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) = x ^{2}** 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)=x**. (For even more @Desmos sophistication – see the end of this post).

^{2}– DesmosBack with Underground Maths again we will use** Gradient Match **to match functions with their gradient functions. This can be used interactively online. All the reources you need and a solution are provided.

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**).

You might like this….

https://howardat58.wordpress.com/2014/08/19/calculus-without-tears-that-is-without-limits/

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Yes – I do Howard!

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