This prompt is suitable for students between the ages of 10 and 14, although it could be made appropriate for younger children by presenting a pictogram and frequency polygon with the bar chart or for older children by adding a histogram. When the bar and pie charts have been presented as a pair, students have made comments related to the following:
- Missing information - there should be labels on the axes of the bar chart (for example, 'frequency' on the vertical axis) and titles.
- Reading the charts - the bigger the piece of the pie chart (or the higher the bar in the bar chart), the greater the amount represented; the charts tell you how many things there are in something; most of the time, pie charts are to do with percentages; the bar on the left is a quarter of the highest bar.
- Construction of the charts - the pie chart has degrees; why is a pie chart harder to draw than a bar chart?
- Interpretation - what do the charts represent?; the pieces of the pie chart are split into 5%, 20%, 25%, and 50%; the charts represent the same information; they show favourite school dinners.
An initial discussion might focus on the data set represented by the charts. How was the data collected? What sampling technique was involved? What was the size of the sample?
To continue the inquiry, students have decided to draw a scale on the bar chart, estimated the frequencies and drawn the pie chart accurately to test if the charts are drawn from the same data set. Whatever scale they use, students will end up drawing the same (or very similar) pie chart. An important lesson to draw out at this point is that pie charts show the proportion of quantities, not the quantities themselves. This can be emphasised by discussing a second prompt showing two pie charts.
The scatter graph introduces the concept of bivariate data and challenges students to compare its meaning with the two charts. Often, a class will argue that the graph is linked because of its similar shape to the bar chart. Students might interpret it as a time series with the line of best fit as a trend line (see box). The inquiry teacher could use the regulatory cards at this point to decide how to proceed. Students might ask the teacher to explain or provide resources so they themselves can inquire into the meaning and purpose of scatter diagrams.