2 Reading and interpreting graphs
What are the variables (or characters) in the story that graphs tell?
The first thing students have to understand in order to read graphs is that they are a visual representation of the relationship between variables. This is important and yet it is often overlooked. Information regarding which variables these are can be found by looking at the labels on the axes. For example, a distance/time graph shows the relationship between time lapsed (or the time of day) and the distance travelled. The x-axis (horizontal) tends to be labelled with the time variable, the y-axis (vertical) with distance.
The first part of Activity 2 is a card sort to make students aware of the variables involved in the graphs. This type of activity helps you to evaluate student learning. You need to keep the group size small to enable all students to engage in the learning activity. In Part 2, the students are asked to use similar approaches with the examples they looked at in Activity 1. The card sort consists of two types of cards: some with graphs and some with descriptions. The activity involves matching a description to a graph and being able to explain the reasons for that choice.
Activity 2: Using card sorts to develop characters in stories
Part 1: Identifying variables in graphs
Preparation
Prepare enough copies of the card sort in Resource 1.
This task works well for work in pairs or in threes. It is less effective for bigger groups because the students will not all be able to see and easily read what is on the cards.
Remember to tell the class that ‘every graph tells a story’.
The activity
Ask the students to look at the card and match the descriptor to the graph.
Tell them that it can be helpful to use the following phrases:
- Is this graph telling me the story that is described on the cards?
- Who are the characters (or the ‘variables’, in mathematical language) in this story?
Part 2: Making your own card sort to identify variables in graphs
Explain to your students what they are required to do in this activity, using the following prompts:
- In Part 1 you used a card sort to become aware of the variables, or characters, that the graphs are telling a story about.
- Look again at the examples you brought in to school and used in Activity 1. What variables are the graphs telling a story about?
- Make your own card sort by writing descriptors similar to the ones you used in the card sort in Activity 2.
- Now exchange these card sorts with other groups and do one another’s card sorts.
Read Resource 4, ‘Using pair work’, to find out more.
Case Study 2: Mr Chadha reflects on using Activity 2
Getting organised for the card sort meant that I had to get several copies of the cards and cut them out – which is time-consuming and also costs money. However, I have since used them with other classes and colleagues have borrowed them as well, so it has been worth it.
I first asked the students to work in pairs on the card sort and to think carefully about the justification for their choices. I then asked them to compare their answers with the pairs of students sitting in front or behind them. What I really liked about these card sorts is that they asked students to focus on variables. They also triggered some really good mathematical discussions.
The students found making their own card sorts straightforward for the graphs in the ‘easier’ pile, but more difficult for those in the ‘harder’ pile – as I had expected. To help them with the harder graphs, I asked them: ‘What was it you did with the easy graphs?’ This helped them to get ‘unstuck’. As a result of this activity, many of the graphs in the harder pile moved to the easier pile. I also asked them to amend the notes they made for the last part of Activity 1, where they created a list of ‘good things to do when constructing graphs’.
By asking the students to bring in examples of graphs, working on developing our own tasks and exchanging these, we now have an impressive amount of teaching material about a large variety of graphs in the class! The students feel proud and seem more self-assured, because they actually made the teaching resources themselves.
 Pause for thought
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1 Using a narrative to help learning