The pot contains 10 counters which are being randomly removed and replaced. How many of each colour do you think are in the pot?
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[Notes for Teacher: The film will go on for ever! It shows a red, green or blue counter being taken from the pot by random selection but in proportion to the number of red, green and blue counters in the pot. Students might make a tally chart to see the relative numbers of counters being pulled out of the pot then divide 10 in the same ratio.]
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Have you read Craig's book yet?
Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...
"How I wish I’d taught maths' is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.
Casio Classwiz Calculator
There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).
As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!
This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...
Teacher, do your students have
access to computers?
Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to a student probability activity.
Change the number of counters in the pot:
You can vary the speed of the animation by sliding the handle below to the left or to the right.
We ask for the probability that a number, integer or fractional, commensurable or incommensurable, randomly chosen between 0 and 100, is greater than 50. The answer seems evident: the number of favourable cases is half the number of possible cases. The probability is 1/2.
Instead of the number, however, we can choose its square. If the number is between 50 and 100, its square will be between 2,500 and 10,000.
The probability that a randomly chosen number between 0 and 10,000 is greater than 2,500 seems evident: the number of favourable cases is three quarters of the number of possible cases. The probability is 3/4.
The two problems are identical. Why are the two answers different?
Joseph Bertrand, Calcul des probabilités, 1889 (translation by Sorin Bangu) presented by Futility Closet.