Often text books (and teachers) put great attention on the procedures for plotting graphs and calculating gradients, rather than developing understanding of relationships that a graph shows (Stump, 1999). It can be more constructive to concentrate on the latter, which involves teaching:

• understanding of how to read information directly from a graph, interpreting each axis individually
• how to describe simple relationships between the axes such as those represented by straight lines
• how to interpret a graph, linking what it represents to a real situation (Friel, Curcio and Bright, 2001; Lingefjard and Farahani, 2018)

This activity gives students practice in plotting graphs in order to develop and consolidate understanding of how to read information directly from a graph.

This activity gives students the opportunity to practise applying their understanding and to clarify their thinking through discussion. To support this, students should plot graphs individually and then answer the question in pairs or small groups.

Plots on graph a are all on the major grid lines, whereas those on graph b are not. The focus of this activity is on plotting points and reading values from a graph, in order to better interpret the information represented in a graph. For this reason scales have been provided.

Observing students as they work often highlights any difficulties they might have. These can often be overcome, through a whole class clarification or redirection part way through the activity.

Differentiation

Sets of data can be adjusted to suit the mathematical skills of students. Some students may be able to select appropriate scales and confidently plot graphs without support.

If some students are working with a teaching assistant, then a list of graph plotting criteria for the TA could help to make this activity more purposeful.