# Mr Barton's Autograph videos - Shape, Space and Measures

#### 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 Shape, Space and Measures. We look at how Autograph can be used to dynamically introduce and investigate the transformations of shapes and circle theorems, discover and test angle facts, and tackle all aspects of Pythagoras and Trigonometry in 2D and 3D!

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!

#### Transformations

2. Reflection

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

3. Rotation

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

4. 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!

5. 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!

6. 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…

20. 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.

30. 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.

31. 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.

33. 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.

35. 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!

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.

64. 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.

65. 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.

#### Angles and Circle Theorems

9. Measuring Angles

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

17. 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.

18. 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?

19. Cyclic Quadrilateral

• 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.

21. 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.

22. 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.

23. 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.

61. 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!

#### Trigonometry (2D and 3D)

33. 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.

34. 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

35. 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!

39. 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.

69. Trigonometry & Pythag 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 in Autograph (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?