Course 4 Unit 2 - Modeling Motion
1st Edition

In the previous units of the Contemporary Mathematics in Context program, students have developed the ability to model and solve problems involving data, change, shape, and chance. In Modeling Motion, concepts and methods of geometry, trigonometry, and algebra are combined to develop powerful tools for representing and analyzing the motion of objects. (See the descriptions of Course 4 Units.)

Unit Overview

This unit introduces two-dimensional vectors and parametric representations of linear and nonlinear motion.

Unit Objectives
  • To describe and use the concept of vector in mathematical, scientific, and everyday situations
  • To represent vectors geometrically and to operate on geometric vectors
  • To describe, represent, and use vector components both synthetically and analytically
  • To use vector concepts to represent linear, projectile, circular, and elliptical motions in a plane with parametric equations
  • To analyze physical motions using parametric models

Sample Overview

The sample material is the fourth investigation of Lesson 2, "Simulating Linear and Nonlinear Motion." In this investigation, students model circular and elliptical motion parametrically. Students draw on their understanding of transformations of function graphs to modify graphs of parametric equations to fit problem situations.

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 4, Unit 7, Functions and Symbolic Reasoning, students intending to pursue college majors in the mathematical, physical, and biological sciences, or engineering develop proficiency in reasoning with and manipulating symbolic representations of exponential, logarithmic, and trigonometric functions. They use trigonometric functions, identities, and polar coordinates to develop an understanding of the geometry of complex numbers. In Unit 8, Space Geometry, students extend their 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.

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