Teaching Adding and Subtracting Integers with Real-World Context
Let’s talk about adding and subtracting integers, one of my favorite topics! I want to give you some ideas for making it engaging and helping students truly understand what they’re doing.
Many teachers say their students forget the rules or come up with “crazy” answers. When students are giving unreasonable answers, we must ask…
Do they have a firm understanding of what positives and negatives are?
Do they understand what they’re actually doing when they operate with them?
When we slow down and build this foundation, students can make sense of the math.
Start with Context: A Vertical Number Line
One of my favorite tools is a vertical number line. I especially love connecting it to sea level, because it gives students a visual and real-world context.
Sea level is at zero.
Numbers above sea level are positive.
Numbers below are negative.
Using sea creatures, we can ask:
“What is the elevation of the seagull?” (Show a seagull at 22 meters above sea level → +22)
“What is the elevation of the clownfish?” (Show a clownfish at 5 meters below sea level → –5)
This gives students a concrete way to understand what positive and negative numbers represent.
Comparing and Ordering Integers
Once students see how positives and negatives are placed on the number line, they can start comparing them.
We can show sea creatures at different locations on a vertical number line and ask, “Can you list the elevations of these animals from greatest to least?”
Students can simply move from the top of the number line to the bottom:
Seagull: +22
Dolphin: +2
Clownfish: –5
Sea Turtle: –25
This kind of ordering helps them see why negatives are less than positives.
Introducing Absolute Value
Absolute value can feel abstract to students. Why are we suddenly “making everything positive”? Instead, when we explain it as “absolute value is the distance from zero,” it has meaning.
In our sea level example, this makes perfect sense:
The clownfish is 5 meters from sea level.
The seagull is 22 meters from sea level.
Then we can challenge students:
“List the animals in order of distance from sea level.”
Here, the sea turtle (25 meters below) comes before the seagull (22 meters above).
This naturally leads into meaningful conversations about absolute value.
Building Toward Integer Operations
Even in sixth grade, before formal operations begin, we can start preparing students with questions like:
“What’s the distance between the dolphin and the seagull?”
“What’s the distance between the clownfish and the sea turtle?”
Students often figure this out by counting or comparing directly on the number line, which is great. They’re operating with integers without even realizing it. Later, when they see problems like 2 – (–5), it makes much more sense.
Adding Integers with Context
Once students are ready, introduce addition in context:
“A seagull is at +10 meters. If he increases his altitude by 5, where is he now?”
→ +15 (10 + 5 = 15)“An octopus is at –20 meters. If he increases his elevation by 5, where is he now?”
→ –15 (–20 + 5 = –15)
Students begin to visualize adding as moving up the number line.
Subtracting Integers with Context
Similarly, subtraction is visualized as moving down the number line:
“A seagull at +20 descends 5 meters.”
→ +15 (20 – 5 = 15)“An octopus at –10 sinks 5 meters.”
→ –15 (–10 – 5 = –15)
This up/down movement makes addition and subtraction intuitive.
Extending to Adding and Subtracting Negatives
Once students see the patterns, you can guide them to extend:
Adding a positive → move up
Subtracting a positive → move down
Adding a negative → move down
Subtracting a negative → move up
Instead of memorizing rules, students rely on patterns they already understand. Vocabulary like additive inverse can come later, after they’ve built intuition.
Going Beyond the Number Line
Eventually, numbers may move far beyond what a physical number line shows:
“What if the seagull is at +10 and increases by 50?”
“What if the octopus starts at –5 and descends 300 meters?”
By this point, students can reason without needing the visual. The foundation is in place.
Final Thoughts
If we start with real-world context and give students a way to see what’s happening, they develop a strong conceptual understanding of integers. They won’t always need a number line, but the visualization helps them make sense of the rules.
Remember: Go slow at first, so students can go fast later!
This approach makes adding and subtracting integers more meaningful, engaging, and lasting.
For a complete pack of integer resources with a large vertical number, moveable sea creature cards, and over 60 exploration word problems, click here.
