# Sampling The Olympics

Mathematics

Level 7Level 8Level 9

What is this sequence about?

This learning sequence aims to develop student understanding of different sampling techniques that can be used to make inferences about a population. It aims to equip students with the skills to collect, present and analyse both primary and secondary data so that meaningful and informed inferences can be made about a population.

Parts of the sequence have been written around the theme of the Olympic Games. The choice to use a theme to explore mathematical concepts is made deliberately, to illustrate one way in which mathematics teaching can be responsive and relevant to contemporary events. The sequence includes suggestions as to how you could adapt these ideas to a local context.

 Big understandings Sampling is a useful tool for us to make inferences about a population. Variation is a natural feature of data. Collecting and presenting data allows us to identify patterns in variation and use these to help predict future events.

The sequence has been written by teachers for teachers, in collaboration with mathematics experts. It has been designed to provide students with rich, engaging learning experiences that address the Victorian Curriculum. The sequence consists of four flexible stages.

There is a strong focus within this sequence on supporting students to develop the four mathematical proficiencies set out in the curriculum: Understanding, Fluency, Problem Solving and Reasoning, as well as their capacity for critical and creative thinking.

Specifically, students will have multiple opportunities to develop their proficiencies of Problem Solving and Reasoning by:

• making choices about the appropriate use of various mathematical manipulatives, strategies and techniques
• conjecturing, hypothesising and inferring
• designing investigations and planning their approaches.

Overview of stages

• 1. An Introduction to Sampling

Suggested Learning Intentions

• To understand that sampling is necessary to make inferences about a population
• To be able to explain and use at least two different sampling techniques

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• 3. Olympic Attitudes

Suggested Learning Intentions

• To understand that different samples taken from the same population can provide different statistical measures, and lead to different inferences being made about the population
• To recognise that bias can influence the sampling process

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• 2. Podiums and the Pool

Suggested Learning Intentions

• To use different tools to represent information, to solve a problem or support an opinion
• To understand the concepts of ‘and’ and ‘or’ when used in the context of probability

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• 4. Does Hosting Help?

Suggested Learning Intentions

• To synthesise and analyse data from a variety of sources to make inferences
• To informally identify outliers and explain their impact

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• Prior knowledge

Before you commence this sequence, it is suggested that you ensure your students are familiar with:

• calculating the mean, mode, median and range of a set of data
• representing the probability of an event as a fraction, decimal or percentage
• working with secondary data.

You can find support for building students’ understanding of these concepts in the Mathematics Curriculum Companion. The Teaching Context and Teaching Ideas related to content descriptions VCMSP232, VCMSP236, VCMSP267 and VCMSP270 may be particularly useful.

Teaching strategies

The Mathematics Curriculum Companion provides teachers with content knowledge, suggested teaching and learning ideas as well as links to other resources. Resources are organised by Mathematics strands and sub-strands and incorporate the proficiencies: understanding, fluency, problem solving and reasoning. The Companion is an additional resource that you could refer to when you are planning how you might use the sequence in your school.

The sequence highlights opportunities to apply the High Impact Teaching Strategies (HITS), which are a component of the Victorian Teaching and Learning Model

Vocabulary

Depending on their progress made, students should be able to understand and use the following concepts and terms by the end of the learning sequence:

 Sample Confidence (in sampling) Population Quantitative data Simple random sampling Primary data Stratified sampling Secondary data Cluster sampling Interest groups Convenience sampling Outlier Systematic sampling Bias Making inference Complementary events Census Two-way table Sample size Venn diagram Sampling error 'and', 'or', and 'not' as probability concepts

You can find definitions of some of these terms in the F-10 Victorian Curriculum Mathematics Glossary.

It is recommended that the explicit teaching of vocabulary occur throughout the learning sequence. The Literacy in Mathematics section of the Literacy Teaching Toolkit provides several teaching strategies with worked examples demonstrating how teachers can use literacy to support student understanding of mathematical language. A further set of strategies demonstrate how can develop students' literacy skills to support their mathematical problem solving.

Assessment

Opportunities for formative and summative assessment are identified at different stages of the learning sequence, usually under ‘Reflect and Consolidate’.

You may want to develop a rubric to assess students’ progress. A range of Formative Assessment resources are available from the Victorian Curriculum and Assessment Authority. This includes a Guide to Formative Assessment Rubrics, a series of modules to support you to develop your own formative assessment rubrics, and sample rubrics across six curriculum areas that demonstrate how you can put formative assessment rubrics into practice in the classroom.

In developing a rubric, you may wish to co-construct assessment criteria with your students. Each stage of the sequence provides sample success criteria for students working at Level 6.

The Victorian Curriculum and Assessment Authority has also published annotated student work samples that provide teachers with examples of student learning achievement in each strand of the Mathematics curriculum.

Victorian Curriculum connections

Contents

Level 7

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 8, but also addresses the following content descriptions from Level 7:

 Content description Stage Mathematics Assign probabilities to the outcomes of events and determine probabilities for events (VCMSP267) Podiums and the Pool Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (VCMSP270) Does Hosting Help? Connect fractions, decimals and percentages and carry out simple conversions (VCMNA247) Podiums and the Pool Critical and Creative Thinking Consider a range of strategies to represent ideas and explain and justify thinking processes to others (VCCCTM040) Podiums and the Pool

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum in Mathematics Level 7:

• Students solve problems involving fractions, decimals, percentages and their equivalences.
• Students identify or calculate mean, mode, median and range for data sets.

Level 8

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 8, addressing the following content descriptions:

 Content description Stage Mathematics Identify complementary events and use the sum of probabilities to solve problems (VCMSP294) Podiums and the Pool Describe events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’ (VCMSP295) Podiums and the Pool Represent events in two-way tables and Venn Diagrams and solve related problems (VCMSP296) Podiums and the Pool Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation (VCMSP297) An Introduction to Sampling Podiums and the Pool Olympic Attitudes Does Hosting Help? Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (VCMSP298) An Introduction to Sampling Olympic Attitudes Investigate the effect of individual data values including outliers, on the range, mean and median (VCMSP300) Does Hosting Help? Plot graphs of non-linear real life data with and without the use of digital technologies, and interpret and analyse these graphs (VCMNA285) Does Hosting Help? Critical and Creative Thinking Consider a range of strategies to represent ideas and explain and justify thinking processes to others (VCCCTM040) Podiums and the Pool

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum in Mathematics Level 8:

• Students explain issues related to the collection of sample data and discuss the effects of outliers on means and medians of data.
• Students use various approaches, including the use of digital technology, to generate simple random samples from a population.
• Students model situations with Venn diagrams and two-way tables and explain the use of ‘not’, ‘and’ and ‘or’.
• Students choose appropriate language to describe events and experiments.
• Students determine complementary events and calculate the sum of probabilities.

Level 9

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 8, but also addresses the following content descriptions from Level 9:

 Content description Stage Mathematics Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (VCMSP324) Podiums and the Pool Does Hosting Help?

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum in Mathematics Level 9:

• Students compare techniques for collecting data from primary and secondary sources.
• Students identify questions and issues involving different data types.

Learning Progressions

The Numeracy Learning Progressions support teachers to develop a comprehensive view of how numeracy develops over time. You can use the Numeracy Learning Progressions to:

• identify the numeracy capability of your students
• plan targeted teaching strategies, especially for students achieving above or below the age-equivalent expected level in the Victorian Curriculum: Mathematics
• provide targeted feedback to students about their learning within and across the progressions.

The sequence is related to the following progressions:

 Learning Progression Level 5 Level 6 - 8 Level 9 Understanding Chance Probabilities Calculating Probabilities N/A
 Learning Progression Level 7 Level 8 Level 9 - 10 Interpreting and Representing Data Shape of Data Displays Graphical Representation of Data Recognising Bias

Click on the Learning Progression to access more detailed descriptions of student learning at each level.