Expected level of development
Australian Curriculum Mathematics V9: AC9M9ST05
Numeracy Progression: Interpreting and representing data: P8
At this level, students plan and conduct a statistical investigation that includes the selection and creation of appropriate displays and conducting independent analysis.
Students should be encouraged to generate their own investigation topics that are relevant to their lives or of personal interest. Teachers can use a range of thinking routines to support this process, such as KWHL (Know-Want-How-Learned).
Over time, students can be expected to work independently, both in class and at home, and to present their findings to the class at the conclusion of the project. The investigation should include representations of multiple datasets, including displays that promote meaningful comparison. Statistical tools that students have used over several years should be evident in their work, such as measures of centre and spread, as well as discussion of how the shape of the distribution and any outliers affect these.
It is still important for teachers to provide some scaffolding, but this should be limited to topic selection and planning. Guide students to obtain the required data for their chosen topic or, in some cases, prompt them to consider whether enough useful data is available. If the teacher can see that the student has chosen a suitable topic and useful data has been obtained, the responsibility for collection, presentation and analysis of data should be released to the students. This is an opportunity for them to demonstrate the skills and knowledge acquired across several previous years.
To support students to work effectively, prepare some back-up investigation topics and datasets for any students who hit a roadblock.
Support students by producing an exemplar investigation beforehand, to explicitly demonstrate expected outcomes of a statistical investigation.
Before beginning, provide explicit information on common sources of large and interesting datasets, such as government and UN resources. Practise accessing and analysing contrived subsets of this data. There will likely be natural points at which to discuss sampling methods and whether the data is representative.
Establish a mid-point check-in, and make the expected level of achievement explicit, to allow students to see progress being made. A fellow classmate could be assigned to peer review another student’s project.
When presenting findings to the class, students should be able to justify their choices, both regarding the displays they have chosen, the comparisons made and the kind of analysis carried out. Their conclusion should be supported by the analysis.
Teaching and learning summary:
- Support students to independently design, plan and conduct a statistical investigation.
- Encourage relevant or interesting topics and ensure suitable datasets are available.
- Probe students with questions regarding their choices and the evidence for their conclusions.
- Support students’ independent work with exemplars, guides, check-ins, peer reviews and alternative options.
- Give opportunities for students to report their findings orally, along with a visual presentation, to justify their decisions and provide evidence to support their conclusions.
- plan, research, design and conduct a statistical investigation
- use the knowledge and skills acquired over previous years in their investigation
- choose appropriate data displays to represent their data
- compare datasets, analyse, draw inferences and interpret results
- report findings, justify decision-making and provide evidence to support conclusions.
Some students may:
- struggle with the independent nature of this task and require support and scaffolding.
- be stubborn with their choice of topic even though little useful data exists for it. Have a plan B and be ready to provide some students with an alternative topic and dataset.
- have knowledge or skill gaps that make it hard for them to do a thorough analysis. Identify these students beforehand with a pre-test, then allow time to teach these skills or modify the task for differentiation, if needed.
- be anxious about presenting to the class. Allow for multimodal presentations, such as a pre-recording, or allow a peer to read a pre-written script.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
We are learning to conduct a statistical investigation of consumer spending habits.
Why are we learning about this?
It’s natural to want to compare yourself. Sometimes this leads to powerful insights. As you continue to mature and become more independent with money, you might want to know how your spending habits stack up. Are you spending too much on eating out? What costs can you expect to incur in the future? Do you need to start a budget? Making these useful comparisons is only possible if you know where to look to find reliable data and ask the right questions.
What to do
- Use the following government resource to get to know the spending habits of the ‘average’ Australian household.
- Australians spend nearly 10 times as much on fashion as they do on gadgets. Can you collect data from you and your friends to verify this claim? You’ll need to calculate both the mean and median for this analysis. (Can you decide which is more useful based on your collected data? Check for outliers!) What does your investigation tell you about the differences between age groups?
- You could repeat this investigation for the other comparisons. Does the sport versus screen claim hold true for teenagers? What about money spent on junk food versus money spent on juices, smoothies and bubble tea?
- Using the average weekly household costs chart, create a table to collect data about your own household spending. Spend some time with your parents filling it in. You might need to help them convert the figures into weekly averages.
- I can conduct a statistical investigation to compare the spending habits of different groups.
Please note: This site contains links to websites not controlled by the Australian Government or ESA. More information here.
A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.Go to resource
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.Go to resource
A worked example is not just a pre-worked question that is given to the students. There are several types of worked examples and ways of using them.Go to resource
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
This multi-step challenge captures students’ knowledge on relative frequency and connects it to visual representation. Students use their skill and knowledge in statistics and probability, and use them concurrently to conduct an investigation.Resource details
Australian Bureau of Statistics
Find all sorts of data on all sorts of topics.Resource details
Bureau of Meteorology
Scroll through topics and statistics on climate science.Resource details
Clearinghouse for sport
This government-funded site hosts the Australian sport and physical activity participation survey.Resource details
By the end of Year 9, students can plan and conduct statistical investigations involving the distributions of multiple numerical datasets. Students report conclusions by using summary statistics to support their reasons.