Expected level of development
Australian Curriculum Mathematics V9: AC9M8ST01
Numeracy Progression: Interpreting and representing data: P7
At this level, students examine different techniques for collecting types of data and begin to consider the challenges of collecting representative data by sampling a population.
Students consider population surveys where data is conducted by census. Discuss some of the issues to consider when collecting samples for surveys, such as accuracy, cost, time, practicality and survey techniques (for example, in person, questionnaire, interview or online).
Students investigate random sampling techniques where each data point of a given population has an equal chance of being selected. They also investigate non-random sampling techniques where data is collected in a way that is convenient for the data collector, for example, putting survey questions to people walking by in a shopping centre.
Explain that statistical data can also be obtained through experimentation and observation whereby a systematic approach is applied methodically; that is, the way the data is obtained, observed, measured, recorded and analysed. The data collected may be qualitative (data that is categorised, such as gender) or quantitative (numerical data, such as temperature).
Critically examine the different sampling methods mentioned above and how the data may have been protected or not protected from various biases. Ask questions about the data and the way it was collected to get students thinking. For example, what information was considered when participants were interviewed in the shopping centre (age, postcode, gender)? Were the average distances travelled by golf balls collected at various holes during a golfing tournament advantaged or disadvantaged by wind?
Teaching and learning summary:
- Discuss survey methods and questioning techniques.
- Investigate different survey methods.
- Discuss the experimental and observational sampling, as well as random and non-random sampling methods.
- Discuss practicalities and implications of various forms of data collection.
- Encourage questioning of data and data collection.
- Introduce the notion of bias and how bias can enter data collections.
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Teaching strategies
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.
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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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Teaching resources
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.
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Are you average? (Part 2)
In this lesson students learn about the ethics of collecting data, whether or not random samples represent a population, size of sample and conducting surveys.
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Are you average? (Part 3)
In this lesson students analyse and report on the distribution of their data for the ‘whole’ school drawing conclusions with respect to different sampling techniques and whether methods chosen were fair and considered.
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Sampling from a population
This resource from AMSI gives detailed explanations for teachers and students on collecting data by survey or census and by experiment and observation. It also touches on the notion of random and non-random sampling.
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Data representation and interpretation
Teachers are shown how, by changing their questions, they can guide students to successfully solve problems and understand new concepts. The topics covered include all the data representation and interpretation descriptors at this level.
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Data collection
This resource describes different methods for collecting data. There are activities linked to each method outlined.
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Guide to good survey design
This extensive guide provides content knowledge and background for teachers on how to design a survey.
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Sample design
This extensive guide provides content knowledge and background for teachers on how to sample a population.
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What makes a good sample?
In this lesson, students examine multiple samples of the same population and learn what it means for a sample to be representative of the population.
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Sampling in a fair way
In this lesson, students consider different methods of selecting a sample. They begin by examining different sampling methods and exploring the concept of bias.
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