Course Description
A deep examination of mathematical topics designed for future elementary school teachers. Visualization. Properties of angles, circles, spheres, triangles, and quadrilaterals. Measurement, length, area, and volume. Transformations, congruence, and similarity.
Athena Title
Geometry Elem School Teachers
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Course Objectives
To strengthen and deepen knowledge and understanding of measurement and basic geometry and how they are used to solve a wide variety of problems. In particular, to strengthen the understanding of and the ability to explain why various procedures and formulas in mathematics work. To strengthen the ability to communicate clearly about mathematics, both orally and in writing. To promote the exploration and explanation of mathematical phenomena. To show that many problems can be solved in a variety of ways.
Topical Outline
CHAPTER REFERENCES ARE TO Mathematics for Elementary Teachers, 3rd edition, by Sybilla Beckmann, Pearson. 1. Visualization of the earth, moon and sun in space: Explaining why there are time zones. Explaining the phases of the moon. (Section 10.1) 2. Basic geometric concepts and objects in 2 dimensions: angles, the sum of the angles in any triangle is 180 degrees (Sections 10.2, 10.3), circles (and spheres) (Section 10.4), triangles, quadrilaterals, and other polygons (Section 10.5), constructions with straightedge and compass (Section 10.6). 3. Basic concepts of measurement: measurable attributes of objects, units and the meaning of measurements, the distinction among length, area, and volume. (Sections 11.1, 11.2) 4. Area of 2-dimensional shapes: area of rectangles (whole number side lengths only), the moving and additivity principles for areas (Sections 12.1, 12.2), areas of triangles (Section 12.3), areas of parallelograms, other polygons, and circles (Sections 12.4, 12.6), approximating areas and Cavalieri's principle (Sections 12.7, 12.5), area versus perimeter (Section 12.8), the Pythagorean theorem and applications (Section 12.9). 5. Solid shapes and their volume and surface area: polyhedra, prisms, cylinders, pyramids, and cones, the 5 Platonic solids (Sections 13.1, 13.2), volume and the moving and additivity principles, understanding volume formulas for prisms, cylinders, pyramids, and cones( Sections 13.3, 13.4). 6. Geometry of motion and change: reflections, translations, rotations, and different kinds of symmetry (Sections 14.1, 14.2); congruence of triangles (Section 14.3), similarity, the behavior of area and volume under scaling (Sections 14.4, 14.5).
Syllabus