Are your students struggling with long subtraction? I have seen so many students have a difficult time with this subtracting strategy over the years. When I was in elementary school, the long subtraction method (also known as standard algorithm) was the only strategy taught for subtracting big numbers.
But, that is not the case today! Sharing a variety of strategies for subtracting multi-digit numbers ensures that every student can find a method that works for them and be successful with subtracting larger numbers.
Interested in learning strategies for adding multi-digit numbers? Check out this blog post!
What is the Long Subtraction Method?
Long subtraction (also known as standard algorithm) is a strategy for subtracting multi-digit numbers that involves stacking the numbers vertically. The solver subtracts from each place value, starting with the column furthest to the right.
To subtract using long subtraction (or standard algorithm):
- Stack the numbers vertically. The larger number should be on top.
- Subtract the ones. If the digit in the minuend is smaller than the digit in the subtrahend, you must borrow. Cross out the digit in the next place value and subtract one. In the example, the 2 in the tens place is crossed out and changed to 1. Then, write 1 in front of the number you are trying to subtract from.
- Repeat the process for each place value, borrowing as needed.
The long subtraction method works well when there is no borrowing or regrouping involved. But, when borrowing and regrouping comes into play, this strategy can be challenging.
For some students, the idea of borrowing from one number to make a new number is just confusing. For other students, crossing out numbers and writing new numbers over others becomes a jumbled mess that is difficult for them to process.
What to Do When Long Subtraction is Hard?
Luckily, other multi-digit subtraction strategies exist that are more visual and require fewer steps. Introducing students to some of these more visual strategies can reduce stress and help them succeed.
In this post, I will share three of my favorite multi-digit subtracting strategies. I’ve provided pictures and step-by-step instructions below. But, if you would prefer a video tutorial, all three of these ways to teach subtraction are also shown in this video.
Subtraction Strategy #1: Compensation
Do you know what all students hate (and me too)? Subtracting across zeros!
The compensation strategy is the perfect strategy to use when subtracting across zeros or when most of the digits in the minuend are smaller than the digits in the subtrahend. This multi-digit subtracting strategy involves rounding one of your numbers to make it more manageable. Then, you add or subtract what was rounded to the difference.
To solve multi-digit subtraction problems using compensation:
- Add or subtract any amount from either number to make it easier to solve. Ideally, you are adding or subtracting an amount that will be easy to add/subtract back in at the end of the problem. For example, the image shows 1 being subtracted from 20,000 to make a number that is easier to subtract from (19,999). 1 is an easy number to add back in at the end of the problem.
- Use long subtraction to subtract.
- Use the opposite operation to add/subtract what was added or taken away in Step 1. In the example, 1 was subtracted in Step 1. So, 1 will be added in Step 3.
Subtraction Strategy #2: Expanded Form
This multi-digit subtracting strategy is a great way to review place value as you teach subtraction.
To solve multi-digit subtraction problems using expanded form:
- Write each number in expanded form. Stack the numbers vertically. Like with the long subtraction method, the larger number should be on top.
- Subtract by place value.
- If the number on top is smaller, borrow from the next place value. Cross out the number being borrowed from.
- Add the borrowed number to the place value by writing “1” in front of the existing number. See Steps 3 and 4 in the image above for an example.
- Keep subtracting from each place value. Borrow as needed.
- Rewrite the difference in standard form.
Subtraction Strategy #3: Number Line
Using number lines to subtract provides another opportunity to review place value and expanded form.
To solve multi-digit subtraction problems using a number line:
- Draw an open number line.
- Write the minuend on the far right side of the open number line.
- Find the value of the largest place value in the subtrahend. In the example image above, 20,000 is the value of the largest place value in the subtrahend.
- Subtract the value of the largest place value in the subtrahend by counting backward. I usually draw a backward jump and write the subtracted amount inside the jump. Write the difference at the end of the jump. See the image above for an example.
- Repeat by counting backward with each place value from the subtrahend. As you subtract, each jump should get smaller because each place value is smaller.
- The final difference will be written on the left-hand side of the open number line.
Subtracting Multi-Digit Numbers Teaching Resources
I’ve just shared three of my favorite strategies for teaching multi-digit subtraction. I find that if a student is struggling with long subtraction, showing them one of these other strategies for subtracting is often the key to their success.
If you’re looking for even more ways to teach subtracting multi-digit numbers, be sure to check out my Addition and Subtraction Units. Each unit shows six ways to teach addition and five ways to teach subtraction with bigger numbers.
Each unit also comes with everything you need to teach adding and subtracting. You’ll find:
- Detailed lesson plans
- Games and centers
- Foldables and Sorts
- Anchor charts
- Exit tickets
- Digital activities
- Final Test
I have Addition and Subtraction Units for all upper elementary grade levels, covering every large number range that you might be teaching. These adding and subtracting lessons take the stress out of planning by providing everything you need with minimal prep work required.
- Addition and Subtraction Unit within 9,999
- Addition and Subtraction Unit within 99,999
- Addition and Subtraction Unit within 999,999
The long subtraction method isn’t the only method for teaching multi-digit subtraction! If you find students struggling with subtracting using standard algorithm, be sure to try out at least one of the other strategies that I’ve shared here.
I hope you find these subtracting methods and resources to be helpful. Be sure to pin this post for later so that you can access these multi-digit subtracting strategies at any time!