Rich Learning Tasks

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Placemats

Questions to facilitate the learning

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Was it easy to tell right away which placemat takes up more space? Why or why not?

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How sure are you about which placemat has the greater area? What did you have to do to check?

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To make your new placemat, did you have to change how wide and how deep your original placemat was,

or only one dimension?

Scaffolding the learning

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Which placemat is wider? Which is deeper? Why do you want to think about both of those things?

•

Suppose you move the black placemat on top of the grey one. What would happen? What would you

do next?

•

Would covering the placemats with plates help? How?

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If you cover each placemat with plates, will you use the same size plate all the time or different sizes?

What’s the point of this task?

This task requires students to compare areas. The task is made more interesting by having the second

placemat somewhat deeper, but also less wide than the first. Students can still superimpose one placemat

on top of the other to make a direct comparison, but will have to do some cutting and rearranging to be

certain which has more area.

There might be students who choose to unitise both areas by putting square or rectangular units on top of

both or by putting ‘plate’ units on top of both, but this is not required.

To make their own placemats, students might copy one of the placemats twice and cut some off or very

slightly enlarge one or both dimensions of one of the existing placemats. There could be discussions

among students about which way they are more secure about (probably doubling and cutting, but

not necessarily).

Extending the learning

Students might be asked to create placemats to meet other conditions, e.g. just as big as the black one,

but wider or as big as more than two but less than three of the black one.

Measurement