# Fibonacci related ideas for outdoor learning week

Discussion in 'Mathematics' started by emserata, Jul 3, 2011.

1. ### emserata

We are spending a week doing as much learning outdoors as possible. I am in Year 6 and have a talented bunch and thought Fibonacci might be a good project. I have a few ideas but wondered if anyone had anymore. I really want to enthuse them about maths and relate it to art and nature as well as do things on a big scale.
So far I have: stick lots of squared paper together and plot out the golden rectangle (LA) and use trubdle wheels, metre sticks and measure it out for HA. We are also going to look for examples of the sequence in nature e.g. petals and start working on the sequence maybe writing it out on a till roll etc?
Hopefully they will do lots of different types of maths as well as have fun. Does this sound OK do you think, any other ideas?
Thank you

2. ### cyolba

Congratulations! You started the 7500th thread on the Maths forum.
You could look at bees and rabbits (I think old Fibo himself was investigating rabbit reproduction when he came across his lovely sequence). There are nautilus shells as well.
As far as the golden ratio is concerned, how about measuring all of the school's windows and seeing which are closest to the golden ratio? How about any sporting things? Dimensions of pitches for football, tennis, netball etc?

cyolba, off to have a cold shower after being unnaturally helpful

3. ### emserata

Thank you cybola, really like the ideas especially measuring windows etc. This being helpful business suits you!

4. ### cyolba

Please edit that post, you're destroying my hard-earned reputation for being a complete arsehole.

cyolba, worried sick at the thought of joining the caring professionals on here

5. ### florapost

are you setting up a chart so you can see how close to the golden rectangle you get with each new square added? ditto with your sequence - having a second sequenc to show nth term - nth - 1 term gets the same sequence - then to show how nth term/ n-1th term gets closer to the ratio - this gives you a cross-check that the quilt measurers have been accurate
pegs in the appropriate corners each time and wind string round them so you can see the golden spiral emerge
you could make some large-size rectangles in various ratios including the golden one - and a square - have a group of kids hold them up, and and get other classes to come out in turn and rate them in order of preferenc to see if the gr does come out favorite as a mini-stats project (when the bbc did this a few years ago, the gr didn't come out as most liked, but as least disliked)
love the petal counting idea
if wet, in the barn - if you have to stay indoors, they could each draw a f quilt - tearing double pages out of a small-squared maths book gives you the perfect paper to do it on
can send you starter ppt etc if you pm me your email - yet another thing i need to upload over summer!

7. ### emserata

Fantastic ideas from everyone; thank you very much. I have loads to work on here, maybe more than a week at this rate!

8. ### Woostarite

Here's an idea: Line up 'n' of your students in a straight line (each acting as lily pad). Put a further student (with an optional frog picture/mask!) at the end of the line. He/she has to get to the other end of the line by making hops over either one student at a time, or two students (hopping over two students at once, and hopping over two students individually, are considered separate moves). Work out how many ways they can get from start to finish. Start with low values of n, and see if they can spot the pattern (which is the Fibonnaci sequence!)

9. ### Woostarite

To clarify with an example, if there is 1 student, you can only hop over them in one way, and get to the finish immediately.
With 2 students, you could hop over the first then the second, or hop over both at once. i.e. 2 ways.
With 3 students, you could hop over each individually, hop over first then the next two at once, or hop over the first two at once then hop over the last, i.e. 3 ways.
It works because to find the number of ways for n students, say F(n), you either hop one student and are then solving the problem with one less student F(n-1), or you could have hopped two then solved for two less students, i.e. F(n-2). Thus F(n) = F(n-1) + F(n-2), i.e. Fibonacci.