Times tables tricks: how to learn the multiplication table for good

Why the times tables still matter

Adults who are fluent at multiplication mostly remember answers rather than work them out. In a 1996 study by LeFevre and colleagues, university students reported retrieving the answer directly on about 80% of single-digit multiplication problems. Every larger calculation rests on these small facts: 37 × 8 is 30 × 8 plus 7 × 8. If 7 × 8 takes you five seconds, every bigger problem that contains it slows down too.

Fewer facts than you think

A 10 × 10 table has 100 cells, but order does not matter: 3 × 8 is the same fact as 8 × 3. Counted once each, that leaves 55 different facts, and a 12 × 12 table has 78 rather than 144. Better still, once you know the 1, 2, 5 and 10 times tables, only 21 facts remain among 3, 4, 6, 7, 8 and 9. That is a short list, and it is the list worth your practice time.

Start with the easy tables

Four tables are almost free. Times 1 leaves a number unchanged, and anything times 0 is 0. Times 10 adds a zero. Times 2 is doubling. Times 5 is half of times 10: for 7 × 5, take 70 and halve it to get 35. This also works for odd whole numbers: 9 × 5 is half of 90, so 45. Secure these four first, because the tricks for the harder tables are built on them.

Doubling for the 4s and the 8s

Times 4 is doubling twice, and times 8 is doubling three times. For 7 × 4, double 7 to get 14, then double again to get 28. For 7 × 8, keep going one more step: 14, 28, 56. Doubling is the easiest operation there is, so chaining it is often faster than hunting for a fact you half remember. Count the doublings under your breath, “one, two, three”, so that you do not lose track.

The 9s: ten times, minus once

Nine times a number is ten times that number minus the number: 9 × 7 is 70 − 7, so 63. Two checks catch mistakes. From 9 × 1 to 9 × 10, the digits of the answer always add up to 9 (6 + 3 = 9), and the tens digit is one less than the number you multiply by. The finger method works too: hold up ten fingers and fold down the seventh; six fingers stay on the left and three on the right, so 63.

The 6s and the 3s

Six times a number is five times it plus one more: 6 × 7 is 35 + 7, so 42. With an even number there is a pattern: 6 × 2 = 12, 6 × 4 = 24, 6 × 6 = 36 and 6 × 8 = 48 all end in the number you multiplied by, and their tens digit is half of it. Three times a number is double it plus one more: 3 × 8 is 16 + 8, so 24. Each trick turns a fact you are unsure of into one you already know.

Borrow from a neighbour

LeFevre and colleagues found that adults do not only retrieve answers. They also use rules, repeated addition, counting in steps (3 × 5 as 5, 10, 15) and derived facts, such as 6 × 7 worked out as 6 × 6 + 6. You can do this on purpose. Squares make good anchors: if you know 7 × 7 = 49, then 7 × 8 is 49 + 7 = 56. A few solid anchors let you rebuild a forgotten fact in seconds.

Name your hard facts

For most people, the trouble sits in a handful of facts among 6, 7 and 8: 6 × 7, 6 × 8, 7 × 7, 7 × 8 and 8 × 8 are common culprits. Rather than reciting the whole table, write down the few facts you hesitate on and give them extra attention. A small rhyme can help for the worst one: “5, 6, 7, 8”, as in 56 = 7 × 8. Your own list will differ, so build it from your mistakes.

A trick is a bridge, not the goal

Tricks get you to the right answer, but they cost time. LeFevre and colleagues found that people were slower to retrieve the problems they most often solved by other procedures. In a study comparing students in Canada and China, Campbell and Xue traced weaker simple arithmetic both to less efficient recall and to greater use of procedures. Use the trick to find the answer, then keep practising until the answer comes on its own.

Test yourself instead of rereading

Looking at a times table on the fridge feels productive but is mostly rereading. In a 2006 study, Roediger and Karpicke found that students who took recall tests on a text remembered it much better two days and a week later than students who only studied it again, even though rereading gave better recall at five minutes and more confidence. For the tables, cover the answer, say it, then check.

Spread practice over days

A 2006 review by Cepeda and colleagues pooled 839 assessments from 317 experiments on spacing out the learning of verbal material, and found that the longer you want to remember something, the longer the best gap between sessions becomes. A 2013 review of learning techniques by Dunlosky and colleagues gave practice testing and spaced practice its highest rating for usefulness. A few minutes a day beats one long session a week.

Mix the tables up

Reciting the 7 times table in order lets each answer lean on the one before: 7, 14, 21, 28. In real use, facts come one at a time and out of order. Rohrer and Taylor found that students who practised different types of problems mixed together did vastly better on a test a week later than students who practised them in blocks. Once you know a table in order, shuffle its facts with the others.

Accuracy first, then speed

Start by getting every answer right, even slowly, and note the facts you miss. Retest those the next day, and drop a fact from your list once you answer it correctly without hesitating. Only then add a timer. Short timed rounds are useful because hesitation becomes visible: a fact that still needs a trick shows up as a pause. Keep rounds short so that tiredness does not turn practice into guessing.

Where Numvolt fits

Multiplication is one of Numvolt’s 15 topics. Its first levels work through the tables up to 12 × 12, and the difficulty adjusts as you play: it rises with correct answers, faster when you are quick, and drops after repeated errors. Each missed question comes back in a review session until you get it right. You can run 15, 30 or 60-second sprints on the topics you choose, and read tricks for times 4, 5, 8, 9 and 11, each with two worked examples and the pitfall to avoid. A duel mode pits two people against each other on one phone.

Further reading

• LeFevre, Bisanz, Daley, Buffone, Greenham & Sadesky (1996), Multiple routes to solution of single-digit multiplication problems, Journal of Experimental Psychology: General
• Campbell & Xue (2001), Cognitive arithmetic across cultures, Journal of Experimental Psychology: General
• Roediger & Karpicke (2006), Test-enhanced learning: taking memory tests improves long-term retention, Psychological Science
• Cepeda, Pashler, Vul, Wixted & Rohrer (2006), Distributed practice in verbal recall tasks: a review and quantitative synthesis, Psychological Bulletin
• Dunlosky, Rawson, Marsh, Nathan & Willingham (2013), Improving students’ learning with effective learning techniques, Psychological Science in the Public Interest
• Rohrer & Taylor (2007), The shuffling of mathematics problems improves learning, Instructional Science