### Real-Life Graphs

One of my favourite resources for real life graphs is a book called "The Language of Functions and Graphs" by Malcolm Swan. A teachers guide and a set of masters for photocopying is available for free online. The tasks are broken into sections for different graph sketching and interpretation skills and they are all based on research that aim to highlight and overcome known misconceptions. They lead the students towards deeper understanding by introducing new ideas using concepts that they can easily understand.

I have used a few of the tasks with classes of varying age and attainment and have always found them extremely successful. A particular favourite of mine is the strawberry picking question below...

Strawberry Picking

The students are asked to sketch a graph representing the described situation with "the number of people" as the x-axis and "total time to pick all the strawberries" as the y-axis.

In general, students engage really well with this task. As expected, many initially draw a straight line with a positive gradient going through the origin. However, when asked to explain what their graphs show, many realise their mistake. This presents the opportunity for a lot of rich discussion between students about why the gradient should be negative. Once this misconception is overcome, it is then possible to think about and discuss the significance of particular points on the graph, such as where it crosses the axes. Students quickly realise that it should not touch the axes, as this makes no sense for the situation.

Some students initially have more difficulty with this task. The trouble is that they want some numbers to be able to draw the graph. They are unhappy with sketching a graph and get confused about how to start. This difficulty can be overcome by finding a student who was able to sketch a graph and asking them to draw in on the board (find a student who has drawn a stereotypical straight line graph going through the origin). The other students can then try to explain what the graph shows. They quickly realise why it is wrong and this enables the rest of the students to commit to their own graphs. This can be followed with rich and interesting class discussion about the features and meaning of a real-life graph.

I have found this task extremely successful as an introduction to real-life graphs. It is such a simple idea and a context that is accessible to all students. I think that the way the problem is worded deliberately leads students towards the stereotypical straight-line graph with positive gradient. This allows us to address this issue of students having over-familiarity with this type of graph. The task also provides plenty of opportunity to think about and consider the important features when sketching and interpreting graphs. It will also make students think twice before going straight in for the obvious graph in the future!

Graph Matching
I like to follow the strawberry picking starter with a matching task from the same set of resources. (One example is below, but there are others depending on the level of the students). The graph sketches in this task encourage students to think about the important features of a graph and students gain a much greater understanding of real-life graphs by the end of the lesson and are much more capable of picking out important and meaningful information from the graphs.