## 6 December 2015

### New GCSE: Real Life Graphs

I have a feeling that I still haven't identified all the new GCSE content. This makes me nervous. I glanced through a textbook last week and spotted a few topics that aren't on my list. For example, I know there's new content for quadratic graphs, but I didn't know that students will also be required to identify the roots of cubic graphs (see example question below). The specification simply says 'recognise, sketch and interpret graphs of ... simple cubic functions'. Previously students have only been required to recognise the shape of cubics - roots didn't come up until A level. Now I've spotted this content in the textbook, I'll need to adjust my plans to ensure I have time to cover this at some point in the next 18 months. The time pressure is increasing.
 A question from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book
Real Life Graphs
I've just taught linear graphs to my Year 10s. My scheme of work tells me that I now have to teach 'real life graphs'. But what does that mean? In this post I will attempt to clarify what comes under this title.

The previous GCSE specification said that students had to 'construct linear, quadratic and other functions from real-life problems and plot their corresponding graphs'. Examples included conversion graphs, 'ready reckoners' (whatever they are...) and distance time graphs.

Here's the relevant extract from the new specification:
The wording is different to the previous specification but it's broadly the same content, with perhaps more emphasis on interpreting contextual graphs. AQA's excellent Teaching Guidance gives us a more detailed description:
There's a lot here! The first four points follow on from linear graphs - for example students will have to interpret a y-intercept as a fixed charge. AQA gives this example question:
There's some great new resources for this kind of graph in AQA's Bridging Unit: Resource Pocket 3. The support provided by AQA is fantastic.

Modelling
The most common examples of 'graphs showing real-life situations in geometry' are those that model water flow. In AQA's sample assessment materials (Question 23 in Higher Paper 3) students are shown a graph representing the depth of water in a container over time. They are asked to identify the corresponding container from a selection (shown below). They are then asked to estimate a rate of change, requiring them to calculate the gradient of a tangent to the curve.

It's worth spending a couple of lessons developing the skills required for the first part of this question (ie identifying the correct container). Thankfully there's plenty of good resources for this topic.

In previous years I've used a 'filling up a bath' card sort (I adapted this from a treasure hunt I found on TES). I don't often use card sorts but I remember this one working well. There's also a good real life graph card sort from Nuffield.

I'm really keen to use Desmos Water Line - this is an online lesson in which students graph the rate at which containers fill with water. They also create their own containers to graph. Desmos lessons are absolutely brilliant so if you have access to tablets or computers then do give it a try. For me it will be a rare but worthwhile visit to the IT Room.
The classic Red Box is full of excellent graphing activities - it's a shame that the image quality isn't great.

Kinematics Graphs
Although I'm teaching real life graphs next week, I'm planning to leave kinematic graphs until I teach compound measures. This will then lead onto rates of change and area under a graph, which I've already blogged about. It doesn't make sense to do kinematic graphs before teaching speed.
We have plenty of resources for distance time graphs. AQA's Bridging Unit has some good questions (extract above). Interpreting Distance-Time Graphs from the Mathematics Assessment Project is excellent. I also like this commentary activity from Transum - The Hurdles Race.

I don't have much on speed time graphs, apart from those listed in my post about finding the area under a graph and those available from Toticity's Mind the Gap Maths Toolbox.

Exponential Graphs
The Higher Tier specification includes contextual exponential graphs. An example question from my Edexcel textbook is shown below. I plan to cover this kind of graph when I teach growth and decay (eg compound interest) next year.
My Plan
Next week I'm teaching 'real life graphs', but what exactly will I teach? Having looked through the new GCSE specification, the sample assessment materials, AQA's Teacher Guidance and a couple of new GCSE textbooks, I now have a clearer idea of what I need to cover. It's taken a lot of effort to determine that I need to do a lesson or two on contextual linear graphs and a couple of lessons on modelling. I'll come back to kinematic graphs, rates of change and areas under graphs after I've done compound measures. I just hope I'll have enough time to cover everything.

Proportional graphs also seem to come up a lot in the new GCSE. Often a context is given in the question. I'll teach these in January when I cover ratio and proportion. @fmaths42 recently wrote a useful post about these graphs which is worth a read.

I hope that this post has been helpful in clarifying the GCSE content on real life graphs. Do let me know if I've missed anything. Don't forget I have a whole page of new GCSE support here.

1. Thanks Jo - as always lots of useful advice and ideas - let me know how you get on with the Desmos Waterline Activity - I'm keen to try this as well.

As a means to summarise and compare different types of graphs before introducing exponential graphs I found this activity has worked very well for me:

http://geogebraintheclassroom.blogspot.co.uk/search/label/Exponential%20Graphs

I definitely agree compound interest is an obvious starting point when it comes to exponential graphs as students can clearly see the practical application but I think its also nice to consider at least one practical example of growth with an integer base as well.

2. Have you seen http://graphingstories.com/? Great for real life graphs...

1. Thanks for this - what a fab website!

3. It looks like there's a lot of overlap between maths and science here. Is anyone working across departments to teach this?

1. Perhaps in some schools, but not normally. Duplication of effort...?