YEAR 8 MATHS FOCUS

Students in Stage 4 can be expected to have some prior knowledge of both dot plots and line graphs, as these types of graph are introduced in Stage 3. They construct, describe and interpret column graphs in Stage 2 and Stage 3; however, histograms, divided bar graphs and sector graphs (pie charts) are not encountered until Stage 4.

Statistical data is part of everyday life. Data may be displayed in tables or graphs, and may appear in all types of media. Graphs provide a visual overview of the substrand under investigation. Students should be aware that while many graphs are accurate and informative, some can be misleading. They need to experience interpreting a wide variety of graphical representations, including column graphs, dot plots, stem-and-leaf plots, divided bar graphs, sector graphs and line graphs. Students should be able to select an appropriate graph to represent the collected data.

recognise variables as categorical or numerical (either discrete or continuous)Literacy

• identify examples of categorical variables (eg colour, gender), discrete numerical variables (eg number of students, shoe size) and continuous numerical variables (eg height, weight) (Communicating) Critical and creative thinking
• recognise that data collected on a rating scale (Likert-type scale) is categorical, eg 1 = dislike, 2 = neutral, 3 = like (Communicating)

investigate and determine the differences between collecting data by observation, census and samplingLiteracy Critical and creative thinking

• identify examples of variables for which data could be collected by observation, eg direction travelled by vehicles arriving at an intersection, native animals in a local area (Communicating)Critical and creative thinking Sustainability
• identify examples of variables for which data could be collected by a census or by a sample, eg a census to collect data about the income of Australians, a sample for TV ratings (Communicating)Critical and creative thinking Civics and citizenship
• discuss the practicalities of collecting data through a census compared to a sample, including limitations due to population size, eg in countries such as China and India, a census is conducted only once per decade (Communicating, Reasoning

identify issues that may make it difficult to obtain representative data from either primary or secondary sourcesCritical and creative thinking Ethical understanding

• discuss constraints that may limit the collection of data or result in unreliable data, eg lack of proximity to the location where data could be collected, lack of access to digital technologies, or cultural sensitivities that may influence the results (Communicating, Reasoning)

explore issues involved in constructing and conducting surveys, such as sample size, bias, type of data required, and ethicsLiteracy Ethical understanding Civics and citizenship Difference and diversity

• discuss the effect of different sample sizes (Communicating, Reasoning)Critical and creative thinking
• describe, in practical terms, how a random sample may be selected in order to collect data about a matter of interest (Communicating, Problem Solving)Critical and creative thinking
• detect and discuss bias, if any, in the selection of a sample (Communicating, Reasoning)

construct appropriate survey questions and a related recording sheet in order to collect both numerical and categorical data about a matter of interestLiteracy Critical and creative thinking Personal and social capability Difference and diversity

• construct a recording sheet that allows efficient collection of the different types of data expected (Communicating, Problem Solving)Literacy Critical and creative thinking Personal and social capability
• refine questions in a survey after trialling the survey (Communicating)Literacy Critical and creative thinking Personal and social capability
• decide whether a census or a sample is more appropriate to collect the data required to investigate the matter of interest (Problem Solving)

collect and interpret information from secondary sources, presented as tables and/or graphs, about a matter of interest, eg sporting data, information about the relationship between wealth or education and the health of populations of different countriesLiteracy Intercultural understanding Ethical understanding Civics and citizenship Difference and diversity

• interpret and use scales on graphs, including those where abbreviated measurements are used, eg ’50’ on a vertical axis representing thousands is interpreted as ’50 000′ (Reasoning)
• analyse a variety of data displays used in the print or digital media and in other school subject areas, eg share-movement graphs, data displays showing sustainable food production (Problem Solving)Information and communication technology capability Critical and creative thinking Sustainability
• identify features on graphical displays that may mislead and result in incorrect interpretation, eg displaced zeros, the absence of labelling on one or both axes, potentially misleading units of measurement (Communicating, Reasoning)

use spreadsheets or statistical software packages to tabulate and graph dataInformation and communication technology capability

• discuss ethical issues that may arise from collecting and representing data (Reasoning)

Construct and compare a range of data displays, including stem-and-leaf plots and dot plots (ACMSP170)

construct and interpret frequency histograms and polygons

• select and use appropriate scales and labels on horizontal and vertical axes (Communicating, Problem Solving, Reasoning)Critical and creative thinking
• recognise why a half-column-width space is necessary between the vertical axis and the first column of a histogram (Reasoning)

construct dot plots

• explain the importance of aligning data points when constructing dot plots (Communicating, Reasoning)

construct ordered stem-and-leaf plots, including stem-and-leaf plots with two-digit stems

• explain the importance of ordering and aligning data values when constructing stem-and-leaf plots (Communicating, Reasoning)

construct divided bar graphs, sector graphs and line graphs, with and without the use of digital technologiesLiteracy

• calculate the length of bar required for each section of divided bar graphs and the angle at the centre required for each sector of sector graphs (Problem Solving)

interpret a variety of graphs, including dot plots, stem-and-leaf plots, divided bar graphs, sector graphs and line graphsLiteracy

• calculate the percentage of the whole represented by different categories in a divided bar graph or sector graph (Problem Solving) Critical and creative thinking
• compare the strengths and weaknesses of different forms of data display (Reasoning)
• identify and explain which graph types are suitable for the type of data being considered, eg sector graphs and divided bar graphs are suitable for categorical data, but not for numerical data (Communicating, Reasoning) Critical and creative thinking
• draw conclusions from data displayed in a graph, eg ‘The graph shows that the majority of Year 8 students who play a musical instrument play a string instrument’ (Communicating, Reasoning)