# The week that was (no.24)

This week was a good week. I found out that our department had passed our SQA verification. Whilst I was confident that we would, it was a relief to get official confirmation. Other than that, my week has been spent focussing on senior classes, trying to sort out change of levels and starting the build up to exam time.

My classes have been working on:

• S2: expanding single brackets and stem and leaf diagrams
• N5: vectors
• AH: inverse matrices, transformations and Euclidean Algorithm

Progress of the week

My S3 class have been working on their retrieval starters for three weeks now. You can read about them here. After a bit of apprehension from some of the class, they are all finally buying into the process. During each starter, lots of questions are being asked and pupils who wouldn’t have normally bothered attempting the starter are now doing it. Pupils are noting down the solutions to questions that they didn’t get correct so that they have something to refer to the next day. The highlight came on Friday when the majority of the class scored over 70% in mini test 3. Lots of smiles and I have noticed an increase of confidence. Positives signs for the rest of S3.

Treat of the week

Ok, so technically this happened on Saturday but I’m still counting it as part of the week. I attended Muckle Grampian in Aberdeen on Saturday. What is Muckle Grampian? It’s a teach meet where teachers meet to share what is going on in our classrooms. It was a fabulous day. I met some wonderful teachers who love to discuss teaching and left at the end of the day buzzing with enthusiasm. This is the kind of event I would love to see happening in schools on a regular occasion but I’m not sure if it ever will. The trouble when having this type of event within a school is that teachers inevitably end up talking about the day-to-day teaching problems rather than sharing practice.

Lessons of the week

My S3s are studying factorising at the moment and I decided to go at it from a slightly different direction. Rather than giving notes I jumped straight into examples. I asked the class to expand these brackets and see what they notice:

Without sharing what they had noticed, I then set them the task of writing this expression in brackets.

Most of the class had the correct answer but a few had yet to spot the connection between the constant term and the coefficient of x. I then asked the class to speak to their partner to share the connection they had noticed. The next ten minutes or so were spent factorising trinomials with positive coefficients. In the next lesson we explored what would happen if we introduced negative coefficients. The conversation around factorising something like x² – 8x – 20 went a bit like this:

Think about or write down two numbers that multiply to make 20 (note: not -20)

Which pair could be used to make an 8? (note: not -8)

Ok, so now we have chosen 2 and 10, how would we use 2 and 10 to make -8?

So our answer is (x + 2)(x – 10)

Previously I would have focussed on writing a list of numbers that multiply to make -20 then choosing which added to negative 8. By removing the focus from the negatives, it became more of a puzzle to solve rather than negative number calculations.

At one point I mentioned the word “algebra”. The pupils stopped and said “Is this algebra?”  I hadn’t specifically mentioned it (although I thought it was obvious) and they just thought of factorising as a little puzzle involving multiplying and adding. I actually think by not making a big deal of it, not completing notes formally and treating as a puzzle meant the class were not intimidated by it. I am hoping that this more informal approach will lead to more confidence when factorising and completing it by inspection rather than a formal procedure.

Weird notation of the week

I have been teaching for a long time and have never seen a pupil write down a vector addition in this way.

Three equals signs!!  The funny thing was, just after I said to the pupil I had never seen this before, I turned to another pupil who had done exactly the same thing.