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Calculus |
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Trigonometry
(2D & 3D) |
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Douglas
Butler Specials |
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1.
Selection and Shapes
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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. |
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58.
Autograph Keyboard
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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 |
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32.
Autograph in 3D
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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 |
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57.
Hiding Thnigs!
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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!
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58.
Images in Autograph
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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! |
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Video |
View
Online |
7.
Edit Axes
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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 |
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60.
Battleships
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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. |
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25.
Straight Lines
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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 |
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26.
Parallel and Perpendicular Lines
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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 |
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27.
The Gradient Tool
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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 |
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43.
Graphing Quadratics
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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. |
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44.
Iteration
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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... |
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52.
Creating Worksheets in Autograph
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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! |
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53.
Creating Number Lines in Autograph
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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. |
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54.
Transformation of Functions 1
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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. |
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55.
Transformation of Functions 2
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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. |
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56.
Follow the Point
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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. |
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66.
Quadrilateral Puzzle
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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. |
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67.
Pizza Puzzle
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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? |
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71.
Find the Line!
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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! |
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Video |
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Video |
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Online |
27.
The Gradient Tool
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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 |
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45.
Tangents and the Gradient Function
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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. |
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46.
Integration - Area Under a Curve
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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. |
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47.
Further Integration
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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... |
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48.
Volume of Revolution Introduction
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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. |
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49.
Volume of Revolution Formula
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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. |
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50.
Further Volumes of Revolution
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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. |
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Video |
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Online |
1.
Selection and Shapes
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In
this first video we look at the issue of Whiteboard Mode and
how we go about creating basic shapes |
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2.
Reflection
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In
this second video we look at three different ways of doing
Reflections in Autograph |
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3.
Rotation
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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! |
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4.
Enlargement
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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! |
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5.
Translation
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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! |
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6.
Combining Transformations
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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... |
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20.
Animation Special
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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. |
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30.
Vectors in 2D
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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 |
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31.
More Vectors in 2D
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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 |
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33.
Cubes and Euler
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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. |
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35.
Planes of Symmetry
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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! |
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36.
Reflections and Rotations in 3D
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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! |
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62.
Line Symmetry in Rectangles
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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. |
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63.
Line Symmetry in Quadrilaterals
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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.
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64.
Matrix Transformations
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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.
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65.
Leap Frog Puzzle
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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. |
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Angles
and Circle Theorems |
Video |
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Description |
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Video |
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Online |
9.
Measuring Angles
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In
this ninth video we look at the basics of measuring angles
in Autograph |
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17.
Angle at the Centre Theorem
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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 |
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18.
Angle at the Centre Theorem - Twist!
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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?... |
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19.
Cyclic Quadrilateral
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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... |
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21.
Angles in the Same Segment
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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. |
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22.
Alternate Segment Theorem
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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. |
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23.
Two Tangents Theorem
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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. |
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61.
Circle Through 3 Points
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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! |
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|
Video |
|
Description |
Download
Video |
View
Online |
33.
Cubes and Euler
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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. |
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34.
Pythagoras & Trigonometry in 3D
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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 |
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35.
Planes of Symmetry
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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! |
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39.
Extras - Trigonometry
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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 |
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68.
Trigonometry and Pythagoras (Part 1)
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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! |
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69.
Trigonometry and Pythagoras (Part 2)
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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… |
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70.
Trigonometry and Pythagoras (Part 3)
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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? |
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Video |
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Description |
Download
Video |
View
Online |
10.
Working with Raw Data
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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! |
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11.
Working with Raw Data - Part 2
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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 |
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12.
Working with Raw Data - Part 3
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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! |
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13.
Working with Raw Data - Part 4
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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 |
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15.
Working with Grouped Data
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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. |
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16.
Working with Grouped Data - Part 2
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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. |
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28.
Scatter Diagrams
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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 |
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29.
Finding the Line of Best Fit
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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 |
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51.
Fitting Functions to Data
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|
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. |
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Probability
and Probability Distributions |
Video |
|
Description |
Download
Video |
View
Online |
37.
Extras - Dice Simulation
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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. |
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38.
Extras - Monte Carlo
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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. |
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40.
Biased Dice & Balls in a Bag
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|
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. |
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41.
Dice and the Binomial
|
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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... |
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42.
Coins and the Geometric
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|
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! |
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|
Video |
|
Description |
Download
Video |
View
Online |
|
Douglas
Butler Special 1 - Reflections
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|
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 |
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Douglas
Butler Special 2 - Normal Distribution
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|
Douglas
Butler, the Autograph creator, looks at a really interesting
way of how we can fit a normal distribution to data using
Autograph |
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Douglas
Butler Special 3 - Bivariate Data
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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 |
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Douglas
Butler Special 4 - Torus (3D)
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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 |
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Douglas
Butler Special 5 - Least Squares Regression
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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 |
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Douglas
Butler Special 6 - Shot Put Investigation
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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 |
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Video |
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Description |
Download
Video |
View
Online |
8.
Christmas Treat
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|
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 |
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14.
Valentines Day Special
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|
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! |
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24.
Easter Special
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|
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! |
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|
For more videos, help and ideas, or to order Autograph 3.3 (you can
download a free one month trial!) just click the icon to visit the
website
Why not subscribe (for free, of course!) to my YouTube channel
to see all my videos and get updates each time a new video is posted?
Or, if you fancy a set of
paper tutorials for you and your students, well I can provide those
as well!
