# Math Tutoring – 3 Basics Steps to Master Reading Mathematics Formulas

Understanding how to read mathematics formulas requires a basic understanding of the formula vocabulary and how to recognize formula reading patterns. We will focus on how to read Mathematical formulas and learn how this formula reading pattern can be used with formulas from different subjects (i.e. Algebra, Geometry, Chemistry, Physics). Knowing how to read Mathematics formulas is essential for maximum understanding and easy memory recall.

It is my hope that you will see a pattern with reading formulas across different subjects. Why is seeing a pattern across subjects so important? Students often feel like they are learning something new each time they are introduced to a Math formula in another class or course. Fact remains, the same methods you use to read formulas in Algebra are the exactly same methods used to read formulas in Trigonometry, Physics, Chemistry, Economics, etc. So the key is mastery of reading formulas in Algebra.

**Step 1:** Understand what a formula is. What is a mathematical formula? An equation (i.e. F = ma) which expresses a general fact, rule, or principle.

**Step 2:** Identify and learn the basic Mathematics equation vocabulary and use as often as possible while doing problems. A good mathematics educator (e.g. tutor, mentor, teacher, …) will help you engage this vocabulary as you are working on your problems. This vocabulary is useful when reading Math instructions, doing word problems, or solving Math problems. Let’s define a basic set of basic Math formula (equations) vocabulary words below:

**Variable –** a letter or symbol used in mathematical expressions to represent a quantity that can have different values (i.e. x or P)

**Units –** the parameters used to measure quantities ( i.e. length(cm, m, in, ft), mass (g, kg, lbs, etc))

**Constant –** a quantity having a fixed value that does not change or vary

**Coefficient –** a number, symbol, or variable placed before an unknown quantity determining the amount of times it will be multiplied

**Operations –** basic mathematical processes including addition (+), subtraction (-), multiplication (*), and division (/)

**Expressions-**a combination one or more numbers, letters and mathematical symbols representing a quantity. (i.e. 4, 6x, 2x+4, sin(O-90))

**Equation –** An equation is a statement of equality between two mathematical expressions.

**Solution –** an answer to a problem (i.e. x = 5)

**Step 3:** Read formulas as a complete thought or statement-do not ONLY read the letters and symbols in a formula. What do I mean? Most people make the repeated error of reading the letters in a formula rather than reading what the letters represent in the formula. This may sound simple, but this simple step allows a student to engage the formula. By reading the letters and symbols only, one cannot associate the formula with particular vocabulary words or even the purpose of the formula.

For example, most people read the formula for area of a circle (A = “pi”r2) just as it is written – A equals pi r squared. Instead of just reading the letters and symbols in the formula, we propose reading formulas like A = “pi”r2 as a complete thought using all the descriptive words for each letter: The area (A) of a circle is (=) pi multiplied by the radius (r) of the circle squared. Do you see how the formula is a complete statement or thought? Therefore, one should read formulas as a complete statement (thought) as often as possible. It reinforces what the formula means in the mind of the reader. Without a clear association of Math formulas with their respective vocabulary, it makes applications of those formulas near impossible.

Example of formulas and the subjects where they are introduced:

PRE-ALGEBRA – Area of Circle: A = “pi”r2

The area (A) of a circle is pi multiplied by the radius (r) of the circle squared

o A- area of the circle

o “pi” – 3.141592 – ratio of the circumference to the diameter of a circle

o r- the radius of the circle

ALGEBRA – Perimeter of a Rectangle: P = 2l+ 2w

Perimeter (P) of a rectangle is(=) 2 times the length(l) of the rectangle plus 2 times the width (w) of the rectangle.

o P- perimeter of the rectangle

o l- measure of longest

o w- measure of shortest

GEOMETRY – Triangles Interior Angles Sum Theorem: mÐ1 + mÐ2 + mÐ3 = 180

The measure of angle 1 (mÐ1), plus the measure of angle 2 (mÐ2) plus the measure of angle 3 (mÐ3) of a triangle is 180 degrees.

o mÐ1 – perimeter of the rectangle

o mÐ2 – measure of a side

o mÐ3 – measure of the width

Knowing the units for each quantity represented in these formulas plays a key role in solving problems, reading word problems, and solution interpretations, but not merely reading the formulas.

Use these steps as a reference and learn how to read Mathematics formulas more confidently. Once you master the basics of formulas, you will be a Learner4Life in different subjects that use Math formulas!