List

Great Expectations: Probability through problems

The resources found on this page offer a new approach to teaching probability.

The articles outline the thinking behind the approach, and explain the research basis for choosing to teach probability in this way.

Then there are resources for teaching the curriculum - rich, hands-on classroom tasks that can be used to teach the necessary concepts at each stage of the secondary probability curriculum.

Finally, there are supplementary resources for exploring the mathematisation of probability. To read more about the research basis for this teaching approach, see 'Towards a new probability curriculum for secondary schools', a paper presented by Dr Jenny Gage, NRICH, at ICME 2012.
Why start with tree diagrams?
article

Why start with tree diagrams?

Why the tree diagram is fundamental to studying probability - and why it should be introduced right from the start.
The dog ate my homework!
problem

The dog ate my homework!

Age
11 to 16
Challenge level
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A practical experiment which uses tree diagrams to help students understand the nature of questions in conditional probability.
Which team will win?
problem

Which team will win?

Age
11 to 14
Challenge level
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A practical experiment which will introduce students to tree diagrams, and help them to understand that outcomes may not be equally likely.
Who is cheating?
problem

Who is cheating?

Age
14 to 16
Challenge level
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A practical experiment provides data. Moving onto expected results provides a context to establish the multiplication rule in probability, and an intuitive approach to conditional probability.
Prize Giving
problem

Prize giving

Age
14 to 16
Challenge level
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What's the fairest way to choose 2 from 8 potential prize winners? How likely are you to be chosen?
The Wisdom of the Crowd
problem

The wisdom of the crowd

Age
11 to 16
Challenge level
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Who's closest to the correct number of sweets in a jar - an individual guess or the average of many individuals' guesses? Which average?
Capture and recapture
problem

Capture and recapture

Age
11 to 16
Challenge level
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How do scientists or mathematicians estimate the size of a population of wild animals?
How Confident Are You?
problem

How confident are you?

Age
11 to 16
Challenge level
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What proportion of people make 90% confident guesses which actually contain the correct answer?
Louis' Ice Cream Business
problem

Louis' ice cream business

Age
14 to 16
Challenge level
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Should Louis go for the safer options, hoping to limit his losses, or would he be better off with a riskier strategy, focusing on maximising his profit?
To insure or not to insure
problem

To insure or not to insure

Age
14 to 16
Challenge level
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Should you insure your mobile phone? It rather depends on whether you focus on the long-term pay-off or the effect of a single event.