Rich Learning Tasks

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Dogs and Cats

Questions to facilitate the learning

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Were there more dogs or cats? How do you know?

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What is the least number of animals there could have been?

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Could there be a whole lot of animals? How?

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What did you notice about how many animals there could have been? Why do you think that happened?

Scaffolding the learning

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Could there be 2 dogs and 2 cats? Why not?

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If there were 3 cats, how many dogs would there be? How many animals?

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If there were 5 dogs, how many cats would there be? How many animals?

What’s the point of this task?

Students will get practice with additions describing a real-life situation. One of the nice things about the

task is that it allows for differentiation; some students will stick with small numbers but some students who

are able might go much higher. Subtraction can be evoked by providing the students a total number of

animals and asking how many there could be of each type of animal.

The task encourages students to observe patterns (e.g. 5, 7, 9, 11, … is possible but 6, 8, 10, 12, … is not)

and reason about why the patterns occur. Some students might even generalise to realise that these

patterns must continue.

Extending the learning

Students might be challenged to change the rules to having 5 more dogs than cats to see how the

possible and impossible numbers change.

Number and Algebra