Multiplication chart 1–12, and how to learn the times tables

A multiplication chart lists every product from 1 × 1 to 12 × 12 in a grid: find one number on the top row, the other down the side, and the answer sits where they meet. It has 144 cells but only 78 different facts, because 3 × 4 and 4 × 3 are the same fact. Learn them in an order, a few at a time, with short spaced practice.

The chart is below, followed by the order Peabody (peabody.kids) teaches the tables in and what the research says about getting them to stick. Peabody is a free AI-driven adaptive learning platform for kids, free through the end of 2026. AI writes the stories; code decides the rest, including every times-table question.

The multiplication chart, 1 to 12

How to read it: for 7 × 8, go along the 7 row to the 8 column: 56. The chart is symmetrical across the diagonal from the top-left corner, which is the whole reason 144 cells shrink to 78 facts. The diagonal itself (1, 4, 9, 16 … 144) is the square numbers.

Why there are only 78 facts to learn

Turning a fact around never changes the answer: 6 × 7 and 7 × 6 are both 42. A child who knows one knows the other, so the chart above has 78 facts in it, not 144: the twelve squares on the diagonal and the 66 pairs on either side of it. Peabody counts it the same way. Its practice brain stores 7 × 8 and 8 × 7 as one fact, though it asks both ways round as separate questions, and Peabody's fact-speed room, Math Dojo, opens dividing once a child has met 24 of the 78 (about 30%).

The order that makes it easier

Learn the tables with the most free facts first. Each table you learn removes facts from the ones after it, so by the time a child reaches the 7s, most of the 7s are already known from other tables. This is the order Peabody's code teaches, and how many new facts each table brings once the earlier ones are known:

Add the column up and it comes to 78. After the 1s, 2s, 10s and 5s, a child already has 42 of the 78. The "hard" tables at the end are short because they are mostly done. The teaching lines in the last column are the ones Peabody's lessons read out before the first example.

What the research says about making them stick

Times-table facts are what researchers call a constrained skill: a fixed, finite set with right answers. That matters, because practice software does best on exactly this kind of skill. Kim and colleagues (2021, AERA Open) pooled 36 studies of educational apps for preschool to grade 3 and found effects largest for constrained skills like counting and number facts, and smallest for open skills like problem solving (Measures Matter). Five findings shape how to practise them.

Space it. Cepeda and colleagues (2008, Psychological Science, 1,354 people) found the best gap between practice sessions grows with how long you want to remember, and that gaps too short hurt more than gaps too long (PubMed). A 2025 meta-analysis of 27 maths studies (Murray, Horner and Göbel, Educational Psychology Review) found spacing beat massed practice at g = 0.28 (Springer). Ten minutes on four days beats forty minutes on Sunday.

Recall, don't reread. Answering from memory teaches more than looking at the chart again. Roediger and Karpicke (2006, Psychological Science) showed it a week later, 56% against 42%, though with prose passages rather than sums (PDF). The same maths meta-analysis is a useful caution: for maths procedures the testing advantage was not reliable, while for facts and vocabulary the case for retrieval is solid. A times table is a fact. Use the chart to look up, then cover it.

Mix the tables once each is known. Practising one kind of problem at a time feels better and teaches less. Rohrer and colleagues (2020, Journal of Educational Psychology) ran a cluster trial with 787 seventh graders: a month later, mixed practice scored 61% and blocked practice 38% (What Works Clearinghouse). Taylor and Rohrer (2010) found 77% against 38% with fourth graders, even though mixed practice looked worse during practice (USF). Those studies used mixed problem types, not times tables, so treat this as the mechanism (choosing which fact you need) rather than a measured times-table result.

Keep sessions short. An Education Week summary of math-fact research (January 2026) recommends two to ten minutes at a time, several times a week, with timed practice only once the facts are known (Education Week).

Speed comes last, and "fast" means about two seconds. Classroom material converges on a right answer within about two seconds as the sign a fact is automatic, with three seconds as a generous ceiling; the research report behind this guide calls that a convention with thin primary backing, not a measured boundary (ERIC study). In the lab, direct retrieval takes 400 to 900 milliseconds (ERIC). A clock on a fact a child does not know yet only measures panic.

How Peabody practises the times tables

Every rule here is ordinary code, written up in full in how Peabody picks the next question.

• A grade sets only the first rung. A third grader starts on multiplying, but a child who has the earlier rungs down climbs to it from any grade, and one who has it down moves on to dividing.
• Rounds of about 30 questions, about 85% already known. At most two new facts a round, each taught first and asked a few questions later. A miss comes back three questions later.
• Quick means 2.5 seconds for times tables. A fact moves up through levels: right with a hint, right first try, quick and right, then quick and right on two different days. Quick facts come back for review after gaps of 1, 3 and 7 days, then three weeks.
• Never the same question again once it is right. 7 × 8 and 8 × 7 are different questions, so each retires on its own. A miss comes back once, later in the round.
• Three boxes, no clock on new facts. In the games every answer is three big tap boxes, and the wrong two are the near misses children make: one group too many or too few, or the neighbouring fact.
• Speed only for known facts. Math Dojo times only facts a child has already got right somewhere; unmet facts get an untimed warm-up first. Belts go white (every fact met), yellow, green, blue, then black at 95% right in under two seconds, and never go down.

The Times Table Board in Numbers is the chart above as a game: the cells vanish in waves and a child fills them back in. Times tables also turn up inside the learning games once a child's ladder reaches them, in Rocket Number Blast, Last Word and Dip & Dash among others. Start free with no sign-up.

What this doesn't show

• Peabody has no published study of its own; none of the numbers above are claims about it.
• The spacing and interleaving studies mostly used older children and other kinds of problem, so their sizes do not transfer to times tables one for one.
• The two-second bar is a classroom convention. A slow right answer is still a right answer.

The multiplication games page lists the games that ask these facts, and 3rd grade math has the lesson parts.

Questions parents ask

Which times table should my child learn first?

The 2s, then the 10s and the 5s. They follow patterns a child already knows (doubling, adding a zero, counting by fives), and with the 1s they cover 42 of the 78 facts. The 3s and 4s come next, then the 9s, which have the times-ten trick.

How long does it take to learn all the times tables?

It depends on the child and the dose, and no study gives a single number. The evidence favours a few minutes on most days over long sessions, and spaced reviews over days and weeks rather than one big push. Expect the last facts (6 × 7, 7 × 8, 8 × 6) to take longest.

Should I use a timer?

Only for facts your child already gets right. Timing unknown facts measures stress, not knowledge. Once a fact is known, a gentle clock helps it become automatic, with about two seconds as the usual classroom target.

Is it fine to use the chart while practising?

Yes, to look things up and to see patterns. Then hide it and answer from memory, because recall is what makes a fact stick. A chart on the wall that is never covered is a lookup table, not practice.

Why does my child know 3 × 7 but not 7 × 3?

Because they have practised the fact in one direction. Point out that the chart is a mirror across its diagonal, then ask the fact both ways round. Peabody asks both forms as separate questions for the same reason.