## 4 January 2016

### Five things you might not know about the new GCSE content #1

This is the first of two posts listing changes to GCSE content that aren't widely known. If you're really familiar with the new GCSE specification then you probably already know all of this. But if you're worried that you might have missed something, read on.

1. Graph Transformations
No more stretching of functions. I missed this one so thanks to @MrBenWard for pointing it out today. This is an odd change - I can't see the rationale. Here's what's in and what's out:
I'm going to have to edit a lot of resources...

Don't forget that the featured transformations (ie reflections and translations) may also be applied to the graphs of y = sinx and y = cosx.

2. Trial and Improvement
Contrary to popular belief, trial and improvement hasn't gone! I thought it had until I saw these tweets from AQA:
AQA's Teaching Guidance says that "students should be able to use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method".

Any trial and improvement questions in the new GCSE may be more challenging than what we're used to, so we can't rely on past exam questions and resources. Here's an example of a new specification trial and improvement question from AQA:
A solid has volume V = x3 + 2x2
The volume of the solid is 90cm3
Work out the value of x to one decimal place.
You must show your working.
Note that the question doesn't explicitly tell the student to use trial and improvement, which is a notable change from previous exam questions.

3. Compound Measures
The new specification lists pressure under compound measures - this is new to maths GCSE. The specification says, "Use compound units such as speed, rates of pay, unit pricing, density and pressure" - see Question 3 in this set of questions from justmaths.co.uk for an example.

In general students should be taught the importance of looking at units in compound measure questions. If speed is measured in km/h then we can see from the units that we need to divide distance by time to get speed. Using this approach students should be able to figure out how to answer any compound measure question even if they're not familiar with the context (eg if a question asks for population density in people/km2 then they simply divide population by area - they know this by looking at the units, no formula required).

It's worth noting that students will need to know the equivalence of the notation m/s and ms-1.

Peter Mattock has written a helpful blog post about teaching pressure. There are some pressure questions in the Toticity Mind the Gap Maths Toolkit which I reviewed here.
 Example question from toticity.co.uk

4. Rounding
It was Mel's post 'GCSE 9-1 New content – Error Intervals' that first alerted me to error intervals and truncating so if you haven't read it then please do. These topics are fairly straightforward to teach, but a few of my top set Year 10 got a truncating question wrong when I tested them on it only a week later... They've been rounding for years and suddenly we're telling them not to round!
 Truncation practice
5. Systematic Counting
The specification says "Apply systematic listing strategies including use of the product rule for counting". Thanks to @MrMattock for drawing these changes to my attention through his blog post 'Multiplicative counting - the different types'.

AQA provides this example question:
"How many numbers between 100 and 200 have at least one digit that is 7?"
I'm not sure this kind of thing needs direct teaching - it just needs a logical approach. This second question from AQA requires the product rule - I think it might be worth spending a lesson or two on this (perhaps more if we extend to combinations and permutations - I will try to find out whether this necessary):
"Daniel has 10 shirts, 8 pairs of trousers and 5 pairs of socks.
a) How many different combinations of shirt, trousers and socks does he have?
b) He chooses a shirt. How many combinations are there now?"
Apart from this lovely PowerPoint from newmrsc on TES, I don't have much in the way of resources for this topic so please send me anything that you have!

Formulae
Finally, just a reminder that your students will need to memorise more formulae than they used to. When the new GCSE was first announced this made the headlines:
"The new curriculum for GCSE maths will see pupils in England spending more classtime studying the subject and memorising mathematical formulae, such as Pythagoras's theorem."
Our students have always had to memorise Pythagoras' Theorem and plenty of other facts, theorems and formulae. I think that the impact of this change was exaggerated. Saying that, I will be annoyed when my students lose marks because they forget the quadratic formula...

I'm pleased that students will no longer be required to memorise imperial to metric conversions because (unlike times tables, Ms Blower), it's entirely practical to look these up online if ever needed.
I hope that this post has been helpful. Don't forget I have a page of new GCSE resources and I've written various posts about new GCSE topics:

Watch out for my next post when I'll list five more changes that you might not know about.

1. Jo, this is an incredibly useful blog and highlights many areas I wasn't aware of, so many thanks on behalf of my whole maths department who have to read this as a compulsory task this evening. You really are making our lives easier.

1. Thanks for the feedback, I'm really pleased to hear this is helpful.

2. Thanks for this - very helpful! Keep them coming :)