Mental maths strategies explained for parents (Australia)

You ask your Year 3 child what 46 + 29 is while you're stuck at the lights. There's a long pause, some finger tapping on the car seat, and finally "Can I get a pencil?" Meanwhile the teacher's newsletter says the class is "working on mental strategies", and you're not sure whether that means memorising more facts or something else entirely.

Mental maths isn't about being a human calculator. It's knowing a few ways to pull numbers apart and rebuild them so a sum is easy to hold in your head. A child with good strategies thinks "46 + 30 is 76, take away the extra 1, so 75" in a couple of seconds.

This guide walks through the main strategies Australian classrooms teach for adding, subtracting, multiplying and dividing in your head, how children choose between them, what the curriculum expects from Prep to Year 6, and short games that build the habit at home.

What "mental maths" really means

When parents hear the phrase, many picture times tables chanted at speed. Quick recall of facts is part of the picture, but schools now separate two things:

• Known facts are answers a child simply remembers, such as 6 + 4 = 10 or 5 × 3 = 15.
• Strategies are ways to work out an answer you don't remember by linking it to facts you do.

A child who knows 7 + 7 = 14 can use it to work out 7 + 8 without counting. That jump from a remembered fact to a new answer is what teachers mean by a mental strategy. It's flexible thinking, and it grows stronger every time your child explains how they got there.

Speed follows on its own. Pushing for quick answers too early tends to produce hidden finger counting, guessing or worry.

The building blocks underneath

Every strategy in this guide leans on three foundations. If one is shaky, the strategies feel like tricks instead of common sense.

1. Pairs that make ten. Knowing 3 and 7, 4 and 6, 8 and 2 without thinking. The guide to number bonds covers how these are taught.
2. Doubles. 5 + 5, 6 + 6, up to 10 + 10, then doubles of tens such as 30 + 30. These unlock near-doubles and fast multiplication. See doubling and halving.
3. Place value. Understanding that 46 means 4 tens and 6 ones, so it can be split into 40 and 6. The place value guide explains why this matters so much.

Strategies for adding in your head

Start from the larger number

For 3 + 9, starting at 9 and counting on three is much quicker than starting at 3 and counting on nine. Young children often don't realise they're allowed to swap the order. The page on putting the bigger number first shows how to make this click.

Bridge through ten

Faced with 8 + 5, borrow 2 from the 5 so the 8 becomes 10. Now it's 10 + 3, which is 13. The same move works with bigger numbers: 47 + 6 becomes 47 + 3 + 3, so 50 + 3, which is 53. There's a full walk-through in make ten and bridging.

Use a nearby double

For 7 + 8, think "7 + 7 is 14, and one more is 15". For 25 + 26, think "25 + 25 is 50, plus 1, so 51". Children who know their doubles love this one because it feels like a shortcut.

Split by place value

For 36 + 27, add the tens (30 + 20 = 50), add the ones (6 + 7 = 13), then join them: 50 + 13 = 63. Many teachers call this the split strategy. It's explained step by step in split, add, join and in the broader guide to partitioning.

Jump along a number line

Keep the first number whole and add the second in hops. For 36 + 27: 36 + 20 = 56, then 56 + 4 = 60, then 60 + 3 = 63. Sketching the hops on a blank line helps children keep their place. See the empty number line guide.

Round and adjust (compensation)

When a number sits just below a ten or a hundred, round it, add, then fix the difference. For 46 + 29, add 30 to get 76, then take 1 away: 75. For 99 + 47, add 100 to get 147, then take 1 away: 146. This is often the fastest strategy of all for numbers ending in 8 or 9.

Strategies for subtracting in your head

Many children believe subtraction means counting backwards, one by one. There are friendlier options.

Think of it as adding

To solve 13 − 8, ask "8 plus what makes 13?" Knowing 8 + 5 = 13 gives the answer. This connection between adding and taking away is the heart of fact families.

Count up to find the gap

For 52 − 47, the numbers are close together, so count up from 47: three to reach 50, then two more to reach 52. The gap is 5. Picture it as the distance between two houses on a street rather than as "taking away".

Jump back

For 74 − 32, take away 30 to reach 44, then take away 2 to reach 42. This mirrors the number line jumps used for adding.

Round and adjust

For 83 − 19, take away 20 to get 63. You took away one too many, so give 1 back: 64. For 63 − 28, take away 30 to get 33, then add 2 back: 35. The adjusting direction often gets muddled at first.

Keep the difference the same

For 62 − 38, add 2 to both numbers: 64 − 40. The gap between them hasn't changed, and 64 − 40 = 24 is easy.

More on the meaning of subtraction sits in the subtraction guide.

Strategies for multiplying and dividing in your head

Once times tables start, the same "use what you know" thinking carries straight over.

• Double, then double again for ×4. 6 × 4: double 6 is 12, double 12 is 24.
• Double three times for ×8. 7 × 8: 14, 28, 56.
• Times ten, then halve for ×5. 16 × 5: 16 × 10 is 160, half of that is 80.
• Times ten, then take one group away for ×9. 9 × 7: 10 × 7 is 70, minus 7 is 63.
• Split one number. 7 × 14: 7 × 10 is 70, 7 × 4 is 28, and 70 + 28 is 98.
• Use quarters of a hundred. 25 × 4 is 100, so 25 × 12 is three lots of 100: 300.
• Halve and halve again to divide by 4. 84 ÷ 4: half of 84 is 42, half of 42 is 21.
• Turn division into a missing multiplication. 56 ÷ 8 becomes "8 times what is 56?" The answer is 7.

Patterns for tens, hundreds and thousands have their own page: multiplying and dividing by powers of ten, and fact recall in times tables explained.

Strategy cheat sheet

Choosing the right strategy

Here's the part that surprises many parents: there is no single correct strategy. Strong mental calculators glance at the numbers first, then pick the move that fits.

Compare these two:

• 48 + 35 suits rounding: 50 + 35 is 85, minus 2 is 83.
• 42 + 35 suits splitting: 70 + 7 is 77.

Ask "What do you notice about these numbers?" before your child starts. Spotting a 9, a near double or a small gap is a skill teachers value highly.

Different children solving one problem in different ways is fine. Show a quicker path afterwards without calling their way wrong.

Talking about strategies at home

The single most useful question you can ask is "How did you work that out?" Asking it after right answers and wrong ones keeps it from feeling like a trap.

• Let them talk first, before offering your own method.
• Write it the way they say it. "I did 40 and 30, then 6 and 9" becomes 40 + 30 = 70, 6 + 9 = 15, 70 + 15 = 85 on paper.
• Praise the reasoning. "I like how you used the double" lands better than "Good, that's right."

The guide to estimating before you add pairs well with this: a quick estimate tells a child whether their mental answer is sensible. For 298 + 405, both numbers round to give about 700, so an answer of 703 looks right and 7003 clearly doesn't. Rounding skills themselves are covered in rounding numbers.

Where mental strategies sit in the curriculum

Written methods such as column addition and column subtraction still arrive later; strong mental strategies make them easier to understand and check.

Calculation strategies run right through Number in the Australian Curriculum: Mathematics, version 9. In Year 1, students add and subtract within 20 using materials, part-part-whole reasoning and a variety of calculation strategies. Year 2 extends this to one- and two-digit numbers, with problems written as number sentences.

Year 3 asks students to add and subtract two- and three-digit numbers by using place value to partition, rearrange and regroup, without a calculator. Multiplication and division of one- and two-digit numbers also bring in a range of calculation strategies. In Year 4, students know multiplication facts to 10 × 10 by heart and develop efficient strategies for solving problems with all four operations. Years 5 and 6 focus on choosing efficient strategies for larger numbers and checking whether answers are reasonable through estimation and rounding. Victoria's Curriculum 2.0 is closely matched, while schools decide the order of topics across each year.

Mental maths from Prep to Year 6

Prep: counting on, knowing small numbers by sight, early pairs that make five and ten.

Years 1–2: bonds to ten and twenty, doubles, counting on from the larger number, bridging through ten, adding tens. Overviews: Year 1, Year 2.

Years 3–4: split and jump strategies with two- and three-digit numbers, rounding and adjusting, times tables built from doubles and tens. Guides for these years: Year 3, Year 4.

Years 5–6: choosing between strategies, multiplying larger numbers mentally, estimating to check, working with decimals and fractions in the head. More detail: Year 5, Year 6.

Five quick games for car trips and kitchen benches

1. Make it ten. Call out a number from 1 to 9; your child shouts its partner to make ten. Move up to partners for 20, then for 100.
2. Double trouble. Take turns naming a number and doubling it. Go as high as you can before someone hesitates.
3. Shopping round-up. At the shops, round two prices to the nearest dollar and add them in your head before checkout.
4. Two ways. Pick a sum such as 38 + 24. Each person must find a different way to solve it, then explain theirs.
5. Target 100. Start at any number under 50. Take turns adding a single-digit or tens amount, saying the new total each time. Whoever lands exactly on 100 wins.

Five playful minutes beat a long session that ends in tears; homework without tears has more ideas.

Common slips and what helps

Counting by ones for everything. Your child counts on fingers even for 9 + 6. Return to bonds and doubles, and model one bridging example out loud.

Adjusting the wrong way. For 46 + 29 they add 30, then add 1 instead of subtracting it. Use coins: "I paid 30 cents but it only cost 29, so I get 1 back."

Losing track halfway. They split the numbers but forget a part. Let them jot down the middle step; mental maths can use a scrap of paper while confidence grows.

Mixing up tens and ones. Adding 30 + 7 and getting 10. That usually points to place value, so revisit tens and ones with bundles of sticks or money.

Freezing under time pressure. Some children know a strategy but blank when rushed. Drop the timer for a while; it's accuracy and explanation that build lasting skill.

If mental maths stays hard

If a Year 3 or 4 child is still counting every step on fingers, can't hold a number in their head for a moment or becomes very upset whenever maths comes up, talk to the teacher.

These guides go further on bigger concerns: signs a child may be behind in maths and maths anxiety in children. This page can't assess your own child; ongoing difficulty with number is best discussed with the school or a qualified professional.

FAQ

Should my child still use fingers for maths?

Fingers are a normal step for young children. The aim is to move beyond counting every single one, using bonds, doubles and tens instead. Don't ban fingers; give your child better tools so they need them less.

What is the compensation strategy?

It means rounding one number to make the calculation easier, then adjusting the answer. For 46 + 29, add 30 to get 76, then subtract the extra 1 to get 75.

One question for this week

Next time a sum pops up naturally, at the shop or while cooking, ask it, wait, then ask "How did you work that out?" Listen without correcting and share your own way afterwards.

If you'd like a broader view of where your child's maths sits, Ziado offers a free check that runs at home in about ten minutes. The questions change based on your child's answers, a portion of the results shows up right away with no account or card required, and signing up unlocks the full placement. Mental strategies aren't given their own separate score, the check isn't designed around NAPLAN, and it doesn't diagnose dyscalculia or any learning or health condition. To see how ongoing practice works, head to Ziado maths; you can try either the Individual or Family plan free for a fortnight, and prices are listed on the pricing page.