Lesson 17 Sets and subsets

# Sets and subsets

Sets and subsets
Overview Resources
An activity to explore classification. Pupils use set diagrams to explore the inclusiveness of properties and overlap of sets.In the process pupils analyse positive integers in terms of multiples and factors and familiar plane shapes in terms of their properties. Concepts of classification, language descriptions and visual representation are explored and developed. Worksheets 1, 2, 3, Scissors, Cardboard rings, made by rolling an A4 card sheet and taping long sides together to make a cylinder, then slicing into rings (optional)
• Explore classification in number and shapes,
• Implications and explain reasoning.
• Types of integers and how they relate to each other: multiples, factors
(divisors), and primes,
• Properties of shapes: side and angle properties of triangles and special quadrilaterals.
• EPISODE 1
Two overlapping sets
Pupils use set diagrams to classify and describe sets of integers with different properties, including overlapping and included sets. Classification skills develop from infancy, including in sets and their overlaps. The difference here is in the mathematical criteria for sets, and the problems of enumeration of sets. Note that we use the phrase ‘set diagram’ rather than the more technical ‘Venn diagram.

Crediting eminent mathematicians is often a secondary priority in pupils’ early construction of mathematical concepts. Pupils explore the difference between the total of the items in each subset and the total overall, and attempt to explain this.
EPISODE 2
Included and excluded sets
This episode introduces a set of numbers which are included in another set. Pupils create included and excluded sets. They describe subsets and consider why they need precise descriptions, Pupils explore the difference between the total of the items in each subset and the total overall, and attempt to explain this.
EPISODE 3
Three sets: pupils explore three intersecting sets.
In many classes this episode may be carried out in a whole class mode, with the teacher selecting the challenge that is most appropriate for the class to work on independently.

Classification of shapes: pupils use a three-set diagram to place shapes in sets and explain what changes would be needed for a shape to fit into another part of the diagram. They use properties such as quadrilateral, equal sides and right angle.
Before you teach the lesson
You may decide to start with the shapes’ episode before addressing numbers. A graded approach with the shapes, parallelling the approach used for integers, would allow pupils to handle two overlapping sets first. That means, for example, pupils using cut-outs or sketches of triangles and quadrilaterals only, and finding ‘shapes that have all sides the same‘ The included set could be ‘with right angle’ in quadrilaterals.