Took a day off from my #MTBoS30 challenge yesterday as I was hiking in New Hampshire with 8 of our boys. Beautiful view from the top despite rain in the morning:
There wasn’t a ton of math happening, but one thing was surprising, and a bit worrying on the theme of number sense. The hike was 5 miles round trip. 2 miles up, including a number of sections like this:
And 3 miles back down. The first mile, both up and down, was less than half an hour for the group. But the last half-mile to the summit, mostly climbing up steep trail like the picture above, took over an hour. My students were very attentive to the signs marking mileage coming up, and weren’t too focused on how long it was taking. Heading down, however, they really struggled to get an idea of how far we were from the trailhead, or how long that would take. They didn’t think that 3 miles was a big deal as we started on the trail down, but were surprised to hear that we probably had more than an hour left after making about a mile of the way down. Then, upon hearing that they were still a mile from the bottom, several students were horrified that they were so far away, unaware of how fast we were moving on the relatively flat lower portion of the trail.
This isn’t a big deal, or a red flag for me mathematically. This type of number sense is tough for many adults, and we were tired and impatient after a long hike. That said, we spent some time this year talking about distance-speed-time questions, and while they often struggled with concepts, it’s a skill I would love them to take to high school, and I didn’t see it in practice. It makes me curious what kind of concrete activities could give students a sense of space and time that they could apply to their everyday lives.
So many questions.