Rich Learning Tasks

145

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Partial Perimeters

Questions to facilitate the learning

•

What is one example of a situation where you lost

of the perimeter? What would happen if you

doubled your length and width? Can you think of other examples?

•

What did you notice about the shapes that lost the least perimeter?

•

Suppose a rectangle has a length double the width. What happens to the perimeter when you cut the

original rectangle to become a square? Suppose you cut it in half the other way, halving the width instead

of the length?

Scaffolding the learning

•

Why might it be easier to start with a 3 x 4 rectangle than a 3 x 5 rectangle if you have to cut it in half?

•

How do you calculate the area of a rectangle? What about the perimeter?

What’s the point of this task?

Students working on this task are likely to calculate many areas and perimeters of rectangles in pursuit of

the required results.

For example, a student who started with a 6 x 9 rectangle with an area of 54 square units and a perimeter

of 30 units might cut it in half to form a 3 x 9 rectangle; the new perimeter is 24 units, which is

of 30.

This would be an example of losing

of the perimeter.

Students may end up noticing that the way they cut the rectangle in half could influence the perimeter

fraction. For example, if you cut a 6 x 12 rectangle in half to make a 3 x 12 rectangle, the perimeter

changes from 36 units to 30 units, a loss of

of the perimeter. But if the cut is made to form a 6 x 6

rectangle, the perimeter changes from 36 units to 24 units, a loss of

of the perimeter—much more. This

previews an important math idea—that longer, narrower shapes have greater perimeters than wider shapes

of the same area.

Extending the learning

Students who are interested might be asked to figure out what other fractions of the perimeter might be

lost. For example, could

of the perimeter be lost?

Measurement