'Measure gradients and see for yourself the relationship between a function and its gradient'
This activity is all about collecting and analysing some results for yourselves. Technology allows us to do some exact measuring and in this case, you will be using a graphing package to measure the gradient of a function at different points in an attempt to see how that gradient varies. You'll repeat this with different functions and work towards a general conclusion about what happens. This work can build nicely on the Classifying sequences activity.
The main aim of this activity is to take the mystery out of the general formulae for deriving functions. Through the investigation, it is hoped that students will discover the important relationship for themselves.
The task is outlined and should be recorded on the Measuring gradients activity sheet.
- Students become familiar with how to plot functions on a graph plotter
- They then work out how to plot a point on the function and have the software measure the gradient at that point.
- For a given function, students measure the gradients at different values of x and record the results.
- This is repeated for a number of different functions.
- Students are asked to look at the nature of the sequences produced by measuring the gradients and relate them to the function itself.
Teacher's Notes (brief)
Why we like this activity ….
This activity allows access to the fundamental principal of calculus, that the gradient of a function at a
given point can be described by another function and that the relationship between the two follows a
pattern. This is important before the details can be mastered! The use of technology replaces the much
less accurate paper and pen and allows students to cut quickly to the chase!
How this activity be used ….
Give the students the electronic document so that results and screen shots can be added when ready
What to expect when using this activity – from our experience
Students need to be good at determining the order of a given sequence. I do this with 'classifying
sequences' and looking at the difference method.
I did it my way!
As a practising maths teacher I know that most of us like to give activities our own little twist and do them 'our way'. It would be great to add a little collection of 'twists' from users. You can either add your twist to the comments section below or e-mail them directly to me at email@example.com In time some of these twists may appear here....