Q I found your column of March 27 about the price of a dish very interesting, as did my pupils. Do you have any other gems using percentages that could stimulate discussion?
A Recently, I was told about a company's negotiations over its annual salary review. The company's negotiator was a mathematician and suggested that, instead of the usual 5per cent increase, they would give them an immediate 20 per cent increase for the two months leading up to Christmas, which would be followed by a 20 per cent reduction of this new rate for the remainder of the 12 months. Good deal? The employees thought so. What do your pupils think?
Let us suppose the average salary of these employees is pound;18,000, monthly earnings being pound;1,500. The 20 per cent increase would give a salary of pound;21,600 (0.2 x pound;18,000 = pound;3,600, pound;18,000 + pound;3,600 = pound;21,600), with monthly earnings of pound;1,800.
This would be a gain of pound;600 over the two months.
After Christmas their pound;21,600 salary is reduced by 20 per cent, which means the earnings after Christmas will be pound;17,280 (0.2 x pound;21,600 = pound;4,320, pound;21600 - pound;4320 = pound;17,280), pound;1,440 per month, less than their original earnings, and over the next 10 months they would lose the pound;600 they gained before Christmas.
If they had taken a 5 per cent increase, the annual salary would be Pounds 18,900. So the employees lose pound;900 and enter next year's negotiations on a lower salary.
There are loads of questions that could be investigated; eg searching for break-even points. What differences, if any, would there be between the highlow earners in the company? Would the overall percentage loss be different between the salary levels? Students investigating percentages are preparing for the world of work, as discussions can arise about how take-home pay is calculated and so on. Data on areas with the lowest average weekly wage can be found at news.bbc.co.uk1hibusiness4319239.stm
Q I have just gained my first teaching post in maths. I have seen the classroom where I am going to teach: the walls are very bare! I wonder if you have any ideas to make it look more interesting. I thought I could use some of the summer break to create some interesting displays.
A Congratulations - Jyou must be really excited. I am sure we can all remember that tremendous buzz from having our first classroom. Even better, you aren't following someone who has already created the space. There are some great posters available on the internet. Ask your head of department if they have any or if they have a budget for you to buy some. Creating your own posters can be fun. Perhaps some posters of famous mathematicians as I suggested in my column of May 5.
I like using the unusual and interesting to add a touch of humour, so I went on a web search for maths mistakes. I came across Dr Donald E Simanek, emeritus professor of physics at Lock Haven, University of Pennsylvania (www.lhup.edudsimanekwhoops.htm).
In 1998, The Department of Environmental Protection of the Commonwealth of Pennsylvania distributed free pocket rulers in an effort to advertise their services to the taxpayer and promote their website. This also promoted imperial and metric units. Take a close look at the ruler they produced.
Dr. Simanek also features the pound;2 coin, which was launched in 1998 to honour British industry: "The artistic designer has used a circle of gears of different sizes in an interlocked array. There are 19 of them. Even if they were sized properly, an odd number of gears meshing around a circle couldn't possibly turn. Each gear turns its neighbor in the opposite direction."
This design was also used in 2002 and 2004. Dr Simanek suggests that someone at the Royal Mint has a sense of humour.
The Mariner I space probe crashed after 293 seconds due to a bar being missed from the variable symbol. This error cost about pound;4,280,000.
en.wikipedia.orgwikiMariner_1 The story of a pound;78 million mistake due to changing from metric to imperial units can be found at mars.jpl.nasa.govmsp98orbiter Other mistakes can be found at members.cox.netmathmistakestop5.htm
Stephen Pile's book Heroic Failures also records some great mathematical mistakes.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.
Email your questions to Mathagony Aunt at email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX