Welcome Welcome to the fourteenth Autograph Newsletter! Each jam-packed edition looks at a specific topic in mathematics and how Autograph can help engage students and enable them to understand the key concepts better.
 Introduction Just like in Newsletter 12, in this edition we draw our inspiration from the wonderful Median maths blog by Don Steward. Don’s activities challenge students to investigate, make conjectures and solve problems, and they have formed the basis of some of my most enjoyable lessons. Several of the activities on Median revolve around geometric proof. This is a topic that many students can have difficulty with, possibly due to its abstract nature, and being able to see the whole picture in terms of the steps that are required to solve the problem. Here is where I feel Autograph can help. By setting up the problems and then playing around with them dynamically, students may be able to see links and relationships that were previously hidden, make further conjectures, and test out their proofs.
 Diagnostic Question Usually we have a Diagnostic Question in this spot, but for this special edition of the newsletter we are instead I wanted to show you the kind of activity Don has on his website. Often these are images which can be copied and used directly, or pasted onto a PowerPoint slide or Word file. Here is a nice way to introduce students to the word of geometric proof using angles in triangles.
 Free Online Autograph Activity Can you Prove it 3? A tricky old construction here that leads to the surprising result that these two angles appear to be always equal. The question is… can you prove it? 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.
Further Activities
The following ideas for activities are also taken from Don Steward’s website. Try them on paper first and then turn to Autograph to look at them in more depth. Click on the image to download the individual Autograph files.
Activity 1 – The Equilateral House
Challenge: A square has an equilateral triangle constructed on each of two of its adjacent sides. The top corner of each triangle is connected to each other and to the far corner of the square. Can you prove that the resulting shape is an equilateral triangle?
 • The situation has been modelled on Autograph • Experiment by moving the positions of the three corners of the triangle around the page • Convince yourself that the triangle is equilateral by measuring the sides or the angles: – Measure sides: click on a side and the distance will be displayed in the status bar at the bottom of the screen – Measure angles: double click on the angle arc and place a tick by Show Label • Does this help you prove that the triangle is equilateral?
Activity 2 – The Mysterious Yellow Triangle
Challenge: Draw any right angled triangle, bisect an angle and construct the perpendicular to the hypotenuse (an altitude). Can you prove that the yellow triangle is isosceles.
 • The situation has be modelled using Autograph • Experiment by dragging the three corners of the right angled triangle around the page • Does this help you prove that the yellow triangle must be isosceles?
Activity 3 – Isosceles Split