Backup Parachutes

I usually try to teach ways to double-check any calculation procedure (by means of initial estimation, making a graph/sketch, etc.). Frequently students resist this: they ask if they can skip the estimation step and just do the direct calculation alone. That's problematic, because it's the estimation which is perhaps the better test of actual comprehension of the overall concepts involved.

New analogy: The double-check is like a backup parachute. Most of the time the main parachute works, but no sane skydiver would take a leap out of a plane without the backup if they can avoid it. If they did, they'd be one tiny glitch away from total disaster.

Edit: I suppose an even better analogy would be the little "drogue parachute" that is deployed for slowdown & stability prior to the main parachute (granted that estimation should occur at the beginning and only partly suggest the full answer). But not everyone knows about that, so I went with "backup parachute" instead.

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