Fibonacci sequence

problem
Favourite

1 Step 2 Step

Age

11 to 14

Challenge level

2 out of 3

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
problem
Favourite

Fibonacci Surprises

Age

11 to 14

Challenge level

2 out of 3

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

Spirals Instead of Sunflowers

Age

11 to 16

Challenge level

1 out of 3

Using logo to investigate spirals
problem

Stringing It Out

Age

14 to 16

Challenge level

1 out of 3

Explore the transformations and comment on what you find.
problem

Golden Powers

Age

16 to 18

Challenge level

2 out of 3

You add 1 to the golden ratio to get its square. How do you find higher powers?
problem

Paving Paths

Age

11 to 14

Challenge level

2 out of 3

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
problem

Golden Fibs

Age

16 to 18

Challenge level

2 out of 3

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!
problem

Golden Fractions

Age

16 to 18

Challenge level

3 out of 3

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.
problem

Simple Train Journeys

Age

5 to 11

Challenge level

1 out of 3

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

Room Doubling

Age

7 to 11

Challenge level

2 out of 3

Investigate the different ways you could split up these rooms so that you have double the number.