Sets and Venn Diagrams
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
- Resource sheets
- The set of shapes from SS1 Classifying shapes on Pages 5 & 6
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
At the end of the session, spend time recording some actions. What do you need to do:
- Next day?
- Next week?
- Next year?
- Primary Magazine
- An introduction to sets and Venn diagrams
- Venn Diagram from WolframMathWorld
- Venn Diagram from wikipedia