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Interpreting Distance-Time Graphs
Before the
  • Assessment Task: Journey to the Bus Stop (15 minutes)
    • Set this task, in class or for homework, a few days before the formative assessment lesson. This will give you an opportunity to assess the work, and to find out the kinds of difficulties students have with it. You will then be able to target your help more effectively in the follow-up lesson.

      • Give each student a copy of Journey to the Bus Stop.
      • Briefly introduce the task and help the class to understand the problem and its context.
        • Read through the task and try to answer it as carefully as you can.

      It is important, as far as possible, students are allowed to answer the questions without your assistance.

      Students should not worry too much if they cannot understand or do everything because in the next lesson they will engage in a similar task that should help them.

      Explain to students that by the end of the next lesson, they should expect to answer questions such as these confidently. This is their goal.

  • Assessing Students' Responses
    • Collect students' responses to the task. Make some notes on what their work reveals about their current levels of understanding and their different problem solving approaches.

      We suggest that you do not score students' work. The research shows that this will be counterproductive, as it will encourage students to compare their scores and will distract their attention from what they can do to improve their mathematics.

      Instead, help students to make further progress by summarizing their difficulties as a series of questions. Some suggestions for these are given on the next page. These have been drawn from common difficulties observed in trials of this unit.

      We suggest that you write a list of your own questions, based on your students' work, using the ideas that follow. You may choose to write questions on each student's work. If you do not have time to do this, select a few questions that will be of help to the majority of students. These can be written on the board at the end of the lesson.

      Common Issues: Suggested Questions and Prompts:

      Student interprets the graph as a picture.

      • For example: The student assumes that as the graph goes up and down, Tom's path is going up and down.
      • Or: The student assumes that a straight line on a graph means that the motion is along a straight path.
      • Or: The student thinks the negative slope means Tom has taken a detour.
      • If a person walked in a circle around their home, what would the graph look like?
      • If a person walked at a steady speed up and down a hill, directly away from home, what would the graph look like?
      • In each section of his journey, is Tom's speed steady or is it changing? How do you know?
      • How can you figure out Tom's speed in each section of the journey?

      Student interprets graph as speed-time.

      • The student has interpreted a positive slope as speeding up and a negative slope as slowing down.
      • If a person walked for a mile at a steady speed, away from home, then turned round and walked back home at the same steady speed, what would the graph look like?
      • How does the distance change during the second section of Tom's journey? What does this mean?
      • How does the distance change during the last section of Tom's journey? What does this mean?
      • How can you tell if Tom is traveling away from or towards home?

      Student fails to mention distance or time.

      • For example: The student has not mentioned how far away from home Tom has traveled at the end of each section.
      • Or: The student has not mentioned the time for each section of the journey.
      • Can you provide more information about how far Tom has traveled during different sections of his journey?
      • Can you provide more information about how much time Tom takes during different sections of his journey?

      Student fails to calculate and represent speed.

      • For example: The student has not worked out the speed of some/all sections of the journey.
      • Or: The student has written the speed for a section as the distance covered in the time taken, such as "20 meters in 10 seconds."
      • Can you provide information about Tom's speed for all sections of his journey?
      • Can you write his speed as meters per second?

      Student misinterprets the scale.

      • For example: When working out the distance, the student has incorrectly interpreted the vertical scale as going up in 10s rather than 20s.
      • What is the scale on the vertical axis?

      Student adds little explanation as to why the graph is or is not realistic.

      • What is the total distance Tom covers? Is this realistic for the time taken? Why? / Why not?
      • Is Tom's fastest speed realistic? Is Tom's slowest speed realistic? Why? / Why not?
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