Archive for September 2011

Welcome to the chain gang

September 29, 2011

You’re in for it now.

Ya done wrong and ya gotta pay the price. It’s the chain gang for you. The Markov Chain gang.

You’re here until yu’ve done your time, and we are gonna make ya work.

Hard labour, kid. Work ’til ya brain burns, ya fingers cramp and ya think ya can’t do no more.

We’re gonna turn ya into a… Mathematician.

OK, enough of the high drama; Markov chains are the last bit of the course content you have to master. Despite my complaining about it, they’re not as bad as I’ve made them out to be. If you remember tree diagrams from year 9, markov chains are just one more step along that path. In short Markov Chain are about semi-independent repeated events. Independent events are probabilistic outcomes that are not affected by prior events; Markov style events are events that are only affected by the immediately prior event – i.e what happened two stages before doesn’t effect the next probability directly. In basic terms, only the last event that occured effects this event – this is not about “winning/losing streaks”.

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To Be, or Not To Be?

September 20, 2011

To Be, or Not to Be?

The name “Hamlet Happens” comes from the old idea that if an army of monkeys were to hit the keys of a typewriter (or word processor) randomly, eventually the whole of Shakespeare’s play Hamlet would be typed. Of course the length of time that we would expect to have to wait for such an extremely unlikely event to happen is billions of times the age of the universe. In this manipulative, letters are drawn at random from the beginning of Hamlet’s soliloquy, “To be, or not to be.” Any word made from those letters (such as TOE), of length five or less, can be entered in the box. When Start is pressed, letters are drawn and recorded. The process continues until your word (in the right order) appears (in blue).

Goal of Instructional Unit

The purpose of this manipulative is to help students recognize that (1) unusual
events do happen, and (2) it may take a long time for some of them to happen.

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Tick-Tock Torture – or the EPI strikes back!

September 18, 2011

So here we go again – it’s time for your second chance at the Extended Practical Investigation (EPI). Before you even begin thinking about this one, you need to think about the first EPI you did.

Spend some time – recall what you had to do – the skills you had to use. Think about the assessment you completed; what was it like – how do you wish you had prepared for it?

Well now you have a second chance – it’s time for the EPI again. You know what the topic is (Determination of acceleration due to gravity by means of a pendulum), so you should be making plans *right now* as to how you are going to use your time.

You only have 3 periods, and you will be using the third to write your report. Here is a file that gives you some more specifics about the project, and here is the marking guide. You should be planning exactly how you will go about using your time. Here is a video that shows a similar experiment to the one you will do:

The student in the above video does some things right, but there are many improvements needed. Think about the following questions (the answers are not simply yes or no!)

  1. Is the mass of the pendulum bob relevant? If yes, why? If no, why should you use one at all?
  2. Is the pendulum string important? Why? What measurements of it should be made? How should it be strung to support the bob? How long should it be/ What length(s) will you use?
  3. How should the pendulum be supported? Does the support matter?
  4. How should the pendulum swing? Straight back and forward or otherwise? How wide should the arc of the pendulum be?
  5. How will you measure the period of the oscillation? From which point to which point? Why?
  6. Have you tried running this experiment at home and seeing what can go wrong with it?
  7. Have you planned your time budget, and who will do what it your group?

Those are some starting questions, and if you don’t feel stressed, YOU SHOULD!

See you in class!