Nicola Randall is a primary maths adviser for HfL

In the aims of the new curriculum for mathematics, it states that a high quality mathematics education provides ‘an appreciation of the beauty and power of mathematics’. What better way to appreciate this beauty than to looking at nature?

The Fibonacci spiral, otherwise known as ‘the hand of God’, is just one of many mathematical patterns that exist within nature. This spiral is a visual representation of a pattern within the Fibonacci sequence. By definition, the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. The first few numbers of the sequence are 1,1,2,3,5,8 and can be worked out in the following way.
1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8
A possible approach to exploring this sequence with your class is to start with a familiar context: a book. ‘The Rabbit Problem’ by Emily Gravett tells the tale of a pair of rabbits living in a field, increasing in number month on month, until December when the field is overrun – but by how many rabbits?

pattern 1

Recording the number of rabbits in the field each month will result in the Fibonacci sequence. An extension of this sequence is to then explore what happens when the numbers are squared, which can be represented visually.

Notice that the edge of the 2² and the 3² squares line up with the edge of the 5² square, the 3² and the 5² line up with the 8² square and so on.

pattern 2

Join the corners of each square using a protractor and you will end up with the Fibonacci spiral, which can be extended as far as you like.

Pattern 3

It’s fun to get pupils spotting the Fibonacci spiral in the great outdoors. It’s surprising just how common it is once you start looking!

Pattern 4

In addition to the Fibonacci sequence, ‘The Rabbit Problem’ stimulates many mathematical links across the curriculum. Here are a few ideas to inspire and motivate your young mathematicians:

  • Solve time related problems and make predictions about the parts of the calendar that are missing.
  • Scale up a recipe in the ‘Carrot Cookery Book’ on the September page.
  • Use the rabbit ration book to explore rationing during WW2 and discuss what the most unobtainable food source would be for other animals such as Foxes. What foods might be rationed for them? This also links nicely with science; food chains and sustainability.
  • Read and interpret the data included in the numerous charts and tables throughout the book, linking with other subjects such as PE for the exercise leaflet.

At a recent TED conference Arthur Benjamin stated: ‘Mathematics is the science of patterns’.

Who knew that it existed within a children’s book?

Pattern in KS1 The Very Hungry Caterpillar is another great book to explore pattern with children and has many links across the curriculum. Why not ask your pupils to represent the food eaten each day using unifix or numicon? Can they describe the pattern? How does it grow? Can they predict the next step in the sequence? This could then lead into some learning about fruit and vegetables and other patterns in nature such as how many leaves grow around each new tomato or exploring the seeds inside an apple – when the fruit is cut in half, are two seeds always visible?

Pattern 5