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| Welcome |
| Welcome to the tenth Autograph Newsletter! Each jam-packed edition looks 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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| Introduction
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| In previous newsletters we have seen how Autograph can be used to enhance the teaching of each of the three types of transformations – reflection, rotation and translations. Now we complete the set with a look at Enlargement. For some students this is the most difficult of them all. Difficulties can emerge when enlarging from a given co-ordinate, finding the centre, determining the scale factor of enlargement, and when entering the world of fractional and negative scale factors. You will be pleased to know that Autograph can help address all of these issues, and can even take you into the wonderful world of enlargements in three dimensions! |
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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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| Enlargement Golf |
| Can you use your knowledge of enlargements to guide the shapes into the black holes? |
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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 this topic require the full version of Autograph. |
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| Idea 1 – Introducing Enlargements |
Download
 1. Introducing Enlargements.agg
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| You can use Autograph to introduce students to the very basics of enlargement, and use the same process to take them right up to fractional and negative scale factors. |
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Challenge your students to predict and  Scribble down where they think the image will appear following an enlargement of scale factor 2 with centre at the circled point |
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When they are ready  click on the object and the centre of the point, right-click and choose Enlargement |
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Choose the scale factor |
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Decide if you want to show construction lines and then click OK |
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Ask the students to predict what happens if you increase the scale factor |
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Use the  Animation Controller to dynamically change the scale factor |
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Now what happens when the scale factor goes below 1? |
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How about when it is negative? |
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Use the Animation Controller to illustrate this, emphasising the smooth progression as the scale factor decreases in size |
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| Idea 2 – Finding the Centre of Enlargement |
| Download
2. Find the Centre.agg
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| This file provides a clear illustration of how to find the centre of an enlargement |
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Challenge your students to predict where they think the centre of enlargement is and Scribble down a prediction |
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Choose one of the dashed lines to start with |
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Drag the circled points to a pair of corresponding corners on the original object and the enlarged image |
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Repeat this for the other three remaining lines until each corner of the two objects has a line passing through them |
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Where these lines meet is the centre of enlargement |
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To set up another example, go to Object > Unhide all, drag the centre of enlargement (and the corners of the object, if you choose) to a new position, then select the point, right-click and choose Hide Object |
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Double-clicking on the enlarged image allows you to change the scale factor, should you wish |
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| Idea 3 – Area Scale Factor |
| Download
3. Area Scale Factor.agg
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| Enlargements are an ideal way to look at area scale factor |
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Challenge your students to predict what will happen to the area of the rectangle if you enlarge it with scale factor 2 |
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Carry out the enlargement as described in Idea 1 |
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Can they explain this answer? |
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Can they now predict the area if the scale factor is 3? |
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How about scale factor ½? |
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Drag the corners of the shape around and change the centre of enlargement to challenge your students further |
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| Idea 4 – Enlargements in 3D! |
| Download
4. Enlargements in 3D.agg
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| You can also use Autograph's unique 3D engine to investigate enlargements in three dimensions, and volume scale factors |
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Challenge your students to predict the co-ordinates of the image of the cube following an enlargement of scale factor 2 from centre (0, 0, 0). |
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How about the volume of the new image? |
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Enlargements in 3D work exactly the same as enlargements in 2D, so just select the point and the cube, right-click, choose your scale factor and click OK. |
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Can your students explain what has happened? |
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Change the centre of enlargement, the enlargement scale factor, or the shape itself to further challenge your students |
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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 enlargements. |
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| Handy Autograph Tip
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Having straight lines that you can move around the page can be extremely useful, not just for enlargements, but also for topics such as lines of best fit on scatter diagrams, or the equations of straight lines. They are nice and easy to create!
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Open Autograph in Standard Mode |
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Make sure you are in Whiteboard Mode |
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Place two points anywhere on the page fairly close together |
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Drag the cursor around both of these points so that they are both selected. Right-click and choose Straight Line from the menu
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Make sure just the line is selected, right-click and choose Edit Draw Options
Here you can change the colour, the weight, and make the line dashed
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Dragging the points around the page allows you to have full control over your straight line |
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