# The week that was (no.16)

This week was a slightly shorter teaching week for me as Wednesday was my moving day. This meant my mind was slightly off from regular school work and more on changing address details, packing boxes, unpacking boxes and endless phone calls. The second last week of term included the Christmas dances, which meant lots of excited pupils, and the staff night out which was a blast.

My classes this week were looking at:

• S2 ratio calculations and Block 5 assessment
• S3 expanding triple brackets and area of 2D shapes
• N5 similarity (length, area and volume) and Block 4 assessment
• AH summation notation and proof by induction

Don of the week

I’ve noticed over the years that many pupils struggle to recognize the different 2D shapes despite regular reference to them. This task from Don Steward allowed my pupils to familiarize themselves with the properties of 2D shapes whilst tackling the problem of designing shapes that have an area of 8cm².

One of my favourite tasks to set when working on area is to sketch 2D shapes which all have a specific area. This time the area was 36cm². The pupils were encouraged to use different dimensions which allowed for exploration of factors. I was pleased to see some of the class use decimal lengths as well.

Mistake of the week

Being a little preoccupied this week with my house move I made a bit of a blunder in my Advanced Higher class. I put up a set of statements that were to be proved using proof by induction. I put together questions from a set of notes I found online. The first question set was this:

Prove by induction that n² + 2n is divisible by 3 for all n ∈ N.

Unfortunately this question was an example of a false conjecture. My poor pupils were very confused about why they couldn’t get the proof to work. Thankfully I teach lovely pupils who were very forgiving of my mistake (I think they are used to all my mistakes by now!!) I need to take my own advice when I tell pupils to read the full question.

Future thinking of the week

This week my N5 classes sat an assessment that was predominantly about quadratic graphs and equations. While they were quite successful with the quadratic equations most were still struggling with quadratic graphs. The main problem is distinguishing between quadratics of the form y = (ax – b)(cx – d) and y = (x + a)² + b. They try to use the same method for finding the turning point for both forms. For example, some identified the turning point from this form y = (x + a)² + b then found half way between the coordinates. I had spent a lot of time working on quadratic graphs so don’t know exactly what went wrong. I need to take some time to think how I can help my pupils learn the different ways to deal with the two forms. Any ideas would be welcome.