Importance of Precision in Math

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Teaching math to your students can be very exciting as you see how your students pick up new concepts and apply it in their lives. As the math teacher, it's important that you teach your math precisely. Learn why in this lesson.

Teaching Math

As a math teacher, you know how important and useful math can be in the real world and how the real world operates is based on math. There are equations for how gravity works and you can calculate the exact position where a marble will fall if you know the direction, speed, and acceleration of the marble.


math precision


Your students will only benefit from these formulas if you teach them with precision. In this context, precision refers to teaching your students exactly how to use formulas and under what situations these formulas are correct. By being precise, you remove the possibility that the students will not understand how and under which conditions a math statement, also known as a math proof, holds true. For example, the equations for how gravity works are only valid when you are on Earth and at reasonable altitudes. If you are too high up in altitude, these equations will give you a wrong answer. You need to explain this to your students so they'll understand how the equations apply in the real world.

A Mathematical Statement

Take for example this conditional mathematical statement.

  • If a < b, then ac < bc.

If c is positive number, then this statement proves true.

  • For a = 3, b = 5, and c = 2, you get 3 < 5, so 6 < 10, a true statement.

But what happens if your c is equal to 0? Why you get 0 < 0, a false statement. Likewise, if c is a negative number such as -1, your statement is likewise false.

Importance of Precision

When you teach this mathematical statement that is known as the multiplication property of equality, you need to be precise in your language so your students know how to use it. You need to teach your students exactly under what conditions a mathematical statement is true. This is true for all mathematical statements. They all rely on exact and accurate definitions. If you are not precise in your math definitions and teaching, then your students may mistakenly use it under conditions where the statement is not true for example when a = 1, b = 2, and c = -1. Under these conditions, ac is no longer less than bc.

To teach this mathematical statement precisely so your students will benefit from it, you need to specify that this statement is only valid when c is a real positive number that is not 0.

  • If a < b, then ac < bc; for real c > 0

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support