'Mathematical modelling: What makes us happy?' is one of our new teaching sequences for V9
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!
Lessons in this sequence
Lesson 1 • Measuring happiness
Students consider factors they believe may influence happiness and consider how we might measure happiness numerically.
Lesson 2 • Does wealth make us happy?
Students use scatterplots to explore the relationship between wealth and happiness for different countries around the world.
Lesson 3 • A closer look at wealth
Students use lines of good fit and regression lines to model relationships in data, interpret gradients and intercepts, and make predictions in context.
Lesson 4 • The wealth and happiness of continents
Students compare scatterplots across continents to examine how relationships vary between subgroups and how context affects interpretation.
Lesson 5 • What else makes us happy?
Students use $r^2$ to compare models and evaluate whether observed relationships support prediction, explanation, or causal claims.
The Australian Academy of Science supports and encourages broad use of its material. Unless indicated below, copyright material available on this website is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) licence.
Curriculum and syllabus alignment
Year 10
Students plan and conduct statistical investigations involving bivariate data. Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association.
Statistics
Construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity
Construct two-way tables and discuss possible relationship between categorical variables
Plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences
In this sequence, students use mathematical modelling to conduct statistical analysis, with a specific focus on exploring relationships between variables using a digital system, CODAP, for efficient calculation. The use of digital systems for statistical analysis allows for calculations to be completed with speed and accuracy, and means that more attention can be given to the interpretation and discussion of statistical results. CODAP has been chosen in this instance as it is free, relatively easy to use, supports a wide range of statistical calculations and models, and is designed for learners.
This teaching sequence supports students to appreciate the usefulness of statistical modelling for understanding the lives and experiences of a diverse range of people and communities, and highlights the rich connections between Mathematics, Humanities and Social Sciences, and Digital Technologies.
The process of mathematical modelling in this sequence
Framing a PROBLEM IN CONTEXT
The problem of determining what makes people happy is difficult to quantify mathematically. Students consider how happiness could be measured, before exploring how researchers do this. They consider a range of different variables that may influence happiness and how data on these variables is collected.
Formulating a MATHEMATICAL PROBLEM
Students extract secondary data from spreadsheets and display the data in a scatterplot using CODAP. They consider independent and dependent variables and some principles to follow when creating a line of good fit by hand.
Solving to produce a MATHEMATICAL RESULT
Students interpret information from scatterplots to make predictions. They use technology to find the equations of lines of best fit and use substitution to make more accurate predictions. They use technology to determine the value of $r^2$ and hence evaluate the strength of correlation of their model.
Interpreting the RESULTS IN CONTEXT
Students interpret the values in the equation of the line of best fit, in order to understand the real-world significance of the gradient and y-intercept of their models. They apply their understanding of correlation to consider how their $r^2$ value impacts the confidence they have in their predictions.
Evaluating if it is an appropriate solution for the PROBLEM IN CONTEXT
Students explore the implications of extrapolation and interpolation on the reliability of predictions made. They are introduced to the distinction between correlation and causation and consider what this means in the context of their models.
'Mathematical modelling: What makes us happy?' is one of our new teaching sequences for V9
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!