Negative Number Lessons

Students need to learn how to work with negative numbers early in their math career.

Learning how negative numbers work is essential for students in early math. Students with a solid foundation in the relationship between negative and positive numbers will have an easier time when faced with more advanced topics. Even seasoned math professionals need to double check their signs, but that is impossible for a student who does not understand how the signs work.

Use a Number Line

Many negative-number lessons begin with a simple number line. A number line is a straight horizontal line with marks to designate integers in order. Be sure that students understand that heading to the right, numbers are always getting bigger and that heading to the left, numbers are always getting smaller. This is a good way to begin teaching addition and subtraction as well, as students can count along the number line to find the answer. For example, if you are doing -3 + 4, have students put their finger on -3, then count to the right 4 places to 1.

Use Money

Students tend to understand negative numbers in terms of money owed to them.

Money is an easy way to help students understand adding and subtracting with negatives. Talk about negative numbers being how much you owe the student and positive numbers as being how much you pay the student. This is helpful in situations where students have trouble seeing that negative numbers appear to get smaller when you add positive numbers. For example, if a student makes this mistake -5 + 3 = -8, then walk through explaining the mistake to them like this: Let's say I owe you $5. Then, I pay you $3. How much money do I still owe you? The answer is $2. Explain that negative numbers are like the money you owe someone, and positive numbers are like the money paid in return. Therefore, -5 + 3 = -2.

Teach "Change, Change"

With adding and subtracting, teach students that they can perform the "change, change" magic to make a problem look easier. "Change, change" means changing the sign of addition to subtraction and the sign of the number being added to positive instead of negative, or vice-versa. For example, 3 + -2 becomes 3 -- 2, and 6 -- (-8) becomes 6 + 8. As long as both the sign of the addition/subtraction and the number to which the function is being applied are changed, then the operation will stay the same in value.

Communicative Property

Understanding the communicative property can be helpful for students. This property states that numbers can be added in any order and you will still end up with the same result. Many times, it is easier for students to see how to add a negative number than it is for them to see how to add a positive number to a negative number. Teach students that when they see -7 + 8 it can be switched to 8 + -7.

Use Counters

Using counters can be an excellent way for students to see how positive and negative numbers cancel each other out when you are adding. Make slips of paper or use poker chips that have + and -- signs on them. If you are doing -5 + 8, then have the students grab 5 "-" counters and 8 "+" counters. Tell the class to line them up side by side on their desk. Every "-" counter cancels out a "+" counter. Ask the students to cancel the pairs of counters, then report what they have left. They will have 3 "+" counters remaining, thus the answer to -5 + 8 is 3.

Multiplication and Division

The multiplication rule is often taught as positive times a positive equals a positive, negative times a positive equals a negative and negative times a negative equals a positive. It is helpful to point out that when the signs are the same, the answer will be positive, and when the signs are different, the answer will be negative. The same rule applies to division; just substitute in the words "divided by" instead of "times."

References

• Purple Math: Basic Number Properties (Associative, Commutative, and Distributive.; Elizabeth Stapel; April 12, 2011
• Home School Math: How to Teach Operations with Integers; Maria Miller; 2003-2011