Skip to content

Times Tables: What Memorising Them Actually Buys You

Recall replaces computation, so the capacity spent working out 7 times 8 goes to the rest of the problem. That is the mechanism, and its limit.

By Published Updated 6 min read

Reign Creative LLC makes IQ Test & Brain Training Games, which this article links to, so we have a commercial interest in it. How we write and check articles.

Key takeaways

  • The benefit of recall is capacity: a product you retrieve costs almost nothing to hold, while a product you compute occupies the same working memory the rest of the problem needs.
  • A twelve-by-twelve grid has 144 cells, but commutativity collapses the 2-to-12 range to 66 distinct products, and only 28 of those avoid 2, 5, 10 and 11 entirely.
  • Retrieval is the end point of a sequence rather than a starting instruction: counting and decomposition strategies produce repeated correct pairings, and recall grows out of those.
  • Drilling speed on facts you do not yet know rehearses the counting, not the recall, so untimed accuracy work comes first and the clock comes second.
  • The demonstrated benefit is within arithmetic. Nothing here supports a claim that memorising tables raises intelligence or improves thinking in general.

Memorising the times tables buys you capacity, not speed. A product you retrieve arrives with almost no cost; a product you work out occupies the same limited holding space that the rest of the calculation needs. That is the whole mechanism, and it explains why people who know their tables are better at multi-step arithmetic rather than merely faster at single facts.

What recall actually buys

Take a two-digit multiplication done in a single pass, as in vertically and crosswise multiplication. The middle column needs two products summed, plus an incoming carry, before you can write a digit. If both products are retrieved, the only thing being held is the carry. If either has to be derived — counting up in sevens, or splitting 7 × 8 into 7 × 4 doubled — that derivation occupies the space where the carry was sitting.

The research picture is consistent with that. A study of multi-step mental addition found that children with faster single-step performance were faster on multi-step problems, and that verbal working memory capacity predicted multi-step speed. The reading is not that single-step speed causes multi-step speed directly, but that fluent components leave room for the steps built on top of them.

The capacity side of this — what working memory is, how much of it there is, and what does and does not change it — is treated directly in what working memory is, and whether training changes it, which is careful about the limits of the evidence.

How many facts there really are

The grid looks intimidating and mostly is not. A twelve-by-twelve table has 144 cells, but multiplication is commutative, so 7 × 8 and 8 × 7 are one fact rather than two. NRICH's article on illustrating number properties with arrays makes this visible: a rectangle turned on its side has the same number of squares, which halves the quantity of facts requiring memorisation.

Counting properly for the 2-to-12 range, where order does not matter, gives 66 distinct products.

Now remove the ones that follow a rule rather than needing storage:

  • Everything involving 2 is doubling.
  • Everything involving 10 is a shift.
  • Everything involving 5 is a shift and a halving, as covered in multiplying by 5, 25 and 50 by dividing instead.
  • Everything involving 11 has its own digit pattern.

Pairs touching 2, 5 or 10 account for 30 of the 66. Of the remaining 36, eight involve 11. What is left is 28 products drawn from 3, 4, 6, 7, 8, 9 and 12 — and even several of those are derivable, since 4 is double-double, 6 is double the threes, 8 is three doublings and 9 is a shift minus one lot.

Twenty-eight facts is a week's work, not a year's. The perception that the tables are an enormous body of material comes from counting the grid rather than counting the facts.

Retrieval is an end point, not an instruction

You cannot decide to recall something. Research on how arithmetic facts develop describes a sequence: children begin with counting strategies, move to decomposition strategies that derive an answer from a related fact, and gradually shift to memory-based retrieval as repeated correct pairings of problem and answer build associations in long-term memory. Retrieval emerges from the earlier strategies rather than replacing them by instruction.

Two consequences follow for an adult relearning the tables.

First, a fact you currently derive is not a failure. It is the normal precursor, and deriving it correctly and repeatedly is what produces the recall. Deriving it wrongly is the problem, because the wrong pairing gets stored just as readily.

Second, speed drills applied too early rehearse the derivation. If 7 × 8 is still being reached by doubling 7 × 4, a clock trains you to double faster. Accuracy first, then speed — an ordering that holds for most arithmetic practice.

A schedule an adult can keep

Nothing exotic is required, and the constraints are practical rather than theoretical.

  • Work in small sets. Ten or twelve facts at a time, drawn from the 28 hard ones, is enough. A whole table at once mostly practises the ones you already know.
  • Self-test rather than re-read. Cover the answer, attempt it, then check. Reading a table through feels productive and produces recognition rather than recall.
  • Mark the misses and return to them sooner. A fact you missed should reappear within the same session and again the next day; a fact you got instantly can wait.
  • Five minutes most days beats an hour on Sunday. Distributed practice is the one scheduling finding robust enough to act on without qualification.
  • Say the whole fact. "Seven eights are fifty-six", not "fifty-six". The association being built runs from the question to the answer, so the question has to be present.

England's national curriculum sets the expectation that pupils have memorised the multiplication tables up to and including 12 by the end of Year 4, with a statutory check of 25 timed questions taken in a two-week window in June. Adults relearning the material have no such deadline, which is an advantage: the pressure that makes the school version stressful is optional here.

Timed or untimed?

The What Works Clearinghouse practice guide on mathematics intervention in the elementary grades includes timed activities among its six recommendations as one way to build fluency, alongside systematic instruction, mathematical language, representations, number lines and word problems. That is a recommendation about building fluency once the material is known, not about how to introduce it.

The practical translation: untimed while a fact is being learned, timed once it is reliably correct. Timing has a real function — it makes derivation impractical and so pushes the answer toward retrieval — but only after the derivation is dependable.

It is also worth saying plainly that timed arithmetic makes some people anxious, and that anxiety costs working memory of its own. If a clock produces worse answers rather than faster ones, that is information about the practice design, not about the person. Untimed rounds are a legitimate permanent choice.

What memorising the tables does not do

The benefit described above is specific and bounded: retrieved facts free capacity for the arithmetic built on them. That is what the cited research addresses, and it is all this article claims.

It does not follow that memorising tables raises intelligence, improves reasoning in general, or transfers to anything outside arithmetic. No evidence offered here supports that, and it should not be inferred. Practising a skill improves that skill; the further claim is a different claim, and it needs different evidence.

Where the app fits

IQ Test & Brain Training Games, our own app at Reign Creative, is an educational game. It does include an IQ-style test, a memory test and a reaction time test, but its Google Play listing describes their results as estimates based on app activities, not clinical or professional assessments. What its multiplication practice does is give the fact practice described above a structure.

The flash-card deck for times tables covers every product from 2 × 2 to 12 × 12, dealt twelve cards per session, with each card self-graded as missed or got it — the self-testing loop above, with the marking done for you. Multiplication Rush runs the same material as timed drills, with difficulties starting at the 1–9 tables and stepping up through 1–12 before reaching two-digit products, and the Accuracy Trainer runs ten questions with no timer at all, with a hint and an explanation available on a miss. The technique library carries the tables as a named topic, on the argument that they are the alphabet the other methods are spelled in. The app itself is described on the IQ Test & Brain Training Games app page.

A workable four-week route: two weeks of untimed flash cards on the 28 hard facts, then two weeks of short timed rounds at the 1–12 difficulty, keeping a list of whichever facts keep reappearing as misses. The wider sequence of methods that recall unlocks is in the mental math practice guide, with the rest of this material in the mental math topic hub and under education and brain training articles.

Good to know

Frequently asked questions

Why is it worth memorising the times tables?
Because a retrieved fact costs almost nothing to hold, while a computed one occupies the same limited capacity the rest of the calculation needs. In a two-digit multiplication you may need six or seven products; if each has to be worked out, the intermediate results start getting displaced before the answer arrives.
How many facts are there really?
A twelve-by-twelve grid has 144 cells, but order does not matter, so the 2 to 12 range contains 66 distinct products. Removing everything involving 2, 5, 10 and 11 — all of which have rules rather than needing memorisation — leaves 28. That is the genuinely hard core.
How should an adult relearn the tables?
Short, frequent self-testing on a small set, untimed at first, writing down the ones you miss and returning to them sooner than the ones you got right. Long single sessions produce a feeling of familiarity that does not survive the week; five minutes most days does.
Should the practice be timed?
Eventually, not initially. A clock rewards whatever strategy you already have, so timing a fact you are still counting out reinforces the counting. Build accuracy untimed, then introduce timing to push the answer from derived to recalled.

Sources

  1. A Framework for Remediating Number Combination Deficits (opens in a new tab)Fuchs, L. S. et al., Exceptional Children (2010) — accessed
  2. Effects of Working Memory, Strategy Use, and Single-Step Mental Addition on Multi-Step Mental Addition in Chinese Elementary Students (opens in a new tab)Ding, Y. et al., Frontiers in Psychology (2019) — accessed
  3. Multiplication tables check (opens in a new tab)Standards and Testing Agency (GOV.UK) — accessed
  4. Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (opens in a new tab)What Works Clearinghouse, Institute of Education Sciences (2021) — accessed

About the author

— The independent app studio that builds the apps covered on this site and publishes every article here. On Google Play it publishes as Reign Collective Apps.

We use AI tools to help research, draft and edit our articles. Each article lists the sources its factual claims rely on, and details about our apps come from their live Google Play listings. No article on this site has been reviewed by an independent expert unless the reviewer is named on it.

Spotted an error? Tell us — how corrections are handled is set out in our editorial policy.

Keep reading