There were two particularly useful comments in response to this problem:
The moment of inertia for rotating a I-beam about its long axis has no practical relevance in structural engineering. This is a fake-world problem, of no interest either mathematically or to engineers.
Even if this task did have practical interest for structural engineers, its presentation here will move the needle on student engagement only a fraction of a degree. The issue here isn’t the usefulness of the application to professionals but the tedious, pre-determined work students do.
When I saw the two boards, I wanted to go get a board and try standing on it. How much weight could we put on the board in each position before it broke? That would be an engaging problem.
I don’t know. That might be an engaging problem.
There are 100 different directions that question can go in terms of the work students do in class and only a handful of them will actual leave kids mathematically powerful and capable.
Watch me ruin the problem:
The maximum load a board can hold before it snaps is given by the formula:
[formula involving cross-sectional area and mass]
Dan weighs 90 kilograms and the dimensions of the board are 2 inches by 4 inches by 70 inches. Will the board hold his weight?
I have no confidence this task will result in the sense of accomplishment and connection the editors of the NYT seem to think it will.
There are other ways to present this kind of task, though. Which is my point. The “real world”-ness or “job world”-ness of the task is one of its least important features.