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Secondary Magazine - Issue 73: An idea for using ICT in the classroom


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 09 November 2010 by ncetm_administrator
Updated on 23 November 2010 by ncetm_administrator

 

Secondary Magazine Issue 73digital photograph with underlying geometric features
 

An idea for using ICT in the classroom – using digital photos to reason geometrically

Issue 71 of the Secondary Magazine included an article that explored how digital images might be imported into a range of different software to provide a motivating starting point for students exploring transformations.

In this issue, this approach is extended to consider how we can use mathematics software to support students to reason geometrically about the shapes and images within carefully selected photographs...

So look at the photograph of The Northgate, Chester...

What sort of curve do you think is formed by the arch?

The Northgate, Chester

How could you prove or disprove your conjecture?

Importing the image into a dynamic geometry package will support you to reason mathematically about your conjecture....

A first instinct might be that the arch forms an arc of a circle....

One approach would be to place some points on the curve...

The Northgate, Chester placing some points on a curve in the picture

If the conjecture is true, then any of the red points, when joined to the ‘centre’ of the circle will form line segments of equal lengths.

The Northgate, Chester showing that segements are of equal lengths

So if we pick out a triangle formed by the two yellow points and ‘guess’ the centre of the circle, we can make a triangle as shown above...

But surely, if the arch is an arc of a circle, the white triangle should be isosceles!

Using the software we can construct a perpendicular bisector and hopefully show where the centre of the circle should be!

The Northgate, Chester finding the centre of the circle

But how do we know where the centre of the circle should be positioned along the green dotted line?

Picking another couple of red points and repeating the construction might help!

The Northgate, Chester - Picking another couple of red points and repeating the construction might help!

So it is beginning to look convincing – but is a third point really needed?

Finally, the software itself will allow you to satisfy yourself that the conjecture is true...

The Northgate, Chester - he software itself will allow you to satisfy yourself that the conjecture is true...

This was just one conjecture and one possible approach....

What alternative approaches could you take?

And how did the lack of actual measurements support the geometrical reasoning?

What about different images with underlying geometric features?

 
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