Rich Learning Tasks

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More Yellow, More Boxes

Questions to facilitate the learning

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Which number did you decide on first? Once you decided that, were you free to choose all the other

numbers or were you forced into choices?

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Which was greater—the number of yellow shapes or the number of boxes? Why?

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Was your total number of shapes an even number or an odd number? Why do you think that happened?

Scaffolding the learning

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Are there more yellow shapes or red ones? Are there more cans or boxes?

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Could there be only 5 shapes altogether?

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Could there be other shapes? How might that help you?

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Could there be other colours? How might that help you?

Extending the learning

Students might be asked to change the second condition to say that there are 3 more boxes than cans.

In this case, one condition requires the total number of shapes to be odd; the other condition requires the

total to be even if only red and yellow cans and boxes are used. Any solution requires the use of another

colour or shape as well.

What’s the point of this task?

This task requires students to sort 3-D shapes (figures/objects) into categories meeting particular

conditions. Students are also exploring how numbers compare—i.e., what numbers are 4 more than

what others, what numbers are 6 more than what numbers—as well as how numbers are partitioned—for

example, realizing that once we decide there are 4 red and 8 yellow shapes and no other colours, we are

seeking to partition the total number of 12 in different ways, only one of which has one part that is 6 more

than the other part.

Because the number of boxes must be 6 more than the number of cans, students need to realise that the

total number of objects must be 7 or more. The task allows for many solutions, e.g. 2 red cans, 1 red box,

and 7 yellow boxes or 3 red cans, 1 red box and 8 yellow boxes. Other colours or shape types can be

added as well.

Although the task requires sorting by only one attribute at a time, the same objects are sorted more than

one way. It is important for students to recognise that a set of objects can be sorted in more than one way.

Allowance is made for students to include shapes or colours other than those required to make the task

more complex and interesting.

Data