Rich Learning Tasks

104

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We Belong Together

Questions to facilitate the learning

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Why else might the shapes in Group 1 go together? Group 2? Group 3?

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Could there be a different shape other than those you chose to add to the group? What would it look like?

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Do you think most shapes you know about are like those in that group or not? Why?

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What properties of shapes do you think are most important to pay attention to?

Scaffolding the learning

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Are these shapes unusual? In what way?

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Would looking at how long the sides are be useful?

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Would looking at the angles be useful?

Extending the learning

Students might change just one of the shapes in each group a little bit and then come up with a new

reason why the two other shapes and the new one go together.

What’s the point of this task?

Shapes have many attributes students can use in describing or comparing them. Rather than asking

for shapes with particular attributes or asking whether a given shape has a given attribute, it is more

interesting to allow students to hypothesise on how shapes were sorted.

Often there is more than one possibility. For example, the first set of shapes could be considered shapes

with all equal sides or shapes with all equal angles or perhaps shapes with lines of symmetry. The second

set of shapes could be considered shapes that are concave (dented in) or shapes with more than 3 sides.

The third set of shapes could be considered shapes with at least 1 right angle (although the right angle

was deliberately turned not to be in the bottom corner in one case) or shapes with fewer than 8 sides.

Allowing for or even encouraging alternate possibilities is helpful to students. Having students create their

own shapes promotes flexibility of thinking.

Geometry