# A Tentative Lesson Structure

I have been naturally falling into a rhythm in my Further Maths classes. This structure seems to work well when students are already on board with Maths (and therefore follow you through headaches and open exploration), and when they are meeting lots of new mathematical structures for the first time.

Table to clarify thinking, and then a record of the lesson below.

Obviously, any attempt to codify what all good lessons looks like is ridiculous.

 Chapter In general In particular – Matrices Why? 1 Provide students with a headache to wrestle with Ask students to solve increasingly complex simultaneous equations Before providing the aspirin, you need to give the headache. Dan Meyer 2 Give students key information that it would not be reasonable for them to discover themselves Lecture on how to multiply matrices (link back to multiplying vectors, which in turn links back to multiplying numbers) Minimise teacher-talk while not wasting time on wishy washy discovery-based learning 3 Ask students what questions they have. Important to do individually first – no cross-contamination “What do you want to know about matrices?’ Now that they have a basic idea, questions start flowing. (Without teacher-input, the blank page is too daunting) 4 Explore! In groups of three or four students? Structured comparison of matrices and numbers. Students need to learn how to behave like a mathematician – conjecture, root around in the darkness, play, prove. 5 Big reveal: you now have the aspirin for your headache After playing around with matrices and working out what the equivalent of division is, you can solve big systems of simultaneous equations Provide an ending to the story, reminder of why this new bit of Maths is useful.

A record of the lesson