Free Dynamic Mathematics Resources
 7. Translations and Vectors
 Welcome Welcome to the seventh 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 In previous newsletters we have looked at Reflection and Rotation, so it was only a matter of time before Translation and Vectors came to our attention. Autograph has the ability to make the study of translations far more dynamic, enabling you to manipulate objects and numbers and instantly see their effect. However, it is with vectors that the software really comes into its own, giving you the power to combine vectors in any way you could imagine, in both 2D and 3D. I hope you find lots of ideas to help bring the study of translations and vectors to life.
 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 Vector Challenge Vectors a and b have been used in some way to create 6 new vectors. Your job is to find out how! 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 – Vectors and Translations on Autograph
There are two main ways of using vectors in 2D on Autograph. The one you choose will be dependent on the task you are doing.
Method 1 – Vector Defined from a point
 • The red object has been translated by the red vector to give the green image. • You can drag the foot of the vector so that it lies on one of the vertices of the red object to show the translation. • Double-click on the vector to change it. • You can even change the vector to and use the constant controller to change the vector.
Method 2 – Vector Defined from two points
 • The blue object has been translated by the blue vector to give the orange image. • You can drag either end of the vector around to see the effect it has on the image itself.
Experiment with both of these methods. Instructions how to create them can be found in the video below.
Idea 2 – Vector Man
Vector man has unfortunately got himself into a bit of a muddle.
 • Can your students drag the points to create vectors to put him back together again? • Scribble down the description of the vector next to each one. • How would these vectors change if you wanted Vector Man to be upside down? (use Drag to see more of the screen if you need). • Encourage your students to create similar puzzles using vectors on Autograph
Idea 3 – Vector Flight Path
Can you guide the spaceship to safety without touching the sides?
 • Left-click on an unoccupied part of the page to make sure no objects are selected • Left-click to select the current position of your point. Left-click on the vector (or vectors) of your choice – the one(s) you select should turn black. • Right-click and choose either:Copy Vector if you have just selected one vector and you want to travel along itNegative Vector if you have selected just one vector and you want to travel along the negative of itMultiply Vector if you have selected just one vector and you want to travel along a multiple of it (either positive or negative)Add Vectors if you have selected more than one vector and you want to add them togetherSubtract Vectors if you have selected more than one vector and you want to subtract them Note: When subtracting vectors, the order which you select the vectors is very important. The second vector you select will be subtracted from the first. • Who can get to safety using the fewest number of vectors? • Encourage your students to create similar puzzles using vectors on Autograph
Idea 4 – Vector Golf in 3D!
What's better than 2D Vector Golf? 3D Vector Golf, of course!
 • Your ball is the point at (−4, −3, −2), and the hole is the centre of black cube at (4, 0, 3) • There are plenty of obstacles in your way, which you are not allowed to hit • Using the same techniques as described in Extension 3, can you get the ball into the hole? • What is the fewest number of shots you need? • Challenge your students to design some nightmare 3D golf holes!
 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 translation.
Handy Autograph Tip
Creating and copying vectors can be a really useful thing to do when building Autograph worksheets
 Open Autograph in Standard Mode. Make sure you are in Whiteboard Mode Place two points anywhere on the page fairly close together In Select Mode drag around the two points, right-click and choose Create Vector Place another point somewhere else on the page Select this point and the vector, right-click and choose Copy Vector. You can now drag the original vector around and the new vector will also move. Add two more vectors to your original vector to create a triangle. Create some copies of this triangle as explained above. If you move one of the original points, all the other triangles should also change. Challenge: Can you create a set of tessellating triangles?
 Curriculum Coverage Not teaching translations or vectors today? No problem, Autograph covers much more including 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.