Course Description
A deep examination of mathematical topics designed for future
elementary school teachers. Length, area, and volume. Geometric
shapes and their properties. Probability. Elementary number theory. Applications of elementary mathematics.
Additional Requirements for Graduate Students:
Graduate students will be expected to do extra assignments and
give a presentation.
Athena Title
Geometry and Problem Solving
Prerequisite
MATH(EMAT) 5001/7001 or MATH(EMAT) 5001E or MATH(EMAT) 7001E
Semester Course Offered
Offered fall and spring
Grading System
A - F (Traditional)
Student learning Outcomes
- To strengthen and deepen knowledge and understanding of measurement, basic geometry, elementary probability, and some elementary number theory and how they are used to solve a wide variety of problems
- 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
- Geometry and measurement: Length, area, and volume, and the fundamental principles that govern them
- Understanding why various formulas for areas and volumes work
- The relationship between perimeter and area
- Measurement in different units and scaling
- Basic geometric shapes and their properties, including the Pythagorean Theorem (for right triangles) and the sum of the angles in triangles
- Constructions with straightedge and compass
- Angles
- Symmetry
- Congruence and similarity, including applications to measurement
- Platonic solids
- Probability: Understanding and calculating probability, including conditional probability; Combinations and Pascal's triangle
- Number Theory: Greatest common divisor and least common multiple; Prime numbers; Decimal representations of rational and irrational numbers; Irrationality of the square root of 2
