# Mr Barton's Autograph videos - Graphing

#### TES Secondary maths resource collections

Collection Author: Craig Barton - Maths AST and creator of www.mrbartonmaths.com

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. The videos can be downloaded, put on your school’s VLE, or simply watched online.

This particular set of videos covers Graphing. We look at all aspects of graphing in 2D including lines, curves and transformations, and then go on to see how Autograph can be used to help students better understand all things to do with calculus.

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.

#### General

1. Selection and Shapes

• 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.

32. 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.

57. Hiding Things!

• 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 for the classroom, involving transformations and the equations of lines. Now you see them, now you don’t!

58. 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!

59. 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!

#### 2D Graphing

7. Edit Axes

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

25. 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.

26. 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.

• 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.

44. 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…

53. Creating Number Lines on 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.

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 Function 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.

60. 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.

• 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.

71. Find the Line Puzzle

• 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!

#### Calculus

• 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. 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

47. Further Integration

• 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.

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.

52. Creating Worksheets on 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!

#### Seasonal Specials

8. 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!).

14. 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!

24. 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!