Matching situations, graphs and linear equations

This resource develops the concept of exploring variables in everyday situations. In addition, students work on finding unknown values from known values, finding relationships between pairs of unknowns, expressing relationships in the form of tables and graphs, and rearranging formulas. The central theme of the work is looking at y = mx + c in practical contexts.

Students work on an extended task about making and selling candles. There are various episodes of paired and individual work as the task builds. Students being by writing an equation for calculating the profit. They are then presented with a table of values and must fit both an equation and graph to fit the values. A consideration is made of intermediate values, for example, having 3.5 candles doesn’t make sense in practical terms. Students explore the practical context throughout the task, an example being; ‘explain the relevance of the x- and y- intercepts. 

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.