Hands-on Activity Learning Distance and Displacement

Learning Objectives

After this activity, students should be able to:

• Explain that distance is the sum of all paths traveled.
• Explain that displacement is a measurement of the direct path from a starting position to an ending position.
• Explain the difference between distance and displacement.

Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

NGSS: Next Generation Science Standards - Science

Common Core State Standards - Math

Materials List

For each group:

• a ruler with cm
• a computer/phone with timer
• a spool or of string

For the teacher:

• a computer

Worksheets and Attachments

Pre-Req Knowledge

Students are expected to:

• Know how to use a ruler and timer.
• Be familiar with the concepts of distance and displacement.

Introduction/Motivation

We have previously discussed distance and displacement. As a review, who can tell me what distance is? (Answer: The extent or amount of space between two things, points, lines, etc.) Who can tell me what displacement is? (Answer: The moving of something from its place or position; the change in position of something.)

In today’s activity, we are going to visualize these concepts to better understand the difference between them.

(Show students the 1:32-minute Food Delivery Robot Ad video.)

After watching that video, what are the benefits of using this technology to deliver pizza? What are the drawbacks? (Let students offer suggestions.)

As the engineer creating this “Nuro” delivery robot, what kinds of things do you think you would have to consider? (Based on student answers, prompt students to think about mapping the route and prod them for ideas about distance/displacement.)

Thinking about the food delivery robot, today we are going to collect data on distance and displacement for our routes to and from school.

Procedure

Before the Activity

• Decide which map to use in the Distance and Displacement Worksheet and insert it into the Word document. The map provided in the attached worksheet is of East Boston. Change the map to fit your local school community.

NOTE:

• In communities where public transport is the main mode of travel for students, consider replacing the Boston map with one of your community that includes bus/train routes.
• In communities where students are driven to school by guardians or the bus, consider replacing the Boston map with one of your community that includes major and minor roads.
• In the Distance and Displacement Worksheet: For the Exit ticket, you can replace “a friend’s house” with a well-known landmark from the community you teach in.
• Make copies of the Distance and Displacement Worksheet, one per student.
• Arrange students into groups of two, or keep them working individually if you have enough materials.

With the Students

Part 1: Introduction / Pre-Activity (15 min)

1. Go over the Introduction / Motivation section.
2. Give each student a copy of the Distance and Displacement Worksheet.
3. Give each student a ruler with centimeters.
4. Have students complete Section 1 of the Distance and Displacement Worksheet (practicing measuring distance and displacement). They will need a ruler.
5. Students who finish early can help classmates or discuss answers.

Part 2: Distance and Displacement Map – Explore! (25 min)

1. Have students work through Section 2 of the Distance and Displacement Worksheet. Note: The attached worksheet uses our local map; you may want to substitute this map with a map of your own area.
1. Students should map their route between school and home using distance and displacement individually. Notes: 
• Students may use their phones (or computers if they do not have access to phones) to look at Google Maps.
• Students will need a ruler, and string (for more complicated paths).

Part 3: Design Challenge (30 min)

1. Have students complete Section 3 of the Distance and Displacement Worksheet (making a maze for a peer to test) and answer the reflection questions. Students will need a ruler, string, and a timer. See example of a maze below:

• For the Exit ticket, you can replace “a friend’s house” with a well-known landmark from the community you teach in.

Part 4: Conclusion (5-10 min)

1. Wrap up the activity with a brief review of what distance is and what displacement is. (Answer: Distance is the length of the path taken by an object. Displacement is the distance between where the object started and where it ended up.)
2. Have students share one thing they learned from this activity.

Vocabulary/Definitions

displacement: The measurement of the direct path from a starting position to an ending position; includes direction.

distance: The sum of all paths traveled.

Assessment

Pre-Activity Assessment

The first worksheet serves as a warm-up to have students determine how to find distance and displacement. Based on student performance, you may choose to spend more time going over the content or move on if students demonstrate competency.

Activity Embedded (Formative) Assessment

Students explore the difference between distance and displacement in the Distance and Displacement Worksheet. There is an opportunity for formative assessment by walking around and listening to partners share ideas about how to calculate distance and displacement.

Post-Activity (Summative) Assessment

After the design challenge, students are asked reflection questions that require them to think critically about the real-world applications of distance and displacement. These reflections provide opportunities for students to think critically and for the teacher to assess content understanding.

Investigating Questions

• How do we describe how far we are from a location?
• How are distance and displacement different?

Troubleshooting Tips

Explain to students how to make a maze; show them the example listed in Part 3 of the procedure.

Individualize the map in the Distance and Displacement Worksheet to your own area.

1. In communities where public transport is the main mode of travel for students, consider replacing the Boston map with one of your community that includes bus/train routes.
2. In communities where students are driven to school by guardians or the bus, consider replacing the Boston map with one of your community that includes major and minor roads.

Activity Extensions

This activity is a great segue to teach students the difference between speed and velocity. An additional option for extension (as mentioned in the Engineering Connection section) is for students to use the concepts of distance and displacement of neighborhood planning to reimagine their neighborhood, making it easier to get to school without moving their houses, the school, or any other buildings.

Copyright

Contributors

Supporting Program

Acknowledgements

This curriculum was based upon work supported by the National Science Foundation under RET grant no. EEC 1407165—at the Research Experience for Teachers in Integrated Nanomanufacturing at the Photonics Center at Boston University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.