Autograph Newsletter 2 – Straight Line Graphs

Welcome to the second 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
Craig Barton
Advanced Skills Teacher, creator of and TES Secondary Maths Adviser. Follow me on Twitter: @TESMaths
Diagnostic Question
Free Online Autograph Activity
Ideas for Extension
Video Tutorials
Handy Autograph Tip
I tend to find that students have a lot of difficulty with the topic of straight line graphs. Perhaps there is something rather abstract about the concepts involved that students cannot relate to. Or, maybe it is the sheer number and complexity of the skills required – reading algebra, substituting, rearranging formula, dealing with negative numbers, understanding co-ordinates – that throws up any nasty misconceptions or weaknesses that students may have and renders them unable to get to grips with the topic as a whole. Again, I feel dynamic geometry has a significant role to play in improving the teaching and learning experience. You are able to instantly manipulate things to tackle students’ questions or in response to their answers, and there is something rather satisfying for students in having a computer validate their efforts. Hopefully you will find lots of useful ideas and resources for aiding the teaching and learning of straight line graphs below.
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.
Reflection Diagnostic Question
Free Online Autograph Activity
Can you use your knowledge of straight line graphs to sink more ships than your opponent?
Battleships Autograph Activity
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 – Using Co-ordinates
Download  1-using-co-ordinates.agg
Can your students move each of the four points to co-ordinates that fit the following patterns:
The x co-ordinate must be 4
The y co-ordinate must be −3
The x and y co-ordinates must be the same
The y co-ordinate must be twice as big as the x
The x and y co-ordinates must add up to 5
Can your students come up with an algebraic way of describing each of these patterns of dots?
When your students are ready, test their predictions by turning on  Slow Plot mode and  enter in the relevant equation
Idea 2 – Move the Points
Download  2-move-the-points.agg
Move the points around and see how the equations of the two lines change. Find pairs of equations which:
Are in the form “x = a number”
Are in the form “y = a number”
Have the same number in front of the x
Have the same number at the end
Have one positive and one negative number in front of the x
What do you notice about the two lines in each of these cases?
Idea 3 – Constant Controller
Download  3-constant-controller.agg
Use the  constant controller to manipulate the values of m and c. The line y = x is used as a reference.
What effect does changing m have on the line?
What happens if m is negative?
How about if m is zero?
What effect does changing c have on the line?
What happens if c is zero?
What can’t you get a vertical line?
Idea 4 – Perpendicular Lines
Download  4-perpendicular-lines.agg
Move the circled points around and keep an eye on the equations of the two perpendicular lines.
Write down the gradients of the two lines and then move the points to a new position
Keep writing down the gradients using the  Scribble tool
What is the relationship between the gradients of perpendicular lines?
Test out your theory on a few more examples
Does this relationship still work for horizontal and vertical lines?
Video Tutorials
The following video takes you through, step-by-step, two different approaches to investigating straight line graphs using Autograph.
Handy Autograph Tip
Sometimes points on Autograph can be a little tricky to see, especially on a whiteboard/projector when viewed from the back of the class. But have no fear – we can highlight them nicely with some lovely little circles!
Open Autograph in Standard Level
Place a point somewhere on your page
Make sure the point is highlighted, right-click and select Circle (Radius) from the menu. Your choice of radius will depend on your scale, but 0.2 tends to work well most of the time.
You can now drag the point around to your heart’s content by clicking on the centre of the point
A nice finishing touch is to add a text-box to keep a record of the co-ordinates of the highlighted point

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