Rich Learning Tasks

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Questions to facilitate the learning

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Do you predict that your pieces will be the same shape as you started with? Why or why not?

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Were your cuts straight up and down or straight across? Did they have to be?

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Once you had created four equal pieces one way, did it help you figure out another way?

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Did all four pieces have to look exactly the same to be equal? If not, what is equal about them?

Scaffolding the learning

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Which shape do you think might be easiest for you to partition? Why?

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Might it help to cut it into two shares first? How would that help?

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Suppose you used a line straight down to get you going. Where would you put that line?

Extending the learning

Students could, of course, partition others of the two shapes that are presented. Or you might ask students

to create a shape that is a little unusual that they think might be easy to partition into four equal shapes.

What’s the point of this task?

This task focuses students on how some shapes can be partitioned to create other shapes. At the same

time, it introduces students to the fractional concept of quarters or fourths. By allowing students the choice

of shapes, differentiation of learning is addressed; for example, compared to the other shapes, the triangle

might be seen as too challenging for some children.

Each of the shapes provided has symmetry to allow for the first cut into halves to be relatively easy. Asking

children to cut up the shapes in as many ways as they can encourages flexibility of thinking.

It may be necessary to point out that equal means equal in area (that if they were pieces of cake, all of

them would be fair), not just equal in number.

Geometry