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Key Stage 4 –

The magic of maths

Student worksheet

Modelling with maths

Mathematics is the science of patterns.

Mathematicians, like Professor Alain Goriely at The

University of Oxford, use these patterns to build

mathematical models.

These can be used to predict the behaviour and

structure of objects that are too small or too big to be

seen in detail, from molecules inside cells to whole

galaxies.

Mathematical models can also be used to engineer

man-made structures that mimic nature. This is called

biomimicry.

One example is looking at how plant

tendrils coil around their supports and

using this to engineer better springs.

Your task

You will be spotting patterns in nature and using them to come up with a

mathematical model.

What to do

1. Work with a partner. Move around the classroom and look at the

images. Count the numbers of repeating parts you can see e.g. how

many petals are on the flowers or spirals in the pinecone? You may

wish to mark the images with a pen to help you count. If you do this

then make sure you wipe your marks away.

2. You will now have a lot of numbers! Write them down in order,

missing out repeated ones.

3. Work with your partner to find a pattern in this sequence.

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Key Stage 4 – The magic of maths

The Fibonacci numbers

Here is Fibonacci's sequence. 1 1 2 3 5 8 13 21 34 55 ...

Write in the square of each number ...

What pattern do you notice?

Create a new sequence by adding up consecutive square numbers. The first number, 6, (1+1+4) has been added

for you. - - 6 ...

What pattern do you notice?

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Key Stage 4 – The magic of maths

Images 1

A

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Key Stage 4 – The magic of maths

Images 2

D

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Key Stage 4 – The magic of maths

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Key Stage 4 – The magic of maths

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