Posted tagged ‘Methods’

Know your limits!

April 18, 2010

It is important to know your (not only mathematical) limits – when you know what you can do and what you can’t do (yet), you know where you need to focus your efforts to improve your skills. This applies to everything in life, not just mathematics.

Have you spent time analysing your own skills in mathematics? Have you looked at the list of skills that you are expect to have (and be able to demonstrate in a test) as you complete each section of study? If you haven’t you can (and should!) read the study design document at this link.

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Popular Populations & Power (or a fistful of Fibonacci!)

March 20, 2010

What does you fist have to with exponential functions? Well aside from wishing you could hit your teacher for making you suffer through Exponential (&Transcendental) functions, it shows you an important sequence of numbers – the Fibonacci (Fibonacci was the first person to bring decimal numerals and place value notation to the west!)  sequence. The fibonacci sequence is:

1, 1, 2, 3, 5, 8, 13 ,21 ,34,…

If you look at the side of your fist, you can see this pattern in the knuckles (not knuckle joints).  The first knuckle is 1. The second knuckle is 1. When you fold your finger over, it makes a curl of three knuckles. When you close your fist (without your thumb) it makes a sequence of five sections. When you include your thumb, it goes to eight – in other words, a fistful of fibonacci (1 knuckle, 1 knuckle, 3 sections in a curl, 5 sections in a fist, 8 sections in a fist and thumb). The Fibonacci sequnce shows up everywhere in nature and art as a ratio called the golden mean. It shows up in places as different as the petals of a rose, sections of a pine cone, the shape of a shell, the Athenean Acropolis, Leonardo Da Vinci’s Mona Lisa and Vetruvian Man, the stock marketthe spiral galaxyDNA, even popular music!

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You can’t dodge this…

February 13, 2010

Matrices are a core part of Mathematical Methods – there is no way to avoid (dodge) this! You must learn the basics of matrix arithmetic (adding, multiplying by a constant, multiplying by another matrix, finding the determinant and inverse) and matrix algebra (solving for an unknown using inverses, managing transformations through matrices)

So what do you have to do to “Enter the Matrix” and make it your plaything? Well, the basic arithmetic and algebra are fairly simple – but you do need to practice – you familiarity with matrices should be the same as your skill with basic timetables – they are the same. Just like junior mathematics was based of simple timestable and basic algebra, Mathematical methods is based on the skills you develop through familiarity with matrices.  So get cracking!

Here are two powerpoints that will help you get a handle on working with matrices. Watch all of the first one, but the second one goes further than you need to understand (don’t worry about shear transformations, rotations or the applications at the end) (unless you want to…) (in which case, please consider arranging for an appointment with the school nurse).

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Get Inspired by your Calculator!

February 8, 2010

So you have this calculator. It’s got lots of buttons, and does a ton of stuff, at least it does according to the manual…

Somehow, it seems more difficult to use for you than everyone else – perhaps an old calculator, like the one on the left would be easier to use…

No – there is a better way – you’ve got to go to TI BOOT CAMP!

Make that calculator work – learn how to make it work for you! VCAA will design exams that assume that you have particular calculator skills – and if you don’t have them – you can’t make your calculator work for you – you are at a disadvantage!

Fortunately, there are some really good websites that will help you become a TI black belt. You should complete one of these videos each night from the Introduction to Graphing, Introduction to Calculator and CAS and Activities using CAS: Systems of Equations sections. You can also use the Atomic Video Tutorials to brush up on some of the basic skills you will need.

Here are some additional notes (1,2,3,4,5,6,8,9 – yes, there is no “7”) to support your learning of this content.

Good luck, and remember to use your Math responsibly – Don’t Drink & Derive!

Add a comment to this post immediately if you are in my class – with your real first name so I know it is you!