What's all this about Fibonacci?

Maestro has moved from the Primary series of Singapore Maths books to the High School series New Syllabus Mathematics. Wow, what a huge step up! Compared with the Primary books, we're having to move at a slower pace now. We don't have a parent's or Home Instructor's Guide, so I need to sit with Maestro and work through this with him.

The problems are very creative, too. There's been a lot of extra problem solving from the outset. Some of the questions are fun, and we'll work on them together. Others are tricky and border on us getting frustrated, so we have to leave them and just move on. (There are no 'working out' diagrams in the answers!)

Hmmm! Did I chose the wrong maths program for Maestro's High School years? I'm hoping not, and as I look ahead into future chapters, I realise that I remember a lot of my High School work.

BUT .. first we have to wade our way through Chapter 3; Number Sequences and Problem Solving. Right there, in the first few pages of that chapter, we're learning about Triangular Numbers, the Fibonacci Sequence and Pascal's Triangle. Hold on; back up! "What's this Fibonacci, Mum? I really don't get it! The triangle stuff seems to make sense, but I don't understand what it means with that Fibonacci sequence."

It's true, I haven't really discussed this with my children before. We've talked about patterns that occur in nature as a generalisation, but not as a mathematical discovery. The New Syllabus Mathematics book only gives a 1/2 page pointed explanation, which assumes that the teacher would fill in a lot of the information, or the child has had some form of introduction to this material before.

We do need to back a bit, and I'm going to opt for some living maths books again. Mariposa will be able to read these with us, and we can also take not of our findings in nature studies.

Here are some books I have ordered, and going by the Amazon reviews, they'll be great additions to our library:

 Blockhead, The Life of Fibonacci
This book is aimed at years 3 to 5, giving a light-hearted introduction to Fibonacci's life.
Some lovely reviews and sample pages, as well as a video presentation, are available via Amazon here.








Growing Patterns
Again, aimed at upper primary grades, but looking at the patterns in nature with some clear photographs.  It looks like a simple book, but again, sometimes that's the best way to invite exploration.
Reviews and samples at Amazon here.

Fibonacci Fun
Aimed at grades 4 - 8, this is an activity book we can use on occasion to keep practicing what we'll be learning.
Review at Amazon here.








Add to those resources some websites, and I think we'll have the makings of some good grounding material.

• Dr Ron Knott's Fibonacci Numbers and the Golden Sequence - was the first site I found on my google search.  It's full of information which I found fascinating, plus some great activity suggestions.

• Thinkquest - this explores the Fibonacci sequence in quite some depth, moving also into Binet's formula, the Fibonacci spiral and the Golden Ratio.  To start using this site, click on 'The Series' in the left sidebar, then use the arrows under the main part of the screen to move along in sequence.  If you hit the 'A' and 'P' icons, you'll see the animations and proofs.

• Brantcan's Fibonacci - gives more of a scientific lean to the study.  To be honest, I need to read through this page more thoroughly, as he talks about sound waves as well.  Fascinating, but I need to get my head around it.  I've marked this webpage in case Maestro really gets the gist of it and wants to explore more.  Additional links and free downloads also available at the bottom of the page.

Looking ahead in Maestro's maths book, I see that some more creative problem solving is going to be happening, so I'm going to read up and make sure I'm well prepared.  I like that we're investigating what develops the curiosity of a mathematician,  and that enquiry is encouraged, but I also think that I'll enjoy a rest from all these mental gymnastics when we hit Fractions and Decimals again!

edited to add:

If you are looking for more information re: Singapore Maths for the high school, there is the choice of doing New Elementary Mathematics, Discovery Mathematics or New Syllabus Mathematics.

Cathy Duffy gives a review of NEM that may be helpful HERE.

Or, check out  Singapore Maths for information on their various books HERE.