fibonacci sequence

							     Numeracy


   Learning objective:
To recognise and explain a
     number pattern.
           Maths is exciting!!!!!
Many of our
ancestors have been
investigating
mathematical
theories for millions
of years?


                                It links to the
                                world around
                                us?

It is not
something that
someone has
just ‘made up’?
Have you ever wondered how many
 spirals a sunflower centre has?
Well, it is all to do with a number sequence which
was discovered over 8000 years ago by an Italian
mathematician called Leonardo Fibonacci.
    He discovered this number sequence


0     1   1    2   3    5    8    13    21

     What are the next numbers in this
                sequence?

     Can you work out the rule for this
             number sequence?

      How can we record our findings?
The next numbers are

34     55   89   144 233 377 610 987 1597

     So what is the rule?
  You add the last two numbers
  together to get the next number!

     This number sequence is called
     Fibonacci numbers.
Ok, so how does this link to sunflowers
and nature?
                        http://www.maths.surrey.ac.uk/ho
                        sted-

  On many plants, the
                        sites/R.Knott/Fibonacci/fibnat.ht
                        ml#plants

  number of petals is
  a Fibonacci number
  and the seed
  distribution on
  sunflowers has a
  Fibonacci spiral
  effect.
Activity:
Put a line under any number in the
sequence. Add up all the numbers above
the line.

What do you notice?

 The total of all the line is one less than
 the second number below the line.

 Is this true every time?
 How can we record our results?
Steps to success
Remember to:

•Work co-operatively with your
partner;

•Read the problem carefully;

•Think of a logical way to calculate
your answers;

•Ask for help if unsure
  Challenge:
  Take any three numbers in the sequence.
  Multiply the middle number by itself.
  Then multiply the first and the third
  numbers together.

Try this a few times.              Tip: Use a
                                  calculator to
                                    help you!
Do the answers have something in
common?
Are there any numbers that do not fit
this rule?
Fibonacci’s number pattern can also be
seen elsewhere in nature:

  •with the rabbit population
  •with snail shells
  •with the bones in your fingers
  •with pine cones
  •with the stars in the solar system
If you have time tonight
Google Fibonacci and see
 where else his number
   sequence appears.