New Gcse: Existent Life Graphs

I guide keep a feeling that I nonetheless haven't identified all the novel GCSE content. This makes me nervous. I glanced through a textbook concluding calendar week as well as spotted a few topics that aren't on my quadratic graphs, but I didn't know that students volition likewise survive required to position the roots of cubic graphs (see instance inquiry below). The specification but says 'recognise, sketch as well as translate graphs of ... unproblematic cubic functions'. Previously students guide keep exclusively been required to recognise the shape of cubics - roots didn't come upward up until H5N1 level. Now I've spotted this content inwards the textbook, I'll demand to adjust my plans to ensure I guide keep fourth dimension to encompass this at some indicate inwards the side yesteryear side eighteen months. The fourth dimension pressure level is increasing.

A inquiry from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book 

Real Life Graphs
I've just taught linear graphs to my Year 10s. My system of piece of job tells me that I straight off guide keep to learn 'real life graphs'. But what does that mean? In this postal service I volition endeavour to clarify what comes nether this title.

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

Here's the relevant extract from the novel specification:

The wording is unlike to the previous specification but it's broadly the same content, alongside perchance to a greater extent than emphasis on interpreting contextual graphs. AQA's first-class Teaching Guidance gives us a to a greater extent than detailed description:

There's a lot here! The commencement 4 points follow on from linear graphs - for instance students volition guide keep to translate a y-intercept equally a fixed charge. AQA gives this instance question:

There's some swell novel resources for this variety of graph inwards AQA's Bridging Unit: Resource Pocket 3. The back upward provided yesteryear AQA is fantastic.

Modelling

The most mutual examples of 'graphs showing real-life situations inwards geometry' are those that model H2O flow. In AQA's sample assessment materials (Question 23 inwards Higher Paper 3) students are shown a graph representing the depth of H2O inwards a container over time. They are asked to position the corresponding container from a alternative (shown below). They are thence asked to gauge a charge per unit of measurement of change, requiring them to calculate the slope of a tangent to the curve.

It's worth spending a distich of lessons developing the skills required for the commencement component of this inquiry (ie identifying the right container). Thankfully there's plenty of practiced resources for this topic.

In previous years I've used a 'filling upward a bath' card sort (I adapted this from a treasure hunt I institute on TES). I don't oft exercise carte du jour sorts but I cry upward this 1 working well. There's likewise a practiced existent life graph card sort from Nuffield.

I'm actually keen to exercise Desmos Water Line - this is an online lesson inwards which students graph the charge per unit of measurement at which containers create total alongside water. They likewise create their ain containers to graph. Desmos lessons are absolutely bright thence if y'all guide keep access to tablets or computers thence do give it a try. For me it volition survive a rare but worthwhile view to the information technology Room.

The classic Red Box is total of first-class graphing activities - it's a shame that the ikon character isn't great.

Kinematics Graphs
Although I'm education existent life graphs side yesteryear side week, I'm planning to leave kinematic graphs until I learn chemical compound measures. This volition thence Pb onto rates of alter as well as surface area nether a graph, which I've already blogged about. It doesn't brand sense to do kinematic graphs earlier education speed.

We guide keep plenty of resources for distance fourth dimension graphs. AQA's Bridging Unit has some practiced questions (extract above). Interpreting Distance-Time Graphs from the Mathematics Assessment Project is excellent. I likewise similar this commentary activeness from Transum - The Hurdles Race.

I don't guide keep much on speed fourth dimension graphs, apart from those listed inwards my post close finding the surface area nether a graph as well as those available from Toticity's Mind the Gap Maths Toolbox.

Exponential Graphs
The Higher Tier specification includes contextual exponential graphs. An instance inquiry from my Edexcel textbook is shown below. I invention to encompass this variety of graph when I learn increment as well as decay (eg chemical compound interest) side yesteryear side year.

My Plan
Next calendar week I'm education 'real life graphs', but what precisely volition I teach? Having looked through the novel GCSE specification, the sample assessment materials, AQA's Teacher Guidance as well as a distich of novel GCSE textbooks, I straight off guide keep a clearer stance of what I demand to cover. It's taken a lot of travail to decide that I demand to do a lesson or ii on contextual linear graphs as well as a distich of lessons on modelling. I'll come upward dorsum to kinematic graphs, rates of alter as well as areas nether graphs afterwards I've done chemical compound measures. I just promise I'll guide keep plenty fourth dimension to encompass everything.

Proportional graphs also seem to come upward up a lot inwards the novel GCSE. Often a context is given inwards the question. I'll teach these inwards Jan when I encompass ratio as well as proportion. here.