Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M8ST02
Numeracy Progression: Interpreting and representing data: P7
At this level, students focus on learning about the different methods used to collect data to create a sample. Students consider whether the data is coming from direct or primary sources or is derived from secondary data.
Students are encouraged to question the data size of a selected sample. How large does the data set need to be for the results of an analysis to be meaningful and as accurate as possible.
Introduce different methods and processes for collecting data, such as simple random, nonrandom, systematic, clustered, convenience, judgement or stratified. Students contrast and compare methods and question the reliability of the data when collected a certain way.
Use the key vocabulary when teaching this area so that students make connections between terminology and its meaning, since statistics can be quite abstract for some students. Ensure students are comfortable with the meanings of ‘random’, ‘sample space’ and ‘sample distribution’ among others.
Teaching and learning summary:
 Discuss and explore different sampling methods and procedures for data collection.
 Ensure students understand and recognise the difference between primary and secondary data and can highlight any potential issues that need to be considered when using secondary data.
 Expand on key vocabulary and include more complex terminology such as 'sample distribution' and 'sample space'.
Students:
 analyse and report on different distributions of data that may have been derived from primary or secondary sources
 investigate a variety of different sampling procedures and recognise these methods as random or nonrandom methods of collection
 expand their vocabulary to include terms such as 'sample distribution' and 'sample space'.
Some students may:
 not realise that a sample size from a large population is used to make generalisations about the population.
 not understand that two different samples from the same population may show variable results.
 underestimate the differences between very small samples sizes versus very large samples sizes.
 underestimate the affect of bias samples.
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.
Learning intention
 I am learning about sampling techniques and the effects on the reliability of statistics.
 I will use several methods to create samples and compare statistics.
Why are we learning about this?
We need to be very aware when looking at data that we are given the whole picture. The way in which a sample is collected and displayed has a significant influence on possible decisions to be made.
What to do
A lolly manufacturer employee weighs a sample of all the lollies made each hour to make sure the correct weight is being produced.
A sample of 10 lollies is taken and statistics are calculated.
Management wants to ensure that the samples are an accurate representation of all the lollies produced. Not only does the advertised weight of each lolly bag have to be accurate so that customers don't complain, but also because sometimes bags of lollies weigh a little more or a little less. The manufacturer wants to make sure that they don't give away the product! The results are recorded in the table below.
What you are going to do is to generate random samples each with 10 pieces of data using different methods.
Sample 1: Random sampling
 Roll a 10sided dice to choose the location of random pieces of data from the table. The piece of data selected will be located by row and column. The first roll will determine the row, the second roll the column. For example, a roll of 3 then 8 would result in the piece of data in the third row and eighth column (8.4).
 There are no repeats, so roll again if the same location on the table is rolled, until 10 pieces of data are collected.
 Collect 5 pieces of data using random sampling.
 Collect 20 pieces of data using random sampling.
Sample 2: Convenience
 Select the first 10 pieces of data, in the first column, off the production line.
 Select the first 5 pieces of data, in the first column, off the production line.
 Select the first 20 pieces of data, in the first two columns, off the production line.
Sample 3: Systematic
 Roll the dice twice as you did in Sample 1: Random sampling. Select every third piece of data until 10 pieces of data are collected.
 Roll the dice to choose a random starting place and select every fifth piece of data until 10 pieces of data are collected.
 Roll the dice to choose a random starting place and then select every seventh piece of data until 10 pieces of data are collected.
Analysis questions
 For each sample generated, calculate the mean, median and range.
 What would you report to management about the lollies produced and the most practical, and accurate, way to generate samples?
 Challenge: If management require a serving size (individual lolly) to be 7.2 grams, does the production line need to be adjusted to meet the weight requirements?
Success criteria
 I can use different sampling techniques to generate a sample from a population of data.
 I can compare statistics from samples to evaluate the effect on the reliability of the statistics.
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Teaching strategies
A collection of evidencebased 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.

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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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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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.

Shooting 3pointers: Part 1
In this lesson students are guided through solving a problem using mathematical modelling.
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Shooting 3pointers: Part 2
In this lesson, students conduct a statistical investigation.
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Are you average? (Part 1)
In this lesson students will plan and conduct a statistical investigation to find the average height of students at their school.
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Obtaining data through sampling: practicalities and implications
This webpage gives specific explanations and guidance for teachers on the topic of sampling and its practicalities and implications.
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Being sceptical
This teacher plan and student lesson focuses on the differences between sample surveys, experiments and observational studies. Students critique reports and investigate how data was collected.
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Sampling from a population: teacher resources
This teacherfacing webpage provides advice on the practicalities and implications of sampling data using different processes and approaches.
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