How to learn the times tables? A guide for parents and teachers

What does multiplication mean?

Multiplication is a short way of adding the same number again and again. 3 × 7 means "3 groups of 7": 7 + 7 + 7 = 21. In our game this is shown at a market stall: there are 3 crates, each crate holds 7 plums, so how many plums are there in total?

That is why a child should first see the groups, not the answer. A child who sees objects arranged in groups understands where 21 comes from and can work it out again when they forget it.

How do you memorise the times tables? Four steps

1. See: show the fact with objects (crates, an egg box, fingers). Let the child find the answer by counting.
2. Skip count: teach counting in sevens: 7, 14, 21, 28 ... This is saying one row of the table in order.
3. Find: ask for the fact without the objects; if the child gets stuck, they can find it by skip counting.
4. Speed up: ask the facts in mixed order. When a fact is answered within a few seconds, without thinking, on several days in a row, it is "known".

Every stall in the game follows these four steps: Count, Skip, Find and Speed up.

Is 3 × 7 the same as 7 × 3? Why half the work is already done

3 × 7 and 7 × 3 give the same answer: 3 crates of 7 plums and 7 crates of 3 plums are both 21 plums. This is called the commutative property of multiplication.

For a child who knows this, most of the 100 facts count twice: once the 2s, 5s and 10s are known, only a few new facts are left to learn in the 7s table (7 × 6, 7 × 7, 7 × 8, 7 × 9). When a fact is known, our game also starts its flipped version at a more advanced step.

In what order should you teach the times tables?

An order that goes from easy to hard, and one that many teachers use too: 2, 5, 10 (the easiest to skip count), then 3, 4 (4 is double 2), then 9 (with the finger trick), then 6, 8 and finally 7. The 1s and 10s are easy anyway: a number times 1 is the number itself, and a number times 10 is the number with a zero on the end.

In the game all stalls are open from the start; the stall with the gold frame is the next one suggested by this order.

Tricks for the hardest times tables

• The 9s finger trick: hold up all 10 fingers. For 9 × 4, fold down the 4th finger from the left: 3 fingers are left on the left (tens) and 6 on the right (ones): 36. It works from 9 × 1 to 9 × 10.
• Digit sum in the 9s: up to 9 × 10, the digits of every answer add up to 9 (18, 27, 36 ...).
• The 5s: the answer always ends in 0 or 5; it is half of 10 times the number (5 × 8 = half of 80 = 40).
• The 4s and 8s: double, then double again. 4 × 7 = double 14 = 28; 8 × 7 = double 28 = 56.
• The 6s: 5 times the number, plus one more: 6 × 7 = 35 + 7 = 42.
• 7 × 8 = 56: remember the sequence "5, 6, 7, 8": 56 = 7 × 8.

How many minutes a day should a child practise?

Short, frequent practice works better than long, rare sessions. A few days a week, 5-10 minutes each time, is usually enough; stopping before the child gets tired makes them happy to come back the next day.

One reason is spaced repetition: a well-known fact does not need to be asked every day, while a hard one should come up more often. Our game tracks this separately for every fact: hard facts come up more often, known ones come back days later.

How are multiplication and division related?

Division is the inverse of multiplication. If you know 7 × 6 = 42, you also know 42 ÷ 7 = 6 and 42 ÷ 6 = 7. The first meaning of division is sharing equally: if 42 plums are shared equally into 7 crates, each crate gets 6 plums.

The game's Missing number mode (? × 7 = 42) makes the step from multiplication to division easier; in Sharing mode, the plums are shared out into crates.

Multiplication chart from 1 to 10

Find where a row and a column meet: the box where row 7 meets column 8 is 56, so 7 × 8 = 56. The chart is symmetrical along its diagonal; this is a picture of the commutative property.

How do you play? Whiteboard mode in class

Choose a stall on the Market screen (2s, 3s ...). In the Count and Skip steps the child taps one of three answers; in the Find and Speed up steps they type the answer with the number keys, and it is checked automatically once enough digits are typed. Each round has 10 questions; 6 answers right first time earn 1 star, 8 earn 2 stars and 10 earn 3 stars. Getting 2 stars in a step unlocks the next one.

There is no penalty for a wrong answer: the right one is shown by counting the crates, the child types it in, and the same fact comes back a few questions later. In Beat the clock mode the goal is to answer as many facts as possible in 60 seconds; this score goes on the leaderboard. The Market notebook uses colours to show which facts are known.

Whiteboard mode is for teachers: you choose the tables and the question type, the problem appears in large print, the class says the answer and the teacher presses Show. Sound is off by default, no ads appear and the children's own progress does not change. The space bar shows the answer and moves on to the next one.

Common mistakes

• Starting memorisation before understanding: a child who has never seen it with objects cannot work out a forgotten fact again.
• Always asking the table in order: a child who counts 7, 14, 21 has to start from the beginning when asked 7 × 6 out of order. Learn in order, then reinforce in mixed order.
• Practising all the tables at once: first the 2s, 5s and 10s, then the others.
• Long, rare sessions: 5-10 minutes on several days instead of one hour-long session.
• Constantly asking the known facts and skipping the hard ones: most of the time should go to the hard facts (the 6s, 7s, 8s and 9s).
• Pushing speed too early: demanding speed without understanding creates anxiety; speed is the last step.