Understanding how to read mathematical formulas requires a basic understanding of 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 (ie algebra, geometry, chemistry, physics). Knowing how to read mathematical formulas is essential for maximum understanding and easy recall of memory.
I hope you see a pattern with reading formulas in different topics. Why is it so important to see a pattern between subjects? Students often feel like they are learning something new every time they are introduced to a mathematical formula in another class or course. The fact is that the same methods you use to read formulas in algebra are exactly the same methods you use 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 (ie, F = ma) that expresses a general fact, rule, or principle.
Step 2: Identify and learn the basic vocabulary of mathematical equations and use it as often as possible while solving problems. A good math educator (eg tutor, mentor, teacher, …) will help you use this vocabulary as you work on your problems. This vocabulary is helpful when reading math directions, doing word problems, or solving math problems. Let’s define a basic set of math formulas (equations) core vocabulary words below:
Variable: A letter or symbol that is used in mathematical expressions to represent a quantity that can have different values (ie, 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 that has a fixed value that does not change or vary.
Coefficient: a number, symbol, or variable placed before an unknown quantity that determines the number of times it will be multiplied
Operations: basic mathematical processes including addition (+), subtraction (-), multiplication
and divide (/)
Expressions: A combination of one or more numbers, letters, and mathematical symbols that represent 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 (ie x = 5)
Step 3: Read the formulas as a complete thought or statement; don’t read ONLY the letters and symbols in a formula. What do I mean? Most people make the repeated mistake of reading the letters in a formula instead of reading what the letters in the formula stand for. This may sound simple, but this simple step allows the student to get involved in the formula. By reading only the letters and symbols, one cannot associate the formula with particular vocabulary words or even the purpose of the formula.
For example, most people read the formula for the area of a circle (A = “pi”r2) as it is written: A equals pi r squared. Rather than 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 times the radius (r) of the circle squared. Do you see how the formula is a complete statement or thought? Therefore, one should read the formulas as a complete statement (thought) as often as possible. Reinforce what the formula means in the reader’s mind. Without a clear association of mathematical formulas with their respective vocabulary, it makes applications of those formulas almost impossible.
Example of formulas and the topics where they are introduced:
PRE-ALGEBRA – Circle Area: 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
or “pi” – 3.141592 – ratio of the circumference to the diameter of a circle
or r- the radius of the circle
ALGEBRA – Perimeter of a Rectangle: P = 2l+ 2w
The perimeter (P) of a rectangle is (=) 2 times the length (l) of the rectangle plus 2 times the width (w) of the rectangle.
or P- perimeter of the rectangle
or l- measure of greater
o w- measure of the shortest
GEOMETRY – Theorem of the sum of the interior angles of triangles: 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 one side
o mÐ3 – width measurement
Knowing the units of each quantity represented in these formulas plays a key role in problem solving, reading word problems, and interpreting solutions, but not just in reading the formulas.
Use these steps as a reference and learn to read math formulas with more confidence. Once you master the basics of formulas, you will be a Learner4Life in different subjects that use mathematical formulas!