Posts Tagged ‘Cubics’

Decending powers of x

September 26, 2014 4 comments

I was in one of my colleagues lessons this week.and he was teaching the class to expand quadratic brackets. As the lesson went on he noticed that a number of pupils had been writing the X squared term, then the constant term then the X term so he pulled the class together to tell them that conventionally we write quadratic equations in decending powers of x. This is excellent practice and something we all should be encouraging, but it made me think “Why decending powers of x?”

When dealing with quadratic, cubics and quartics up to GCSE and A-Level level we use the convention of decending powers. This is common in all sorts from expanding through long division, even in linear function we use descending powers. However, when we start with series expansions, such as binomial or Taylor’s, we switch to ascending powers. I’m also fairly certain that everything in my second and third year university modules on polynomials was in ascending powers too.

Now don’t get me wrong, I’m happy with the fact we have different conventions here, and I’m not against using them. I’m just inquisitive, and would love to know if there is a reason, and if there is what that reason is. If you do know, I’d love to hear it!

Graphs, Graphs and Further Graphs

March 28, 2014 Leave a comment

Recently my Year 11 class have been doing a lot of work around graphs. Not plotting graphs, but the stuff that comes under the banner of “further graphs”, so recognising, sketching and transforming quadratics, cubics, logarithmic graphs, exponential graphs and everyone’s favourite trigonometric graphs.

I hadn’t taught it to a KS4 class before, so I had a good long think about it and created some new resources, and rejigged a couple from A Level classes! You can see all the resources on TES here.

I started off with a match up, I gave them a number of graphs and the equations they matched too, some they had met before, some they hadn’t, but I gave them calculators and whiteboards and 15 minutes to have a crack at it. The class responded really well to this and a number of them managed to correctly match up all the graphs to the equations without any help whatsoever. The rest of the lesson was spent sketching and solving quadratics, they had touched on this before, but were glad to revisit it.

The next lesson was spent on cubics, sketching and solving and becoming familiar with the shapes, and how to factorise ones with a constant term of zero.

The next lesson was spend on transforming graphs, this was a lesson adapted from my A level class and it worked well, the class fully getting to grips with graph transformations. To finish the unit I then did the lesson from the standards box on trig graphs. They also responded well. I’ve not use all the activities from the standards box, but I have always found the ones I have used have gone well!

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