Every maths trick your child learns is a bet. Either it deepens how they see numbers, or it papers over the fact that they don't. The trouble is that both kinds of trick look identical in week one: the child gets the answer, faster than before, and everyone is pleased.
The difference only shows up later — sometimes two grades later — when the trick meets a problem it wasn't built for. The child who understood why it worked adapts; the child who only memorised the moves is stranded, usually in front of a test, usually concluding they are bad at maths. They aren't. They were sold a shortcut with a hidden toll booth.
This article is the sorting guide. Twenty tricks that are genuinely strategies — each with the one-line reason it works — and five popular ones we'd gently steer you away from, with the receipts.
Strategy or gimmick? The distinction that decides everything
A strategy works because of place value and number relationships, and a child who uses it can say why. Doubling one number and halving the other works because you're keeping the same total area, just reshaping the rectangle. That understanding transfers to numbers the child has never met.
A gimmick works instead of them. It's a dance of digits — draw the wings, cross the arrows, add a zero — that produces answers while bypassing the thinking. The cognitive scientist Daniel Willingham has a line teachers quote for good reason: memory is the residue of thought. A trick that removes the thought leaves no residue; when the trick expires, nothing remains.
Every trick below has a "why it works" a nine-year-old could repeat back. That's not decoration; that's the test.
The 20 keepers
Addition and subtraction
1. Bridging through 10. For 8 + 5, take 2 to make 10, then add the remaining 3: 13. Why it works: our number system is built in tens, so 10 is a resting place — every sum near it becomes two easy steps.
2. Bridging through 100. For 97 + 25, take 3 to make 100, then add 22: 122. Why it works: same landmark idea, one storey up — a child who bridges through 10 already owns this.
3. Compensation (round and adjust). For 46 + 29, do 46 + 30 = 76, then take 1 back: 75. Why it works: adding a friendlier number and repaying the difference leaves the total unchanged.
4. Left-to-right addition. For 47 + 38, add the tens first (70), then the ones (15): 85. Why it works: it starts with the biggest part of the answer, matching how we estimate, and keeps place value in view rather than hidden in a carried digit.
5. Doubles and near-doubles. For 7 + 8, use double 7 plus 1: 15. Why it works: doubles are among the earliest facts children secure, so neighbouring sums can lean on them.
6. Making tens in a list. For 7 + 5 + 3, pair the 7 and 3 first: 10 + 5 = 15. Why it works: addition can be done in any order, so you're allowed to hunt for pairs that make ten.
7. Subtraction by adding up. For 62 − 58, climb from 58: 2 to reach 60, then 2 more — the gap is 4. Why it works: subtraction is the distance between two numbers, and short distances are easier to walk than to compute.
8. Constant difference. For 62 − 38, shift both numbers up by 2: 64 − 40 = 24. Why it works: sliding both numbers the same amount doesn't change the gap between them.
9. Round-and-adjust subtraction. For 83 − 19, do 83 − 20 = 63, then give 1 back: 64. Why it works: you subtracted 1 too many, so the answer owes you 1 — compensation again, wearing a minus sign.
Multiplication and division
10. Doubling and halving. 16 × 25 = 8 × 50 = 4 × 100 = 400. Why it works: halving one factor and doubling the other keeps the product the same — same rectangle, different shape.
11. ×4 as double-double. For 26 × 4, double 26 (52), double again: 104. Why it works: 4 is 2 × 2, so multiplying by 4 is just doubling twice.
12. ×8 as double-double-double. For 7 × 8: 14, 28, 56. Why it works: 8 is 2 × 2 × 2 — three doublings, each one easy.
13. ×5 as ×10 then halve. For 18 × 5, do 18 × 10 = 180, then halve: 90. Why it works: 5 is exactly half of 10, so five groups is half of ten groups.
14. ×9 (and ×99) by compensation. 7 × 9 = 70 − 7 = 63; 34 × 99 = 3,400 − 34 = 3,366. Why it works: nine groups is ten groups with one group removed — and the same logic scales straight up to 99.
15. ×11 as ×10 plus one more group. 35 × 11 = 350 + 35 = 385. Why it works: eleven groups is ten groups and one more — no digit-sandwich mnemonic required.
16. ×25 as ×100 then quarter. 32 × 25 = 3,200 ÷ 4 = 800. Why it works: 25 is a quarter of 100, so 25 of anything is a hundred of it shared four ways.
17. Partitioning. For 14 × 6, split the 14: (10 × 6) + (4 × 6) = 60 + 24 = 84. Why it works: this is the distributive law in casual clothes — the same law long multiplication and, later, algebra depend on.
18. Deriving near facts from known facts. Stuck on 6 × 7? Use 6 × 5 = 30 and 6 × 2 = 12: together, 42. Why it works: multiplication facts live in families, and a child who can travel between them is never truly stuck — this is the engine behind learning tables in the right order.
19. Dividing by 5 as ÷10 then double. For 340 ÷ 5: 340 ÷ 10 = 34, doubled is 68. Why it works: there are twice as many fives as tens in any number, because each ten holds two fives.
Fractions and percentages
20. The percentage flip. 8% of 50 = 50% of 8 = 4. Why it works: a% of b always equals b% of a, because both are just a × b ÷ 100 — so a child can always pick the easier direction.
Twenty tricks, one idea: use a landmark you own to reach a place you don't, and know why the road holds your weight.
A good trick is a strategy your child can explain. A bad trick is a debt — and it comes due two grades later.
The 5 "tricks" that hurt
None of these are taught maliciously. Most are taught by kind adults trying to get a child through Friday's test. But maths-education researchers Karp, Bush and Dougherty have documented a whole family of these in their well-known "Rules That Expire" articles for Teaching Children Mathematics: rules that are true just long enough to be believed, then quietly false forever after.
1. The fraction "butterfly method." Cross-multiply the diagonals, multiply the bottoms, draw the wings — and add fractions with zero understanding of common denominators. It handles exactly one case: two fractions, nothing else. Faced with three fractions, or a mixed number, the butterfly has no move to make. Worse, it teaches the child that fraction addition is a digit ritual rather than the question "what same-sized pieces can these both be cut into?" — which is the entire concept.
One family we heard from watched this play out in slow motion. Their daughter, then in Grade 5 (Class 5 in India, Year 6 in England), aced fraction addition all year with the butterfly method — genuinely aced it, full marks. In Grade 6 she met ⅓ + ¼ + ½: three fractions, no butterfly. She had nothing. Her tutor had to go back and teach common denominators from zero, and this time the lesson came with an "I thought I was good at this" bruise attached. The method hadn't saved time. It had borrowed it, at interest.
2. "Just add a zero" to multiply by 10. It works beautifully for whole numbers — right up until decimals arrive, where it breaks catastrophically: 3.5 × 10 is not 3.50. The child who was taught why ×10 works (every digit shifts one place-value column to the left) sails through decimals. The child who was taught to append a character to a string does not.
3. Order-of-operations and expansion mnemonics before structure. Acronyms like FOIL (and its cousins) hand children a fixed choreography for one specific situation — two brackets, two terms each — instead of the general idea of distributing every term. Give that child three terms in a bracket and the dance floor is gone. Mnemonics are fine as a label for something already understood; as a substitute for the structure, they set a trap with a two-year delay.
4. The 9-times-table finger trick as a final destination. Fold down the seventh finger, read off 63 — it's charming, and as a bridge it's harmless. The harm is when it becomes home: a ten-year-old still routing every 9s fact through their hands has been spared the far more useful discovery that nine groups is ten groups minus one (strategy 14) — reasoning that also unlocks ×99, ×19 and half the compensation family. Fingers as scaffolding, fine; fingers as the building, no. (The same logic applies to finger counting in general — the stage is healthy, the terminus isn't.)
5. Keyword-hunting in word problems. "Altogether means add. Left means subtract. Of means multiply." Until: "Riya had some marbles, gave 7 to her brother, and had 12 left — how many did she start with?" The keyword says subtract; the problem requires addition. Keyword lists train children to skip the one step word problems exist to test — actually reading the situation — and they are a reliable factory for the errors parents later file under carelessness. (Which is rarely what it looks like.)
The litmus test: one question to ask tonight
You don't need a teaching degree to audit your child's toolkit. Next time they produce a fast answer, ask warmly: "Why does that work?"
A child using a strategy will tell you something about tens, or doubles, or groups — clumsily, perhaps, but recognisably about numbers. A child using a gimmick will say "it just does," or "that's the trick," or will re-perform the moves at you, slightly louder.
If you get the second answer, don't ban the trick on the spot — nobody did anything wrong here, not the child and not whoever taught it. Just keep asking the question, and feed in the real reason when the moment is right ("you know what's funny — nine sevens is just ten sevens minus a seven"). Gimmicks rarely need evicting. They get quietly outgrown the moment something sturdier moves in.
And if the "why" questions reveal that several tricks have nothing underneath them, that's worth knowing too — it's often the first visible sign of a missing skill from a grade or two back, a far more useful diagnosis than "bad at maths" and a far easier one to fix. A quick check against what tends to be automatic at each grade shows which foundations the tricks should be standing on.
Where daily practice fits
Strategies become fluent the same way anything does: small, regular, successful use. That is exactly what CREST Champs' free daily adaptive practice is built for — a few minutes a day, pitched at the edge of what your child can do, quietly rewarding the child who can say why a strategy works. And when one keeps failing, the engine goes looking for the prerequisite underneath it — because that, not the trick, was the problem all along.