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
