Course 1 Unit 5 - Patterns in Space and Visualization
1st Edition

Patterns in Space and Visualization is the fifth unit in Course 1 of the Contemporary Mathematics in Context program. By the time students begin this unit, they will have developed the ability to make sense of real-world data through the use of graphical displays and summary statistics. They will be able to recognize important patterns of change between related variables and use linear equations to model real-world problems. Students will also have developed skills in algorithmic problem solving and learned how to model a variety of situations with vertex-edge graphs. (See the descriptions of Course 1 Units.)

Unit Overview

Patterns in Space and Visualization develops student visualization skills and an understanding of two- and three-dimensional shapes and their properties.

Unit Objectives
  • To use visualization to interpret and reason about situations in space
  • To classify, construct, and sketch models of space-shapes
  • To use plane- and space-shapes to model real-life situations
  • To find appropriate measures (perimeter, area, volume) of plane- and space-shapes
  • To classify polygons and analyze their properties
  • To identify and explain the different kinds of symmetry for plane- and space-shapes

Sample Overview

This sample material consists of the second investigation and homework (MORE) set from Lesson 2, which develops and reviews the concepts of measurement of two- and three-dimensional shapes. The sample investigation revisits the Pythagorean relationship by considering what the length of the diagonal of a television screen reveals about the shape of the screen. Perimeter, area, and volume concepts are revisited and extended in other investigations of this lesson.

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 2, students develop an understanding of coordinate methods for representing and analyzing relations among classes of geometric shapes and use coordinates to represent geometric transformations and to understand their effects and that of their compositions. Students also develop the ability to model and analyze physical phenomena with triangles, quadrilaterals, and circles and to use trigonometric relationships to solve problems.

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 application 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; and to visualize and sketch surfaces and conic sections defined by algebraic equations.

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