TES Maths: Inspect the spec - probability

Tailored to the new GCSE specification, top tips and resources to help students make sense of Venn diagrams in probability

Craig Barton

TES Maths, Inspect The Spec, GCSE, New Specification, Probability, Venn Diagrams, Set Notation, Sets, Independence, Dependence, Mutually Exclusive, Secondary, KS4, Year 10, Year 11

Explore the requirements for using and interpreting Venn diagrams in probability as part of the new specification 

Everyone is talking about functions and frequency trees, but what else has changed with the advent of the new specification? And what resources are available to help? Throughout this series, TES Maths aims to find out.

What does the specification say?

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

P6: Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams

P9h: Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

What's the same?

There is a lot more emphasis on probability in the new specification, which now has its very own section. And, while the old classics such as single events, sample space diagrams, experimental probability and tree diagrams remain, there is a new guest at the probability party - the Venn diagram.

What has changed?

All students will need to be familiar with the basics of Venn diagrams. They may be asked to fill in a blank diagram or calculate simple probabilities from one. They'll almost certainly need to be comfortable with the accompanying set notation, including ∪, ∩, ∈, A' and ε. It is the notation that students are likely to find most challenging. While they may have encountered Venn diagrams at primary school, the sight of those squiggly lines can result in a few confused expressions.

Higher students are in for a real treat, as they must now be able to calculate and interpret conditional probabilities through, among other things, Venn diagrams. Many AS-level statisticians find this tricky, so it remains to be seen how challenging the examination questions actually are.

How can TES Maths can help?

As ever, the wonderfully talented authors of the TES Maths community have stepped up to the mark to lend a hand. Here is a selection of my favourite resources to help support the teaching of this topic:

  1. Rich Venn diagram number task
    Before tackling the notation, get students comfortable with creating and sorting using a Venn diagram using this rich activity, including problem-solving opportunities.
  2. Introduction to set notation
    Support students as they start to use set theory to solve probability problems with this differentiated lesson from TES Author, Pixi_17.
  3. Handy starter activity
    Use this rich task to consolidate students' understanding of Venn diagram notation, as well as their calculation skills.
  4. Venn diagram challenges
    Engage students with this collection of in-context problems, in which they must not only interpret diagrams, but also create their own.
  5. Complete Venn diagram lesson
    Starting with notation and progressing quickly onto tricky calculations, this well-structured lesson comes complete with accompanying worksheets.
  6. Exploring events worksheet
    Pitched at the right level for higher students, this worksheet explores the properties of independent, dependent, mutually exclusive and non-mutually exclusive events.
  7. Conditional probability video
    Show students how to set up Venn diagrams and use them to calculate conditional probability in this clear, step-by-step video.
  8. A-level Venn diagram lesson
    The ultimate test for your higher students, this unfiltered A-level presentation is guaranteed to make them feel more confident about the GCSE content!

Craig Barton, TES Maths adviser

Craig is a secondary maths teacher in the North of England.

Find more resources to support the changes to the GCSE maths specification by taking a look at the rest of the series.