Do your students struggle with adding or subtracting positive and negative integers? This can be a mind-blowing concept for some students when first introduced, but it doesn’t need to be. Here are 4 ways to teach this so all students understand:

__Start with Something Familiar: Money__

I introduce the topic of negatives by having a discussion about where they might have seen negative numbers. Someone might talk about temperature, particularly if this lesson happens to be during winter, if I’m lucky, a student might bring up coordinate places (cue perfect segway into the number line approach!), but invariably someone always mentions owing money. We have a classroom economy system, and it sometimes happens that a student might go into debt, so they’ve seen negative amounts of money. We just call it “debt” or “money owed.” Now though, we can discuss it as negatives.

Discuss what happens when money is earned or money is lost; this is adding and subtracting with negatives! Pull out the play money and an account register like this one I made here. Let the students have some hands on practice adding and subtracting dollars by giving them different real-world scenarios.

__The Number Line/Coordinate Plane__

If it happens that your students have already worked with 4 quadrant coordinate planes, then this method will be easy to help your students visualize adding and subtracting with negatives. I prefer the x and y axis plane, because you have both the horizontal and vertical number lines, but if it hasn’t been introduced to your students yet, just use whatever number line is familiar to your students.

Number lines allow students to not only compare integers, but to begin to view positive and negative numbers as opposites. To encourage this, I have students draw on transparency and label the x and y number lines on their papers using rulers to ensure spacing is even and exact. e fold the lines in half and discuss how the numbers are the same unit value (absolute value review here!), but negative is the opposite of positive, meaning it’s been removed. Put together, two opposite integers of the same value cancel each other out, giving a value of zero. This step is important for students to grasp for when we eventually get into equations with integers, but it is also helpful in understanding subtracting or adding negatives.

__No Such Thing as Subtracting__

After teaching these methods, I then prep my students for a mind bender. I tell them there is no such thing as subtraction. It doesn’t exist; subtraction is just adding a negative! There is a great video clip of a PBS Math Club debate on this topic that you can watch here:

We then do some practice problems to drive the point home. I box the signs with the number it is attached to to help the students visualize how the subtraction sign is acting as an added negative.

__Commutative Property__

This one is short and sweet. I do a quick reteach of the commutative property. We’ve now looked at how the subtraction sign can be attached to a number to become an added negative. Commutative property helps students put this understanding to work by switching around different expressions. 4 – 7 is the same as -7 + 4. This helps students see how the minus/negative sign is attached to the number “behind” it. It also gives students the “permission” to move around the numbers into whatever order is easier for them to solve and adds some extra perspective into their practice.

__Integer Song – Summary Activity__

Finally, I give students the rules of adding and “subtracting” positive and negative numbers. My notes for them are brief and given only after teh previous discover activites.

- If both numbers have the same sign add the values. Keep the sign the same.
- If each number has a different sign, subtract the values. Give the answer the sign of the larger number
- If there is a minus next to a negative, the 2 signs combine to become a positive(relate this to taking away debt). Then follow the above rules.

I type these notes up to give students a printed handout which they keep in a sheet protector in their math binders. Get your copy of my Integer Operations Rules Handout on my Teachers Pay Teachers Store.

We end this intro unit by singing a song to the tune of “Row, Row, Row Your Boat.”

*Same sign, add and keep. *

*Different signs, subtract!*

*Keep the sign of the bigger number,*

*and it will be exact. *

Once we’ve finished all these activities, it’s time for some assessment to see where students are. This Formative Benchmark Negative Operations Quiz is great to get a good idea of where, or even if, students are still tripping up.

__Bonus Strategy – Bird Beak__

This year, one of my students came up with her own method of remembering rule 3: a minus sign next to a negative sign becomes a plus/positive sign. She drew this:

She thought it looks like a bird eating. Any time she sees the “eyes,” she knows to draw the beak and a the plus sign underneath.