# Number Sense – Long Distance Hiking

Did a mini 3-act task today. Showed my students a bunch of pictures of the High Sierra where I’ll be hiking on the John Muir Trail this summer, for instance:

Anyway, then I took a few questions, and we looked at some maps. I told them I plan on hiking close to 300 miles, and asked how long they thought it would take.

Answers ranged from 2 days to 3 months, which I was pretty fascinated by. Most students were in the 1-2 week range — way faster than I’ll be hiking, but within the scope of reason — in particular for kids who usually move around the world much faster than that.

Then students had to name the information they needed to solve. They all knew they needed speed, but there was some interesting discussion about the remaining variable. Once we nailed down that I would only hike for some of the day, I told them I expected to hike about 2 miles per hour, and that I would hike from 7:00 am to 6:00pm with 3 hours of breaks in between.

Here, students struggled mostly to keep their work organized. They work well with distance, speed and time — they have several methods to work with, in particular proportions or d = rt — and had all the pieces. Got some really interesting answers. I really liked one girl who got 18.75 days, then told me that it would take 18 days and 18 hours. We then had a fun conversation about what that meant about the time I would finish.

We did several more similar examples as a class, then more practice on their own, variants of the above talking about road trips or bike tours. I really emphasized organization of work, and pushed something I haven’t before — drawing a vertical line to divide the workspace when solving a multi-step problem. One of our 7th grade teachers has done an incredible job with this, and I’m excited to teach her students next year with that in the toolbag. I don’t love telling them exactly how to solve a problem like this one, but organized and well-labeled work will be an asset to them in a huge range of academics, and I’ll be excited if I see students continuing that organization.

Also, great moment during student practice — a student solved a problem about a cross-country road trip. They were driving slowly — 5 hours per day to see the sights — and took 11 days to cross the country. She was really concerned that it took so long to get from the east coast to the west coast! Loved that she was able to be metacognitive about the problem.

All in all a fun lesson. Next time I need to connect their curiosity about my trip more concretely to the mathematical questions at hand, and try to find some more graphics and representations to give kids a foothold in what’s actually happening.