Detective maths quest: patterns

Quick answer

Patterns are repeating or growing sequences that help us predict what comes next. As a detective, you can find patterns in shapes, numbers, or events by looking for what repeats or changes in a logical way.

Learning outcome

By the end of this page, you will be able to find and extend simple repeating and growing patterns using objects, drawings, or numbers.

• You can spot a pattern in a sequence of shapes or numbers.
• You can continue a pattern by adding the next shape or number.
• You can describe how a pattern grows or repeats.
• You can make your own pattern using a rule.

Why this matters

Patterns are everywhere around us! When you play a song, you might notice it has a repeating beat. When you build with blocks, you might make a pattern with red, blue, red, blue. Recognising patterns helps you understand how things work and makes it easier to solve puzzles, play games, and even predict what happens next in stories. Patterns are also the foundation for learning multiplication, algebra, and problem-solving later in school.

How it works

Patterns follow a rule. There are two main types:

1. Repeating patterns – These repeat the same group of items over and over. For example, red, blue, red, blue, red, blue.
2. Growing patterns – These change in a logical way. For example, one block, then two blocks, then three blocks. Each step adds one more.

As a detective, you can look for the rule by:

• Looking at the first few items.
• Checking if they repeat or grow.
• Figuring out what comes next based on the rule.

Examples you can see

Let’s look at some detective clues to find patterns.

Repeating Pattern Example

Imagine you see this sequence of shapes:

Circle, Triangle, Square, Circle, Triangle, Square, ?

What comes next?

Look at the first three shapes: Circle, Triangle, Square. Then it repeats: Circle, Triangle, Square.

So, the next shape is a Circle.

Growing Pattern Example

Look at this pattern:

1, 3, 5, 7, ?

What number comes next?

Each number increases by 2:

• 1 + 2 = 3
• 3 + 2 = 5
• 5 + 2 = 7
• 7 + 2 = 9

The next number is 9.

Real-Life Detective Clues

Imagine you are a detective solving a mystery at a birthday party. You find a trail of cake slices:

• First slice: 1 piece
• Second slice: 2 pieces
• Third slice: 3 pieces
• Fourth slice: 4 pieces

What comes next?

This is a growing pattern. Each slice has one more piece than the last.

So, the fifth slice will have 5 pieces.

Try it as a mini adventure

Adventure: The Pattern Detective Mission

You are a detective solving a mystery. You find a trail of clues that form a pattern. You must find the next clue to solve the case!

1. First clue: Red block
2. Second clue: Blue block
3. Third clue: Red block
4. Fourth clue: Blue block
5. Fifth clue: ?

What is the next clue?

It's a Red block. This is a repeating pattern: Red, Blue, Red, Blue, Red.

Challenge: Make your own pattern

Draw or build a pattern with 5 steps. Use shapes, colours, or objects. Then, write the rule for your pattern. For example:

• Rule: "I am using red, blue, green, red, blue, green."
• Next step: "The pattern repeats, so the next item is red."

Common mistakes

• Mistake: Thinking that a pattern always starts with the same shape or number.
• Why it happens: Children might be used to patterns that start the same way and forget that patterns can begin with different items.
• Fix: Look at the first few items to see the repeating or growing rule, not just the first one.

• Mistake: Confusing growing and repeating patterns.
• Why it happens: Sometimes it's hard to tell if a pattern is growing or just repeating, especially if it's short.
• Fix: Ask: "Does the pattern get bigger each time, or does it repeat the same group?"

• Mistake: Skipping a step when continuing a pattern.
• Why it happens: Children might rush to guess the next item without thinking about the rule.
• Fix: Count or look carefully at each step. What is the pattern doing?

Parent and carer guide

Help your child become a pattern detective by:

• Playing pattern games like "What comes next?" with everyday objects like toys, food, or blocks.
• Looking for patterns in nature, like leaves, flowers, or footprints.
• Encouraging them to draw or build their own patterns and explain the rule.
• Noting if they get confused between repeating and growing patterns – it’s normal to mix them up at first.
• Using fun phrases like "Detective mode: What's the rule?" to make it playful.

Remember: It's okay to make mistakes. Patterns take practice. Keep the fun going and keep asking "What comes next?"

Practice questions

1. What comes next in this pattern: Red, Blue, Red, Blue, Red, ?
2. Continue the pattern: 2, 4, 6, 8, ?
3. Which shape comes next in: Triangle, Square, Triangle, Square, ?
4. What number comes next in: 10, 15, 20, 25, ?
5. Complete the pattern: 1, 2, 4, 5, 7, 8, ?

Answers:

1. Blue
2. 10
3. Triangle
4. 30
5. 10

FAQ

What is a pattern in maths?

A pattern is a sequence of numbers, shapes, or events that follow a rule. It can repeat or grow.

How do I know if a pattern is repeating or growing?

If the same group of items keeps appearing, it’s repeating. If each step gets bigger or changes in a way, it’s growing.

Can patterns be found in music?

Yes! Music has patterns in beats, rhythms, and melodies. For example, a beat like "clap, snap, clap, snap" is a repeating pattern.

How can I help my child at home?

Look for patterns in daily life. Ask questions like "What comes next?" or "What rule are we following?"

Why do we learn about patterns?

Patterns help us predict what happens next, solve puzzles, and understand how things change. They’re the foundation for algebra and problem-solving.