As this is an extremely late post for the last of the “12 Days of Christmas” series it is very brief.

I received this card just after New Year from my aunt:

I’ve seen this before but I still find it fairly funny and it is a useful reminder of the problems with trying to shoehorn a physical / applied situation onto a maths problem!

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.

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

Watching an episode of Peppa Pig this morning (Season 3, Episode 11) I was quite excited to see the quadratic formula on a board at Daddy Pig’s work.

I found it interesting that they wrote it with the \( \bigtriangleup \) notation. I always introduce this notation for the discriminant but have never actually used it in the quadratic formula.

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.

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.