12 Days of Christmas: Day 11 – Further Maths Polynomials Cardsort

Over the last couple of years I have particularly enjoyed teaching and writing interesting questions that concern Vieta’s Formulae. These relate the sums of products of roots of polynomials to the coefficients of the polynomial.

I have always liked these, and have a very vivid memory of a Russian lecturer in one of my first undergraduate lectures expressing surprise that we weren’t formally taught them as part of the normal A-Level in Maths. He confidently told us that in Russia they are done in primary school!

Last year I created a card sort for this topic which turned out to be trickier than I anticipated. It has taken two different classes now a whole lesson to complete but it has generate some fantastic mathematical discussions.


If you download the file to use in the classroom from here I would love to know what you think.

12 Days of Christmas: Day 10 – Thirdsday

Sometimes being late with posting has it’s advantages!

Thursday 3rd January was deemed a day to celebrate the number 1/3. It was named Thirdsday by James Propp (@JimPropp) who has written a fascinating and very detailed post about why he thinks 1/3 deserves more recognition and some interesting facts about 1/3 here.

Since this post lots of cool things have been written on the theme of Thirdsday and Matt Parker (@standupmaths) has produced an excellent video:

Unfortunately being late to posting also has its drawbacks. I was going to talk about the classic geometric series

\( \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \frac{1}{256} +\cdots \)

which converges to a third. However the excellent Zoe Griffiths st Think Maths has already published a lovely classroom activity involving this.

Over at The Aperiodical they have rounded up some nice Thirdsday related posts.

I’ve put a reminder in my phone to spend some time preparing a more interesting post in time for the next Thirdsday – 3/1/30 Keep an eye out for that…

12 Days of Christmas: Day 8 – Reflections on A-Level Exams 2018

As it is New Year’s Day and I am beginning to think about getting students ready for the next round of exams in May/June it seems a sensible time to share the brief reflections I wrote on the 2018 Series of AS and A-Level mary’s exams. They focus on the AQA papers as that is the board I am currently using.

The cumulative grade boundaries were interesting to look at.


Download the file here if you want to read them.

12 Days of Christmas: Day 6 – Matrix Transformations

I have some catching up of posts to do so today I shall be sharing 3 fairly short posts.

For the first I’m sharing a resource that I have used with both Year 12 Further Mathematicians and Year 11 Level 2 Further Mathematicians. Matrix representations of linear transformations appear in the syllabi for both of  the qualifications just listed previously.

I’m always quite reluctant to just teach this as a memory test so I use this self guided sheet that students can work through before having a whole class discussion about the transformations.


Download the file here if you want to use it.


12 Days of Christmas: Day 5 – Christmas Market Simultaneous Equations

On Boxing Day, I went with my family to the Nottingham Winter Wonderland.


While in the Alpine style bar I bought 2 mulled wines, a hot spiced apple juice, 1 fully loaded raclette fries (shown in the picture above) and one ham and mushroom pizza. The total cost of these was £27.50.

In a slightly contrived situation the tables around me bought the following with the associated total cost:

Table in front: 1 ham and mushroom pizza, 4 mulled wines, 3 hot spiced apple juices and 2 fully loaded fries. £50.50

Table behind: 1 hot spiced apple juice, 1 fully loaded fries. £10.50

Table to the left: 3 hot spiced apple juices, 2 fully loaded fries. £23.50.

The question is: “How much did each item cost?” Of course I would like to know the cost of each item (my memory and keeping of receipts is poor!) but I am really more interested in the method used to get the answer…

12 Days of Christmas: Day 4 – Integration by Substitution

Integration is a tricky topic to teach at A-Level (and beyond really) as so much comes down to experience. You only get good at Integration by doing lots of integrals and building up experience of  different techniques.

Integration by substitution is very powerful but deciding on a substitution can be tricky and is often something students find hard. Because of this I wrote a small card sort where students first have to match an integral with an appropriate substitution and then do the integration.


If you want to use it the file is available here .

12 Days of Christmas: Day 3 – Fortran 2018

Those of you who know me well know that I am quite a fan of programming and due to my background the languages I am most expert in are probably Fortran and Matlab.

Excitingly a new standard – Fortran 2018 – was approved and published on the 28th November. If you so wish you can buy it from here.

Helpfully John Reid as usual has produced a document detailing the differences from the last standard – which can be found from the Fortran Working group page here.

Fortran has certainly moved on from the original restrictions on line length (with certain columns reserved for describing the type of information on the card).

I’m particularly interested in the new parallel features, though given my job now I’m unlikely to have much of a chance to play with them.

The paid for Intel compiler already seems to have quite good support for this new variant of Fortran. If you are interested in Fortran it is certainly worth following @DoctorFortranon twitter – this is the Twitter handle of Steve Lionel who used to work for Intel and whose comments on forums I found very useful!