- Topics At a Glance
- Variables
- Variables as Unknown Quantities
- Variable Notations
- Constants
- Expressions and Equations
- Rearranging Expressions
- Commutative Properties
- Associative Properties
- Distributive Properties
- Factoring (Distributive Property in Reverse)
- Combining Like Terms
- Eliminating Parentheses
- Simplifying
- Equations, Functions, and Formulas
- Equations
- Functions
- Independent and Dependent Variables
- Formulas
- Applications to Toolbox
- Evaluating Expressions by Substitution
- Evaluating Formulas by Substitution
**Geometric Formulas**- Four-Sided Shapes
- Three-Sided Shapes
- Circles
- Unit Conversion
- Temperatures
- Weights
- Distances and Speeds
- Money
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

Formulas wouldn't tell us squat if we couldn't then turn around and apply them to situations in the real world. Fortunately, we can do just that. Formulas can help us figure out how to deal with, plan for or manipulate objects of all different shapes and sizes, both two-dimensional and three-dimensional. The two-dimensional ones are easier, as you may imagineâ€”let's start there. We're not a throw-you-in-the-deep-end-of-the-pool-to-teach-you-to-swim kind of people.

Two-dimensional shapes appear a lot in the world. A soccer field is a rectangle, the body of a bicycle may be a triangle, and some cakes have circular tops. These are all three-dimensional objects, but with two-dimensional *parts*. Practical considerations aside, two-dimensional shapes are good for math problems because we can draw them on paper. Because most paper that we know of is more or less two-dimensional.

We will go through some familiar shapes in the next few pages. For each shape we will give you a formula for the **perimeter**, meaning the distance around the outside of the shape, and a formula for the **area**, meaning the size of the surface covered by the shape. Perimeter is measured in units of length such as inches, feet or miles. Area is measured in units of length *squared*, such as square inches, square feet or square miles. Perimeter usually works better in poetry. For example, Robert Frost never would have been such a hit if he'd written that he had "square miles to go before I sleep."