Woodturning is my absolute favourite example of volumes of revolution and in this activity we extend this to even consider Rose Engines. What's a Rose Engine you ask? Well read on to find out...

Exercises demonstrating how to use Autograph to visualise mathematical concepts in the classroom.

A set of Autograph Activities finding equations to model butterflies. Motivated by a question on Twitter to @autographmaths, I started investigating equations for modelling the shape of butterflies for which polar coordinates were helpful and then considered a moving butterfly for which cartesian coordinates were a more natural fit. A nice fun modelling exercise which could be very simply extended to other butterfly shapes, different routes, multiple butterflies, etc.

An Autograph Activity allowing you to visualise the meaning of a distance-time graph for a journey with one stop.

Using linear programming to solve a practical example with Autograph Mathematics.

An Autograph Activity visually demonstrating a distance-time graph. You can adjust the length of the various parts of the journey.

An Autograph Activity to demonstrate why the angles in a triangle add up to 180 degrees. The interesting thing about this activity is that it has no numbers! So really it is a demonstration that the angles in a triangle when put together form a straight line. This activity was inspired by the awesome Oliver Byrne's 'The Elements of Euclid'. Mathematics is not just about numbers, using colours in this example hopefully demonstrates that.

Approximate the area under a curve using rectangles, and use Autograph Mathematics' Animation Controller to investigate what happens when the number of rectangles is increased.

Autograph Mathematics is used to solve 2 = x³ numerically using the method of iteration.

Using Autograph Mathematics to explore the Geometric Distribution.

Adding, subtracting and creating scalar multiples of vectors in Autograph Mathematics.

Autograph Mathematics Slow Plot mode is used to encourage students to predict what coordinates the quadratic graph will go through before using the software for confirmation.

Explore quadratic functions using Autograph Mathematics. Learn how to enter equations and use Slow Plot, Scribble Tool and the Constant Controller.

Using Autograph Mathematics to investigate domain and range of functions.

Explore the unique properties of the exponential function using Autograph Mathematics.

Graphs of trigonometric functions have an interesting link to the unit circle. In this video we investigate this link using Autograph Mathematics.

Autograph Mathematics helps you examine your understanding of the differentiation of trigonometric functions. Does it matter if we use radians or degrees?

Transforming shapes with Autograph Mathematics. Investigating rotation, enlargement, reflection and translation.

Using Autograph Mathematics to plot the parametric form of the Lissajous equation.

An Autograph Activity for exploring a classic interlocking solid star puzzle. Can you rearrange the 6 identical pieces to form a star?

Autograph Mathematics provides a fantastic way to visualise the error in lines of best fit. In this activity we use this visualisation to manually find the line of best fit.