Read more about the purpose of the MAP *Classroom Challenges*…

## 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

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.
- 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.
- 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
*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 for making posters. The cards should be cut up beforehand. - You will also need a supply of graph paper to give to students who request it. There are some projector resources to support your teaching.

### Time needed

15 minutes before the lesson, a 90-minute lesson (or two 45-minute lessons), and 10 minutes in a following lesson (or homework). Timings are approximate and will depend on the needs of the class.

### Mathematical Practices

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

- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others

### Mathematical Content

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

### Resources

#### Lesson (complete)

- distance-time_complete.pdf ( 2049.2K PDF/Acrobat 26 Feb 2014)

#### Projector Resources

- distance-time_slides.ppt ( 301K MS PowerPoint 25 Feb 2014)

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP *Classroom Challenges* for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to map.info@mathshell.org.

Can you help us by sending samples of students' work on the *Classroom Challenges?*