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Maths History

Fibonacci and rabbit numbers

Introduce a famous sequence through a story and patterns.

Quick answer

The Fibonacci sequence is a special pattern of numbers where each number is the sum of the two numbers before it. It starts with 0 and 1, and the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. This pattern appears in nature, art, and even in stories about rabbits!

Learning outcome

By the end of this page, you will understand how the Fibonacci sequence works and see how it appears in nature and real life. Success signs:
  • You can explain what the Fibonacci sequence is
  • You can continue the Fibonacci pattern from 0 to 21
  • You can find examples of Fibonacci numbers in nature or your everyday life
  • You can make your own Fibonacci pattern with objects or drawings

Why this matters

The Fibonacci sequence is not just a fun pattern – it’s found all around us! From the spirals in a sunflower to the shape of a nautilus shell, this sequence helps us understand how nature builds itself. Learning about it helps you see maths in the world around you, not just in books or school.

How it works

Let’s start with a simple idea. The Fibonacci sequence begins with two numbers: 0 and 1. Then, to get the next number, you add the two numbers before it. Here’s how it works step by step:
  1. Start with 0 and 1
  2. 0 + 1 = 1
  3. 1 + 1 = 2
  4. 1 + 2 = 3
  5. 2 + 3 = 5
  6. 3 + 5 = 8
  7. 5 + 8 = 13
  8. 8 + 13 = 21
Each number is the sum of the two numbers before it. So the pattern goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

Examples you can see

Let’s imagine a story about rabbits to help you understand the pattern. Story of Fibonacci’s Rabbits Once upon a time, a pair of rabbits was born. Every month, they had a new pair of rabbits. But these rabbits were special – they never died and each new pair of rabbits started having babies after one month. Let’s count how many pairs of rabbits we have each month:
  • Month 1: 1 pair (the original pair)
  • Month 2: 1 pair (the original pair, still the only pair)
  • Month 3: 2 pairs (original pair + new pair)
  • Month 4: 3 pairs (previous 2 + new pair)
  • Month 5: 5 pairs
  • Month 6: 8 pairs
  • Month 7: 13 pairs
Each number in the Fibonacci sequence shows how many pairs of rabbits there are each month. You can also see this pattern in nature. For example, the number of petals on a flower often follows the Fibonacci sequence:
  • Lilies have 3 petals
  • Roses have 5 petals
  • Delphiniums have 8 petals
  • Chrysanthemums have 21 petals

Try it as a mini adventure

Let’s go on a Fibonacci adventure! Adventure: Fibonacci Flower Hunt 1st time: Look for a flower with 3 petals. 2nd time: Look for a flower with 5 petals. 3rd time: Look for a flower with 8 petals. 4th time: Look for a flower with 13 petals. 5th time: Look for a flower with 21 petals. Can you find a flower that matches each Fibonacci number? You can draw or take photos of the flowers you find. This is like being a Fibonacci detective!

Common mistakes

  • Mistake: Thinking that the Fibonacci sequence starts with 1 and 1.
    Why it happens: Some people confuse it with other number patterns.
    Fix: Remember, the Fibonacci sequence starts with 0 and 1.
  • Mistake: Adding the wrong numbers to get the next number.
    Why it happens: It’s easy to mix up which numbers to add.
    Fix: Always add the two numbers just before the one you’re trying to find.
  • Mistake: Forgetting to start with 0 and 1.
    Why it happens: The first two numbers are not always obvious.
    Fix: Always start with 0 and 1, then continue the pattern.

Parent and carer guide

As a parent or carer, you can help your child understand Fibonacci numbers by:
  • Using everyday objects like counters or blocks to show the pattern
  • Looking for Fibonacci numbers in nature together, like petals on flowers or spirals in pinecones
  • Playing Fibonacci games, such as counting how many Fibonacci numbers you can find in a week
  • Encouraging your child to draw or build the pattern with art or blocks
  • Reinforcing that it’s okay to make mistakes – learning is a process
It’s okay if your child doesn’t get it right away. The Fibonacci sequence is a big idea, and it takes time to understand. Celebrate small wins and keep exploring together.

Practice questions

  1. What are the first 6 Fibonacci numbers?
  2. Continue the Fibonacci sequence: 0, 1, 1, 2, 3, 5, ?
  3. What comes next in the Fibonacci sequence: 2, 3, 5, 8, ?
  4. Which Fibonacci number comes after 34?
  5. What is the 8th number in the Fibonacci sequence?
Answers:
  1. 0, 1, 1, 2, 3, 5
  2. 8
  3. 13
  4. 55
  5. 13

FAQ

What is the Fibonacci sequence?

The Fibonacci sequence is a pattern where each number is the sum of the two numbers before it. It starts with 0 and 1.

Where can I find Fibonacci numbers in nature?

You can find Fibonacci numbers in flowers, pinecones, shells, and even in the spiral of a galaxy. For example, the number of petals on a flower often follows the Fibonacci sequence.

Why is the Fibonacci sequence important?

The Fibonacci sequence shows how nature builds itself. It helps us understand patterns in the world around us, and it’s used in art, music, and even architecture.

Can I make my own Fibonacci pattern?

Yes! You can use objects like blocks or counters. Start with 0 and 1, then add the two previous numbers to get the next one. Try making it with your hands or drawing it on paper.

Is Fibonacci only for maths?

No, Fibonacci is used in art, music, nature, and even in computer science. It’s a pattern that shows up in many different areas of life.