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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 165
Course Title: Geometric Reasoning for Elementary and Middle School Teachers
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

This course introduces some basic concepts of geometric and measurement that underlie these concepts in elementary and middle grades, with a focus on collaborative learning and technology. Prerequisites: MATH 102 and MATH 150 (or higher).

Prerequisite(s) / Corequisite(s):

MATH 102 and MATH 150 (or higher).

Course Rotation for Day Program:

Offered even Fall.

Text(s): Most current editions of the following:

A TI-84 calculator is required for this course.

Geogebra, a freeware program, is required.

Developing Essential Understanding of Geometry: Grades 6-8
By Sinclair, N., Pimm, D., and Skelin, M. (NCTM)
Navigating through Geometry in Grades 3-5
By Gavin, M. K., Belkin, L. P., Spinelli, A. M., and St. Marie, J. (NCTM)
Course Objectives
  • To learn about the axiomatic nature of geometry.
  • To read, write, and critique basic geometric proofs.
  • To explore concepts of Euclidean geometry.
  • To use technology as an integral part of the process of  formulation, solution and communication of geometric ideas.
Measurable Learning
  • Solve mathematical problems using geometric thinking.
  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
  • Apply transformations and use symmetry to analyze mathematical situations.
  • Use visualization, spatial reasoning, and geometric modeling to solve problems.
  • Recognize  two- and three-dimensional  geometric shapes and describe their characteristics.
  • Know  simple geometrical concepts and facts and their applications: point, line, plane, parallel, perpendicular, sum of the angles of a triangle is 180 degrees, the Pythagorean theorem.
  • Perform elementary geometric constructions with ruler and compass, and with dynamic geometry software (Geogebra).
  • Compute  perimeters, areas, and volumes of elementary geometric objects: rectangle, circle, triangle, cone, pyramid, cylinder, sphere.
  • Demonstrate understanding of the concept of measurement units in both the standard and metric systems, be able to convert measurements within systems (e.g. yards to inches) and from one system to another (e.g. miles to kilometers).
  • Measure lengths, angles, area (including  surface area), and volumes in standard and metric units.
  • Understand congruence and similarity and apply them to solve problems.
  • Apply transformations to geometric figures and determine if such transformations are isometries.
Topical Outline:
  • Shapes
  • Location
  • Transformations
  • Spatial Visualization
  • Decomposition and Rearrangement
  • Imagery
  • Geometric Tools
  • Classification and Definitions
  • Ratio and Proportional thinking for dilations
  • Trigonometry
  • Tesselations

Recommended maximum class size for this course: 20

Library Resources:

Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

Prepared by: Ann Schlemper Date: May 22, 2014
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

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