Mental Maths Strategies for Kids: Partitioning, Bridging and More

Mental maths isn't about being fast or being "a natural". It's about having a few reliable strategies and knowing which one suits the numbers in front of you. A child who knows that 46 + 29 is the same as 46 + 30 − 1 doesn't need to be quick; they just need to see it. Here are the five strategies that do most of the work in primary school, each with worked examples and what to say to your child.

The foundation: number bonds#

Before any strategy works, children need instant recall of the pairs that make 10:

0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5

"Instant" means no counting, the way you'd know your own phone number. These bonds then scale up:

• If 3 + 7 = 10, then 30 + 70 = 100 and 13 + 7 = 20.
• If 6 + 4 = 10, then 0.6 + 0.4 = 1.
• Bonds to 100 in tens and ones: 37 + 63 = 100, because 30 + 60 = 90 and 7 + 3 makes one more ten.

Practise bonds in tiny bursts. Hold up fingers and ask "How many more to make 10?" Play "I say 4, you say…" ("6!") at the bus stop. Our number sense collection has printable bond games for younger children.

Strategy 1: Partitioning#

What it is: splitting numbers into tens and ones (or hundreds, tens and ones), working with each part, then putting them back together.

Worked examples

• 46 + 37 → 40 + 30 = 70, and 6 + 7 = 13, so 70 + 13 = 83
• 87 − 34 → 87 − 30 = 57, then 57 − 4 = 53
• 23 × 4 → 20 × 4 = 80, and 3 × 4 = 12, so 80 + 12 = 92
• 156 + 230 → 156 + 200 = 356, then + 30 = 386

Say this: "Can you split one of the numbers into tens and ones?"

Watch out for: subtraction where the ones won't go. With 62 − 27, partitioning both numbers gives 60 − 20 = 40 and 2 − 7, which stops children in their tracks. Partition only the second number instead: 62 − 20 = 42, then 42 − 7 = 35. Or use counting up (below).

Partitioning is also the bridge to written methods later. The column method is really just partitioning, written down neatly.

Strategy 2: Bridging through 10#

What it is: when an addition or subtraction crosses a tens boundary, stopping at the ten on the way. It relies completely on number bonds.

Worked examples

• 8 + 5 → 8 + 2 = 10, then + 3 = 13 (split the 5 into 2 and 3)
• 47 + 8 → 47 + 3 = 50, then + 5 = 55
• 53 − 7 → 53 − 3 = 50, then − 4 = 46
• 196 + 7 → 196 + 4 = 200, then + 3 = 203

Say this: "How far is it to the next ten?"

A useful relative of bridging is counting up for subtraction, especially when the numbers are close together. Think of it as finding the gap:

• 82 − 57 → from 57 to 60 is 3, from 60 to 80 is 20, from 80 to 82 is 2. 3 + 20 + 2 = 25
• 1,003 − 996 → 996 to 1,000 is 4, then 3 more. 7

It's also exactly how you work out time intervals. From 9:45 to 11:20 is 15 minutes to 10:00, an hour to 11:00, and 20 more minutes: 1 hour 35 minutes. Change from a shop works the same way.

Strategy 3: Compensation (round and adjust)#

What it is: rounding one number to something easy, calculating, then correcting for the change. It's the strategy that makes "awkward" numbers like 9, 19, 99 and 4.99 easy.

Worked examples

• 46 + 29 → 46 + 30 = 76, but that's 1 too many, so 76 − 1 = 75
• 83 − 19 → 83 − 20 = 63, but we took away 1 too many, so 63 + 1 = 64
• 6 × 19 → 6 × 20 = 120, but that's 6 too many, so 120 − 6 = 114
• 3 items at 4.99 → 3 × 5 = 15, minus 3 × 0.01, so 14.97

Say this: "Is either number close to a ten or a hundred? What would be easier?"

Watch out for: the sign of the correction in subtraction. This is the commonest mental maths mistake in the later primary years. With 83 − 19, children round to 20, subtract, and then subtract 1 again because "it was 1 less". Ask them to explain it with money: "If I take away 20 pounds instead of 19, I've taken 1 pound too many. Do I need to give it back or take another?"

Strategy 4: Doubling and near doubles#

What it is: using known doubles to work out facts that are close to them, or to multiply by 2, 4 and 8.

Worked examples

• 7 + 8 → double 7 is 14, plus 1 more = 15
• 25 + 26 → double 25 is 50, plus 1 = 51
• 35 × 4 → double 35 is 70, double 70 is 140
• 13 × 8 → double 13 = 26, double = 52, double = 104
• 150 + 149 → double 150 is 300, minus 1 = 299

Say this: "Do you know a double close to that?"

Doubles are often the first facts children know by heart, which makes this one of the earliest strategies they can use. Young children enjoy doubling with mirrors: put three counters in front of a mirror and see six.

Strategy 5: Halving, and halve-and-double#

What it is: using halving to make multiplication easier, especially with 5, 25 and 50.

Worked examples

• 5 × 48 → 10 × 48 = 480, half of that is 240 (multiplying by 5 is multiplying by 10 and halving)
• 16 × 25 → halve one, double the other: 8 × 50 = 4 × 100 = 400
• 14 × 15 → 7 × 30 = 210
• Half of 76 → half of 70 is 35, half of 6 is 3, so 38

Say this: "Can you make one of the numbers easier by doubling it, if you halve the other?"

Halve-and-double works because you're rearranging the same amount: 16 groups of 25 is the same as 8 groups of 50. Show it with an array of counters, cut in half and placed side by side, if your child is unconvinced. Secure times tables make this strategy much more useful.

Choosing a strategy#

The best mental mathematicians look at the numbers first, then choose. Show your child this table and ask them which strategy they would use before they start each calculation.

There is rarely one right strategy. 64 + 39 can be done by partitioning, bridging or compensation, and all three get 103. What matters is that your child has a choice.

As a rough guide to when each strategy usually appears (school years and curricula vary by country):

• Ages 5–7: number bonds to 10, doubles to 10 + 10, counting on, bridging single-digit additions like 8 + 5.
• Ages 7–9: partitioning 2-digit numbers, bridging through tens, near doubles, counting up for subtraction, adding and subtracting 9 and 11 by compensation.
• Ages 9–11: compensation with larger numbers and money, halving and doubling for multiplication, all of the above with decimals (0.7 + 0.3 = 1, so 2.7 + 1.3 = 4).

If your child is older but missing an earlier step, go back to it without fuss. A 10 year old who doesn't have instant bonds to 10 will find every later strategy harder, and a few weeks on bonds will make more difference than more practice of the advanced methods.

How to practise without drilling#

Mental maths improves with short, regular talk about how answers were found, more than with timed sheets.

Teachers often call this a "number talk", and it works just as well at home. Hearing three different methods for the same sum is worth more than doing twenty sums one way.

Other quick practice ideas:

• Target 100: roll two dice to make a 2-digit number. Keep adding rolls mentally. First to get within 5 of 100 without going over wins.
• Shop prices: "If I buy both, how much is that?" in a real shop, or with a catalogue at home.
• The numbers game: pick six number cards and a target number between 100 and 500. Use any operations to get as close as you can.
• Short practice sheets: our mental maths worksheets have ten-question sets grouped by strategy.

For more everyday chances to use these strategies, from recipes to bus timetables, see our guide to everyday maths at home. Younger children who are still building early addition can start with our addition pages.

Choose one strategy this week, show it with three examples, and then ask your child to make up a problem for you to solve the same way. If they can invent a problem that suits the strategy, they understand it.