Holy Venn Diagram

Possibly the best Venn Diagram, ever.

Two words – absolute genius.

Witty, visually appealing but, most importantly, mathematically correct.

Sets and Venn Diagrams have been on the IGCSE syllabus for some time, and made it onto the new GCSE syllabus, so we’ve all got to teach them. Project this image onto your whiteboard, sit back and put your feet up – job done. You could spend hours telling your classes about intersections and unions, or you could just show them this and they’ll grasp it in a moment.

The image is just one of many great diagrams, charts and infographics to be found in Stephen Wildish’s fantastic book: Chartography – worth a tenner of anyone’s money.

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9 – 1 Grade Boundaries

9 - 1 IGCSE Maths Grade Boundaries

As most readers will know, this year sees GCSE maths grading change from A* to E to 9 – 1.  There has been much speculation as to what the grade boundaries will be for each new level.

The first (that I have found) to publish the grade boundaries are Cambridge, for their IGCSE and can be seen above.  Below, I have converted them into percentage scores (easier for all – and pupils & parents in particular to understand)

Higher Tier:

9 – 80%, 8 – 68%, 7 – 58%, 6 – 47%, 5 – 36%, 4 – 27%, 3 – 22%

Foundation Tier:

5 – 73%, 4 – 58%, 3 – 43%, 2 – 29%, 1 – 14%

The official table from Cambridge can be found here

Important Note – These grade boundaries are for the Cambridge International Examinations board only, for their IGCSE exam. The grade boundaries for different exam boards and for GCSE maths will be different.  The information above is all that I have available at the time of writing.

However, the grade boundaries above will be of interest to those who sat Cambridge IGCSE and might also serve as a useful ball park figure to estimate grade boundaries for other boards.

It should also be noted that, unlike last year, grade boundaries for GCSE (and A Levels) will not be published the day before results day (although they will be made available to schools the day before).  Grade boundaries will be published on the same day as the results (Thursday 17th August for A & AS Levels, Thursday 24th August GCSEs)

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Maths Fail #5

Ooops! A whole generation of youngsters could be scarred for life.



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Trust me, I’m a maths teacher

There are two types of mathematicians (or 10 if you are into binary) – pure mathematicians and applied mathematicians.  I am firmly in the latter camp. That’s not to say I don’t enjoy solving a tricky trig problem, just for the sake of it, but it is applying maths to the real world that really floats my boat.

And so it was with great delight that I stumbled across The Game of Trust , an interactive insight into game theory, and how it can be applied to building trust, whether that be in negotiations, the first world war trenches or pretty much any situation where risk and reward depends on your choices.

The site analyses  different strategies – cheat, co-operate, copy etc. I won’t tell you what strategy to follow, visit the site now and invest 30 minutes or so playing the game, you will be rewarded (can you trust me when I make that statement? Visit the site and you can decide what category I’m in!)

But, without giving too much away, it does tell us that game theory says:

Without the non-zero sum game, trust cannot evolve

And in these increasingly turbulent times, we need trust more than ever.

So whether your negotiating with a teething toddler, a truculent teenager or a paranoid politician try and find an outcome that benefits you both – it’ll be in your best interests. Trust me, I’m a mathematician.

[Here’s that link again in case you missed it The Game of Trust – visit it now and invest 30 minutes of your time, it’s worth it]

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The Sausage Sandwich Game

Red sauce, brown sauce or no sauce at all – checking for bias at the BBC

One of the great pleasures of a Saturday morning is being able to linger over your breakfast whilst listening to the wit and whimsy of Danny Baker on Radio 5. A highlight of his show is the sausage sandwich game in which two listeners compete to answer questions that only that day’s celebrity guest could possible know.

Today’s guest was Wayne Bridge, who will soon be moving house, and one question was how many letters separate the first letter of his new street and the first letter of the last foreign country he visited. So, for example, if he is moving to Filbert Street and the last country he visited was Japan, the answer would be 5, as there are five letters separating F and J.

The contestants were given three options:

  1. Less than 6 letters separating them
  2. Between 6 and 12
  3. More than 12

“What a great question” I thought, no use using Google – only Mr Bridge would know the answer to that. But is it a fair question? Can you use maths to help you decide if the three options are equally likely, or is this an example of bias at the BBC, the smoking gun its opponents have been hunting for? I fired up my spreadsheet, grabbed some paper and a sharpie and began to crunch the numbers …

I wont bore you with the full calculations now, but here is brief look at my methodology. (You could safely skip this bit if you wish.) Take the letter K as the first letter of the street name. The probability of K being the first letter is 1/26 (26 letters in the alphabet). To be separated by less than six letters it could have 5 letters above it (F to J), or 5 letters after it (L to P) or it (the country) could begin with K, so if K is the first letter of the street, there are 11 letters the country could start with to have a separation of less than six. So the probability is 1/26 x 11/26. For the second option (separation between 6 and 12 letters) the probability is 1/26 x 12/26 and for the third option, a separation of greater than 12 there are only 3 possibilities: X, Y and Z, so the probability is 1/26 x 3/26. Repeat this process for each letter of the alphabet and sum the probabilities.

And the results are in! (If you skipped the above paragraph, you need to rejoin now).

The chances of three options are below:

  1. Less than 6 letters separating them 38%
  2. Between 6 and 12 35%
  3. More than 12 27%

So not too much difference between the first two options, but picking a separation of more than 12 letters would not be a good choice.

I think we can conclude that the the BBC has done its best to be fair, although it has succumbed to a little negative bias against the more than 12 separation. It does, however, raise the fascinating question of whether the question could have been made more equal for all options. If the summer holiday weather remains as rubbish as it has begun today, I may just ponder that problem a little longer.

But what we can be sure of, is that The Danny Baker Show remains the broadcasting highlight of the week.

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