Welcome 
Welcome to the second Autograph Newsletter! Each jampacked 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

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 coordinates – 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. 




Free Online Autograph Activity

Battleships 
Can you use your knowledge of straight line graphs to sink more ships than your opponent? 

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 Coordinates 
Download
1usingcoordinates.agg


Can your students move each of the four points to coordinates that fit the following patterns: 

• 
The x coordinate must be 4 
• 
The y coordinate must be −3 
• 
The x and y coordinates must be the same 
• 
The y coordinate must be twice as big as the x 
• 
The x and y coordinates 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
2movethepoints.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
3constantcontroller.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
4perpendicularlines.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, stepbystep, 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, rightclick 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 textbox to keep a record of the coordinates of the highlighted point 


