Syllabus Bites Introducing Venn diagrams

Syllabus links

Stage 4 Mathematics Statistics and Probability: Probability 2

The Board of Studies NSW Syllabus for the Australian Curriculum in Mathematics K-10 prescribes the study of Venn diagrams in Stage 4 Statistics and Probability, substrand Probability 2.

A student:

  • communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA4-1WM

  • applies appropriate mathematical techniques to solve problems MA4-2WM

  • recognises and explains mathematical relationships using reasoning MA4-3WM

Students:

  • Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292)

This series addresses the following dot points. The dots point(s) addressed in this Syllabus Bite are shown in bold.

  • interpret Venn diagrams involving two or three attributes

  • describe regions in Venn diagrams representing mutually exclusive attributes

  • describe individual regions or combinations of regions in Venn diagrams representing non-mutually exclusive attributes, using the language 'and', exclusive 'or', inclusive 'or', 'neither' and 'not'

  • construct Venn diagrams to represent all possible combinations of two attributes from given or collected data

  • use given data to calculate missing values in a Venn diagram

  • interpret given two-way tables representing non-mutually exclusive attributes

  • describe relationships displayed in two-way tables using the language 'and', exclusive 'or', inclusive 'or', 'neither' and 'not'

  • construct two-way tables to represent the relationships between attributes

  • use given data to calculate missing values in a two-way table

  • convert between representations of the relationships between two attributes in Venn diagrams and two-way tables

This series addresses all five Working Mathematically components.

  • Fluency: Students practise drawing Venn diagrams and constructing two-way tables.

  • Understanding: Students interpret Venn diagrams and two-way tables.

  • Reasoning: Students use given data to calculate missing values in Venn diagrams and two-way tables. They deduce the meaning of regions within these organisers.

  • Problem Solving: Students solve a variety of problems including problems with multiple solutions. They use both formal and informal methods.

  • Communicating: Students describe relationships displayed in Venn diagrams and two-way tables using appropriate terminology.

Each Syllabus Bite includes a bonus activity containing material that can extend suitable students beyond the scope of the syllabus.