Further Maths Specification Mapping

Yesterday Luciano (@DrTrapezio) tweeted asking if anyone had a document comparing the A-Level content across different exam boards. I’m convinced that I have seen exactly this in the past but I can’t find it now. Sue de Pomerai (@SuedePom) mentioned that she had a copy of one for further maths and emailed it to Luciano, who has asked me to put it up and share with people. So this was a nice easy #summerblogchallenge  post today.

This file is now available on my web site here and looks a bit like thisScreenshot 2015-09-04 22.12.03

The file is ordered around the MEI further mathematics modules and then the location of each topic in the specification of the other boards is given. It is pretty much complete, but I think there are a few AQA topics missing (for example Viète’s formulae) and don’t we cover simultaneous equations with matrices in Edexcel FP1 and FP2.

I think this document is very interesting and I wish more boards did some of the topics that MEI do, for example the Cayley-Hamilton theorem and Lagrange interpolating polynomials.


No Plan Starters

Short post tonight….

Next year I will be moving about classrooms a fair bit, not least because I will be frequently moving between main school and sixth form. As we don’t have movement time, on those occasions I will sometimes want to have a starter that I can get the students working on quickly whilst I wait for the ‘computer to log on etc.

Because of this I have produced the sheet below with a few options to go on the back cover of the exercise books, with the intention that after a while i will be able to just say, for example,  “Task 7 and write a few numbers on the board. 

 There is nothing new or revolutionary here, but I thought I would share it in case it is useful for anyone. A pdf is available here.

You may notice that i have also put a RAG123 key at the bottom. After being inspired by many people on Twitter, I’m excited to be trying this properly for the first time this year.



Yeaterday I picked up my free copy of The Times with my My Waitrose Card and on page 3 it had this puzzle: 

 The rules are deceptively simple

  • You must place the numbers 1-9 in the 9 squares, using each number only once. 
  • The number in each circle should be equal to the sum of the four surrounding squares. 
  • Each colour sum is correct. 

This puzzle turns out to be trickier than it looks, and this was the intention according to this little bit of history. The puzzle was created by Jai Gomer of Kobayaashi Studios. 

The three pictures below show my workings to solve this puzzle.  

 To start with we have 9 unknowns and 7 equations so clearly an indeterminate system; hence brute mathematical force alone won’t be sufficient. Applying a bit of logic we can deduce two of the numbers. At this point I thought great, now I have 7 unknowns but 7 equations. However this was very foolish of me, as in fact we only really have 5 equations for our remaining 7 unknowns. And so, I had to make a few educated guesses on the likely magnitudes of some of the unknowns based on the totals that they contributed to. Once I had done this, the other unknowns dropped out fairly easily and a quick verification at the end showed that I had all the values correct. It could have been different though if I had been incorrect with these educated guesses. 

So I have a few unanswered questions

  • Have I missed something? Could I have done it without these educated guesses?
  • Could I remove one condition and the solution still be unique? 
  • Would colour totals split into 3,3,3 squares instead of 2,3,4 lead to easier or harder puzzles?

I shall ponder these….


Mathematician’s Quote Posters

Inspired by Kim’s (@kimThomasLee) post about maths quotes and needing to fill a bit of space on a display board I thought I would see if I could quickly produce some posters of quotes using the Retype app for iOS.

Here are the results:

Maths_quotes_1 Maths_quotes_2 Maths_quotes_3You can download the full resolution images from the links below.