Math in Our World: Ling’s Hiking Trail

Ling likes hiking. She and her family have a favorite trail near their house. Ling isn’t sure how long the trail is, but she knows that it has the following features:

  • Scenic overlooks at the halfway point and the end of the trail
  • Memorial benches every 1/3 of the trail
  • Bridges over streams every 1/4 of the trail
  • Trail markers called “blazes” every 1/6 of the trail

Some of her favorite parts of the trail are near these features:

  • Her favorite swimming spot is at the first bridge.
  • If you sit on the second bench and look up at the tallest tree there’s a bald eagle nest.
  • There is an amazing waterfall at the fifth blaze.
  1. Using pictures, models, or numbers to show what is happening.
  2. What do you notice? What do you wonder?
  3. What mathematical questions can you ask about this situation? Answer all the questions you can!
  • You may wish to sketch the trail as a number line, labeling different features.
  • How long could the trail be? What if it was 12 kilometers? What would that look like on a map?

Show your work to someone else, and explain your thinking. Did they understand?
Ask whether they have any other questions you can answer!

Design a trail map. Label it with features that occur at regular fractional intervals on the trail. How long is the trail? What are the features? How many of each feature does your trail include?