# TES collection Autograph Videos - from Mr Barton

#### Autograph Videos - from Mr Barton

Autograph is a piece of mathematical software that many schools have tucked away on their network somewhere, but that often only gets used to draw the odd straight line or curve. This is as big a crime as using an iPad as a coffee mat.

Autograph can do so much more, enabling you to dynamically demonstrate to your students topics as diverse as transformations, cumulative frequency diagrams, the fundamental theorem of calculus and the outcomes of rolling several dice. Autograph can be used with all ages and abilities, from primary school students right up to Further Mathematicians with eyes on a mathematics degree.

This collection is a series of videos put together by me which aim to give you a few ideas of how you could use Autograph in your classroom. You do have to put up with my annoying voice, but hopefully there will be enough tips and suggestions for beginners and advanced users to help you get over that. A new video will be added each week, and if you have any requests for specific topics to be covered, just email me at teachers@mrbartonmaths.comand I will do my best to meet your requests.

Selection and Shapes

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

Reflection

• Here we look at three different ways of doing Reflections in Autograph.

Rotation

• This time we look at how we can carry out Rotations in Autograph.

Enlargement

• Here we look at how we can carry out Enlargements in Autograph which also leads us to our first viewing of a Dynamic Text Box!

Translation

• 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!

Combining Transformations

• This time 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…

Edit Axes

• Now we take a closer look at the Edit Axes menu to get our Autograph page looking exactly how we want it.

Christmas Treat

• A Special Christmas Edition of Mr Barton’s Autograph Videos which has a look at the online Autograph Player (with a festive twist!).

Measuring Angles

• This time we look at the basics of measuring angles in Autograph.

Working with Raw Data

• Now 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!

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

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!

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.

Valentine’s Day Special

• 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!

Working with Grouped Data

• 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.

Working with Grouped Data 2

• 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.

Angle at the Centre

• 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.

Angle at the Centre - 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?

• We look at our second Circle Theorem - this classic Cyclic Quadrilateral Theorem. After quickly constructing and demonstrating the theorem, we also have a look at a nice little extension question involving parallelograms.

Animation Special

• 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.

Angles in the Same Segment

• 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.

Alternate Segment Theorem

• 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.

Two Tangents Theorem

• 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.

Easter Special

• 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!

Straight Line Graphs

• 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.

Parallel & Perpendicular Line

• 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.

Scatter Diagrams

• 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

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.

Vectors in 2D

• 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.

More Vectors in 2D

• 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.

Autograph in 3D

• 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.

Cubes and Euler

• 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.

Pythagoras and 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

Planes of Symmetry

• 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!

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!

Extras – Dice Simulation

• 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.

Extras – Monte Carlo Method

• 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.

Extras – Trigonometry

• 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.

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.

Dice and the Binomial

• 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…

Coins and the Geometric

• 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!

• 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.

Iteration

• 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…

• 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.

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.

• 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.

The Keyboard

• 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!

Importing Images

• 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!

Co-ordinate Battleships

• 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.

A Circle Through 3 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!

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.

• 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.

Matrix Transformations

• 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.

Leap Frog Puzzle

• 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.