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### Number and algebra

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### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Great Expectations: Probability Through Problems

### Probability Articles

### Why Start with Tree Diagrams?

### Probability Calculations from Tree Diagrams

### Learning Probability Through Mathematical Modelling

### Tree Diagrams, 2-way Tables and Venn Diagrams

### Independence and Dependence

### Conditional Probability Is Important for All Students!

### Probability Resources for Teaching the Curriculum

### Which Team Will Win?

### The Dog Ate My Homework!

### Who Is Cheating?

### Prize Giving

### Exploring the Mathematisation of Probability

### The Wisdom of the Crowd

### Capture and Recapture

### How Confident Are You?

### Louis' Ice Cream Business

### To Insure or Not to Insure

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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.

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.

Age 11 to 14

Why the tree diagram is fundamental to studying probability - and why it should be introduced right from the start.

Age 11 to 16

Progression from natural frequencies to proportions to the multiplication rule, and hence to probability trees.

Age 11 to 16

Moving from the particular to the general, then revisiting the particular in that light, and so generalising further.

Age 11 to 18

Representing frequencies and probabilities diagrammatically, and using the diagrams as interpretive tools.

Age 11 to 18

When are events independent of each other? Sampling with and without replacement.

Age 11 to 18

Understanding statistics about testing for cancer or the chance that two babies in a family could die of SIDS is a crucial skill for ALL students.

Age 11 to 14

Challenge Level

A practical experiment which will introduce students to tree diagrams, and help them to understand that outcomes may not be equally likely.

Age 11 to 16

Challenge Level

A practical experiment which uses tree diagrams to help students understand the nature of questions in conditional probability.

Age 14 to 16

Challenge Level

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.

Age 14 to 16

Challenge Level

What's the fairest way to choose 2 from 8 potential prize winners? How likely are you to be chosen?

Age 11 to 16

Challenge Level

Who's closest to the correct number of sweets in a jar - an individual guess or the average of many individuals' guesses? Which average?

Age 11 to 16

Challenge Level

How do scientists or mathematicians estimate the size of a population of wild animals?

Age 11 to 16

Challenge Level

What proportion of people make 90% confident guesses which actually contain the correct answer?

Age 14 to 16

Challenge Level

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?

Age 14 to 16

Challenge Level

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.