Lesson plan

Lesson 10: Measuring Long Distances Over Uneven Terrain

teaches Common Core State Standards 7.RP.A http://www.corestandards.org/the-standards
teaches Common Core State Standards MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards MP5 http://corestandards.org/Math/Practice/MP5

Lesson 10: Measuring Long Distances Over Uneven Terrain

This lesson is optional. It is the first of four lessons where students explore ways of measuring long distances. Over the course of these lessons:

  • Students first think about different ways to measure distances of various lengths and in which situations different methods might work better.
  • They then read about and build a trundle wheel (also known as a surveyor wheel or measuring wheel) that is commonly used to measure walking distances.
  • They design a walking course for a 5K race on their school campus. (The course should be one lap of about 500 m. The actual race would go around the course multiple times.)
  • They use their trundle wheel to measure the path of the walking course and make a scale drawing of the course on a map or satellite image of the school grounds.

In this first lesson, students brainstorm ideas about how to measure long distances, possibly over uneven terrain. Students work in groups to try out the accuracy and effectiveness of different methods. Some of the methods involve proportional reasoning. Students engage in many aspects of mathematical modeling (MP4) and will use appropriate tools (MP5) when they are planning and trying out  methods of measurement.

As with all lessons in this unit, all related standards have been addressed in prior units. This lesson provides an optional opportunity to go deeper and make connections between domains.

Lesson overview

  • 10.1 Optional Activity: How Far Is It? (5 minutes)
  • 10.2 Optional Activity: Planning a 5K Course (10 minutes)
  • 10.3 Optional Activity: Comparing Methods (20 minutes)

Learning goals:

  • Choose a method and appropriate measuring tools to measure the length of a path.
  • Compare and contrast (orally and in writing) methods for measuring distances.
  • Compare measurements of a path and represent (in writing) the difference between measurements as a percentage.

Learning goals (student facing):

  • Let’s measure long distances over uneven terrain.

Required materials:

  • Measuring tapes
  • Meter sticks
  • Yardsticks

Required preparation:

  • Choose a path outside of the classroom that students can measure the length of.
  • The length should be between 50 and 100 meters (long enough that it cannot be measured directly with a tape measure.
  • Ideally it should include some curves or elevation changes (but not stairs).
  • A long hallway would also be okay, especially if it goes around corners.
  • This is not part of the 5K course, rather it is just a path to test measuring methods.


  • Access the complete Grade 7 glossary.


  • This lesson builds on the standard:CCSS.2.MD.A.1MS.2.MD.1MO.2.GM.B.4
  • This lesson builds towards the standard:CCSS.7.RP.AMO.7.RP.A






IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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