Mental strategies for subtraction
Theory
Mental strategies for subtraction are ways to take one number away from another in your head, without a written column sum. This Year 3 maths page explains the split strategy, jumping back on a number line, bridging to ten, counting up to find the difference, compensation and constant difference for numbers near a ten or hundred. Curriculum: VC2M3A02 / AC9M3A02.
A mental strategy is an easy way to work out a subtraction in your head. Instead of writing a column sum, you break the job into small steps. The best strategy depends on the numbers, so it helps to know a few.
The split strategy breaks the number you take away into tens and ones, then subtracts each part. Bridging means jumping back to the nearest ten first. Counting up finds the difference by counting on from the smaller number, which is quick when the numbers are close.
Compensation rounds the number you take away to an easy ten or hundred, then adjusts the answer. Constant difference moves both numbers up by the same amount, which keeps the difference the same: \(93 - 58\) has the same answer as \(95 - 60\). It also helps to remember that subtraction undoes addition: because \(34 + 16 = 50\), you know \(50 - 34 = 16\).
Mental subtraction has no formula, but these facts are what make the strategies work.
How to subtract in your head
- Look at the numbers. If they are close together, count up from the smaller number to find the difference. If they are far apart, plan to take the second number away in parts.
- Break it into easy steps. Use the split strategy (tens then ones) or jump back on a number line. Bridging to the nearest ten first keeps each step simple.
- Use compensation near a ten. If you take away a number like \(29\) or \(99\), take away the round ten or hundred, then add the extra back.
- Or keep the difference constant. Add the same amount to both numbers so the second one becomes a round number. \(93 - 58\) becomes \(95 - 60 = 35\).
| \(80 - 50\) | \(=\) | \(30\) |
| \(6 - 2\) | \(=\) | \(4\) |
| \(30 + 4\) | \(=\) | \(34\) |
So \(86 - 52 = 34\).
Split the \(7\) into \(2\) and \(5\) so you land on \(50\).
| \(52 - 2\) | \(=\) | \(50\) |
| \(50 - 5\) | \(=\) | \(45\) |
So \(52 - 7 = 45\).
| \(57 + 3\) | \(=\) | \(60\) |
| \(60 + 2\) | \(=\) | \(62\) |
| \(3 + 2\) | \(=\) | \(5\) |
The difference is \(5\), so \(62 - 57 = 5\).
\(99\) is \(1\) less than \(100\). Take away \(100\), then add \(1\) back.
| \(253 - 100\) | \(=\) | \(153\) |
| \(153 + 1\) | \(=\) | \(154\) |
So \(253 - 99 = 154\).
Common pitfalls
Frequently asked questions
What are mental strategies for subtraction?
They are ways to subtract in your head without a written column sum. Common ones are the split strategy, jumping back on a number line, bridging to ten, counting up to find the difference, and compensation. You pick the strategy that fits the numbers.
What is the split strategy for subtraction?
The split strategy breaks the second number into tens and ones. Take the tens away, take the ones away, then add the two results. For \(86 - 52\), work out \(80 - 50 = 30\) and \(6 - 2 = 4\), then \(30 + 4 = 34\).
How do you use bridging to subtract?
Bridging means jumping back to the nearest ten first. For \(52 - 7\), take away \(2\) to land on \(50\), then take away the other \(5\) to reach \(45\). Splitting the number you subtract so you stop on a ten makes the second step easy.
What is compensation in subtraction?
Compensation rounds the number you take away to an easy ten or hundred, then adjusts. For \(253 - 99\), take away \(100\) to get \(153\), then add \(1\) back because you took away \(1\) too many, giving \(154\).
What is the constant difference strategy?
Add the same amount to both numbers so the number you take away becomes a round ten or hundred. The difference does not change. For \(93 - 58\), add \(2\) to both numbers to get \(95 - 60\), which is \(35\).
How do you find the difference between two numbers?
When two numbers are close together, count up from the smaller number to the larger one. For \(62 - 57\), count on from \(57\): \(3\) more makes \(60\), then \(2\) more makes \(62\), so the difference is \(5\).
How is subtraction related to addition?
Subtraction undoes addition, so every subtraction has a matching addition fact. Because \(34 + 16 = 50\), you know \(50 - 34 = 16\). This helps you find a missing number by adding back.