Here’s the problem:

An airplane is flying at 36,000 feet directly above Lincoln, Nebraska. A little later the plane is flying at 28,000 feet directly above Des Moines, Iowa, which is 160 miles from Lincoln. Assuming a constant rate of descent, predict how far from Des Moines the airplane will be when it lands. [1]

**Question:** Which student demonstrates better understanding? Why?

## Student A

## Student B

## Student C

## Student D

[1] Problem courtesy of Phillips Exeter Academy. Hat Tip: Alison Blank

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Student A has some incorrect wording I think (subtract 720 from 160?). The work is there, but the reasoning is not obvious: where did the 4.5 come from at the beginning?

Student B seems to get the scenario, but the method does not scale well.

Student C seems to have done the same method as B, but with more words.

Student D has the correct answer and the most scalable method, but lacks the explanation of the others. I would probably have done it in this same way: Interpret the words as a more traditional math problem, work through the math problem, reinterpret the answer.

It is a basic linear problem and they all “get it.” Being able to effectively communicate the complex processes of the mind in arriving at a solution is an entirely different thing. Mathematicians will appreciate D while engineers might appreciate B but english majors and other right-brainers might better appreciate C. In the end I consider A the brightest of the lot in general terms.

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