Guatemalan Sinkhole

Taught this lesson today. Pouring on the 3-Act tasks in 3-D geometry (one more coming after February break).

Challenges:

1. Much harder to estimate than with the filing cabinet 3-act from two days ago.

2. Numbers are a bit unwieldly.

3. One of the ideas I wanted to emphasize–flexibility with the units we choose–was tough to get through. They wanted to use feet because feet are familiar, and that was all.

4. I’m conflicted about having students work in terms of pi vs calculating with 3.14 vs estimating. I want them to be able to do all three, and most importantly, to intuit which is most appropriate given the context. I didn’t give them calculators here, pushing them to estimate. Many students didn’t, and got bogged down in decimals.

Wins:

1. Cylinder in relief. Showing students lots of textbook diagrams, or cylindrical jars, or etc doesn’t do the whole job. Lots of examples are objects that have a cylindrical hollow. Really useful conceptual piece.

2. Reading! Love that Robert Kaplinsky includes the articles.

3. Kids were engaged. They wanted to know more. Also became a challenge, but initial buy-in was awesome.

Big Takeaway:

The fundamental questions kids wanted to answer when they were confronted with the task were not the same questions I posed. They didn’t care as much about the volume of the hole, or the cost of filling it, as much as they cared about how it happened, if it could happen in Boston, and how many people died. This was an example where the real-world-ness of a task became a detriment–students were distracted from the mathematical thinking I wanted them to learn from. The filing cabinet 3-act would never need to be solved in the real world–no one has ever actually needed to cover a filing cabinet in post-its, much less a filing cabinet with dimensions that are multiples of the post-it dimensions. But it was engaging, and they were asking questions that led to mathematical learning.

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