# Lesson 10

Measuring Long Distances Over Uneven Terrain

### Lesson Narrative

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.

### Learning Goals

Teacher Facing

• 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.

### Student Facing

Let’s measure long distances over uneven terrain.

### 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.

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