The Mental Math Strategies Your Kid Is Being Taught, in Plain English

For families 23 October 2026

Your kid's worksheet says "use compensation." You know the answer. You have no idea what compensation is. Here is the whole list.

The homework says: Use compensation to find 36 + 19.

You know it is 55. You have known it was 55 since roughly 1991. What you do not know is what compensation is, why the sheet is asking for it, or why the answer alone is apparently not the point any more.

So you show your kid the way you were taught. Stack them up, nine and six is fifteen, carry the one. And your kid — who is eight, and certain — tells you that is not how they do it.

Here is the thing nobody puts on the worksheet: you already use almost every strategy on that page. You use them in restaurants and supermarkets and whenever you work out whether something is actually a deal. You have just never seen them written down, because when you were at school nobody named them. They were what the kids who were quick at mental math did in their heads, silently, and the rest of us assumed it was a talent rather than a method.

The names are new. The methods are not.

The one piece of research worth knowing first

In 2015, researchers at the University of Chicago followed 438 first- and second-graders and their parents across a school year. They measured the children's math achievement and the parents' math anxiety, and they asked how often parents helped with math homework.

Children of math-anxious parents learned less math across the year, and became more math-anxious themselves.

But only in one condition: when those anxious parents frequently helped with the homework. Where anxious parents stayed out of it, the effect did not appear. Reading achievement was unaffected either way, which rules out a lot of the obvious alternative explanations.

That is an uncomfortable finding and it is easy to take the wrong lesson from it. The lesson is not don't help. It is that anxiety is contagious, it travels down the pencil during homework, and the fix is not to help more or less but to change what helping looks like.

Which is mostly what this page is for. It is much harder to be anxious about a method you understand.

The early ones

Roughly Grades 1 to 3.

Making ten

What it is: move a bit from one number to the other so one of them becomes 10, because 10 is easy.

7 + 5. Take 3 off the 5 and give it to the 7. Now it is 10 + 2. Twelve.

Why it exists: adding to 10 is instant for almost everyone, and this converts a fact a child has to remember into one they can see. It is the first real strategy most children meet, and nearly everything later is built on it.

What it's called where: making 10 in Alberta and Ontario. British Columbia writes it as making or bridging 10. Quebec's program talks about 5 and 10 as anchor points — points d'ancrage — which is the same idea with different furniture.

Bridging ten

What it is: making ten's twin, for when you are going the other way, or crossing a ten rather than landing on it.

15 − 7. Go down to 10 first, which costs 5. You still have 2 left to take off. Eight.

43 + 9. Go up to 50, which costs 7. Two left over. Fifty-two.

Why it exists: it turns every crossing of a ten into two easy steps instead of one hard one, and it is the engine under most two-digit mental arithmetic for the rest of a child's life.

Doubles and near doubles

What it is: children learn doubles fast — 6 + 6, 8 + 8 — and then use them as anchors for everything nearby.

7 + 8 is double 7 plus one, or double 8 minus one — whichever the child sees first.

Why it exists: it is memory doing real work. A dozen memorised facts cover thirty or forty more.

Worth knowing: there is a lovely variant for numbers two apart. 6 + 8 is double the number in between — double 7, fourteen. Children usually find this one themselves and are delighted by it.

The two-digit ones

Roughly Grades 3 to 5.

Compensation

The one on your homework sheet. Also the one you use most often without knowing it.

What it is: round an awkward number to an easy one, do the easy sum, then undo the difference.

36 + 19. Nineteen is awkward. Twenty is not. Add 20 to get 56, then give one back. 55.

You already do this. When something costs $4.99 and you think "that's five dollars, near enough," that is compensation. When you add $12.98 and $7.99 by calling them $13 and $8 and taking three cents off at the end — compensation.

It works for multiplication too. 7 × 9 is 7 × 10 less one seven: 70 − 7 = 63. That is why the nine times table feels easier than the sevens. It isn't; it just has a better trick.

What it's called where: Alberta and Ontario both use the word compensation exactly. BC writes compensating. It is one of the most consistently named strategies across Canada, which is a decent sign that it earns its place.

Decomposing

What it is: break numbers into friendly parts, handle the parts, put them back.

46 + 38. Forty and thirty is seventy. Six and eight is fourteen. Seventy and fourteen is 84.

Why it exists: it is what the stacked column method is doing, but visibly, in an order that makes sense out loud, and without the carried digit that so many children write down and then cannot explain.

What it's called where: every province names this one, often from Grade 1. You will also see partitioning, and in Ontario's wording, decomposing turns up in the expectations very early.

Counting up

What it is: stop subtracting. Find the gap instead.

72 − 45. Do not take 45 away from 72. Start at 45 and walk up. Forty-five to fifty is 5. Fifty to seventy is 20. Seventy to seventy-two is 2. Five, twenty, two — 27.

Why it exists: a cashier handing you change has never once borrowed from the tens column. They count up from the price to the note, because it is faster and almost impossible to get wrong. The number you end up with has a name worth using at home: the difference.

This is the single most useful one on the list for anyone who finds subtraction unpleasant, and it is the one adults adopt most readily once they see it.

The multiplication ones

Roughly Grades 4 to 7.

Halving and doubling

What it is: multiply by the easy relative, then adjust.

× 5 is always half of × 10. 14 × 5? Fourteen times ten is 140. Half is 70.

× 4 is double, then double again. × 8 is three doublings — 7, 14, 28, 56.

Why it exists: doubling is the one multiplication nearly everyone can do without thinking, so the whole times table can be reached by repeated doubling from a handful of starting points.

What it's called where: Alberta names halving, doubling, repeated doubling directly, and Manitoba uses nearly identical wording. Ontario gets to the same place with the phrase double and double again, which is friendlier out loud.

Breaking a factor apart

What it is: split one of the numbers into two easy pieces, multiply both, add them.

8 × 15 is 8 × 10 plus 8 × 5. Eighty and forty. 120.

7 × 12 is 7 × 10 plus 7 × 2. Seventy and fourteen. 84.

Why it exists: it makes every two-digit multiplication reachable without paper, and it is the same move as the long multiplication algorithm — just done in an order you can say.

The name: this is the distributive property, which sounds like university and is in fact what your child is doing in Grade 5. Worth saying the words at some point, because that phrase comes back in algebra and it is nice to meet it as an old friend.

The grown-up ones

Grades 6 and up, and useful for the rest of your life.

Benchmark percentages

What it is: get 10%, then build everything else out of it.

10% is a decimal point moved one place left. Everything useful comes from there:

5% is half of 10%
15% is 10% plus half of it
20% is 10% doubled
1% is 10% of 10%, so 13% is 10% plus 1% three times

A 15% tip on $43. Ten percent is $4.30. Half of that is $2.15. Together, $6.45.

This is not a shortcut invented by a blog. Ontario names the method directly in Grade 6, and the Grade 7 material works it out on the page: to find 5% of 72, find 10% of 72 and then halve it — 7.2 ÷ 2 = 3.6. The thing you may have thought was your own private restaurant trick is, as of a few years ago, on the curriculum.

Common denominators and equivalent fractions

What it is: two fractions with different bottom numbers cannot be compared until they share one.

Which is bigger, 5/8 or 3/5? Eight and five both go into 40. 5/8 becomes 25/40; 3/5 becomes 24/40. 5/8 wins, by a fortieth.

The words: the bottom number is the denominator — how many parts the whole is cut into. The top is the numerator — how many of those parts you are taking. Forty is the common denominator; 25/40 and 5/8 are equivalent fractions.

Why this one matters more than it looks: a large study tracking children in the US and UK found that how well a child handled fractions and division at around age 10 predicted their algebra achievement in high school — still holding up after accounting for IQ, working memory and family income. Fractions are not one topic among many. They are the gate.

Unit rate

What it is: work out what one of something costs, then compare.

Not just per item — per year, per use, per wear. $800 boots that last four winters cost $200 a winter. $300 boots that last one cost $300. The expensive ones are cheaper.

A caution on the name: Ontario says unit rate; BC says unit price. If you use one and your child has been taught the other, that is a vocabulary gap, not a math one.

So what do you actually do with this

Not a worksheet. That is the one thing the research is clearest about.

The useful version is smaller and much less formal: say these out loud when they come up naturally. Work out the tip at the table and narrate it. Ask which pack is the better deal in the aisle and let them argue. When they get one wrong, say which method would have caught it rather than which digit was wrong.

Two things make that work better than it sounds.

Do the math yourself, badly, in front of them. A parent who is visibly working something out — and occasionally getting it wrong and fixing it — is teaching the thing that actually transfers, which is that being stuck is a normal step and not a verdict.

Play rather than test. The difference between "what's 15% of 40?" and both of you racing to get it is entirely in who is being measured. In the first, your child is. In the second, nobody is.

That is the whole idea behind the Numbers game we are building at Coroplay — a board of questions you play with your kids rather than at them, where the parent is a player and not the examiner, and where the hints name these strategies properly so everyone picks up the vocabulary on the way through. It is not required. Any of the above works at a dinner table with no equipment at all.

But if you have ever stood in a kitchen holding a worksheet that said use compensation and quietly wondered when math changed — it did not. It just started telling you what it was doing.

Strategy names in this piece are drawn from the published curriculum documents of Alberta, Ontario, British Columbia and Quebec. Where provinces use different words for the same method, both are given — the method is identical, and the gap is only ever vocabulary.