1. All pupils can recognise patterns in numbers
L.O.
All pupils can recognise patterns in numbers

2. Patterns 1:

3. All pupils can recognise patterns in numbers
L.O.
All pupils can recognise patterns in numbers

4. Patterns 2:
According to an old Indian myth, Sissa ben Dahir was a courtier for a king. Sissa worked very hard and invented a game which was played on a board, similar to chess and played on the same board.
The king decided to reward Sissa for his dedication and asked what he would like. Sissa thought carefully and then said,
"I would like one grain of rice to be put on the first square of my board, two on the second square, four on the third square, eight on the fourth and so on."
The king thought this was a silly request but went ahead with it.
Draw a brief diagram to understand the problem.
How many grains of rice did Sissa get on the 64th square?
How much rice did Sissa get in total?

5. All pupils can recognise patterns in numbers
L.O.
All pupils can recognise patterns in numbers

6. So the mathematician bought a pair of rabbits.
Patterns 3:
A very famous mathematician wanted to buy a sailing boat so his old teacher suggested that he could breed rabbits, then sell their fur until he had enough money to buy his boat.
So the mathematician bought a pair of rabbits.

7. Patterns 3:
 He had to calculate how long it would take to save enough money for his boat and from this came a famous problem:
If a pair of rabbits gives birth to another pair every month, then after two months each new pair gives birth to another pair, and so on, how many pairs of rabbits would there be after a year?
(Think about it - it's tricky. Remember the original pair keeps breeding too).  

8. Patterns 3:

9. All pupils can recognise patterns in numbers
L.O.
All pupils can recognise patterns in numbers

10. Patterns 4: Leonardo of Pisa: You know, Leonardo the son of Bonacci.
The one who lived from about 1170 to 1250 in Pisa.  
Well, Leonardo is better known as Fibonacci.
Fibonacci's number sequence (1,1,2,3,5,8,etc) has been discovered in some very interesting places. In branching plants, flower seeds and petal and leaf arrangements, on the outside of pineapples and inside apples as well as within pine cones. All involve the Fibonacci numbers.

11. Patterns 4:
Investigate how the numbers of the sequence relate to each - you will make another amazing discovery!
Try dividing each number into the number that follows it, e.g. 2 into 3, 3 into 5, 5 into 8 and so on.
Try finding the average of your answers.
This is the type of strange phenomenon that intrigues mathematicians.
If you have discovered a pattern to the answers, you have found an answer that is very close to what is sometimes known as the "golden mean".

12. They named this special relationship of the parts the "golden ratio".
Patterns 4:
Golden items are considered very valuable and quite rare. The "golden mean" has been a number used to investigate natural and man-made objects and the size of one part of the object to another part.
When mathematicians examined what they considered to be perfect objects; a building like the Acropolis, a finely made and tuned violin, the human body, they discovered that the parts of the objects were in the same ratio as Fibonacci's numbers were to each other.
They named this special relationship of the parts the "golden ratio".  

13. All pupils can recognise patterns in numbers
L.O.
All pupils can recognise patterns in numbers

14. Try wrapping rectangles in the Golden Ratio around one another.
Patterns 5:
This diagram gives you an idea of the proportions of a Golden Rectangle . It is divided into two pieces, and the ratio of the two parts (a to b) is the Golden Ratio .
If you investigate even further you will find that the two parts together (a+b) is the same ratio to just the left part (a)!
Try wrapping rectangles in the Golden Ratio around one another.  

15. There are more 'golden shapes ' to be found in geometry and in nature:
Patterns 5:
There are more 'golden shapes ' to be found in geometry and in nature:
the nautilus shell or spiral, squares and triangles have all been investigated.
The Golden Rectangle is said to be one of the most visually pleasing rectangular shapes. What do you think? Many artists think so and have used the shape within their artwork.

16. All pupils can recognise patterns in numbers
L.O.
All pupils can recognise patterns in numbers

17. Extension: Research Fibonacci or the Golden Ratio.
Where and when else does it occur?
Come up with both in depth natural and manmade examples.

18. All pupils can recognise patterns in numbers
L.O.
All pupils can recognise patterns in numbers