- Ask students to work in small groups of two or three students.
- Give each group the Card Set A: Distance-Time Graphs and Card Set B: Interpretations together with a large sheet of paper, and a glue stick for making a poster.

- You are now going to continue exploring matching graphs with a story, but as a group.
- You will be given ten graph cards and ten story cards.
- In your group take a graph and find a story that matches it. Alternatively, you may want to take a story and find a graph that matches it.
- Take turns at matching pairs of cards. Each time you do this, explain your thinking clearly and carefully. If you think there is no suitable card that matches, write one of your own.
- Place your cards side by side on your large sheet of paper, not on top of one another, so that everyone can see them.
- Write your reasons for the match on the cards or the poster just as we did the example in class. Give explanations for each line segment.
- Make sure you leave plenty of space around the cards as, eventually, you will be adding another card to each matched pair.
The purpose of this structured group work is to encourage students to engage with each other's explanations and take responsibility for each other's understanding.
Slide P-3 of the projector resource summarizes these instructions.
You have two tasks during the small-group work: to make a note of student approaches to the task, and to support student reasoning.
Make a note of student approaches to the task:
Listen and watch students carefully.
Note different student approaches to the task and any common mistakes. For example, students may interpret the graph as a picture, or students may read the graph from right to left.
Also notice the ways students check to see if their match is correct and how they explain and justify a match to each other. You can use this information to focus a whole-class discussion.
Support student reasoning:
Try not to make suggestions that move students towards a particular match. Instead, ask questions to help students to reason together.
If you find one student has produced a solution for a particular match, challenge another student in the group to provide an explanation:
- John matched these cards. Sharon, why do you think John matched these two cards?
If you find students have difficulty articulating their decisions, then use the sheet Suggested Questions and Prompts to support your own questioning of students.
In trials of this lesson, some students had difficulty stating where home is on the graph.
- For this graph, where does the journey start? Is that home?
- Give me a graph that shows a journey starting away from home.
- For this graph, does the journey end at home? How do you know?
If the whole class is struggling on the same issue, you could write a couple of questions on the board and hold an interim, whole-class discussion. You could ask students who performed well in the assessment to help struggling students.
Some of the cards are deliberate distracters. For example, a student who matches Card 2 and E indicates that they think that graphs are pictures of the situation.

Allow students time to match all the cards they can.