# Autograph Newsletter 3 – Angles

 Welcome Welcome to the third 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 Students are first introduced to angles at an early age, and they keep cropping up throughout all of their maths education. Starting with the introduction of degrees and how to measure angles, the topic progresses through angle rules, bearings, right up to the concept of radians and trigonometric identities. Dynamic software, like Autograph, can help with all aspects of the topic of angles. By making the most of the ability to instantly manipulate things, as well as hiding and revealing information, we can hunt for relationships, test them out and work towards proofs. The days of drawing hundreds of examples on the classroom board have long gone! Hopefully you will find lots of ideas and resources to help with the teaching and learning of angles in this newsletter.
 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 Angle Facts Can you spot each of the key angle facts using this interactive activity? Change the slope and position of the lines and see if they are still true. 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 straight line graphs require the full version of Autograph. Click on the image to download the individual Autograph files.
Idea 1 – Make the Angle
Students are challenged to create three angles of given sizes, and then use Autograph to check the accuracy of their attempts.
 • What strategies did you use? • Which angle was the most difficult to make? • How do you know when an angle is greater than 90°? • How about greater than 180°? • How far off where your guesses? • Use the  Scribble Tool to mark the students’ predictions and any workings out • Note: You can change the target angles to whatever you like, and to reveal the size of the angles, simply double-click on the angle and place a tick by Show Label
Idea 2 – How big is the Angle?
Extending the previous idea by this time asking students to estimate how big a set of angles are.
 • What strategies do you use when estimating the sizes of angles? • What size do you know your angle is definitely greater than? • How about definitely smaller than? • Can you think of a clever strategy for estimating angles greater than 180°? • Again, make use of the  Scribble Tool to mark the students’ predictions and any workings out • Note: To adjust the size of the angles, simply drag the ends of the arms of the angles into new positions
Idea 3 – Bearings