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3 times table pattern clues

Simple patterns, shortcuts and visual clues that make the 3 times table easier to remember.

Quick answer

3 times table pattern clues help you learn the 3 times table more easily by spotting simple patterns in the numbers, like how the digits in each answer add up to a multiple of 3, or how the numbers go up by 3 each time.

Learning outcome

By the end of this page, you will be able to spot and use patterns in the 3 times table to help you remember the answers quickly and easily. Success signs:
  • You can count in 3s from 0 to 36
  • You can spot that the digits in each answer add up to a multiple of 3
  • You can use the pattern to check if a number is in the 3 times table
  • You can solve 3 times table problems using the pattern clues

Why this matters

Knowing the 3 times table helps you solve bigger maths problems faster. You use it when sharing 3 cookies with friends, counting 3-legged animals, or working out how many wheels are on 3 cars. The patterns make it easier to remember the numbers and spot mistakes. If you know a pattern, you can even guess the answer before calculating it.

How it works

The 3 times table is made by adding 3 each time, starting from 0. You can see patterns in the numbers, like how they go up by 3, or how the digits of each answer add up to a number that is also a multiple of 3. These patterns are like clues that help you remember the table more easily.

Examples you can see

Let’s look at the 3 times table and find the patterns:
3 × 0 3 × 1 3 × 2 3 × 3 3 × 4 3 × 5 3 × 6 3 × 7 3 × 8 3 × 9 3 × 10 3 × 11 3 × 12
0 3 6 9 12 15 18 21 24 27 30 33 36
Pattern 1: Counting up by 3s Each number is 3 more than the last one. If you start at 0, you go 0, 3, 6, 9, 12, 15, and so on. Pattern 2: Digits add up to a multiple of 3 If you add the digits of each answer, the total is always a multiple of 3:
  • 3 × 4 = 12 → 1 + 2 = 3
  • 3 × 7 = 21 → 2 + 1 = 3
  • 3 × 9 = 27 → 2 + 7 = 9
  • 3 × 12 = 36 → 3 + 6 = 9
Pattern 3: Even and odd numbers If you look at the answers, you’ll notice that 3 × even = even, and 3 × odd = odd:
  • 3 × 2 = 6 (even)
  • 3 × 3 = 9 (odd)
  • 3 × 4 = 12 (even)
  • 3 × 5 = 15 (odd)

Try it as a mini adventure

The Pattern Detective Adventure You are a detective who needs to find the secret pattern in the 3 times table to solve a mystery. The mystery is hidden in a treasure chest, but the chest only opens if you can find the clues. Your first clue is to count in 3s from 0 to 36:
  • 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
Your second clue is to check if these numbers are in the 3 times table by adding their digits:
  • 12 → 1 + 2 = 3
  • 21 → 2 + 1 = 3
  • 27 → 2 + 7 = 9
  • 36 → 3 + 6 = 9
Now, solve this riddle: If a number is in the 3 times table, what must the sum of its digits be? The answer is a multiple of 3. Can you find the treasure by using these patterns?

Common mistakes

  • Mistake: Thinking that all numbers that add up to 3 are in the 3 times table. Why it happens: Confusing the rule for the 3 times table with other number rules. Fix: Remember that 3 × 1 = 3, so 3 is in the 3 times table, but 12 is also in the 3 times table because 1 + 2 = 3, which is a multiple of 3.
  • Mistake: Forgetting that 3 × 0 = 0. Why it happens: Not remembering that multiplying by zero always gives zero. Fix: Remember that any number multiplied by 0 is 0.
  • Mistake: Not seeing that the numbers go up by 3 each time. Why it happens: Not counting in 3s regularly. Fix: Practice counting in 3s every day to build the pattern in your head.

Parent and carer guide

As a parent or carer, you can help your child learn the 3 times table by:
  • Counting in 3s together, like when walking or playing games
  • Using the digit sum trick to check answers
  • Practicing with flashcards or online games
  • Encouraging your child to look for 3s in everyday life, like 3 wheels on a tricycle or 3 legs on a chair
  • Not pushing too hard, but making it fun and regular
If your child gets stuck, ask them to count in 3s or add the digits of the answer to see if it's a multiple of 3. It’s okay if they don’t get it straight away – learning times tables is a process.

Practice questions

  1. What is 3 × 8?
  2. What is the sum of the digits in 3 × 9?
  3. Is 24 in the 3 times table? Why or why not?
  4. What is 3 × 11?
  5. What is 3 × 0?
Answers:
  1. 24
  2. 9
  3. Yes, because 2 + 4 = 6, which is a multiple of 3
  4. 33
  5. 0

FAQ

What is the 3 times table?

The 3 times table is the list of answers you get when you multiply 3 by 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

How can I remember the 3 times table?

You can remember it by counting in 3s, using the pattern that the digits of each answer add up to a multiple of 3, or by using repeated addition (like 3 + 3 + 3 = 9).

Why do the digits of 3 times table answers add up to multiples of 3?

This is a special rule in maths. If you add the digits of any number in the 3 times table, the result will always be a multiple of 3. It’s one of the clues that helps you check your answers.

What if I forget a 3 times table fact?

You can use the pattern clues to help. Count in 3s, or add the digits of the answer to see if it’s a multiple of 3. You can also use repeated addition or skip counting to figure it out.

Can I use 3 times table patterns in other maths?

Yes! Patterns in the 3 times table help with division, fractions, and even algebra. They make maths easier and more fun to learn.