Bivariate data 

Overview

During these lessons students will develop skills and understanding to explain relationships from deterministic linear models, where the relationship is obvious through patterns, to statistical linear models, where the relationship is not immediately obvious.

Students will:

• connect multiple representations for linear relationships

• appreciate the importance of collecting and representing data to identify relationships

• develop and interpret lines of best fit, with or without technology

• apply lines of best fit to extract inferences and predictions for real life situations.

Outcomes:

• MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts

• MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context

• MA5.1-6NA determines the midpoint, gradient and length of an interval, and graphs linear relationships

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-16SP investigates relationships between two statistical variables, including their relationship over time

• MA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures 

• MA5.3-2WM generalises mathematical ideas and techniques to analyse and solve problems efficiently 

• MA5.3-19SP investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decision-making processes 

Students will:

• connect multiple representations to describe linear relationships 

• appreciate the need to acquire data to uncover relationships between quantities that are not immediately obvious 

• describe quantities in linear relationships as dependent or independent.

Outcomes:

• MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts

• MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context

• MA5.1-6NA determines the midpoint, gradient and length of an interval, and graphs linear relationships

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-16SP investigates relationships between two statistical variables, including their relationship over time

Students will:

• develop techniques for generating a line of best fit by eye 

• use technology to develop lines of best fit through linear regression models 

• understand and apply lines of best fit to make predictions through interpolation and extrapolation 

• interpret the correlation coefficient to rate the strength and direction of a correlation.

Outcomes:

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-16SP investigates relationships between two statistical variables, including their relationship over time

• MA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures 

• MA5.3-2WM generalises mathematical ideas and techniques to analyse and solve problems efficiently 

• MA5.3-19SP investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decision-making processes

Students will:

• interpret lines of best fit to make inferences and predictions 

• apply lines of best fit to gain insights into real life situations.

Outcomes:

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-16SP investigates relationships between two statistical variables, including their relationship over time

• MA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures 

• MA5.3-2WM generalises mathematical ideas and techniques to analyse and solve problems efficiently 

• MA5.3-19SP investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decision-making processes

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