Mental strategies for addition & subtraction
Theory
Mental strategies turn hard calculations into easy ones. This Year 5 maths page explains levelling for addition, constant difference for subtraction, bridging to the next ten, rounding and adjusting, and counting up, with number-line pictures and advice on choosing the best strategy.
Levelling (compensation for addition): move an amount from one number to the other so one becomes a round number. The total stays the same: \(3997 + 486 = 4000 + 483\).
Constant difference (for subtraction): add the same amount to both numbers. The gap between them stays the same: \(6004 - 2998 = 6006 - 3000\).
Bridging: jump to the next ten (or hundred) first, then add the rest. \(56 + 27\) is \(56 + 4 = 60\), then \(60 + 23 = 83\).
Counting up: to subtract two numbers that are close, count up from the smaller to the larger. \(8003 - 7995\): \(5\) up to \(8000\), then \(3\) more, so \(8\).
Round and adjust: add a round number, then fix the extra. \(394 + 278 = 400 + 278 - 6\).
Each strategy keeps the answer the same while making the numbers friendlier:
Levelling for addition
- Find the number closest to a round number and how much it needs.
- Move that amount from the other number.
- Add the new, easier numbers.
Constant difference for subtraction
- Make the number being subtracted round by adding to it.
- Add the same amount to the first number.
- Subtract the new numbers.
Counting up
- Jump from the smaller number to the next round number.
- Jump on to the larger number.
- Add the jumps: that is the difference.
| \(699 + 1\) | \(=\) | \(700\) |
| \(238 - 1\) | \(=\) | \(237\) |
| \(700 + 237\) | \(=\) | \(937\) |
\(699 + 238 = 937\).
| \(3997 + 3\) | \(=\) | \(4000\) |
| \(486 - 3\) | \(=\) | \(483\) |
| \(4000 + 483\) | \(=\) | \(4483\) |
\(4483\).
| \(298 + 2\) | \(=\) | \(300\) |
| \(403 + 2\) | \(=\) | \(405\) |
| \(405 - 300\) | \(=\) | \(105\) |
\(403 - 298 = 105\).
| \(56 + 4\) | \(=\) | \(60\) |
| \(60 + 23\) | \(=\) | \(83\) |
Split \(27\) into \(4 + 23\). The answer is \(83\).
| \(400 + 278\) | \(=\) | \(678\) |
| \(678 - 6\) | \(=\) | \(672\) |
Adding \(400\) adds \(6\) too many, so take \(6\) off: \(672\).
| \(3994 \to 4000\) | \(:\) | \(6\) |
| \(4000 \to 7000\) | \(:\) | \(3000\) |
| \(6 + 3000\) | \(=\) | \(3006\) |
\(7000 - 3994 = 3006\).
| \(397 + 3\) | \(=\) | \(400\) |
| \(65 - 3\) | \(=\) | \(62\) |
| \(400 + 62\) | \(=\) | \(462\) |
Adding \(3\) to both numbers made the total \(6\) too big. The \(3\) must come off the \(65\). The answer is \(462\).
Common pitfalls
Frequently asked questions
What is levelling in addition?
Levelling moves an amount from one number to the other so one becomes a round number. The total does not change: \(699 + 238 = 700 + 237 = 937\).
What is the constant difference strategy?
Add the same amount to both numbers in a subtraction so the second becomes round. The difference stays the same: \(403 - 298 = 405 - 300 = 105\).
What is bridging to ten?
Jump to the next ten first, then add what is left. \(56 + 27\): \(56 + 4 = 60\), \(60 + 23 = 83\).
When should I count up to subtract?
When the two numbers are close together, such as \(8003 - 7995\). Count up \(5\) to \(8000\) and \(3\) more: \(8\).
If I add 2 to one number in levelling, what happens to the other?
Take 2 from the other number, so the total stays the same.