How to teach multiplication, step by step.

1. Start with what multiplication means

Before any memorising, show that multiplication counts equal groups. Three bags with four apples in each is 3 groups of 4, or 3 × 4. Use real objects first: buttons, coins or pasta shapes.

Then arrange the objects in an array, with rows and columns: 3 rows of 4 dots. An array makes two big ideas visible. You can count it as 4 + 4 + 4 (repeated addition), and if you turn it on its side it becomes 4 rows of 3, so 3 × 4 = 4 × 3.

3 × 4 = 4 + 4 + 4 = 12

2. Build skip counting

Counting in 2s, 5s and 10s is the bridge from addition to multiplication facts. Chant, clap or hop the sequences, then ask questions such as “how many fives make 30?” Skip counting gives a child a reliable way to work out a fact they have not memorised yet.

3. How to teach multiplication tables in an easy-first order

Do not teach the tables from 1 to 12 in order. Start with the tables that are easiest to reason about, then use them to unlock the harder ones:

1. ×2, ×10 and ×5: doubles, place value, and half of ten.
2. ×1 and ×0: short rules once groups make sense.
3. ×9: ten groups minus one group, so 9 × 6 = 60 − 6 = 54.
4. ×4 and ×8: double, double again, then double once more for ×8.
5. ×3 and ×6: ×3 is double plus one more group; ×6 is ×5 plus one more group.
6. ×7 last: by now the turnaround rule means almost every ×7 fact is already known.

The turnaround rule (3 × 7 = 7 × 3) roughly halves the number of facts to learn, so point it out early and often. Our times table tricks show each of these routes with worked examples.

4. How to teach multiplication facts so they stick

Aim for a child who can work out a fact before asking them to remember it. Then practise little and often: five to ten minutes a day beats an hour on Sunday. Mix older facts with new ones, and ask for the answer from memory before checking, because retrieving a fact is what makes it stick. Multiplication games are an easy way to get those short daily sessions without a fight.

How to teach multiplication by grade

In the US, the Common Core standards spread multiplication over three years:

• Grade 2: the foundations. Children use addition to find the total of objects in rectangular arrays of up to 5 rows and 5 columns. Focus on equal groups, arrays and skip counting.
• Grade 3: the main year. Children learn what multiplication and division mean, multiply and divide within 100 and, by the end of the year, know from memory all products of two one-digit numbers. For third graders, follow steps 1–4 above across the year.
• Grade 4: bigger numbers. Children multiply up to a four-digit number by a one-digit number and two two-digit numbers, using place value. This is where rules such as the multiply by 11 trick build confidence.

In England, the national curriculum expects children to recall the multiplication tables up to 12 × 12 by the end of Year 4, which is also when the multiplication tables check takes place.

How to teach multiplication to struggling students

• Go back to objects. If the facts are not sticking, the meaning often is not secure yet. Rebuild arrays with counters.
• Shrink the target. Work on two or three facts at a time, not a whole table.
• Teach strategies, not just answers. A child who knows 5 × 7 = 35 can reach 6 × 7 by adding one more 7.
• Hold off on timed tests. Build accuracy first; pressure before accuracy tends to create anxiety rather than speed.
• Look for the pattern in mistakes. Is it one table, the turnaround facts, or losing count while skip counting? Fix that one thing.

If a child still struggles a lot after steady practice, talk to their teacher. Persistent difficulty with number facts can have many causes, and a school can help look into it.

What comes after the times tables?

Once facts are secure, children enjoy seeing that bigger calculations can be done in their head too. The Trachtenberg method turns multiplication into short digit-by-digit rules, and our Trachtenberg Kids app teaches them as guided lessons with a free ×11 lesson to start.