My grandmother started walking a mile a day when she was ninety.
We have no idea where she is now!
`That was just a joke`
If instead of walking a mile everyday, if she walked 99% of the distance she walked the previous day, at least we would know how far she would eventually have travelled assuming she walked one mile on the first day.
How far would she have travelled after a suitably large number of days?
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Consider the infinite(?) number sequence:
1, 0.99, 0.9801 ...
This is a geometric sequence with first term 1 and common ratio 0.9
The sum of the sequence is (1 - 0.99n)/(1 - 0.99)
When n is sufficiently large the term 0.99n tends to zero.
The sum is then 1/(1 - 0.99)
= 100 miles!
Check this answer by generating the sequence and its sum on a spreadsheet
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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...