The following page contains an index of all my Autograph Maths tutorial videos. They are arranged by broad categories. I hope you find them useful in getting to grips with the wonderful piece of software.

**Contents:**

Handy Autograph Tricks and Tips

Probability and Probability Distributions

**Key Autograph Skills back to contents**

In this first video we look at the issue of Whiteboard Mode and how we go about creating basic shapes. Please Note: This is a good video to start with if you are unfamiliar with Autograph, regardless of the topic you are covering.

A feature of Autograph that many people are unaware of (or close down as quickly as possible!) is the Autograph Keyboard. In this video we take a look at some of the useful things that the Autograph keyboard can do, both in the program itself and in other applications. You emails may never be the same again

In preparation for the next few videos, we take a look at some of the important tools needed for getting the most out of Autograph’s unique 3D engine

58. Importing images in Autograph

Another incredibly useful feature of Autograph is the ability to import images onto the graph page. In this video we take a look at how easy it is to import images into Autograph, and then take a look at some potential lesson applications, including working out the equation of lines on the London Underground and helping out the Human Cannonball!

**Handy Autograph Tips and Tricks back to contents**

52. Creating Worksheets in Autograph

Just a quickie here about how you can use Autograph to add that finishing touch to your perfect worksheet. Whether you want a lovely set of axes, some square paper, or some old fashioned graph paper, Autograph can satisfy your needs. We also look at a handy way of getting the size of the grid and the number range just right!

53. Creating Number Lines in Autograph

Following on from our work on worksheets last week, this time we take a look at how Autograph can be used to very quickly create an incredibly flexible number line. This can then be used in class to help with the teaching of topics including place value, scales, sequences and negative numbers.

An incredibly useful feature of Autograph is the ability to hide a variety of things. These include points, shapes and lines. In this video we look at how to hide objects and then suggest a few interesting applications, involving transformations and the equations of lines. Now you see me, now you don’t!

**Straight Lines back to contents**

In this seventh video we take a closer look at the Edit Axes menu to get our Autograph page looking exactly how we want it

In this video we take a look at an activity I like to use with my classes called Co-ordinate Battleships. I use this either to revise the equations of straight line graphs or even to introduce the topic. Teams take it in turn to launch their missiles (in the form of straight line graphs) in order to sink the ships (the co-ordinates). We look at how you can easily create this page on Autograph, and then some possible extension work after the sea battles are over.

Here we look at two different approaches to investigating the equations of straight lines on Autograph, both of which make good use of Autograph’s excellent dynamic textboxes, and one which uses the Constant Controller

26. Parallel and Perpendicular Lines

This week we follow-up our work on straight lines with a look at how you might tackle the topics of parallel and perpendicular lines on Autograph

Following on from the last couple of weeks where we have looked at straight line graphs, this time we take a look at Autograph’s excellent Gradient Function. We see how useful it can be for studying straight lines, and as a way of introducing older students to the joys of differentiation and calculus

Here is a quick idea for an activity that should help your learners practise identifying the equation of a line from the points that lie on it. A line is constructed, and a point attached to it, but the line is then hidden! Can your students figure out the equation of the line by moving the point up and down? Can they work out the gradient? You about the y-intercept? Fire up the turtle and test out their answer!

**Other Graphs back to contents**

We are going to be looking at graphing on Autograph for the next few weeks, and what better way to start than by looking at some of the different ways we can represent quadratic equations graphically. This includes tables of values, factorising, completing the square and equations from three points.

I was surprised that one of my Year 13 students wasn’t aware of the lovely fact that you can draw a circle through any 3 points, so long as those 3 points do not lie on a straight line. After an example with compasses and a ruler failed to convince him, I turned to Autograph, and this is the result!

Following a request from Mr Howard of Bolton School, this week we look at how Autograph can be used to help students visualise how the iterative process works. We look at three different examples which lead to convergence, divergence, and something rather odd…

**Transformation of Functions back to contents**

54. Transformation of Functions 1

The first in the Transformations of Functions Trilogy of videos where we look at how we can use Autograph to introduce students to the topic of transforming graphs. We see how to enter the f(x) notation, and how to make best use of the wonderful constant controller to get all the stretches, shifts and squashes that you could possibly want.

55. Transformation of Functions 2

Part 2 of the Transformations of Functions Trilogy of Autograph videos. This time we take a peek at a nice way of getting the exact shape function you are looking for without having to worry about a horrendous equation.

The Transformation of Functions Trilogy comes to a close with this final video all about how you can use Autograph to play “Follow the Point”. Being able to predict the co-ordinate of a point following a transformation is increasingly becoming a popular exam style question, and is a really useful skill for the students to develop, and it can be examined thoroughly using Autograph’s dynamic features.

**Calculus back to contents**

Following on from the last couple of weeks where we have looked at straight line graphs, this time we take a look at Autograph’s excellent Gradient Function. We see how useful it can be for studying straight lines, and as a way of introducing older students to the joys of differentiation and calculus

45. Tangents and the Gradient Function

This week we continue our look at the world of 2D graphing by examining how we can use the tangent tool and the gradient function to investigate quadratic curves. This offers a slick way of illustrating why two quadratic curves have the same gradient function.

46. Integration – Area Under a Curve

This week we move from differentiation to integration by taking a look at how Autograph can be used to introduce students to the concept of the area under the curve. The good news is that Autograph can easily and clearly illustrate estimating the area using rectangles as well as the classic Trapezium and Simpson rules. We also make nice use of the Animation button to see what happens as our number of divisions increases.

Following on from last week’s video, this time we look at how to use Autograph to cope with integration’s little twists, such as dealing with negative areas, working out the area between a curve and the y-axis, and working out the area between a curve and a line. This will set us up nicely for next week when we enter the world of 3D…

48. Volume of Revolution Introduction

In my opinion, there is no better way of illustrating the concept of Volumes of Revolution to students than using Autograph’s unique 3D engine. Watch their delight at the area under the curve spins neatly around the x-axis to form a lovely 3D shape bringing what can be a very abstract concept to life. This video will set us up nicely for next week when we look at how to use Autograph to derive the Volume of Revolution formula.

49. Volume of Revolution Formula

Following directly on from Video 48, this week we look at how we can use Autograph’s unique 3D engine to demonstrate to students exactly where the formula for the volume of revolution comes from. This provides a nice insight into limits and the fundamental theorem of calculus.

50. Further Volumes of Revolution

In the final Autograph Video of 2011 we take a look at some of the lovely shapes you can make using Volumes of Revolution. We hint at how it is possible to derive the formulae for some common 3D objects (for more on this see Mr Barton’s “Autograph Activities” textbooks!), how you can create volumes around the y-axis, and finally we look at some of the fascinating shapes you can form with areas between curves and lines. Plenty to keep you busy until the end of the year.

**Transformations back to contents**

In this first video we look at the issue of Whiteboard Mode and how we go about creating basic shapes

In this second video we look at three different ways of doing Reflections in Autograph

In this third video we look at how we can carry out Rotations in Autograph. See Video 20 for an nice animated twist with Rotations!

In this forth video we look at how we can carry out Enlargements in Autograph which also leads us to our first viewing of a Dynamic Text Box! See Video 20 for an nice animated twist with Enlargements!

In this fifth video we complete the set of Transformations by looking at how we can carry out Translations in Autograph. Mr Barton also sorts out the screen size issue!

In this sixth video we look at how we can use Autograph to combine Transformations, and there is even a little puzzle for you to have a think about…

In a special edition of Mr Barton’s Autograph Videos we look at the use of Autograph’s very impressive Animation function and how you might use it in the context of angles, points and transformations.

This week we look at how we can use Autograph to model Vectors in 2D, including the multiple of a vector and adding and subtracting two vectors

This week we take a look at how we can make the study of vectors in 2D more dynamic, which culminates in a suggestion for a nice little starter activity that you can try on your students

This week we learn how to construct a 2x2x2 cube in Autograph, which will come in very handy when we come to look at Pythagoras in 3D, Planes of Symmetry and Vectors in the next few weeks. There is also a nice little link to Euler’s famous formula.

We make good use out of our cube again this week, this time by taking a look at the surprisingly tricky question of: “how many planes of symmetry does a cube have?”. Autograph’s 3D mode provides a lovely way of displaying the answer. Oh, and for the record, I got this question wrong!

36. Reflections and Rotations in 3D

Your students have mastered reflections and rotations in 2D, they are getting a bit cocky, they are thinking maths is easy. Well, let’s see how they cope with another dimension!

62. Line Symmetry in Rectangles

A common misconception amongst students (and myself, actually!) is that a rectangle has 4 lines of symmetry. In this video we look at how we can use Autograph to illustrate this concept in a simple, effective way and thus dispel the myth once and for all. Along the way we look at hiding objects and parallel lines.

63. Line Symmetry in Quadrilaterals

This is the much-anticipated(!) sequel to last week’s Line Symmetry in Rectangles. Here we look at how we might create an Autograph page to look at line symmetry more generally by allowing us to alter the original shape. This requires a sneaky use of vectors, and this technique may have applications in other Autograph activities that you may wish to create.

Should you find yourself needing to teach the transformation of matrices, it would be nice to have some dynamic geometry package to help you along the way through this very visual topic. This is where Autograph steps in! In this video we look at carrying out simple transformations, and then a few twists: using the animation controller to repeat the transformation, using a constant controller to change elements of the matrix, and finally combining two matrix transformations together.

**Angles and Circle Theorems back to contents**

In this ninth video we look at the basics of measuring angles in Autograph

An introduction into the wonderful world of circle theorems on Autograph

17a. Angle at the Centre Theorem

This week we take a look at how to construct Circle Theorems using Autograph, beginning with the Angle at the Centre Theorem. We also see how understanding this theorem leads us to another theorem for free! Autograph’s dynamic nature makes it perfectly suited to demonstrating circle theorems to your students

18. Angle at the Centre Theorem – Twist!

Whilst we are on a roll with the Angle at the Centre Theorem, why not have a quick look at a nice little twist? We can use Autograph to set up some circumstances where the theorem doesn’t seem to work. Has maths been broken, or can your students figure out what is going on?…

This week we look at our second Circle Theorem – the classic Cyclic Quadrilateral Theorem. After quickly constructing and demonstrating the theorem, we also have a look at a nice little extension question involving parallelograms…

21. Angles in the Same Segment

This week we look at our third Circle Theorem – the classic Angles in the Same Segment Theorem. There is also a quick demonstration of how to set up a nice looking label for points, and a twist that you might want to try on your students.

This week we look at our fourth Circle Theorem – the notoriously difficult Alternate Segment Theorem. Can Autograph help us understand when this theorem works and when it doesn’t? There is also a look at how to construct tangents and a sneaky way of measuring angles.

In a jam-packed edition of Mr Barton’s Autograph Videos we look at all things to do with Tangents, including the Two Tangents Theorem. This also leads us to discover a slick way of marking the intersection of two lines on Autograph and how to measure the length of line segments.

**Trigonometry (2D and 3D) back to contents**

This week we learn how to construct a 2x2x2 cube in Autograph, which will come in very handy when we come to look at Pythagoras in 3D, Planes of Symmetry and Vectors in the next few weeks. There is also a nice little link to Euler’s famous formula.

34. Pythagoras & Trigonometry in 3D

Let’s put last week’s cube into good use by looking at how we can use it to help illustrate the difficult topics of Pythagoras and Trigonometry in 3D

In this video we take a look at the third of Autograph’s wonderful Extras pages – Trigonometry. Here we see where the graphs each of the trigonometric ratios comes from using the unit circle, and observe the effect on the graphs where we manipulate some constants

68. Trigonometry and Pythagoras (Part 1)

The first of the Trigonometric Trilogy! In this week’s video we take a look at a clever way of using Autograph to practice working out the length of missing sides using Trigonometry (sin, cos and tan) and Pythagoras. We begin by constructing a right-angled triangle, and then use a sneaky technique to cover up a measurement. The finished article can then be used in class or at home for infinite trigonometry practice! More on this next week!

69. Trigonometry and Pythagoras (Part 2)

The second of the Trigonometric Trilogy! Following on from last week’s work, we take a look at how we can use Autograph to help students practise finding the sizes of missing angles in right-angled triangles using Trigonometry. The advantage of doing this on Autograph is you can easily generate as many examples as you want and quickly check the students’ answers. One more part to come next week…

70. Trigonometry and Pythagoras (Part 3)

All good things must come to an end, and the same is also true for our Autograph Trigonometric Trilogy! In this final video we go out with a bang by taking a look at how we can use Autograph to test students’ understanding of the classic isosceles triangle questions that seem to be a favourite of the examiners. Can students use their knowledge of sin, cos and tan in right-angled triangles to solve these problems?

**Statistics back to contents**

In this tenth video I deal with a request from Lucius Evans who wanted to look at some of the Statistical functions on Autograph. Here we look at some of the things you can do with Raw Data, including dot plots and box and whisker diagrams. More stats to come next week!

11. Working with Raw Data – Part 2

Following a suggestion from none other than Autograph creator Douglas Butler, we take another look at some of the things you can do with Raw Data on Autograph, including quickly creating a data set

12. Working with Raw Data – Part 3

Douglas Butler returns again! This time with a great suggestion for introducing the Normal Distribution via a look at the fascinating world of IQ. The also encompasses Autograph’s wonderful scaling option for nasty looking data!

13. Working with Raw Data – Part 4

In a jam-packed edition we start to look at how Autograph can group raw data for us and how this opens up a whole new set of possibilities in terms of mathematical diagrams, including cumulative frequency curves, histograms and stem and leaf

In our final look at data for a while (you can have too much of a good thing) we tackle an issue with commas and how to alter the sizes of your groups.

16. Working with Grouped Data – Part 2

Yes, yes, I know I said last week was the last data one, but a request came through on the emails, so I thought I had best cover it whilst we are on a roll! So, this week we look at different ways of entering grouped data, another way of comparing data, and we take another look at the Results Box.

Seeing as we are now experts with straight line graphs, this week we look at how we can use Autograph to study Scatter Diagrams, Lines of Best Fit and Correlations

29. Finding the Line of Best Fit

Following on from our work on Scatter Diagrams, we take a look at how the Line of Best Fit is calculated. This provides a valuable link from Key Stage 4 maths to A Level Statistics as Autograph is able to clearly demonstrate the method for finding the least squares regression line

Following a request from Science teacher Mr Richardson, here is a video explaining how you can use Autograph to fit functions to various data sets. It doesn’t matter if the relationship in your data is linear, quadratic or exponential decay, you can be sure that Autograph can handle it.

**Probability and Probability Distributions back to contents**

This week we take a look at one of the excellent Autograph Extras pages. The Dice Simulation page is fantastic for allowing your students to explore the concepts of experimental probability, sample sizes and distributions.

In this video we take a look at the second of Autograph’s wonderful Extras pages – the Monte Carlo Method. We see how this can be used to make an estimate for the value of pi, combining together important aspects of geometry and probability.

40. Biased Dice & Balls in a Bag

This week we take a look at how Autograph can be used to introduce students to the concept of experimental probability. You can very quickly set up a probability distribution function of your choice (fair dice, biased dice, numbered balls in a bag, you name it!), take samples of varying sizes, and create diagrams from the data. All of this may just help a tricky topic sink in a bit better.

In this video we continue our look at statistics and probability by seeing how Autograph can be used to introduce the concept of the binomial distribution. We look at the classic example of tossing a coin to create dot plots and box and whisker diagrams, and then we introduce a nice little twist…

Continuing our theme of all things statistical, this week we take a look at how Autograph might be used to introduce students to the concept of the Geometric Distribution, with a little helping hand from the Animation Controller!

**Seasonal Specials and Puzzles back to contents**

A Special Christmas Edition of Mr Barton’s Autograph Videos which has a look at the online Autograph Player (with a festive twist!). To have a play with the file yourself, just click here

In a special “loved-up” edition of Mr Barton’s Autograph videos, we look at a romantic (mathematical) alternative to chocolates and flowers to send to the love of your life to let them know you care. Happy Valentines Day!

Egg-sactly what you need this time of year – an Easter themed Autograph video. Here we take our first proper look at Autograph’s very impressive 3D engine and how you can use it to create planes and rotate curves around lines to make 3D objects. Happy Easter!

The first of the Autograph Puzzle Trilogy! Here we look at a lovely pencil and paper puzzle inspired by Don Steward’s amazing Median Maths Blog. Place any 3 points on a page and start leap-frogging over them. After a few leaps, do you notice anything? More importantly, can you explain/prove it? We look at how Autograph may be able to help us get to grips with what is going on.

The second of the Autograph Puzzle Trilogy! Here we look at another a lovely pencil and paper puzzle inspired by Don Steward’s amazing Median Maths Blog. Students are given four co-ordinates and asked to consider the shape that would be formed by joining up the midpoints of pairs of these co-ordinates. What type of quadrilateral is it? How do they know? We can then turn to Autograph to construct the puzzle and investigate it even further.

The final part of the Autograph Puzzle Trilogy! This week we take a look at the “Pizza Problem” – what is the maximum number of pieces you can cut a pizza up into making straight line slices? This is something I have always investigated using good old-fashioned pencils and rulers, but Autograph just adds that extra dimension, allowing students to move the cuts around without the need for lots of rubbings out. Can you and your students spot the pattern? Can you explain why?

**Official Autograph Videos back to contents**

Some really lovely videos from the Autograph team can be found here