How to Learn the 3 Times Table: Patterns and Tricks

The 3 times table is often the first "odd" table children meet after the easy 2s, 5s and 10s. The answers don't end in a neat pattern like 0 and 5, so it can feel harder at first. But the 3s have a lovely hidden pattern of their own, and learning them well pays off twice, because the 6s and 9s are built straight on top of them.

What is the 3 times table?

Fact	Answer	Fact	Answer
1 × 3	3	7 × 3	21
2 × 3	6	8 × 3	24
3 × 3	9	9 × 3	27
4 × 3	12	10 × 3	30
5 × 3	15	11 × 3	33
6 × 3	18	12 × 3	36

What does "3 times" actually mean?

Before any tricks, make sure your child can picture it. 3 × 4 means three groups of four, or four groups of three. Lay out counters, or look at a dot array of 3 × 4: three rows of four dots, twelve in all. Turn it on its side and it's four rows of three, which shows why 3 × 4 and 4 × 3 are the same fact. Children who can see a fact can rebuild it when they forget.

Trick 1: How do you count in threes?

Counting in threes is the backbone of the table. Say it together on walks or in the car: 3, 6, 9, 12, 15, 18… Tap a finger for each step so your child can see which fact they're on: the seventh finger is 21, so 7 × 3 = 21. Once the counting is smooth, stop counting and start asking facts out of order, so it doesn't stay a chant.

Trick 2: What is the digit-sum pattern?

Add up the digits of any answer in the 3 times table and you always get 3, 6 or 9:

• 12 → 1 + 2 = 3
• 15 → 1 + 5 = 6
• 18 → 1 + 8 = 9
• 21 → 2 + 1 = 3, and the cycle of 3, 6, 9 starts again

This gives your child a way to check an answer. If they say 3 × 8 = 23, the digits add to 5, so it can't be right. The same check works for big numbers too: 3 + 6 + 9 = 18, and 1 + 8 = 9, so 369 is in the 3 times table.

Trick 3: What is the 3-6-9 grid?

Draw a noughts-and-crosses grid. Starting at the bottom left, write 1, 2, 3 going up the first column, then 4, 5, 6 up the second and 7, 8, 9 up the third. The top row now reads 3, 6, 9, the middle row 2, 5, 8 and the bottom row 1, 4, 7. Finally, write a tens digit in front: nothing on the top row, 1 on the middle row and 2 on the bottom row:

Row	Read left to right
Top (no tens)	3	6	9
Middle (1 ten)	12	15	18
Bottom (2 tens)	21	24	27

That's the 3 times table from 3 × 1 to 3 × 9. Children love drawing it, and it shows how the last digits cycle through 3, 6, 9, 2, 5, 8, 1, 4, 7.

How do you work out the tricky 3s facts?

Use facts your child already knows as stepping stones:

• 3 × 7: 3 × 5 = 15, then two more threes: 15 + 6 = 21.
• 3 × 8: double 3 × 4: 12 + 12 = 24.
• 3 × 9: 3 × 10 = 30, take away one three: 30 − 3 = 27.
• 3 × 12: 3 × 10 = 30, plus 3 × 2 = 6, so 36.

Splitting a fact like this is the same idea as the area model: a 3 by 7 rectangle cut into a 3 by 5 piece and a 3 by 2 piece.

Why is the 3 times table worth learning well?

Because three more tables grow out of it. The 6 times table is the 3s doubled (3 × 7 = 21, so 6 × 7 = 42). The 9 times table is the 3s tripled, and the 12 times table is the 3s times four. That's why the 3s come before the 6s and 9s in the best order to learn times tables.

How can you practise the 3 times table at home?

• Five minutes a day on the 3 times table practice page, which starts without a timer.
• Play "Fizz" on a car journey: count from 1 and say "Fizz" instead of any number in the 3 times table.
• Once your child is confident, try a short speed round to build fluency.
• Print a 3 times table worksheet for a quick check on paper.

Little and often works far better than long sessions. See why 5 minutes a day beats an hour.