Train maths quest: patterns

Quick answer

Patterns are repeating or growing sequences that help us predict what comes next. In this train maths quest, you'll spot patterns in train timetables, distances, and platform numbers to solve puzzles and travel to the next destination!

Learning outcome

By the end of this page, you will be able to find and continue patterns in train schedules, distances, and platform numbers using repeated and growing sequences.

• You can identify what comes next in a pattern of train times
• You can spot the rule that makes a pattern grow or repeat
• You can use patterns to solve simple train travel puzzles
• You can create your own train pattern clues

Why this matters

Patterns help us understand how things work in the world around us. When you're on a train, you can use patterns to know when the next train will come, how far it travels, or which platform it will arrive at. Recognising patterns helps you solve problems faster and makes you feel like a detective!

In school, patterns help you learn multiplication tables and understand number relationships. In games and real life, patterns help you predict what happens next, like when you're playing a board game or planning your day.

How it works

Patterns are sequences of numbers, shapes, or events that follow a rule. There are two main types:

• Repeating patterns – These repeat the same sequence over and over, like: red, blue, green, red, blue, green
• Growing patterns – These get bigger each time, like: 1, 2, 3, 4, 5 or 2, 4, 6, 8

To solve a pattern, you:

1. Look at the first few items in the sequence
2. Find what changes or repeats
3. Use that rule to predict what comes next

Examples you can see

Imagine you're on a train journey with your family. You're looking at the train timetable to plan your trip. Here's a pattern you might see:

What pattern do you see here? The train numbers go up by 2 each time (101, 103, 105, 107, 109). The times go up by 15 minutes each time (9:00, 9:15, 9:30, 9:45, 10:00). The platforms go up by one letter (A, B, C, D, E).

Let's look at a growing pattern with distances:

Each time, the train travels 5 more kilometres. The pattern is growing by 5 each time. If the train continues this pattern, the next stop would be at 25 km.

Try it as a mini adventure

Train Maths Quest: The Pattern Puzzle

You're on a train journey to visit your grandparent's house. You've been given a secret clue to help you find the next train to catch:

1. You are at Platform 2
2. Next train: Platform 4
3. Next train: Platform 6
4. Next train: Platform 8
5. Next train: Platform ?

What platform should you go to next?

Answer: Platform 10

Why: The pattern is growing by 2 each time (2, 4, 6, 8, 10).

Challenge: Now try to find the pattern in these train times:

1. Train 101: 10:00
2. Train 104: 10:20
3. Train 107: 10:40
4. Train 110: 11:00
5. Train 113: ?

Answer: 11:20

Why: The train numbers go up by 3 (101, 104, 107, 110, 113) and the times go up by 20 minutes each time.

Common mistakes

• Mistake: Thinking the pattern is just the first few numbers and not looking for the rule.
  Why it happens: Children get excited about the numbers and don't think about what changes.
  Fix: Always look for what changes between each number, not just what the numbers are.
• Mistake: Adding the wrong amount when continuing a growing pattern.
  Why it happens: They might add 1 instead of 2, or 5 instead of 10.
  Fix: Count the difference between each number to find the rule, then apply it.
• Mistake: Confusing repeating and growing patterns.
  Why it happens: Both look like sequences, but they work differently.
  Fix: Ask "Does it repeat the same thing?" or "Does it get bigger each time?"

Parent and carer guide

Help your child by:

• Looking at train timetables together and spotting patterns
• Playing pattern games with everyday items like buttons, toys, or food
• Encouraging them to explain their thinking when they find a pattern
• Using real-life situations like cooking or shopping to find patterns
• Not worrying if they get it wrong – ask them to explain their thinking

What to say: "Can you see what comes next in this pattern?" "How do you know that's the right number?"

What not to do: Don't rush to tell them the answer. Let them try and make mistakes. They're learning!

Practice questions

1. What comes next in this pattern: 2, 4, 6, 8, ?
2. Find the rule in this pattern: 5, 10, 15, 20, 25
3. What platform comes next: A, C, E, G, ?
4. Complete the train pattern: 102, 105, 108, 111, ?
5. What distance comes next: 0, 3, 6, 9, ?
6. What time comes next: 9:00, 9:15, 9:30, 9:45, ?
7. What comes next in this pattern: 1, 3, 6, 10, ?
8. Find the rule: 2, 4, 8, 16, 32
9. Complete the platform pattern: 1, 3, 5, 7, ?
10. What time comes next: 8:00, 8:30, 9:00, 9:30, ?

Answers:

1. 10
2. Adding 5 each time
3. I
4. 114
5. 12
6. 10:00
7. 15
8. Multiplying by 2 each time
9. 9
10. 10:00

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 in a predictable way.

How do I find a pattern?

Look at the first few items in a sequence, then ask: "What changes between them?" or "What rule makes this happen?"

Why are patterns important?

Patterns help us predict what comes next, solve problems, and understand how things work in the world around us.

Can patterns be in real life?

Yes! Patterns are everywhere – in music, nature, cooking, and even in train schedules and games.

How can I practice patterns at home?

You can look at train timetables, play with blocks or toys to make patterns, or find patterns in your daily routine like breakfast, lunch, dinner times.