and relate circles to rotating objects, angular velocity, and the graphs of trigonometric functions

#### Sample Overview

This sample material consists of Investigations 2 and 3 from Lesson 2, "Triangles and Trigonometric Ratios." In Investigation 2, students explore conditions that guarantee two triangles are similar and special cases of similar right triangles. The trigonometric ratios sine, cosine, and tangent are introduced. In the third investigation, students use trigonometric ratios for indirect measurement in several different contexts.

#### 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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#### How the Geometry and Trigonometry Strand Continues

In Course 3, students develop the ability to reason formally in geometric settings. Deductive reasoning is used to prove theorems concerning parallel lines and transversals, angle sums of polygons, similar and congruent triangles and their application to special quadrilaterals, and necessary and sufficient conditions for parallelograms.

In Course 4, geometry and algebra become increasingly intertwined. Students develop understanding of two-dimensional vectors and their applications and the use of parametric equations in modeling linear, circular, and other nonlinear motion. In addition, students intending to pursue programs in the mathematical, physical, and biological sciences, or engineering extend their ability to visualize and represent three-dimensional surfaces using contours, cross sections, and reliefs to visualize and sketch surfaces and conic sections defined by algebraic equations.

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