When you subtract, you’re finding the difference between two numbers. One way to do that is by counting back from the larger number. For example, if you want to know what 7 – 3 is, you can start at 7 and count back three numbers: 6, 5, 4. That means 7 – 3 = 4.
Counting back is a basic math skill that’s super helpful for understanding how subtraction works. It helps you really see what’s happening when you take one number away from another. It’s also a good way to build a strong foundation before moving on to more complicated subtraction methods.
In this article, we’ll cover what counting back is, some helpful techniques, tips, and examples to get you started.
What is Counting Back?
Counting back is a simple way to subtract one number from another. It’s a visual way to find the difference between two numbers.
Counting back is really just a practical way of showing how subtraction works. It helps demonstrate the idea of “taking away” a smaller number from a larger number.
When you subtract, the larger number you start with is called the minuend, and the smaller number you’re taking away is called the subtrahend.
Easy Techniques for Counting Back
Counting backward is simple once you get the hang of it. Here are a couple of techniques that can help.
Using a Number Line
A number line is a visual representation of numbers, typically arranged horizontally and in order. To count backward using a number line, start at the larger number (the minuend) and then count backward the number of spaces indicated by the smaller number (the subtrahend).
Let’s say you want to solve 22 – 6. Find 22 on the number line, and then count back six spaces. You’ll land on 16.
Number lines make subtraction more concrete and are especially helpful for visual learners. It’s easy to see how the numbers relate to each other.
Finger Counting
Another technique is to use your fingers to count backward. For example, if you’re solving 8 – 2, start by holding up two fingers. Count back from 8 by two numbers (7, 6), lowering a finger for each number you count. When you’ve lowered all the fingers, the last number you said is the answer.
Just be aware that finger counting works best with small numbers, since most of us only have 10 fingers.
Tips and tricks to count back
Counting backward can be tricky, but there are a couple of strategies that might make it easier.
Reaching a “friendly number” (multiples of 10)
It’s often easier to do math in your head when you work with multiples of 10, so try to adjust the equation to reach a “friendly number.”
Here’s how to use friendly numbers to make counting back simpler: Break down the number you’re subtracting (the subtrahend) to reach the nearest multiple of 10.
Let’s say you’re trying to solve 96 – 26. First, recognize that 96 – 6 = 90, which is a friendly number. Then, subtract the remaining 20 from 90. You’re left with 70, which is the answer.
Breaking down the subtrahend
Another way to simplify counting back is to break the subtrahend into its place values. In other words, separate the number into tens, ones, hundreds, etc.
Then, subtract each place value separately, starting with the tens, then the ones, then the hundreds, and so on.
For example, if you’re calculating 853 – 208, subtract 200 first (853 – 200 = 653), then subtract 8 (653 – 8 = 645).
Counting Backwards: More Than Just Subtraction
Counting back is really just the opposite of counting forward. In math, we call this an “inverse relationship.” So, if you’re counting forward, you’re adding. Counting backward means you’re subtracting. You can even use addition to double-check your subtraction!
One trick to make counting back easier is something called “compensation.” This means adding or subtracting the same amount from both numbers in your problem to create easier numbers to work with. For instance, instead of 15 – 7, you could think of it as 16 – 8, which is easier to solve in your head.
Mastering counting back is a basic skill that helps with more advanced math later on. It’s all about understanding how numbers relate to each other.
Let’s Practice!
Okay, let’s put these skills to work. Here are a couple of worked-out examples to show you how it’s done:
- 13 lollipops – 5 lollipops = 8 lollipops
- 8 balloons – 2 balloons = 6 balloons
- 76 – 24 = 52
Now, it’s your turn! Try these problems:
- What is 15 – 7?
- Jack has $20. He spends $8. How much does he have left?
- What is the difference between 35 and 12?
Click to reveal the answers!
- 8
- $12
- 23
How did you do? Keep practicing, and you’ll be a subtraction whiz in no time!
To Conclude
Counting back is a straightforward subtraction strategy that can be mastered using tools like number lines, finger counting, and “friendly” numbers. It’s a foundational skill that’s key to developing strong math skills.
The more you practice counting backward, the more confident and fluent you’ll become. So, whether you’re helping a child learn math or brushing up on your own skills, make counting back a regular part of your routine. With consistent practice, you’ll find it becomes second nature, unlocking a deeper understanding of subtraction and setting the stage for more complex mathematical concepts.