Welcome Welcome to the tenth 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 In previous newsletters we have seen how Autograph can be used to enhance the teaching of each of the three types of transformations – reflection, rotation and translations. Now we complete the set with a look at Enlargement. For some students this is the most difficult of them all. Difficulties can emerge when enlarging from a given co-ordinate, finding the centre, determining the scale factor of enlargement, and when entering the world of fractional and negative scale factors. You will be pleased to know that Autograph can help address all of these issues, and can even take you into the wonderful world of enlargements in three dimensions!
 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 Enlargement Golf Can you use your knowledge of enlargements to guide the shapes into the black holes? 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 this topic require the full version of Autograph.
Idea 1 – Introducing Enlargements
You can use Autograph to introduce students to the very basics of enlargement, and use the same process to take them right up to fractional and negative scale factors.
 • Challenge your students to predict and  Scribble down where they think the image will appear following an enlargement of scale factor 2 with centre at the circled point • When they are ready  click on the object and the centre of the point, right-click and choose Enlargement • Choose the scale factor • Decide if you want to show construction lines and then click OK • Ask the students to predict what happens if you increase the scale factor • Use the  Animation Controller to dynamically change the scale factor • Now what happens when the scale factor goes below 1? • How about when it is negative? • Use the  Animation Controller to illustrate this, emphasising the smooth progression as the scale factor decreases in size
Idea 2 – Finding the Centre of Enlargement
This file provides a clear illustration of how to find the centre of an enlargement
 • Challenge your students to predict where they think the centre of enlargement is and  Scribble down a prediction • Choose one of the dashed lines to start with • Drag the circled points to a pair of corresponding corners on the original object and the enlarged image • Repeat this for the other three remaining lines until each corner of the two objects has a line passing through them • Where these lines meet is the centre of enlargement • To set up another example, go to Object > Unhide all, drag the centre of enlargement (and the corners of the object, if you choose) to a new position, then select the point, right-click and choose Hide Object • Double-clicking on the enlarged image allows you to change the scale factor, should you wish
Idea 3 – Area Scale Factor