Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M7ST01
Numeracy Progression: Interpreting and representing data: P5
At this level, students will develop a robust statistical vocabulary. This includes defining and distinguishing between discrete numerical data and continuous numerical data. To illustrate the differences, students should be asked to collect sets of data from their peers. They should describe the differences in the results from each dataset and use these observations to construct definitions.
When collecting data, attention should be paid to the way it is organised and errors that might arise in its collection. To what degree of accuracy does continuous data need to be measured to be informative? Depending on the type of data they are collecting, students might use a list, table or spreadsheet, tally marks, words or numerals. The usefulness of each warrants discussion. Students are expected to know what kind of data they will collect based on the question they ask.
The process of calculating statistical measures is the imperative. Students can identify the mean, median and mode as measures of central tendency and the range as a measure of spread. They should understand the purpose of summarising each and the insights gained by interpreting them. Summary statistics need to be calculated by hand for small data sets, with a calculator for larger sets, and with spreadsheet software for very large sets. These statistics are used to make statements comparing datasets.
Vocabulary to describe the visual features of data is equally important. When presented with a variety of data displays, students can comment on the shape of the distribution, referencing its symmetry or skew. These terms should be defined in relation to the mean and median so that students can make predictions about them from the shape of the distribution. Students can notice outliers visually and numerically, and comment on how removing them will affect the summary statistics.
Teaching and learning summary:
 Use key vocabulary: discrete, continuous, categorical, numerical, distribution, symmetry, skew, outlier.
 Demonstrate how to calculate range, mean, median and mode by hand and with digital technologies.
 Provide many examples of measures of central tendency and spread.
 Explicitly teach mean versus median as best measure of centre in positively and negatively skewed data.
Students:
 understand the differences between categorical and numerical (discrete and continuous) data
 calculate the range, mean, median and mode by hand and with the aid of a calculator or spreadsheet software
 describe the usefulness of measures of central tendency and spread
 determine the most appropriate measure of central tendency for a skewed distribution
 make reasonable predictions about the mean and median from a given data display.
Some students may:
 be disorganised in how they collect data.
 find it difficult to use the terms 'mean', 'median' and 'mode' instead of 'average', 'middle' and 'most frequent'.
 grasp the distinction between discrete and continuous.
 find data analysis and interpretation abstract in comparison.
 regularly mistake positive and negative skew.
 want to make inferences beyond the scope of the data.
 infuse personal biases into their analysis.
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
 We are systematically collecting data about fuel consumption over an extended period.
 We can accurately measure the centre and spread of the data.
 We can recognise patterns in the data that may inform decisionmaking.
Why are we learning about this?
Everything we do generates data, and this data is valuable. Using statistics to analyse data, we can answer almost any question we can think of. We need to be careful to gather the right data, measure it accurately and make sensible interpretations. In this activity we will collect, measure and visualise data about our vehicle fuel consumption.
What to do
1. Monitor your family’s (or a friend’s family’s) car fuel consumption with statistical rigour for at least a week. You’ll need to be patient, as good data analysis takes time. To spot patterns and trends, we need enough data. Maybe you have a big road trip coming up – that could be the perfect opportunity to try out this activity.
 Begin data collection the day the tank is filled and keep going until it’s empty. Measuring litres consumed each day would require special equipment, so instead record the total volume of fuel in the tank, then monitor the kilometres travelled each day.
 Set up some routines to ensure you get an accurate measurement each day. Let the car user know what you are doing, so they can remind you too. At the end of each day, you will need to read the car’s odometer.
 Challenge: if you have access to several vehicles, try to keep track of them all, using multiple copies of the table. Comparison is one of the most useful forms of statistical analysis.
 Labelling data: try to label your data as discrete or continuous. This may depend on the display output shown in the car.
2. Collect and record data in a table like the one below.
Date  Distance travelled (km)  Notes 
Monday 21 Nov  48  
3. Display the data using spreadsheet software, such as Excel, or create a graph or chart by hand.
 If using a spreadsheet, enter your values and find the tool that analyses the data for you and creates a graph or chart. In Excel, you would use the Data Analysis tool. Here is an example.
 Why do you think I chose a line graph to display this data?
 What design choices could I have made to improve the readability and usefulness of this graph?
4. Before doing any calculations, we can sometimes spot patterns in the data that begin to ‘tell a story’. This data has been collected randomly and there is no discernible pattern. Your data will be collected, therefore it is not random data.
5. Calculate the measures of central tendency (mean, median and mode) and measure of spread (range) for your data. You can use spreadsheet technology to help you.
 How spread is your data?
 Do the kilometres travelled fluctuate heavily, or is it consistent?
 Does anything from your notes explain why?
 Did you have many ‘average’ days in which your kilometres travelled was like the mean? Why might this be?
 What recommendations would you make to your family or friend based on the data?
 Is your usage above or below Australian averages? The Australian Bureau of Statistics has plenty of data you can consult.
Success criteria
 I can carefully collect and accurately measure realworld data.
 I can recognise patterns in my data and consider whether they are significant.
 I can make recommendations based on statistical analysis.
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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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Differentiated teaching
Differentiation involves teachers creating lessons that are accessible and challenging for all students.
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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.

Australian Bureau of Statistics
This is the official website of the ABS. Use this as a resource to access secondary data on Australia.
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Data investigation and interpretation
A comprehensive resource that examines the statistical investigation cycle and how to examine and interpret secondary data.
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Statistics
A teacherfacing resource on how to teach and assess statistics within the classroom. It contains big ideas, activities, good teaching tips and common misunderstandings.
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Common online data analysis platform (CODAP)
CODAP is free educational software for data analysis that runs in a browser. There are data sets available for analysis as well as tools for analysing your own data.
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Reading and interpreting data
This webpage discusses the importance of data literacy and how to make sense of tables and graphs. It includes teaching ideas and background content knowledge.
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Assessment
By the end of Year 7, students can acquire data for discrete and continuous numerical variables. Students can calculate the mean, median and mode and discuss central tendency to gain meaningful insights into the distribution of data sets.

Top drawer teachers: activities
A series of statistical activities for students covering a wide range of investigative skills, as well as catering for a range of learners.
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About average
This printable worksheet aims to develop students’ sense of how to measure individuals in a given sample and to develop fluency with median, mean and mode.
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Unequal averages
This printable problem asks students to think about the properties and therefore the meaning behind mean, median and mode.
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Mean, median, mode, range: quick check
This interactive allows quick and repetitive practice with the statistical terms 'mean', 'median' and 'mode'. Finding the range of the data set is also available for those wanting the challenge.
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Sports salaries
In this sequence, students explore variation in the salaries of NBA players. Using realworld data, they calculate means and medians, draw graphs, compare findings and investigate the implications of random sampling.
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Sampling and estimating: counting trees
This lesson is designed to assess students’ ability to estimate a population using proportion and sampling techniques.
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