# Secondary Maths Collection - "Autograph Videos - from the Autograph Team"

**TES Secondary maths resource collections**

**Collection Author:** Craig Barton - Maths AST and creator of www.mrbartonmaths.com (TES Name: mrbartonmaths)

Alongside Mr Barton’s weekly set of Autograph videos, there is also this Collection kindly put together by the very talented Autograph team. Here you will find lots of ideas, tips and tricky for getting the most out of Autograph for all ages and abilities. My personal favourites are the videos on volumes of revolution, transformations in 3D and the human cannonball!

**General Autograph Tips**

- Autograph can be used to great effect to enhance a lesson, but to do this you need to follow the simple three step rule.

- In this starter activity you will be introduced to Object Selection and the Right-click Menu, which are used in most Autograph files.

**Whiteboard Mode and the Onscreen Keyboard**

- If you use Autograph with a projector or interactive whiteboard then it is best to use Whiteboard Mode

- Share your work with people who don’t have Autograph installed using the Autograph player

**Videos for all ages**

- There may be some occasions when you want to prepare a file in advance of the lesson. For example Pin Boards are great for geometrical reasoning but the construction is not very helpful.

- In the 1920s, some very large structures were built along the South Coast of England to deal with the increasing threat of aerial attack.

- Modelling the path of a human cannonball by inserting an image into Autograph .

**Videos for Key Stage 3 (age 11 to 16)**

- We are going to explore the connection between the angle at the centre of a circle and the angle at any point on the circumference.

- Using Autograph to demonstrate different types of transformation: translation, enlargement, rotation and reflection.

- Because of the extra dimension transformations are somewhat different in three-dimensions. In this activity we will see what those differences are.

- Addition, subtraction and multiplication of vectors in Autograph.

- In this activity we explain how to enter equations and introduce Slow Plot, the Scribble Tool and the Constant Controller.

- In this activity we will demonstrate a link between the graphs of trigonometric functions and the unit circle.

**Videos for A Level Pure (age 16+)**

**A Goat Grazing Half a Square Field**

- One of the classic “goat grazing a field” geometry problems demonstrated.

**Differentiating Trigonometric Functions**

- We begin by plotting the sine curve and its gradient function in degrees and use this to motivate the introduction of radians.

- A simple visual introduction to calculus.

- We are going to investigate the vector equations of a line x = a + kb and a plane y = a + kb + µc

- The concepts learnt in the investigation of areas can also be applied to volumes of revolution. Suppose the region under the curve y = f(x) between x = a and x = b is revolved around the x-axis to form a solid. What is the volume of this solid? How can we approximate the volume?

- Investigating the exponential function by consider the function y = a^x and its derivative.

**Finding the Area under a Curve**

- How can we find the area A under the curve y = f(x) between x = a and x = b?

- The Binomial approximation is often used for approximating powers of numbers close to 1, but how close to 1 do we need to be in order for the approximation to be any good?

- In this investigation into a strange property of cubics, students would normally first be introduced to a special case, for example y = (x -2)(x + 3)(x + 4), and then asked to look at this more general case.

- Many equations cannot be solved using conventional methods. In such cases we need to use numerical methods to find solutions.

- Many different types of equation can be entered in Autograph: cartesian, trigonometric, exponential, hyperbolic, implicit, conics, polar, parametric, piecewise and differential. In this activity we look at a parametric form of the Lissajous equation.

- Create a plane and a cone in Autograph and investigate the intersections.

**Videos for A Level Applied (age 16+)**

- Using Autograph to visualise the solution to a linear programming problem.

- The drag acting on a falling object increases as it accelerates. The terminal velocity is achieved when the drag is equal to the force due to gravity, so the net force is zero.

- Analyse the weights of babies to determine how unusual a given weight is.

- It is possible to import a bivariate data set into Autograph but in this activity we are going to see how to create a dataset from points and we will then use that dataset to demonstrate least squared regression.

**Poisson and Normal Approximations to Binomial**

- Both the Poisson and Normal distributions can be used as approximations to the Binomial, but for which values of n and p are the approximations any good?

- The Central Limit Theorem tells us that regardless of the parent distribution, the distribution of the sample means will have a Normal distribution.

**Douglas Butler Video Specials**

**Douglas Butler Special 1 - Reflections**

- A special treat from the Autograph guru Douglas Butler who shows us some really nice things you can do with reflection on Autograph, including looking at the beauty of nature and the talent of the Red Arrows pilots.

**Douglas Butler Special 2 - Normal Distribution**

- Douglas Butler, the Autograph creator, looks at a really interesting way of how we can fit a normal distribution to data using Autograph.

**Douglas Butler Special 3 - Bivariate Data**

- This time Douglas Butler takes us through how we can do scatter graphs and lines of best fit on Autograph by looking at an interesting relationship between the weights of babies and the gestation period.

**Douglas Butler Special 4 - Torus (3D)**

- What do you get when you rotate the equation of a circle about a line in 3D?… there is only one man to tell you the answer to that - Mr Douglas Butler.

**Douglas Butler Special 5 - Least Squares Regression**

- An excellent video from Douglas Butler which reveals a simple and highly effective way of demonstrating to students where the least squares regression line comes from.

**Douglas Butler Special 6 - Shot Put Investigation**

- A fascinating video from Douglas Butler who uses Autograph to investigate why the optimal angle for a shot put to be thrown is not 45 degrees but 31! Let’s hope the 2012 Olympic Committee are watching.