What is the Fibonacci sequence?

It is a list of numbers that starts 1, 1, 2, 3, 5, 8, 13, 21, where you make each new number by adding the two numbers just before it. For example, 5 + 8 = 13.

Why do so many flowers have a Fibonacci number of petals?

Plants grow new petals and leaves in a spiral that packs them as efficiently as possible to catch light and rain. This growth pattern naturally produces petal counts like 3, 5, 8, 13, 21 and 34, which are Fibonacci numbers.

Where can my child spot Fibonacci patterns at home?

Look at sunflower seed heads, pinecones, pineapple skin, the petals on daisies and lilies, and the curling shape of a snail or nautilus shell. Counting the spirals or petals is a great real-world maths game.

Fibonacci was the nickname of Leonardo of Pisa, an Italian mathematician who lived around 800 years ago. He helped popularise the sequence in Europe, which is why it carries his name.

Is the Fibonacci sequence suitable for primary-school children?

Yes. It only needs simple addition to extend, and the spirals and petals give children something concrete to count and check, making it a friendly first taste of patterns and number sequences.

Fibonacci Patterns in Flowers and Shells

Math Interactive lesson Free to play

Fibonacci patterns in nature are the appearance of the Fibonacci sequence — the list of numbers where each one is the sum of the two before it (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on) — in the way living things grow. Many flowers have a Fibonacci number of petals: lilies have 3, buttercups 5, many daisies 13, 21 or 34. The seeds in a sunflower head and the bumps on a pinecone form interlocking spirals whose counts are usually neighbouring Fibonacci numbers, such as 34 and 55.

The sequence was named after Leonardo of Pisa, known as Fibonacci, an Italian mathematician of the 13th century. It matters because it links simple addition to real shapes children can see and count outdoors, turning a maths idea into a hands-on hunt.

Learners grasp three key ideas: how to extend the sequence by adding the two previous numbers, how to count petals and spirals to test whether a pattern is Fibonacci, and how a Fibonacci spiral curls like a snail or nautilus shell.

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A secret code in nature

🌻🐚🌼 Nature's Secret Number Pattern Did you know that flowers, pinecones, and seashells all share a hidden counting trick? It is called the Fibonacci pattern (say it: fib-oh-NAH-chee). Once you learn it, you will start spotting it everywhere — in your garden, at the beach, even in a slice of pineapple! 🔍 Your mission: become a nature detective and crack the code. Tap Next to begin!
Build the number ladder

The Fibonacci Numbers The pattern is a list of numbers. To get the next number, you add the two numbers before it. It starts like this: 1 1 2 3 5 8 1 + 1 = 21 + 2 = 32 + 3 = 53 + 5 = 8 So what comes after 8? Add the last two: 5 + 8 = ? 11 13 16
Drag the next number

Keep the Ladder Going You are getting good at this! Drag the right tile into each empty box. Remember: add the two numbers before it. 8 13 ? 34 ? Tip: 8 + 13 = 21, and 21 + 34 = 55 55 21 40
Count the petals

Petals Love Fibonacci Here is the magic: most flowers have a Fibonacci number of petals! Tap each petal to count them. Petals counted: 0 Lilies have 3, buttercups have 5, daisies often have 34 — all Fibonacci numbers!
Match the flowers

Detective Challenge: Real Flowers Each flower below has a Fibonacci number of petals. Tap a flower to check if its petal count is really in the pattern! Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34… 🌷 Lily — 3 petals 🌼 Buttercup — 5 petals 🌸 Delphinium — 8 petals 🌻 Marigold — 13 petals
The spiral shell

The Curling Spiral When you draw squares using Fibonacci numbers and curve a line through them, you get a beautiful spiral — the very same shape as a snail's shell! 🐌 Tap the squares from smallest to biggest to grow the spiral.
Spot it yourself

Where Else Is It Hiding? Now you are a real Fibonacci detective! Tap each thing below to reveal whether it hides the pattern. 🌻 Sunflower seedsspirals: 34 & 55 🌲 Pinecone8 & 13 spirals 🍍 Pineapple skin8 & 13 rows 🧱 Brick wallall the same Three of these hide Fibonacci. One does not — can you find it?
You cracked the code!

🏆🌻🐚 You Cracked Nature's Code! Amazing work, detective! Here is what you learned: 🔢 The Fibonacci pattern adds the two numbers before to get the next: 1, 1, 2, 3, 5, 8, 13, 21, 34… 🌼 Most flowers have a Fibonacci number of petals. 🐚 Fibonacci squares curl into a spiral — like shells and snails. 🌻 Sunflowers, pinecones and pineapples hide the pattern too! Your challenge: go count the petals on a real flower this week. Nature is full of secret maths! 🌷✨

Frequently asked questions

What is the Fibonacci sequence?: It is a list of numbers that starts 1, 1, 2, 3, 5, 8, 13, 21, where you make each new number by adding the two numbers just before it. For example, 5 + 8 = 13.
Why do so many flowers have a Fibonacci number of petals?: Plants grow new petals and leaves in a spiral that packs them as efficiently as possible to catch light and rain. This growth pattern naturally produces petal counts like 3, 5, 8, 13, 21 and 34, which are Fibonacci numbers.
Where can my child spot Fibonacci patterns at home?: Look at sunflower seed heads, pinecones, pineapple skin, the petals on daisies and lilies, and the curling shape of a snail or nautilus shell. Counting the spirals or petals is a great real-world maths game.
Who was Fibonacci?: Fibonacci was the nickname of Leonardo of Pisa, an Italian mathematician who lived around 800 years ago. He helped popularise the sequence in Europe, which is why it carries his name.
Is the Fibonacci sequence suitable for primary-school children?: Yes. It only needs simple addition to extend, and the spirals and petals give children something concrete to count and check, making it a friendly first taste of patterns and number sequences.

Fibonacci Patterns in Flowers and Shells

What this Spark covers

Frequently asked questions

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