# 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.

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

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