Rich Learning Tasks

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Fill Me In

Questions to facilitate the learning

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Did all of the shapes have to be squares? Could they be?

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What colours did you use in your patterns? Could there have been other colours?

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Could the 2nd and 3rd shapes be completely different from the 1st and 4th?

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Once you had one pattern, did it help you figure out others?

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What made your patterns correct? What makes them patterns?

Scaffolding the learning

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What patterns could you make that start with a yellow square? Do any of them have a red square in

them in the right spot?

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Could the 4th shape be exactly the same as the second one? Does it have to be?

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How will you make sure that what you create really is a pattern?

What’s the point of this task?

This task helps students realise that a few terms in a pattern may not show the pattern; there are, in fact,

an infinite number of possible patterns containing any small set of terms. Rather than starting with the

yellow and red squares and asking students to continue the pattern different ways, the two given terms are

spaced apart; it is usually trickier for students when any of the first few terms are missing, even though it is

really not an essentially different task than if the first two terms were given.

Both shapes given were squares and so some students will assume all the shapes must be squares, even

though that is not the case. Similarly, yellow and red were used, so some students will assume all shapes

must be yellow and red, whereas others will realise other colours can be introduced.

Extending the learning

Students might be challenged to create patterns that meet certain conditions, e.g. there are a lot more

yellow shapes than red ones OR there are at least three different shapes in the pattern OR the 5th and

7th shapes have to be the same.

Patterns