Geometric Reasoning for Elementary and Middle School Teachers
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.
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) Recommended
Navigating through Geometry in Grades 3-5
By Gavin, M. K., Belkin, L. P., Spinelli, A. M., and St. Marie, J. (NCTM) Recommended
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.
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.
Decomposition and Rearrangement
Classification and Definitions
Ratio and Proportional thinking for dilations
Recommended maximum class size for this course: 20
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.