The following collection of resources have been assembled by the TES Maths Panel. They can be downloaded for free by registering on the TES website.
I can’t think of a single piece of technology or any scientific advance of the last few centuries that hasn’t been somehow touched by calculus. It is an idea central to sixth-form mathematics syllabuses in all qualifications; the following resources illustrate a variety of the manners in which it can be tackled.
Top 10 resources:
1. Calculus activity
Why wait until a student opts for post-16 maths to introduce calculus? This collection aims to whet the appetites of GCSE students and informally discusses the underlying principles, exposing students to some key vocabulary in the process.
2. Introduction to differentiation
This spreadsheet helps illustrate four key concepts of differentiation via interactive spinner buttons. Students can investigate differentiation from first principles along with rates of change of quadratic, exponential, and trigonometric functions.
3. Optimisation
Optimisation problems form an essential early exposition of the wide-ranging footprint of calculus. This resource not only gets students to solve a manufacturing problem but promotes a discussion about why the ideal solution is not always used in industry.
4. Integration spot the mistake
An endless source of frustration for teachers is the unfathomable ability of some students to apply self-concocted integration rules. This resource turns the tables and gives students the opportunity to pick holes in some questionable solution attempts.
5. Calculus countdown
This activity from nrich enables students to consolidate a sophisticated understanding of functional notation and differential operations.
6. A2 mathematics: Differentiation
It’s essential that students at this level begin to see how results are derived; there are so many ‘rules’ that they risk appearing arbitrary if no method behind them is demonstrated. This resource will help with regards the product and chain rules, and differentiation of trigonometric and exponential functions.
7. Volumes of revolution
In a similar vein, this set of documents uses some useful computer-generated illustrations to confound the mystery in students’ minds regarding the volume of revolution formulae.
8. Parametric differentiation jigsaw
Everyone loves a tarsia even when it contains some ferocious looking parametric differentiation. Even the upper sixth doesn’t have to be spent relentlessly completing textbook drill.
9. Differential equations treasure hunt
Furthermore, sixth-formers needn’t even be restricted to their seats. Increase their kinetic energy levels with this treasure hunt encompassing a variety of questions on a theme of differential equations.
10. The Mathematics of woodturning
An article from Autograph guru, Simon Woodhead. He suggests using volumes of revolution to model objects made using the centuries-old technique of woodturning.
Owen Elton, TES Maths panel
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