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Autograph Newsletter 10 – Enlargement

May 26, 2014 - Autograph, Autograph Newsletters
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.
Contents
Introduction
Diagnostic Question
Free Online Autograph Activity
Ideas for Extension
Video Tutorials
Handy Autograph Tip
Introduction
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!
Diagnostic Question
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.
Reflection Diagnostic Question
Free Online Autograph Activity
Enlargement Golf
Can you use your knowledge of enlargements to guide the shapes into the black holes?
Enlargement Golf
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.
Ideas for Extension
The following ideas for extending this topic require the full version of Autograph.
Idea 1 – Introducing Enlargements
Download  1. Introducing Enlargements.agg
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.
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
When they are ready  click on the object and the centre of the point, right-click and choose Enlargement
Choose the scale factor
Decide if you want to show construction lines and then click OK
Ask the students to predict what happens if you increase the scale factor
Use the  Animation Controller to dynamically change the scale factor
Now what happens when the scale factor goes below 1?
How about when it is negative?
Use the  Animation Controller to illustrate this, emphasising the smooth progression as the scale factor decreases in size
Idea 2 – Finding the Centre of Enlargement
Download  2. Find the Centre.agg
This file provides a clear illustration of how to find the centre of an enlargement
Challenge your students to predict where they think the centre of enlargement is and  Scribble down a prediction
Choose one of the dashed lines to start with
Drag the circled points to a pair of corresponding corners on the original object and the enlarged image
Repeat this for the other three remaining lines until each corner of the two objects has a line passing through them
Where these lines meet is the centre of enlargement
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
Double-clicking on the enlarged image allows you to change the scale factor, should you wish
Idea 3 – Area Scale Factor
Download  3. Area Scale Factor.agg
Enlargements are an ideal way to look at area scale factor
Challenge your students to predict what will happen to the area of the rectangle if you enlarge it with scale factor 2
Carry out the enlargement as described in Idea 1
Can they explain this answer?
Can they now predict the area if the scale factor is 3?
How about scale factor ½?
 Drag the corners of the shape around and change the centre of enlargement to challenge your students further
Idea 4 – Enlargements in 3D!
Download  4. Enlargements in 3D.agg
You can also use Autograph’s unique 3D engine to investigate enlargements in three dimensions, and volume scale factors
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).
How about the volume of the new image?
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.
Can your students explain what has happened?
Change the centre of enlargement, the enlargement scale factor, or the shape itself to further challenge your students
Video Tutorials
The following video takes you through, step-by-step, some of the ways you can use Autograph to look at the topic of enlargements.
Handy Autograph Tip
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!
Open Autograph in Standard Mode
Make sure you are in Whiteboard Mode
Place two points anywhere on the page fairly close together
Drag the cursor around both of these points so that they are both selected. Right-click and choose Straight Line from the menu
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
Dragging the points around the page allows you to have full control over your straight line

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