SUMMERMATH

FUNDAMENTAL MATH CONCEPTS

TOPIC DESCRIPTIONS

This course selection information describes the choices for Fundamental Mathematical Concepts (FMC) Topics. Students choose a topic from one of the five areas in mathematics listed below, which will be the area of focus for the four weeks of the program. No matter what topic is chosen, work will focus on problem solving and on ideas that help more generally in future studies of mathematics.

This is a rare opportunity to learn without the pressure of grades or homework and to try out new ways of learning!

Topic Titles:

Topic Descriptions:

Algebra:

Algebra will focus on the concept of variable.  Beginners will construct variable expressions to fit real world situations, and then learn how to manage information by representing it with pictures, words, tables, and equations.  More advanced students will work on patterns, equations, and functions along with their applications.

Geometry:

The emphasis in this topic area is on investigating, constructing, and reasoning about fundamental geometric objects.  Students will learn about the tools of geometry:  straightedge, compass, paper folding, and the geometry software, Geometer's Sketchpad.  These tools will be used to study similarity, congruence, transformations, and more. 

Trigonometry:

This topic emphasizes modern and ancient applications of triangle trigonometry and the trigonometric functions.  Trigonometry is a great way to link geometry and algebra and to experience the function concept. 

Pre Calculus to Calculus:

The focus here is on the idea of function, thinking about functions graphically, numerically, symbolically, and verbally and putting all these representations together!  If time permits, students will also experience the beginnings of calculus.

Calculus:

In this focus topic functions are taken to the limit - specifically, to limits that define the derivative and integral of a function. Students make use of mathematical software that allows them to dynamically simulate rates of change (think velocity) and the process of accumulation (think of the area of a curvy region).