In most of the world, children learn multiplication tables the same way: recite them from 1 to 10 (or 12), in order, every evening — in classrooms and kitchens from Chennai to Lagos to Leeds. It's how their parents learned, and their parents before them.
Almost no research supports that order. Not because recitation is evil, but because 1-to-12 is an ordering by label, not by difficulty or usefulness — it front-loads none of the facts that make the others easy. It's why so many children cruise through the 2s and 5s, then hit the 7s like a wall and stay there for a term.
There is a better sequence, and it comes with a pleasant surprise: followed in the right order, the "hard" tables mostly stop existing. The 8s become a doubling exercise. The 9s become a subtraction. What's left genuinely needing memorisation is a set of facts you can count on your fingers — ironically.
Why 1-to-12-in-order fails
Taught in label order, the tables present themselves as 144 separate facts — a 12-by-12 wall of independent memorisations, to be laid brick by brick, table by table. That's a heavy load for anyone, let alone an eight-year-old, and it explains the classic pattern: the early tables go in easily (they're small numbers, drilled often), and each later table feels harder than the last, because each is being memorised cold, with no help from the ones before it.
But the facts aren't independent. They're a dense web of relationships — doubles, halves, one-more-groups, one-less-groups — and the right order teaches the relationships first, so that each new table is mostly generated from the previous ones rather than memorised from scratch. Roughly fifteen facts get memorised; the rest get derived, faster and faster, until deriving is indistinguishable from knowing.
This isn't just a cute reframe. Researchers who study how children acquire arithmetic facts — Arthur Baroody's work is the standard reference — have found that children who use known facts to derive unknown ones develop both fluency and flexibility, and that the deriving itself is what wires the facts in for good.
The sequence
Here is the order, with the reason each table earns its place:
- 2s first. They're the doubles, which children usually half-know already from addition. Everything downstream leans on them.
- 10s. The easiest table in the book — it's place value doing the work — and the anchor for two other tables to come.
- 5s. Each 5s fact is half the matching 10s fact: 7 × 5 is half of 70, so 35.
- 4s. Double the 2s: 7 × 4 is double 14, so 28.
- 8s. Double the 4s: 7 × 8 is double 28, so 56. The table with the fearsome reputation, reduced to one extra doubling.
- 3s. One of the few tables that's genuinely new material — a short memorisation job, made easier because it comes this late.
- 6s. Double the 3s: 7 × 6 is double 21, so 42.
- 9s. The 10s minus one group: 9 × 6 is 60 − 6, so 54. No finger origami required — and this version of the 9s keeps working at 19, 29 and 99, where the finger trick quietly retires.
- The leftovers. Whatever the web hasn't already caught — a handful of stubborn residents like 6 × 7 = 42, 7 × 8 = 56 and 6 × 8 = 48. Drill those, individually and by name, not all 144. (The 11s and 12s, where taught, largely take care of themselves: 11 groups is 10 groups plus one more, and 12 groups is 10 groups plus 2 groups — 7 × 12 is 70 + 14, so 84.)
Most systems expect this whole edifice to be standing by around the end of Grade 3 or during Grade 4 (Class 3–4 in India, Year 4–5 in England), so a child mid-journey is not behind — they're mid-journey.
The bookkeeping reveal: 144 facts is really about fifteen
Watch what happens to that intimidating 12-by-12 grid when you do the honest accounting.
Start with 144 facts. Commutativity — 6 × 7 is the same fact as 7 × 6 — removes nearly half of them at a stroke, leaving 78 genuinely distinct facts. Now remove the 1s (nothing to learn), the 2s, 5s, 10s and 11s (each generated by a strategy above), and the square numbers, which children tend to absorb early because they're memorable. What remains is roughly twenty facts — and the doubling families (4s from 2s, 8s from 4s, 6s from 3s, 12s from 10s-plus-2s) and the 9s-from-10s move dissolve most of those on contact.
The stubborn core — the facts that resist every strategy and simply have to be known — comes to around fifteen, with 6 × 7, 7 × 8 and 6 × 8 as the famous ringleaders.
Your child doesn't need to memorise 144 facts. They need about fifteen — and a way of seeing that generates the rest.
That's why "we're stuck on the sevens" is almost always a misdiagnosis. There is no seven wall. There are three or four unfriendly facts wearing a seven, and everything else in that table belongs to a family your child may already own.
One mother we heard from watched her 8-year-old grind at "the sevens" for months — recitation every evening, no movement. Then she stopped teaching the 7 table and started asking different questions: "What's double 7 × 3?" (double 21 — 42, which is 7 × 6). "What's 7 × 10 minus 7?" (63, which is 7 × 9). The sevens fell in a week. They were never the problem; the order was. Every fact in that table had a relative willing to help — the recitation script just never introduced them.
How to practise (whatever the order)
The sequence sets up the facts; practice is what makes them automatic, and the same two principles that govern how many minutes of practice a day actually work govern tables in particular.
Retrieval, little and often. Flashcards, an app, oral quizzing in the car — a few minutes daily, with the child producing answers rather than re-reading a chart. Keep it low-stakes: this is a game, not an audit.
Mixed and spaced. Once a table is introduced, questions should come shuffled across everything learned so far, not in tidy blocks. "7 × 4, 3 × 9, 8 × 5" is practice; "2 × 7, 3 × 7, 4 × 7…" is a pattern the child rides without retrieving anything.
Division facts travel with multiplication, not after it. The moment 3 × 7 = 21 is secure, ask "so 21 ÷ 7 is…?" Taught together, they're one fact family; taught a year apart, division becomes a brand-new mountain that didn't need to exist.
And a gentle flag: if daily fact practice has run for a couple of months and a child of 9 or 10 is still deriving everything from scratch — or still routing small facts through their fingers — the tables may not be the real story. Multiplication stands on comfortable addition and doubling, and when those wobble, the fix is usually a skill from a grade or two earlier, not louder recitation.
What recitation is still good for
Let's be fair to the family tradition. Chanting a table has real virtues: rhythm, confidence, a sense of the sequence's shape, and a pleasant ritual that grandparents can run without an app. As a first pass over a new table, it's genuinely useful.
Where it stops helping is retrieval out of sequence — which is the thing school actually demands. No test asks for the 7 table in order; it asks for 7 × 8, cold, between two unrelated questions. Education systems have noticed: England now runs a national multiplication tables check in Year 4 (ages 8–9) built on exactly this — randomly ordered facts with a few seconds each, a format recitation alone simply cannot prepare a child for.
So keep the chanting if your household enjoys it. Just don't let it be the only practice — a child can recite a table perfectly and still not have it.
Where daily practice fits
Everything above — the sequence, the mixing, the spacing, the division pairing, the hunt for the three or four genuinely stubborn facts — is exactly what CREST Champs' free daily adaptive practice runs automatically. A few minutes a day, facts asked out of sequence at the edge of what your child can do, derived-fact strategies rewarded, and a quiet step backwards to doubling or addition whenever that turns out to be the real gap. You bring the child and the breakfast table; the order takes care of itself.