If there was one skill I wish my students had a better understanding of on their first day of Algebra 1, it would be adding and subtracting integers. It is almost as if they are taking a guess with every single question, just hoping they might get it right!
Because the lack of understanding is so wide-spread, I often spend several class periods reteaching this skill in the way that I have had the most success — I keep the rules simple.
Simplify the Rules
I found this to be the #1 key to helping my students master adding and subtracting integers. Basically, there are two rules for adding integers, and it all comes down to whether or not the numbers have the same signs.
Same Sign
- Add the numbers
- Keep the sign
Opposite signs
- Subtract the numbers
- Use the sign of the “larger” number
That really is the gist of adding integers at its most basic level. I always put “larger” in quotation marks because I’m not talking about the value of the number in the question; rather, I have the students just rely on their intuitive understanding of numbers. Let’s look at some examples.
In this example, we see the numbers have the same sign; they are both negative. We just add the numbers and keep the sign. Easy.
In this next example, I walk my students through the process of determining the numbers have opposite signs. Based on our rule, we subtract the numbers (9 – 4) and we use the sign of the “larger” number. Since 9 is bigger than 4, we use its sign, and our answer is positive.
If this example, my students would again find the numbers have opposite signs, so we subtract. Again, 9 is bigger than 4, so we use the sign that goes with 9.
Putting the process in terms of a straightforward rule, really seems to help my students. After repeating this process for a couple of class periods, it really seems to click.
But what about subtracting integers?
I tell my students that those adding rules are hard enough; we definitely don’t want to memorize anything more, right? (They always agree.) So instead, we change every subtraction problem into an addition problem; then we can use our rules of addition.
Change “-” into “+ -“
Change “- -” into “+”
This “rule” takes a little more convincing, but when they realize this creates an addition problem, the students usually get on board.
I train my students to rewrite a “minus a minus” to a plus, so we can use our two addition rules.
Student Cheat Sheet
It takes some time to really get these rules solidified, so I like to give my students a “Cheat Sheet,” that they can refer to as they are really getting the hang of it. I would love to share this resource with you! Just fill out this form to get the full-sized file.
