Free Dynamic Mathematics Resources
 1. Reflections
 Welcome Welcome to the new 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
 Contents Introduction Diagnostic Question Free Online Autograph Activity Ideas for Extension Video Tutorials Handy Autograph Tip
 Introduction Reflection is a topic that lends itself particularly well to being taught in a visual and dynamic way. Students who may struggle with the numeric and algebraic components of mathematics may have a flare for the more visual topics such as reflections, and if you can hook them in then it is likely to have a positive knock-on effect throughout the rest of their studies. Autograph enables you to easily and dynamically manipulate objects and lines to interactively cover every conceivable aspect of reflections, testing your students' special awareness to the very limit!
 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 Reflection Golf Can you change the line of reflection in order to fit the green object into each of the black holes? What is the equation of the line of reflection 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 the topic of reflection require the full version of Autograph.
Idea 1 – Simple Reflection
Introduce students to the idea of reflections using vertical and horizontal lines.
 • If I move the blue object to the left one square, where do the reflected objects move? • If I change the position of the lines of reflection (drag the circled points), how do the reflected objects move? • If I wiggle the top left corner of the blue object, which corners of the reflected objects will wiggle?
Use the  Scribble Tool to mark the students' predictions
Idea 2 - Diagonal Reflection
Develop your students' understanding of reflection by looking at diagonal lines of reflection.
 • If I move the blue object down one square, where do the reflected objects move? • If I change the position of the lines of reflection, how do the reflected objects move? • If I wiggle the top left corner of the blue object, which corners of the reflected objects will wiggle?
Use the  Scribble Tool to mark the students' predictions
Idea 3 - Any Reflection
Why be limited by simple lines of reflection? Here, simply drag the circled points around to create any line of reflection you choose
 • Can you describe how to reflect objects in the line y = 2x?
Idea 4 - Combined Reflections
Now the ultimate reflections test - can your students visualise combined reflections? Here, the blue object has been reflected in the green line to produce the green image, and then the green image has been reflected in the orange line to produce the orange image!
 • If I move the blue object down one square, where do the reflected objects move? • If I wiggle the top left corner of the blue object, which corners of the reflected objects will wiggle? • How could we get from blue to orange in a single transformation?
 Video Tutorials The following video takes you through, step-by-step, some of the ways you can use Autograph to look at the topic of reflections. Reflections are found everywhere in nature. In this tutorial you will learn how to use Autograph's  Insert Image to explore the reflectional symmetry in a butterfly.
Handy Autograph Tip
Using  Redo is a really nice way of taking your students step-by-step through a demonstration that you have already prepared. For example:
 Open Autograph in Standard Level Make sure you are in Whiteboard Mode In Point Mode plot points at (−4, 3), (−2, 3), (−2, 1) and (−4, 1) In Select Mode drag around all four points, right-click and select Group to Shape from the menu Enter the equation y = x Left-click on the centre of the square and the line, right-click and select Reflection from the menu Now Undo (in the Edit menu or using Ctrl-Z) enough times until you are back to your blank page You can then ask the following questions, and after each one Redo (also in the Edit menu or using Ctrl-Y) to reveal the next stage: • What shape would points at (−4, 3), (−2, 3), (−2, 1) and (−4, 1) form? • What does the line y = x look like? • Where would the square appear if I reflected it in the line y = x?
 Curriculum Coverage Not teaching reflections today? No problem, Autograph covers much more including statistics, probability, graphing, vectors, coordinate geometry, shapes and transformations, numerical methods, cartesian equations, parametric equations, polar equations, differential equations, calculus, trigonometry and all in two- and three-dimensions. Douglas Butler's series of 7 Autograph Tutorial Videos provide a perfect overview of curriculum coverage.
 Free Autograph Activities If you need free Autograph Activities that can be used without Autograph installed try Mr Barton's Autograph Activities.
 Getting Started If you are just getting started with Autograph try the Video Training Series and the Training Manual with step-by-step instructions.
 Worksheets Autograph trainer Alan Catley has created an impressive collection of student worksheets which can all be downloaded and used for no charge.
 Video Tutorials Watch videos by Craig Barton, Douglas Butler, Hassan Lakiss and Janet Smith.
 Books Prefer printed material? Download sample chapters from the Autograph Activities books.
 Courses and Trainers If you prefer face-to-face training attend a training course or book a trainer to come to your school.
 Be Inspired Been using Autograph for a while and looking for new ideas? For inspiration try Owen Elton's Matheminutes blog, and the blog from Autograph's creator Douglas Butler. Jonny Griffiths has three resources sites which make use of Autograph: Rich Starting Points for A Level Core Mathematics, Making Statistics Vital and Carom Maths. A complete list of useful websites can be found on Douglas' TSM Resources website.
Keep in Touch