“Today we are going to look at Pythagoras”
Cue whoops and cheers...no? Deathly silence instead?!
It's a tough one, “my mum could never to Pythagoras so I can't” is my all time favourite line from a post 16 student.
Having been based with dance students re sitting GCSE maths, often not for the second time, I had to become more creative in my approach. The benefit of teaching post 16 resit is that the misconceptions are there, and students are not shy about explaining and sometimes oversharing why they can't do things or what has gone wrong in the past. From this I learnt that when my students looked at Pythagoras questions they could label the hypotenuse easily but not the opposite and adjacent. Then they could recall beautifully the Pythagoras proof of cutting squares out and making right angles triangle activity they did in year 10 but couldn't answer a missing side question. This is where we were and it’s my job to piece together a way forward.
Let's start with labelling, from experience making things easy to remember and build on the knowledge that's already there is a good plan. So we label the hypotenuse first. Always opposite the right angle. Learners in my experience are often OK with this skill. I discuss labelling in the blog post about trigonometry if you want to know more about this. What we were struggling with when looking at Pythagoras was that we didn't know when we were adding and when we were subtracting. Over the years I tried many many many approaches and I began to think about how we often think of mnemonics and acronyms to help learner's get along and that's when I came up with SASSY LASS.
As you can see all it is is the steps that you need to do in the right order:
Square, add or subtract, square root, for the longest you add and the shortest you subtract. As I teach resit students only now, I know students have previously been taught a2+b2=c2 . I must explain that the starting point activity of this lesson aims to establish if students can recall a2+b2=c2 and apply it correctly then that is what we use. I only use SASSYLASS as an option for those who cannot use a2+b2=c2 correctly.
Once we can apply SASSYLASS correctly I like to then look at rearranging a2+b2=c2 and extending learners to using a2+b2=c2. I am not limiting them to only using SASSYLASS. SASSYLASS is merely a starting point for them to get into Pythagoras and in my experience may give learners the confidence to tackle harder questions once they have practised the skills involved. Aiming for conceptual understanding is always key but as educators we often have to find a path through the fog and SASSYLASS affords me that.
Tremaine is a talented dancer and studies level 2 dance. However, he hasn’t got a grade 4 in maths and has to resit whilst studying dance. As much as we have a positive relationship Tremaine really doesn’t want to be in maths class. He would rather be dancing, the canteen, the library, anywhere but maths! We began to look at Pythagoras and our starting point starter cue Tremaine “Eh no, I ain’t doing to Greek squares and cutting and that!”
Tremaine clearly remembers the proof lesson he must have had in his school career! After some calming down I asked Tremaine what this was: a2+b2=c2
“I aint squaring nothing. I hate this triangle (swear)”
This is our starting point. Tremaine isn’t alone, many resitters have the fear of Pythagoras.
I explained that to sort out these triangles we needed to have a little bit of sass. I suddenly had Tremaine and everyone’s attention.
We start by squaring the numbers in the question. We then eliminate in the LASS, are we looking for a long or a short? In this example we are looking for a long so we add the squared numbers. Then we square root.
In this example we square the numbers. We are looking for a short so we subtract (circle the final S in LASS) and then we square root.
Working through examples of SASSY LASS the whole class was ready to start work. Some were using a2+b2=c2 and some were using SASSY LASS. All thankfully ended up at the same answer and within our 90 minute session we even managed to reach 3D problems. Tremaine ended the lessons by saying “You know that triangle (swear)? Bossing it now aren’t I?!”
