The Fibonacci numbers

Golden Sunflower

Can you see a spiralling pattern in the image above? It is a similar kind of pattern you might see on pine cones, pineapples, the arrangement of leaves and the petals of flowers.

Can you continue this sequence? 0, 1, 1, 2, 3, 5, 8, 13, 18, 31, …………

If you count the numbers of tiny flowers and seeds in each sunflower head, starting in the centre and working your way out, you will find, more or less, this is the numerical pattern that is formed. Plants don’t know the Fibonacci series, so why do they grow this way? Well, it turns out that this is the most efficient way to pack many objects into a small space. Petals into a flower, seeds into a fruit, bracts into a cone and leaves onto a branch.

Another amazing thing about these numbers, is that when you study the ratio of one Fibonacci number to the next, you get closer and closer to one peculiar number, an irrational number, called “phi” or the “golden ratio”. Try these ratios (fractions) on your calculator:

1/1; 2/1; 3/2; 5/3; 8/5; 13/8; 21/13; 34/21; ………….

If you convert these to decimal numbers what happens? I’d love to read your answers in the comments section. If you are interested in finding out more about the beauty of maths in nature, check out this YouTube video, “Nature by Numbers”.

Read more at Science Ray “The Fibonacci Sequence in Nature – The Mystery of the Golden Ratio” and  at How Stuff Works “Fibonacci Numbers“.

Japanese Multiplication on YouTube


Screenshot from YouTube

On Friday, Michelle and Abby and I were very lucky to be able to attend a Country Education Project seminar “21st Century Learners in Rural Communities” with Stephen Heppell. Stephen Heppell is a leading educator and global consultant, ‘architect’ of 21st century learning spaces and engaging and distinguished guest speaker  from UK. I wrote another post about the seminar at Technoscience.

One of the exciting examples of learning strategies using web2.0 tools was this YouTube video of Japanese multiplication. Many in the audience were left pondering “How does it work?” and spent time scratching intersecting lines on their serviettes! Your learning task today is to practise five long multiplication problems using this method and then try to explain to your partner how it works. Go to the video and leave a comment about whether you think it is a good method for long multiplication.

Your homework tonight is to ask an adult if they know any maths tips and tricks to make mental arithmetic easier. One tip I learnt from a market vendor was that 88% of 25 is the same as 25% of 88, which is an easier task to calculate. It works for all percentages – Why is this so?

Nature by Numbers


Image Source

Maths is often considered boring or difficult by many people, but I am looking forward to showing this video (Nature by Numbers) to my Year 6/7 students after the holidays – it captures the simple beauty of maths in nature, using magnificent images created by Cristobal Vila.  The music and flow of this short video is just beautiful. Thanks Denise, our art teacher at Hawkesdale, for this link.