Rich Learning Tasks

171

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Two Points

Questions to facilitate the learning

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What does the reflected shape look like? Does it have to look like that?

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Were the points on the original triangle that were reflected onto the two black dots arranged in exactly the

same way as the two black dots?

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Was the reflection line equally far from both of the dark dots? Did it have to be that way?

•

Was the original triangle on the left or the right of the two reflected dots? Could it have been either?

Scaffolding the learning

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What shape do you think the reflected shape has to be? Why?

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What would that shape look like if the dots were vertices of it?

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What if the dots were on two different edges of it?

What’s the point of this task?

This task encourages students to visualise the effects of a reflection. Because only a small bit of the

reflected image is shown and none of the original image or reflection line is shown and because students

can choose to use those dots as any part of the reflection image, there are many, many possible solutions.

The reflection line could actually go through the dots or be parallel to the line that joins them or could

intersect the line that joins them.

A decision was made not to tell students that the image needs to be a triangle, since the original was,

but students who are comfortable with reflections should realise this. Some students will assume that

the reflection line must be parallel to the segment formed by the two dots, but, of course, that is not

necessarily the case.

Extending the learning

Students might be asked to determine the original, reflection line and reflection image if three dots were

shown. In this case, there is much less latitude.

Geometry