YEAR 8 MATHS FOCUS

describe compound events using the following terms:

• • ‘at least’, eg rolling a 4, 5 or 6 on a standard six-sided die may be described as rolling ‘at least 4’
  • ‘at most’, eg rolling a 1, 2, 3 or 4 on a standard six-sided die may be described as rolling ‘at most 4’
  • ‘not’, eg choosing a black card from a standard pack of cards may be described as choosing a card that is ‘not red’
  • ‘and’, eg choosing a card that is black and a king means that the card must have both attributes
• pose problems that involve the use of these terms, and solve problems posed by others (Communicating, Problem Solving)
• describe the effect of the use of ‘and’ and ‘or’ when using internet search engines (Communicating, Problem Solving)

classify compound events using inclusive ‘or’ and exclusive ‘or’, eg ‘choosing a male or a female’ is exclusive as one cannot be both, whereas ‘choosing a male or someone left-handed’ could imply exclusivity or inclusivity

• recognise that the word ‘or’ on its own often needs a qualifier, such as ‘both’ or ‘not both’, to determine inclusivity or exclusivity (Reasoning)

interpret Venn diagrams involving two or three attributes

• describe regions in Venn diagrams representing mutually exclusive attributes, eg a Venn diagram representing the languages studied by Year 8 students

The image shows a Venn diagram with 2 separate ovals inside a rectangle.

• There are 50 students who study French; 32 students who study Mandarin; 18 students who study neither language; and no student who studies both languages (Communicating, Problem Solving, Reasoning)
• 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’, eg a Venn diagram representing the sports played by Year 8 students

There are 25 students who play both basketball and football; 46 students who play basketball or football, but not both; 19 students who play neither sport; and 71 students who play basketball or football or both (Communicating, Problem Solving, Reasoning)

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, eg the number of members that have both attributes or the number of members that have neither attribute (Problem Solving, Reasoning)

interpret given two-way tables representing non-mutually exclusive attributesLiteracy Critical and creative thinking

• describe relationships displayed in two-way tables using the language ‘and’, exclusive ‘or’, inclusive ‘or’, ‘neither’ and ‘not’, eg a table comparing gender and handedness of students in Year 8

There are 63 male right-handed students, ie 63 students are neither female nor left-handed; there are 114 students who are male or right-handed, or both (Communicating, Problem Solving, Reasoning)

construct two-way tables to represent the relationships between attributes

• use given data to calculate missing values in a two-way table (Problem Solving)

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