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.