Welcome Welcome to the fourth Autograph newsletter! Each jam-packed edition will look at a specific topic in mathematics and how Autograph can help engage students and enable them to understand the key concepts better. Hope you enjoy it! Craig Barton Advanced Skills Teacher, creator of www.mrbartonmaths.com and TES Secondary Maths Adviser. Follow me on Twitter: @TESMaths
 Introduction I have found that students are aware of calculus long before they study it in a mathematics classroom. Often they have heard it mentioned in movies or TV shows, and witnessed seeming incomprehensible scribbles on blackboards by bearded brain-boxes. Bearing this in mind, there is a danger that students can become overawed by the concept and methods involved with calculus before they have even got going. If we are not careful, it can become a rather abstract and daunting topic, which is clearly a major problem as the majority of advanced mathematics is built upon its foundations. Fortunately, help is at hand! By using dynamic geometry software we can bring the topic to life, looking at where it all comes from, right up to the most advanced features. In this newsletter we look at how we might use Autograph to introduce and study the first part of calculus – differentiation.
 Diagnostic Question Diagnostic questions are ideal to use at the start of the lesson to enable you to get a quick and accurate picture of your students’ levels of understanding. They are designed in such a way that common misconceptions that your students may hold should steer them to one of the incorrect answers, thus allowing you to learn where the problems lie from their responses. Typically I give my class 30 seconds thinking time and then ask them to hold up their fingers: 1 for A, 2 for B, etc.
 Free Online Autograph Activity The Rules of Differentiation Can you discover the rules for differentiating quadratic functions? Can you then apply this to other polynomials? These Autograph activities do not require the full version of Autograph to run them. You just need to install the free Autograph Player (you will be guided through how to do this), which means you can use these activities in the classroom or set them for your students to do at home.
Ideas for Extension
The following ideas for extending the topic of differentiation require the full version of Autograph. Click on the image to download the individual Autograph files.
Idea 1 – Differentiation from First Principles
Demonstrate to your students where the concept of differentiation comes from by using the concept of a limit.
 • The file shows a calculation for the gradient of the line segment joining the two points • The second point has an x value of “1+h” • Use the  Constant Controller to gradually reduce the value of h • Drag and zoom in around the two points as h gets smaller • Let the students see that the gradient of the line segment is approaching that of the curve • What value does this gradient tend towards? • You can then try your points in a different position • You can also double-click on the curve and type in a new equation
Idea 2 – The Gradient Function
Autograph has a lovely feature that allows you to instantly plot the gradient function of any function