# Autograph Newsletter 5 – Rotation

 Welcome Welcome to the fifth 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 Following on from Newsletter 1 on reflection, here we turn our attention to another of the transformations – rotation. For many students, this is the most difficult of the transformations, and I can certainly sympathise. I find rotations difficult to picture in my head and interpret on paper. Fortunately, there is dynamic geometry software such as Autograph to help students (and me!) out. The ability to manipulate objects and points, immediately change the angle of rotation, and hide crucial information, allows us to put together a package of resources and activities to really bring the topic of rotation alive. We can even venture into the world of 3D!
 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 Rotation Golf! Can you change the centre of rotation and the angle in order to fit the red object into each of the black holes? Describe the rotation in each case. 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. Click on the image to download the individual Autograph files.
Idea 1 – Find the Centre
Turn the topic of rotation on its head by challenging students to find the three centres of rotation
 • The blue object has been rotated about three different centres of rotation by 90, 180 and 270 degrees clockwise to produce the three images. • Can you work out the three centres of rotation? • Use the Scribble Tool  to mark the students’ predictions. • If students are struggling, move the blue object to the right one square and look at the new positions of the images. • To reveal the centres of rotation, click the Object menu and choose Unhide all. • If I now move the blue object up one square, how will the rotated images move? • You can set up more examples like this using the techniques in the video below.
Idea 2 – Rotation Patterns
Can your students make nice patterns using rotations?
 • Can your students see how my pattern has been put together? • Try moving one of the shapes on the right and see what happens. • Can your students make a pattern using just one shape? • How about using two or three? • Why do some patterns have gaps and others have no gaps? • If your students want to share their patterns, email[email protected]. • The techniques to carry out the rotations are explained in the video below.
Idea 3 – Combining Rotations