Introducing Calculus

rates-of-change

New on the GCSE specification we have interpretation of the gradient at a point on a curve. I want to introduce this to my very able Year 11 (UK age 15-16) class this week. As this class is also studying for AQA’a Level 2 Further Mathematics Qualification I want to go beyond the GCSE specification. Talking of the Further Maths specification – a wonderful find – thank you Craig Barton  – so many wonderful resources for this specification. Thanks too, to Mark Greenaway, Thomas Whitham Sixth Form College and on YouTube, Raw Maths, Jerry Jam and Riley Maths.

Some resources – I plan on using:

Perhaps after initial explanations with reminders about what they already know about distance time graphs and emphasising that a gradient is a rate of change, a good starting activity, A tangent is … from Underground Mathematics which emphasises rather well that a tangent is a local property of a graph.

I want them to draw some tangents and see how accurate they can be, so I’ll give everyone a good size graph of f(x) = x2 and have them draw tangents at x=0, 1, 2, 3 and 4, something that has worked well with A Level students. We can use Desmos to check our work, Tangents to f(x)=x2 –  Desmos. (For even more @Desmos sophistication – see the end of this post).
gradient-on-a-curve-desmos

Back with Underground Maths again we will use Gradient Match to match functions with their gradient functions. This can be used interactively online. All the resources you need and a solution are provided.
gradient-match-underground-mathematics

Further Resources
AQA – Bridging the Gap – Pocket 3 is on Graphs and Real Life Contexts; this includes Distance Time Graphs and Velocity Time Graphs.

OCR’s Topic Check In 7.04 Interpreting Graphs     7.04

There are several resources for teaching this topic on AQA’s All About Maths including clear PowerPoints and suggested lesson activities.
(Free for AQA Centres, find out how to register).

2 comments on “Introducing Calculus

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