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| Welcome |
| Welcome to the new Autograph Newsletter! Each jam-packed edition
will look at a specific topic in mathematics and how Autograph can help
engage students and enable them to understand the key concepts better. |
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| Hope you enjoy it! |
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| Craig Barton
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| Advanced Skills Teacher creator of www.mrbartonmaths.com and TES Secondary Maths Adviser
Follow me on Twitter: @TESMaths
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| Introduction
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| Reflection is a topic that lends itself particularly well to being taught
in a visual and dynamic way. Students who may struggle with the numeric
and algebraic components of mathematics may have a flare for the more visual
topics such as reflections, and if you can hook them in then it is likely
to have a positive knock-on effect throughout the rest of their studies.
Autograph enables you to easily and dynamically manipulate objects and
lines to interactively cover every conceivable aspect of reflections, testing
your students' special awareness to the very limit! |
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| Diagnostic Question
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| Diagnostic questions are ideal to use at the start of the lesson to enable
you to get a quick and accurate picture of your students' levels of understanding.
They are designed in such a way that common misconceptions that your students
may hold should steer them to one of the incorrect answers, thus allowing
you to learn where the problems lie from their responses. Typically I give
my class 30 seconds thinking time and then ask them to hold up their fingers:
1 for A, 2 for B, etc. |
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| Free Online Autograph Activity
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| Reflection Golf |
| Can you change the line of reflection in order to fit the green object
into each of the black holes? What is the equation of the line of reflection
in each case? |
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| These Autograph activities do not require the full version of Autograph
to run them. You just need to install the free Autograph Player (you will
be guided through how to do this), which means you can use these activities
in the classroom or set them for your students to do at home. |
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| Ideas for Extension
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| The following ideas for extending the topic of reflection require the
full version of Autograph. |
| Idea 1 – Simple Reflection |
Download
 simple-reflection.agg
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| Introduce students to the idea of reflections using vertical and horizontal
lines. |
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If I move the blue object to the left one square, where do the reflected
objects move? |
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If I change the position of the lines of reflection (drag the circled
points), how do the reflected objects move? |
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If I wiggle the top left corner of the blue object, which corners of the
reflected objects will wiggle? |
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Use the
 Scribble Tool to mark the students' predictions |
| Idea 2 - Diagonal Reflection |
| Download
diagonal-reflection.agg
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| Develop your students' understanding of reflection by looking at diagonal
lines of reflection. |
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If I move the blue object down one square, where do the reflected objects
move? |
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If I change the position of the lines of reflection, how do the reflected
objects move? |
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If I wiggle the top left corner of the blue object, which corners of the
reflected objects will wiggle? |
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| Use the
Scribble Tool to mark the students' predictions |
| Idea 3 - Any Reflection |
| Download
any-reflection.agg
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| Why be limited by simple lines of reflection? Here, simply drag the circled
points around to create any line of reflection you choose |
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Can you describe how to reflect objects in the line y = 2x? |
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| Idea 4 - Combined Reflections |
| Download
combined-reflections.agg
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| Now the ultimate reflections test - can your students visualise combined
reflections? Here, the blue object has been reflected in the green line
to produce the green image, and then the green image has been reflected
in the orange line to produce the orange image! |
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If I move the blue object down one square, where do the reflected objects
move? |
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If I wiggle the top left corner of the blue object, which corners of the
reflected objects will wiggle? |
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How could we get from blue to orange in a single transformation? |
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| Video Tutorials
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| The following video takes you through, step-by-step, some of the ways
you can use Autograph to look at the topic of reflections. |
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Reflections are found everywhere in nature. In this tutorial you will
learn how to use Autograph's
 Insert Image to explore the reflectional symmetry in a butterfly. |
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| Handy Autograph Tip
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Using
 Redo is a really nice way of taking your students step-by-step through
a demonstration that you have already prepared. For example: |
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Open Autograph in Standard Level |
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Make sure you are in Whiteboard Mode |
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In Point Mode plot points at (−4, 3), (−2, 3), (−2,
1) and (−4, 1) |
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In Select Mode drag around all four points, right-click and select Group
to Shape from the menu |
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Enter the equation y = x |
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Left-click on the centre of the square and the line, right-click and select
Reflection from the menu |
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Now Undo (in the Edit menu or using Ctrl-Z) enough times until you are
back to your blank page |
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You can then ask the following questions, and after each one Redo (also
in the Edit menu or using Ctrl-Y) to reveal the next stage:
• What shape would points at (−4, 3), (−2, 3), (−2,
1) and (−4, 1) form?
• What does the line y = x look like?
• Where would the square appear if I reflected it in the line y =
x?
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