This prompt was designed by Mark Greenaway (an advanced skills teacher in the UK) after a discussion about the nature of inquiry prompts. Mark contacted inquiry maths with an idea for a prompt. He proposed to play the first part of a YouTube clip of a drag race and encourage students to ask questions. This idea seemed similar to Dan Meyer's 3-Act lessons with an initial stimulus set in a practical or real world context (see box below). In inquiry maths lessons, the structure of a lesson is not determined beforehand. Students are invited to play a large part in determining how the inquiry proceeds. It is also the case that many prompts are deliberately 'de-contextualised' to encourage students to provide their own context (and that context might indeed be a race).
In view of these considerations, Mark designed a first version of the diagram above without labels on the axes. This prompt could have led to a very open, multi-faceted inquiry with students interpreting the graph in different ways. However, as the topic was distance-time graphs, Mark gave students more structure by labelling the axes - thereby hinting at possible contexts for the inquiry.
The students' questions and comments about the prompt (below) show a high degree of knowledge about the graph, although still with questions and ambiguities to be resolved:
The responses suggest the class could move quickly onto changing features of the prompt and exploring new situations. Perhaps, they could change one of the axes to 'speed', especially as it appears in the formula. Could they plot speed against time and speed against distance for the same journey. How do the three graphs compare?
Mark Greenaway runs his own website, which is highly recommended for its comprehensive coverage of ideas for the mathematics classroom. You can follow Mark on twitter @suffolkmaths.