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Practising Mathematics: Developing the mathematician as well as the mathematics

How can your students work like mathematicians?

An engaging selection of tasks contain activities from many areas of mathematics including: Number work, Ratio and Proportion, Algebra, Geometry, Probably and Statistics.

 

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Activities

Are males better drivers?

These group tasks scaffold an investigation into whether males are better drivers. Student discussions that lead to decisions are required at each phase of the investigation.

Area in graphs

The focus of considering the graph presented here is the importance of the area of each portion of a bar representing the value or frequency of the variable plotted.

Awareness of outliers

In considering measures of centre, particularly the mean, it is important to be aware of the influence of outliers.

Balancing act 1

Results from class investigations about balancing on one foot are used to make inferences about different groups or larger populations.

Balancing act 2

The question of "How long can typical year X students stand on one foot with their eyes closed?" is extended to compare two different populations, perhaps boys and girls, or children and adults.

Biased data

It is important for students to realise that the data they collect may be biased in many different ways. The activity explores accuracy and precision.

Categorical and numerical data

This investigation distinguishes between categorical and numerical data.

Conflicting reports

Two conflicting newspaper articles challenge students’ beliefs in the truth of media reports, which is sometimes unfounded.

Contrasting the median and mean

This activity is designed to help students distinguish between means and medians in symmetric and skewed data sets.

Dice duels

This digital object allows students to explore the mathematical principles of bias through investigations with loaded dice.

Differences in heights

Differences in samples can suggest differences in populations. This activity has data sets with height measurements for children of different ages.

Graph investigator

Using data to investigate a range of questions, students learn about the specific features, uses and advantages of different graph types for appropriate representation of data. 

Home internet survey

This digital object models the process of a statistical investigation. Students select a question and are guided through the steps of the investigation to make conclusions supported by evidence. 

How long is a piece of string?

This investigation uses body-based measurements to estimate the length of a piece of string, using the mean arm span of students as an effective measure of centre. 

How much is lots?

‘How much is lots?’ is a student activity from the CSIRO website archive that explores ‘lots’ as a quantifying term.

Increasing sample size

This activity compares the distributions of smaller samples with larger samples to determine when a sample is representative of the larger population. 

Interpreting box plots

With comparative box plots, the overlap can indicate that there are differences in the underlying populations.

Investigating us

A pedagogical framework is a useful aid for a series of lessons about conducting a statistical investigation. It includes ways to incorporate digital curriculum resources and other ICT materials, as well as advice on assessment. 

Judging associations

The examples presented give students the opportunity to judge the strength of an association from the appearance of scatter plots.

Mean, median and mode

This activity distinguishes among mean, median and mode through modelling with paper strips.

Media claims activity

This activity is based on an extract from a newspaper. It challenges students to think about the sampling method and the way in which the results are extrapolated from a non-representative sample. 

Melbourne Cup data

The Melbourne Cup is a context rich in data and data types. Different investigations from this context require informed selection of graphical representation based on both the question asked and the data type.

Mystery bag

In this classroom activity, students draw a sample from a bag of tiles and try to predict the contents of the bag. 

Paperclips

This investigation uses a tag-release-recapture method to estimate the number of paperclips in a container. The resource includes a student worksheet, video clip and student work sample.

Plots and outliers

An outlier in a single variable data set can be identified by drawing a box plot. Outliers in two variable data can be identified if their removal from the data set strengthens the correlation between the two variables.

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