MATH 240 Geometry for Elementary/Middle School Teachers Course objectives: 1. Use inductive reasoning and conjecturing to explore topics including properties of polygons and polyhedrons, symmetry, transformations, geometric constructions, and measurement. 2. Use a dynamic geometric computer environment to explore geometric topics appropriate for students in the middle grades. 3. Model strategies for teaching geometry to students in grades K-8. Usual course content: Unit One: Polygons. Key concepts in this unit include properties and characteristics of polygons, Pythagorean theorem, Pythagorean triples, angle measure, geometric constructions, Euler line, nine-point circle, Gauss' theorem about the construction of regular polygons with straight edge and compass, star polygons, pierced polygons, and symmetry. Unit Two: Polyhedrons. Key concepts in this unit include characteristics and properties of polyhedrons, Platonic and Archimedean solids, kaleidocycles, Euler's formula, planes of symmetry, cross sections, and three-dimensional tessellations. Unit Three: Transformations. Key concepts include constructing and describing translations, rotations, reflections, glide reflections, and magnifications, combinations of transformations, algebraic representations of transformations, transformations as groups, similar and congruent figures, and indirect measure. Unit Four: Measurement. Key concepts include deriving formulas for surface area and volume of a sphere, solving non-routine problems related to area and volume, and investigating alternative formulas for area using the computer. Unit Five: History of Geometry. This unit takes a historical look at the geometric concepts investigated during the semester. As a class, students will construct a timeline depicting key events and people in the history of geometry from an early formula for the area of circles developed by the Egyptians in 200 BC through fractal geometry. Unit Six: Topology. This unit looks at topics in topology including the Mobius strip, Konigsberg Bridge problem, cut points and the four-color theorem. Technology: Students are required to purchase a copy of the Geometers Sketchpad, available from Key Curriculum Press. Students who may benefit: Students in this course are preparing for certification in elementary education with an elementary mathematics major or minor. This course will not count toward the secondary mathematics major or minor. This course is part of a core of required courses for the elementary mathematics program. Follow up courses: Students will often take either MATH 210 Algebra for Elementary/Middle School Teachers or MATH 301 Advanced Topics in Elementary Mathematics after completing MATH 240.