Sequences and times tables

Quick answer

Sequences and times tables are connected because times tables show patterns that repeat in a predictable way, like counting by 2s, 5s, or 10s. When you know your times tables, you can spot and continue number patterns easily.

Learning outcome

By the end of this page, you will understand how times tables create number sequences, and you will be able to spot and continue simple number patterns using multiplication facts.

• You can find the next number in a sequence by using your times table facts.
• You can make your own number patterns using times tables.
• You can explain how multiplication and sequences are linked.

Why this matters

Sequences and times tables help you think like a mathematician. When you see a pattern, you can predict what comes next. This skill is useful in games, science, music, and even cooking! Understanding sequences helps you solve problems faster and build strong math skills for the future.

How it works

Sequences are numbers that follow a rule. When you multiply the same number over and over, you create a pattern. For example, if you start with 3 and keep adding 3, you get the sequence 3, 6, 9, 12, 15, 18… This is the 3 times table in sequence form.

Each number in the sequence is a multiple of 3. You can think of it like:

1. 3 groups of 1 = 3
2. 3 groups of 2 = 6
3. 3 groups of 3 = 9
4. 3 groups of 4 = 12

So, the sequence 3, 6, 9, 12 is just the 3 times table written out in order.

Examples you can see

Here’s how the 5 times table looks as a sequence:

Notice how each number in the sequence is 5 more than the last one. This is because you're adding 5 each time, which is the same as multiplying by 5.

Try it as a mini adventure

Adventure: The Treasure Hunt Sequence

You are going on a treasure hunt. The clues tell you to:

1. Start at 2
2. Count by 2s to find the next clue
3. Keep going until you find the treasure

What sequence do you follow?

• First clue: 2
• Second clue: 4
• Third clue: 6
• Fourth clue: 8
• Fifth clue: 10
• Sixth clue: 12
• Seventh clue: 14
• Eighth clue: 16
• Ninth clue: 18
• Tenth clue: 20

Can you guess what the next clue would be? It's 22!

Now, try this: What if the treasure hunt starts at 3 and you count by 3s? What would the sequence be?

Common mistakes

• Mistake: Thinking that 4 x 3 = 12, but then skipping to 14 instead of 16 in the sequence.
• Why it happens: Forgetting that each step in a sequence adds the same number (in this case, 4).
• Fix: Always add the same number each time. If you're counting by 4s, add 4 to get the next number.
• Mistake: Using 5 x 3 = 15, then saying the next number is 18 instead of 20.
• Why it happens: Mixing up the times table facts or thinking 5 x 4 = 20 but not remembering that you're counting by 5s.
• Fix: Use your times tables to check the next number. If you're counting by 5s, 15 + 5 = 20.

Parent and carer guide

Help your child understand sequences by:

• Using everyday objects like buttons, toys, or snacks to make a pattern (like 2 buttons, 4 buttons, 6 buttons).
• Playing a game where you say a number and they count by a specific number (e.g., “Start at 3, count by 3s”).
• Reinforcing that each number in a sequence is the same amount more than the last one.
• Encouraging them to say the next number in a sequence out loud.
• Practising times tables in order to help with sequence patterns.

Remember, it’s okay if they make mistakes. Sequences take time to understand. Be patient and celebrate small steps!

Practice questions

1. What is the next number in this sequence: 4, 8, 12, 16, ?
2. Continue the sequence: 7, 14, 21, 28, ?
3. What number comes next in this pattern: 3, 6, 9, 12, ?
4. Complete the sequence: 5, 10, 15, 20, ?
5. What is the next number in this sequence: 9, 18, 27, 36, ?

Answers:

1. 20
2. 35
3. 15
4. 25
5. 45

FAQ

What is a sequence?

A sequence is a list of numbers that follow a rule, like counting by 2s or 5s.

How are sequences and times tables connected?

Times tables show patterns. When you write out a times table, it makes a sequence where each number is the same amount more than the last one.

Why do we learn sequences?

Sequences help you predict what comes next and solve problems faster. They are used in science, games, music, and even in nature!

Can I make my own sequence?

Yes! Just pick a number and keep adding the same amount. For example, start at 6 and count by 6s: 6, 12, 18, 24…

What if I forget a times table?

You can still make a sequence by adding the same number each time. For example, if you forget 7 x 3, just add 7 three times: 7, 14, 21.