Mental strategies for addition
Theory
Mental strategies for addition are quick ways to add in your head, taught in Year 3 maths. This page explains the split strategy, the jump strategy on a number line, bridging to ten, compensation, levelling, making a ten and turn-around facts, so students can pick the easiest way to add. Curriculum: VC2M3A02 / AC9M3A02.
A mental strategy is a way to add numbers in your head, without writing them one under the other. You break the numbers into friendly parts and add them step by step.
The split strategy breaks each number into tens and ones, then adds the tens and ones separately. The jump strategy keeps the first number whole and jumps on in parts, often shown on a number line. Bridging to ten fills up to the next ten first, and compensation adds a tidy ten and then adjusts. Levelling moves a little from one number to the other so that one of them becomes a tidy number; the total does not change.
A turn-around fact reminds you that you can add two numbers in either order: \(8 + 35\) gives the same answer as \(35 + 8\). Starting with the bigger number often makes the adding easier.
How to add two numbers in your head
- Look at the numbers. Notice if one is close to a tidy ten (like 19 or 39), or if both are two-digit numbers.
- Break a number into easy parts. Split it into tens and ones, or round it up to the next tidy ten to make the adding simple.
- Add step by step, then adjust. Add the parts one at a time. If you rounded up, take off the extra at the end.
More handy strategies
- Make a ten first. When you add three numbers, look for two that make a tidy ten, such as \(3 + 7\) or \(13 + 7\), and add those first. You can add numbers in any order. Brackets show the pair you add first: \((13 + 7) + 18\) means add \(13 + 7\) first.
- Add tens and hundreds like ones. For \(430 + 260\), add the hundreds (\(400 + 200\)) and the tens (\(30 + 60\)), then join them.
- Add 9, 19 or 99 by rounding. Add \(10\), \(20\) or \(100\) instead, then take \(1\) off.
- Levelling. If one number is just below a tidy hundred, move a few from the other number to fill it up: \(297 + 38\) becomes \(300 + 35\).
- Missing numbers. To find what makes a total like \(100\), count on from the first number: first to the next tidy ten, then by tens to the total.
| \(50 + 30\) | \(=\) | \(80\) |
| \(3 + 4\) | \(=\) | \(7\) |
| \(80 + 7\) | \(=\) | \(87\) |
Add the tens, add the ones, then join the parts: \(53 + 34 = 87\).
| \(43 + 30\) | \(=\) | \(73\) |
| \(73 + 5\) | \(=\) | \(78\) |
Keep \(43\) whole, jump the tens, then the ones: \(43 + 35 = 78\).
| \(67 + 3\) | \(=\) | \(70\) |
| \(70 + 5\) | \(=\) | \(75\) |
Split the \(8\) into \(3 + 5\): the \(3\) fills up to \(70\), then add \(5\).
| \(27 + 20\) | \(=\) | \(47\) |
| \(47 - 1\) | \(=\) | \(46\) |
\(19\) is one less than \(20\), so add \(20\) then take \(1\) off: \(\$46\).
| \(13 + 7\) | \(=\) | \(20\) |
| \(20 + 18\) | \(=\) | \(38\) |
\(13\) and \(7\) make a tidy \(20\), so add them first, then add \(18\): \(38\).
| \(63 + 7\) | \(=\) | \(70\) |
| \(70 + 30\) | \(=\) | \(100\) |
| \(7 + 30\) | \(=\) | \(37\) |
Count on to the next ten, then to \(100\). The missing number is \(37\).
| \(400 + 200\) | \(=\) | \(600\) |
| \(30 + 60\) | \(=\) | \(90\) |
| \(600 + 90\) | \(=\) | \(690\) |
Add the hundreds, add the tens, then join them: \(690\).
| \(57 + 100\) | \(=\) | \(157\) |
| \(157 - 1\) | \(=\) | \(156\) |
\(99\) is \(1\) less than \(100\), so take \(1\) off: \(57 + 99 = 156\).
| \(297 + 3\) | \(=\) | \(300\) |
| \(38 - 3\) | \(=\) | \(35\) |
| \(300 + 35\) | \(=\) | \(335\) |
Move \(3\) from \(38\) to \(297\) to make a tidy \(300\). The total stays the same: \(297 + 38 = 335\).
Common pitfalls
Frequently asked questions
What is a mental strategy for addition?
A mental strategy is a way to add numbers in your head, without writing them in a column. You break the numbers into easy parts and add them step by step.
What is the split strategy?
The split strategy breaks each number into tens and ones. Add the tens, add the ones, then join the two parts. For \(53 + 34\), \(50 + 30 = 80\) and \(3 + 4 = 7\), so the answer is \(87\).
What is the jump strategy for addition?
The jump strategy keeps the first number whole and jumps on in parts, often on a number line. For \(43 + 35\), start at \(43\), jump \(30\) to reach \(73\), then jump \(5\) to land on \(78\).
What does bridging to ten mean?
Bridging to ten means filling up to the next ten first. For \(67 + 8\), add \(3\) to make \(70\), then add the other \(5\) to get \(75\).
What is the compensation strategy?
Compensation adds a tidy ten and then adjusts. For \(64 + 29\), add \(30\) to get \(94\), then take \(1\) off because \(29\) is one less than \(30\), giving \(93\).
How do I choose which addition strategy to use?
Look at the numbers first. Use compensation when a number is near a tidy ten like \(19\) or \(99\), use bridging when adding a small number crosses a ten, and use the split or jump strategy for two two-digit numbers. Any strategy that gives the right answer is fine.
What is levelling in addition?
Levelling moves an amount from one number to the other to make a tidy number. For \(497 + 26\), move \(3\) across: \(500 + 23 = 523\). Both sums have the same total.