Add and Subtract on the Number Line
What Is the Number Line?
Did you know that all numbers are arranged on a number line? Curious to learn more? Check out our article on the number line.
How Do We Add and Subtract on the Number Line?
Addition and subtraction come to life in a very natural way on the number line:
Addition: Find the first addend on the number line, then make a jump to the right that matches the second addend.
Subtraction: Start at the number you have (the minuend), then make a jump to the left that matches the number you’re taking away.
Distance: When you subtract two numbers that are close together, the easiest way is to place them both on the number line and count how many steps it takes to move from one to the other.
Why Does It Matter for Kids?
The number line gives kids a simple, visual way to connect two sides of number sense: order and quantity. Order is easy to spot — numbers are lined up one after another: 0, 1, 2, 3, 4, 5, and so on. Quantity shows up in the steps: the number 5 is the five steps it takes to get from 0 to 5.
Research shows that seeing arithmetic on a number line creates a clear mental picture for kids. Moving to the right for addition and to the left for subtraction gives them a universal model for these otherwise abstract operations.
As kids get older, the “empty number line” becomes an even more powerful tool. It helps them handle tricky skills like bridging across tens and multiplication, while also strengthening their understanding of addition and subtraction as inverse operations.
How Do We Teach?
When kids walk along the number line, they always move in one of two directions. To the right, numbers get bigger — each step adds 1. We show “add 4” as an arrow that combines four steps to the right. To the left, numbers get smaller — each step takes away 1. That’s why subtraction is always an arrow to the left.
Kids can place arrows one after another to carry out several moves in a row. For example, adding 2 and then 3 is the same as adding 5. Or adding 4 and subtracting 3 works out to adding just 1.
Breaking one move into two can make calculations easier. For instance, to add 7 to 8, kids can first add 2 to reach 10, then add 5 to get 15. Or they might add 10 instead of 7 to get 18, and then step back 3 — which also gives 15. All of these strategies are easy to show with arrows on the number line.
Addition
Steps Forward on the Number Line
Addition on the number line means taking steps to the right. For example, if you start at 8 and take 4 steps to the right, you land on 12:
8 + 4 = 12
You can also look at it this way: how many steps does 8 need to reach 12? The answer is 4.
Distance on the number line
Distance on the number line up to 20 (objects and numbers)
Four single steps can be shown as one longer step of 4:
8 + 1 + 1 + 1 + 1 = 8 + 4
Notice that the equal sign here isn’t just an “answer button.” It’s a statement that two number expressions mean the same thing.
If you add 2 and then 3, it’s the same as adding 5 in one go. Kids can see this both with fish in a tank and with arrows on the number line.
Adding in two steps is especially helpful when crossing a ten. For instance, to add 8 to 27, you can first take 3 steps to reach the nearest round number, 30, then make the remaining 5 steps:27 + 8 = 27 + 3 + 5 = 30 + 5 = 35
Visual addition and subtraction
How many steps?
Visual addition and subtraction
2-step addition with pictures
Moving on a number line
2-step addition with pictures
Moving on a number line
Crossing tens (up to 100)
Subtraction
Two Ways to Subtract
On the number line, subtraction first shows up as moving backward — steps to the left. Taking 3 steps to the left is the same as subtracting 3.
Basic subtraction (up to 10)
Subtracting part-by-part
Alongside counting steps left, subtraction can also be seen as the distance between two numbers. For example, the length of a little worm stretched between 7 and 12 is exactly 12 – 7. That’s 5 steps on the number line: from 7 to 8, then 8 to 9, 9 to 10, 10 to 11, and finally 11 to 12.
It’s important not to get confused: subtraction is about how many steps it takes to get from one number to another. Related problems can look a bit different. For instance, how many numbers are there from 17 to 48 on the number line? That’s one less than 48 – 17. But if you write down all the numbers from 17 to 48 inclusive, you’ll get one more than 48 – 17.
Thinking of subtraction as distance makes it easier to cross tens. For example, to solve 81 – 72, move from 72 up to 80 — that’s 8 steps — and then 1 more step to reach 81. Altogether, 81 – 72 = 8 + 1 = 9. Written out like this, it may look unusual, but on the number line it’s simple and clear.
Subtraction can also be done by moving to the right. For example, to subtract 47 from 65, you can first subtract 45 to land on the round number 20, then subtract 2 more:65 – 47 = 65 – 45 – 2 = 20 – 2 = 18.
Measuring with a ruler
Measure length (in 2s)
Number line (up to 100)
Intervals on number line
Distance on the number line
Distance on the number line up to 100 (numbers only)
Addition strategies
Crossing tens (up to 100)
Addition and Subtraction
There and Back
On the number line, it’s easy to see that if you add something to a number and then subtract the same amount, you end up right back where you started.
Mathematicians call addition and subtraction inverse operations.
Subtraction
Using addition to subtract
With real objects, this idea isn’t always so obvious. For example, kids might not realize that if 3 people get on a bus and then 3 different people get off, the total number of passengers is still the same.
What if you add more than you subtract? For instance, adding 8 and then taking away 3 is really the same as adding 5.
Many mental math strategies combine both addition and subtraction. For example, to add 38 and 9, you can add 10 instead — a little more than needed — and then subtract 1, the extra you added.
Visual addition and subtraction
2-step addition with pictures
Addition and subtraction
Using addition to subtract
Moving on a number line
Using addition to subtract
Moving on a number line
Using addition to subtract
Big Ideas
Arrows on the number line later grow into vectors or operators. When kids place one arrow after another, carrying out operations step by step, they’re already getting an early glimpse of the idea of composing operators or functions.
Rounding is another powerful concept in working with numbers. We first estimate the result of a calculation, then, if needed, make small adjustments to reach the exact answer.
