Fibonacci sequence

problem
Fibonacci surprises

Age

11 to 14

Challenge level

Play around with the Fibonacci sequence and discover some surprising results!
problem
Fibonacci deduction

Age

11 to 14

Challenge level

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?
problem
Farey Fibonacci

Age

16 to 18

Challenge level

Investigate Farey sequences of ratios of Fibonacci numbers.
problem
Building gnomons

Age

14 to 16

Challenge level

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
problem
Simple train journeys

Age

5 to 11

Challenge level

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
problem
First forward into Logo 11: sequences

Age

11 to 18

Challenge level

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
problem
Colour building

Age

11 to 14

Challenge level

Using only the red and white rods, how many different ways are there to make up the other rods?
problem
Plus or minus

Age

16 to 18

Challenge level

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
problem
Pythagorean fibs

Age

16 to 18

Challenge level

What have Fibonacci numbers got to do with Pythagorean triples?
problem
Fibonacci fashion

Age

16 to 18

Challenge level

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?