Final Exam reminders

Final exams are coming – but should not increase your stress dramatically.  Finals in ToK are 5% of your semester grade and will likely have a minimal effect on your semester grade unless you fail to take the test.  The test will have three main parts: a 50-60 question multiple choice section, a written portion (think paragraph), and a puzzle/challenge.

The content for the final exam will be material covered this semester.  The material in our math unit will take greatest priority – 20-30 questions will come from the math unit, so start your review there.  If you’d like to start studying now, you should generate a list of concepts and authors that are most important.  Show the list to Mr. Braman and he will tell you if you’re on the right track.

Probability and human decision-making

There are many who would say that math is not part of the natural world.  Yet there are many similarities between the natural world and mathematical models that can replicate the functioning of the complex, dynamic world we live in.  We have studied fractals, iteration, and probability.  We have considered the Monty Hall problem and the Prisoner’s dilemma – both attempt to mathematically explain the optimal outcome.  Optimization requires a mathematical way to consider choice.

Today, we considered the dilemmas – Pig, Panther, Porridge and the Tower of Hanoi.  The real conundrum wasn’t ‘how do you solve the puzzle;’ the real challenge was ‘how can I explain the optimal outcome mathematically?’  Try to convey the optimal outcome in your journal.  Can you convey an answer for the Tower of Hanoi with 5 rings?  With 10 rings?  With ‘n’ rings?

Here are a few others to keep your brain busy.  Swap