Planning tool

Australian Curriculum Mathematics V9: AC9M10ST05

Numeracy Progression: n/a

At this level, students conduct statistical investigations to a sophisticated standard, using continuous numerical and categorical bivariate data.

The teaching and learning focus provided in Year 9 should be considered as the foundation when planning this unit. However, explicit instruction will be required so that students can include more complex displays, such as box plots and scatterplots, and conduct more effective analysis in their investigations. Box plots will be useful for students when comparing datasets, and examples of this should be provided. This is an excellent opportunity to examine NAPLAN data. Introduce new vocabulary so that students can accurately analyse scatterplots. It should be expected that students consider the strength, direction and linearity of numerical variables in their analysis.

In class, work through real-world examples with students to build understanding of how bivariate data is used, and how spreadsheets can help. Consider the relationship between advertising and revenue, study and grades, exercise and heart rate, schooling and income, or rainfall and plant life. These examples can be presented with either numerical or categorical variables and could be used to teach the construction of two-way tables. It is important to discuss the relationship between variables, the validity of inferences and the limitations of analysis. At this point, it may be worthwhile reviewing the difference between correlation and causation. Use online examples of this fallacy and have students complete a short research task. To ensure students don’t take their inferences too far, provide sentence builders to help students write reasonable concluding statements. A discussion of Bayesian inference could be added to extend student understanding.

Use a similar framework to investigations conducted in the previous year but strengthen the focus on student independence. Allow students to experiment with topics that may not prove fruitful and take this as an opportunity for reflection. Encourage students to look for correlation and reiterate the correct way to describe it using linear terminology. Students should also consider how well their linear model fits the data and whether it has predictive power. Students can use language such as 'for every change of ___ unit in X, there is a change of ___ units in Y’ and refer to the slope or gradient of the line-of-best-fit. Assess students' plans before allowing them to move forward in their investigation. If necessary, support them to go back to the drawing board rather than provide a ready-made back-up plan. Ensure students report their findings to you or to the class. They will need to consider any limitations when drawing and describing inferences from their results, including whether a different model may have been more appropriate.

Teaching and learning summary:

• Provide extensive explicit instruction and worked examples for the new displays, vocabulary and skills associated with bivariate data.
• Compare and contrast examples that use numerical and categorical data.
• Guide students, with less scaffolding than at previous levels, to plan and investigate two variables and infer a possible relationship.
• Provide frequent questioning to encourage critical and creative thinking when planning, analysing, evaluating and drawing inferences or conclusions.
• Identify or explain the role of each variable.
• Provide examples for students to follow and obtain an understanding of what is expected of them.
• Discuss the natural and mathematical limitations of statistical inference, particularly without knowledge of a range of more complex models.