Adding Integers – There Are Two Simple Rules

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This past week my math classes learned how to add Integers. Adding Integers is the next logical step after learning about Absolute Value since understanding Absolute Value is essential to understanding how to add Integers.

To review: Integers are the set of whole numbers and their opposites. Absolute Value is the distance a number is from zero on the Number Line.

When we began the lesson on adding Integers, I introduced the students to two acronyms I’ve used for many years. I’ve found these acronyms are simple ways to help students remember the rules for Integer addition.

The first rule is SSS. SSS stands for Same Sign Sum. When you add two Integers with the Same Sign, either both positive or both negative, you take the sum of their Absolute Values and then give the Sum the Sign the two Integers had in common. I often joke with my students that math is easier to do than explain at times. This may be one of those cases. Perhaps an example is called for.

Take the expression 2 + 3. Both the 2 and the 3 are positive. The Absolute Value of 2 is 2 and the Absolute Value of 3 is 3. When you take the sum of 2 and 3 you get 5. Since both addends, the 2 and the 3, are positive, the sum of 5 is also positive.

All this may sound unduly complicated, very New Math or Common Core, but it makes sense to the students. It makes even more sense when you add two negative integers.

Say you want to add (-4) + (-6). The Absolute Value of (-4) is 4 since (-4) is 4 units from zero on the Number Line. Similarly, the Absolute Value of (-6) is 6. When you add the Absolute Values of (-4) and (-6) the sum is 10. Because both of the original addends were negative, the sum will also be negative. Thus, (-4) + (-6) = (-10).

In class we show this using Integer Counters. Positive Integers are represented by yellow chips. Negative Integers are represented by red chips. This helps the students visualize the math. Once they grasp the concept using the chips, we move to the Number Line. By the time they are asked to work out a few exercises on their own, most are ready to do so with mastery and enthusiasm because they really understand the concept.

The second acronym, DSD, stands for Different Sign Difference, and is used for adding Integers with Different Signs. The long version is as follows: When adding two Integers with different signs, you subtract the Absolute Value of the Integer with the lesser Absolute Value from the Absolute Value of the Integer with the greater Absolute Value. The difference between the Absolute Values is the sum of the two Integers, and the sign of the sum is the sign of the Integer with the greatest Absolute Value becomes the sign of the sum.

If you’re having trouble making sense of all that, here is an example.

Find the sum of (-12) + 6. The Absolute Value of (-12) is 12 and the Absolute Value of 6 is 6. Now subtract the Absolute Values. 12-6=6. Once you have calculated the difference, the answer is given the same Absolute Value as the original addend with the greater Absolute Value, in this case (-12). Therefore, the answer is (-6).

Change the expression a bit and the answer changes a bit.

Find the sum of 12 + (-6). The Absolute Value of 12 is 12 and the Absolute Value of (-6) is 6. Now subtract the Absolute Values. 12 – 6 = 6. Once you have calculated the difference, the answer is given the same Absolute Value as the original addend with the greater Absolute Value, in this case, positive 12. Therefore, the answer is 6.

Standing alone, each of these exercises may not seem relevant. However, understanding each will become vitally important when the students start solving equations and have to isolate variables. But that’s for a future post.

As always, I remain,

The Exhausted Educator