Download Fibonacci numbers

Year 7 Maths Investigation - Fibonacci Numbers Project
Leonardo Fibonacci was a mathematician who is most famous for describing the following number pattern:
1, 1, 2, 3, 5, 8, 13, 21, …………
Your task :
PRODUCING
1.
What’s the next number in the Fibonacci sequence ?
2.
List the next 20 numbers that are part of the sequence ?
INVESTIGATING
3.
How is the pattern formed ?
SOME CALCULATIONS
4.
Write out the first 15 Fibonacci numbers.
a) Look at every third number. What sort of number is it ?
b) Look at every fourth number. What is it divisible by ?
c) Look at every fifth number. What is it divisible by ?
5.
Follow these steps :
a) Take any three Fibonacci numbers in a row.
b) Multiply the first and the third number together.
c) Multiply the middle number by itself.
d) Find the difference between the answer you got for part b and the answer you got for
part c.
e) What pattern did you notice ?
6.
a) Add up the first five Fibonacci numbers. Compare your answer with the seventh number.
b) Add up the first ten Fibonacci numbers. Compare your answer with the twelfth number.
Is there a pattern when you compare this with your result to part a ?
c) Add up the first fifteen Fibonacci numbers. By looking at your results for parts a and b,
work out what the seventeenth number is going to be.
7.
It’s possible to make different Fibonacci sequences by using different starting numbers.
Copy and complete these sequences.
a)
b)
c)
d)
e)
2, 2, 4, 6, 10, __, __, __,
0, 4, 4, 8, __, __. __,
0, 0, __, __, __,
6, __, 8, __, 18, __,
__, 5, __, 11, __, __,
f)
g)
h)
i)
j)
1, 2, 3, 5, 8, __, __. __,
10, 1, 11, 12, __, __. __.
10, 10, 20, 30, __. __. __.
9, __, 9, __, __. __,
__, 4, __, 20, __, __,
Year 7 Maths Investigation - Fibonacci Numbers Project
Continued . . . . . . . . . . .
DESIGN
8.
Write 2 of your own Fibonacci sequences. Take out some of the numbers as in Question 7,
and ask another person to work out the missing numbers in your sequence.
MATHS AND NATURE
9.
Fibonacci sequences are commonly found in nature. Make a list of 10 of these. (Hint: use the
internet).
10.
Choose 3 from your list and describe the background behind each one. (Pictures and diagrams
are a useful tool here).
RESEARCH
11.
Who was Leondardo Fibonacci ?
12.
What was his real name ?
13.
Where did he live ?
14.
When did he live ?
15.
Outline something you found interesting about him ?
16.
What other mathematical discoveries did he make ? Describe one.
BIBLIOGRAPHY
Include a list of the internet sites and books you used for this project.
Presentation : Prepare a booklet
Due date : _____Friday _________