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# Language of Math

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Author: Katie Smith
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To understand mathematical terms as a separate language rather than a misuse of letters, words and symbols as we otherwise know them.

This packet will provide an introduction to the common words, letters, and symbols used in math problems, and an explanation of when and how they differ from other everyday usages.

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Tutorial

# Language of Math

Learning math involves wrapping your head around a rather unusual concept -- forgetting what you know.

As you move through your math classes, you'll find things that look familiar used in entirely different ways.  Let's take the letter c, for example.  You're familiar with the letter c.  It comes after b, and before d.  As Sesame Street taught us, c is for cookie.  Or c is for cat.  You have a capital C and a lowercase c.  We know all about c.  But:  did you know that "c" is a "scalar"?  And that a  "scalar" is any "real" number?  Did you know that some numbers are "real"?  What does that say about about the rest of the numbers?  Did you know that "b" is the "y-intercept",  "m" is the "slope" of a line, "x" is a "variable"?

To clarify, c isn't always a scalar, b isn't always an intercept, m isn't always the slope, and x isn't always a variable.  You are welcome, at any time, to return to your English class and use them to write the words chocolate cake, bubblegum, money and x-ray.  But in math, we use these letters (and a whole lot more -- symbols, too) to represent things.  We have conventions -- letters, words, symbols, etc that we all agree will be used to represent a particular thing.  Sometimes there's a reason we picked that representation, sometimes there's not.  (That thing you're sitting on?  Why is it called a "chair"?  Why are you reading this on a "computer"?)

This packet will introduce you to some of the terms used in math, and help you to start building the vocabulary you need to dive right in.

# Vocabulary

Some common math terms, with definitions, are included below:

Coefficient:  A number placed in front of a variable (Example: In each of the following, the coefficient is three:  3x2  or 3x or 3xy)

Degree:  A sort of ranking of polynomials, defined by the exponent.  x2 is a second-degree term.  x3 is a third-degree term.  x6 is a sixth-degree term, and so forth.  The degree of a polynomial is defined by the greatest degree in any term. Also called order.

Independent variable/Dependent Variable:  The 'x' variable is often refered to as an independent variable.  That means that you can pick any value here, and your outcome (y) will depend on what you pick.  (For this reason, y is called the dependent variable).  How many hours you work each day would be an INDEPENDENT variable (often depending on when the alarm clock goes off).  How much money you earn would be the DEPENDENT variable (it depends on how many hours you worked).

Order:  See Degree

Polynomial:  The sum of several terms which contain variables raised to whole-number, positive exponents.

Quadratic Formula:  The quadratic formula can be used to solve a second-order polynomial ax2 + bx +c = 0 by inserting the coefficients a, b, and c into the formula (-b±(b2-4ac)1/2)/2a

Slope:  You'll see the word slope when dealing with linear equations.  Slope refers to how your line "looks" as you go from left to right.  Is it going up? (That's a positive slope).  Or is it going down? (That's a negative slope).  If it were a hill, would it be a steep hill (that's a bigger number for your slope) or a gentle rolling hill (that's a smaller number for your slope).

Term:  A "part" of a polynomial.  In the polynomial 3x2 + 2x + 1, there are three terms.

Variable:  Variables are always changing.  The letters x and y are used as place holders.  (See also independent variable and dependent variable).

Y-intercept:  This term tells you where your line (or equation) crosses the y-axis on your graph.  The numerical value where it crosses is your y-intercept.

## .

Often times, letters are used in math to represent a particular concept, variable or mathematical term.  Common uses of letters are given below.  See the Vocabulary section above for words you're not familar with!

a:  You'll see the lowercase a in your math classes when we talk about solving quadratic equations.  It represents the coefficient in front of the first term (the second order term) of the quadratic equation.

b:  The lower case b is often used to represent the y-intercept of a linear equation.  It is also seen in solving quadratic equations -- in this case, it refers to the coefficient of the second (first order) term of the equation.

c:  When solving quadratic equations, c represents the coefficient of the 3rd term.

m:  In a linear equation, m refers to the slope, or steepness, of a line.

x:  The letter x will be used to represent the independent variable.

y:  Y is typically used to represent the dependent variable.

x,y, and z:  On a 3-dimensional graph, the x-axis goes left to right, the y-axis goes up and down and the z-axis goes into the page and out at you.