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Interpreting Distance-Time Graphs
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to interpret distance-time graphs and, in particular, to help you identify students who:

      1. Interpret distance-time graphs as if they are pictures of situations rather than abstract representations of them.
      2. Have difficulty relating speeds to slopes of these graphs.
  • Formative Assessment Task: Journey to the Bus Stop
    • Students are presented this scenario: Every morning, Tom walks along a straight road from his home to a bus stop, a distance of 160 meters. The graph shows his journey on one particular day. Students are asked to describe what may have happened, including how fast Tom walked, and to assess whether all sections of the graph representing Tom's journey are realistic.

  • Common Core State Standards
    • Common Core State Standards for Mathematical Practices Common Core State Standards for Content

      This lesson involves a range of mathematical practices from the standards, with emphasis on:

      1. Reason abstractly and quantitatively.
      2. Construct viable arguments and critique the reasoning of others.

      This lesson involves mathematical content in the standards from across the grades, with emphasis on the following Domain.Cluster:

      • 8.F: Construct a function to model a linear relationship between two quantities.
      • 8.F: Describe qualitatively the functional relationship between two quantities by analyzing a graph.
  • Lesson Structure
    • The lesson unit is structured in the following way:

      • Before the lesson, students work on a task designed to reveal their current understandings and difficulties. You review their work and create questions for students to answer in order to improve their solutions.
      • During the lesson,
        • A whole-class introduction provides students with guidance on how to work through the first task.
        • Students then work in small groups on a collaborative discussion task, matching verbal interpretations with graphs. As they do this, they translate between words and graphical features, and begin to link the representations.
        • This is followed by a whole-class discussion about applying realistic data to a graph.
        • Students next work in small groups, matching tables of data to the existing matched pairs of cards. They then explain their reasoning to another group of students.
        • In a final whole-class discussion, students draw their own graphs from verbal interpretations.
      • After the lesson, students return to their original task and try to improve their individual responses.
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