Mental strategies for addition & subtraction
Theory
A mental strategy rewrites a calculation as an easier one with the same answer. Levelling makes a round number in addition; constant difference shifts both numbers in a subtraction so the gap stays the same.
A mental strategy rewrites a calculation as an easier one that has exactly the same answer.
Levelling is for addition: move an amount from one number to the other to make a round number, adding to one and taking the same from the other.
Constant difference is for subtraction: add the same amount to both numbers. The gap between them stays the same, so the answer does too.
Two strategies rewrite a calculation as an easier one with the same answer:
| Strategy | Use for | What to do |
|---|---|---|
| Levelling | addition | add to one, take the same from the other |
| Constant difference | subtraction | add the same to both numbers |
How to use these strategies
- Look for a number close to a round number (like \(198\) or \(3997\)).
- Levelling: for addition, add to one number and take the same from the other.
- Constant difference: for subtraction, add the same amount to both numbers, then work out the easier calculation.
| \(198 + 47\) | \(=\) | \(200 + 45\) |
| \(=\) | \(245\) |
Add \(12\) to \(4988\), take \(12\) from \(955\).
| \(4988 + 955\) | \(=\) | \(5000 + 943\) |
| \(=\) | \(5943\) |
Add \(1\) to both numbers.
| \(302 - 199\) | \(=\) | \(303 - 200\) |
| \(=\) | \(103\) |
Add \(3\) to both numbers.
| \(5009 - 3997\) | \(=\) | \(5012 - 4000\) |
| \(=\) | \(1012\) |
Common pitfalls
Frequently asked questions
What is levelling in addition?
Levelling moves an amount from one number to the other to make a round number. \(198+47\) becomes \(200+45=245\).
What is constant difference?
In subtraction, adding the same amount to both numbers keeps the difference the same. \(302-199\) becomes \(303-200=103\).
Why does constant difference work?
The answer to a subtraction is the gap between the two numbers. Moving both the same way keeps that gap unchanged.
When should you use a mental strategy?
When one number is close to a round number, so a small adjustment makes the calculation easy to do in your head.