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Departmental Workshops: Sets and Venn Diagrams


Created on 22 February 2011 by ncetm_administrator
Updated on 04 April 2013 by ncetm_administrator

Departmental Workshops - Structured professional development activities    
 

Sets and Venn Diagrams

Overview

This unit explores the teaching and learning of Venn diagrams and sets. It is intended to support teachers working on the GCSE Linked Pair Pilot and is subject content for the Methods qualification. You will be invited to consider sorting and what is important when developing students’ understanding of sets and Venn diagrams. You will then explore some strategies and activities which may support you in the planning of a group of lessons to include in your scheme of work focussing on Venn diagrams, sets and probability

Objectives related to this topic are:

  • understand and use Venn diagrams and set notation to solve problems
  • use Venn diagrams to represent the number of possibilities and hence find probabilities

Materials required

Suggested activities

Activity 1: Getting Started

Working in pairs, sort the shapes into two groups

  • regular polygons, and
  • shapes with at least one line of symmetry.

Are there some shapes which come in both groups?
Are there some shapes which come in neither group?
Now draw a Venn diagram with two interlocking circles, on a piece of A3 paper. Arrange your shapes in the correct regions. You may want to compare your answer with that of another pair.
Now change the criteria and re – sort.
What criteria would you choose to have the intersection as large as possible? As small as possible? To have the greatest number of shapes in the two sets? Etc.

Working as a department, think of some situations where you use sorting and categorising
E.g. storing files on a computer, classifying plants. Make a list which you can share with pupils.

Activity 2: Sample learning activities


As a team use the following resource sheets to explore the suggested learning activities:

Sets 1 - Extract from the NCETM Primary Magazine Issue 29

In this activity the teacher invites learners to determine the categories she has chosen for the two sets using their knowledge of number properties

Sets 2 – Shading worksheet

Learners use the diagrams on the worksheet to understand the notation for different regions in the Venn diagram

Sets 3 - Set logic

Learners use their knowledge of set notation to categorise pictures of road signs

Sets 4 – Notation card sort

Learners match diagrams, word and symbols in this multiple representation exercise

Sets 4a – Even Multiple cards

This resource can be used with Sets 4 Notation Card sort. Learners match groups of numbers and their descriptions

Sets 4b – Quadrilateral cards

This resource can be used with Sets 4 Notation Card sort. Learners match groups of quadrilaterals and their descriptions

Sets 5 – Always, sometimes, never

Learners decide if statements relating to set notation are always, sometimes or never true

Sets 6 – The link to probability

Learners explore the differences and similarities of Venn diagrams containing names and those containing the number of elements in the set.

Sets 7 – Probability

Learners match probability statements to a Venn diagram

Sets 8 – Working on an examination question

Learners are given a diagram form an examination questions. They are given a framework in which to write down things that they know, and suggest possible questions that they could answer before being shown the questions that were posed in the examination.

Activity 3: Sets 9 - So what’s good about these activities?

Read ‘Eight Principles for Effective Teaching’ on resource sheet Sets 9 (taken from Malcolm Swan in the Standards Unit ‘Improving Learning in Mathematics’ resource).

In pairs or small groups discuss the ways in which the sample activities fit and don’t fit with these principles.

Collect other Venn Diagram and Set activities which fit with some of the Eight Principles.
Sort these activities into a progression which can be developed into a unit of work to be included into your team’s scheme of work.

Embedding in practice

Hooks for Learning

Action points

At the end of the session, spend time recording some actions.  What do you need to do:

  • Next day?
  • Next week?
  • Next year?

Further reading

 
 
 

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