# Interpreting Distance–Time Graphs

## 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:

- Interpret distance–time graphs as if they are pictures of situations rather than abstract representations of them.
- Have difficulty relating speeds to slopes of these graphs.

## Introduction

- 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.
- A whole-class introduction provides students with guidance on how to work through the first task. Students then work in small groups, 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.
- Finally, students return to their original task and try to improve their individual responses.

## Materials required

- Each student will need two copies of the assessment task
*Journey to the Bus Stop,*a mini-whiteboard, a pen, and an eraser. - Each small group of students will need copies of the cut-up
*Card Set A: Distance–Time Graphs*,*Card Set B:**Interpretations*,*Card Set C:**Tables of Data*, a large sheet of paper, and a glue stick. - A supply of graph paper to give to students who request it. There are some projector resources.

## Time needed

15 minutes before the lesson, a 100-minute lesson (or split into two shorter lessons), and 10 minutes in a following lesson (or homework). Timings are approximate and will depend on the needs of the class.

## Lesson Type

## Mathematical Practices

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

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- 8.F: Define, evaluate, and compare functions.
- 8.F: Use functions to model relationships between quantities.