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Yes, they’ve done it! Three stupid DC-CAS questions out of three!
The question is really asking students to compare four 4-place decimals to see which one is the smallest. However, the company that wrote this felt it was necessary to make this into a "story problem" with a context. The problem is that in the real world, this problem makes almost no sense. Especially if you have ever cut down or measured a tree. It so happens that I have done both. The first difficulty is that trees don’t have the same diameter or circumference at all locations. If you measure at, say, 2 inches off the ground, well, you are going to have a very difficult time measuring at all because there are lots of roots and rocks and plants in the way, and you will find it nearly impossible to hold your tape measure level unless you have a whole bunch of helpers. Plus: where exactly is “ground level”? It varies, especially on sloping ground. In general, the higher you go on a tree trunk to measure the diameter, the narrower the tree will be. For legal purposes, one measures the distance around the tree at “breast height.” But whose breast, and which part thereof? It would depend on the age of the person, among other things. Allow me to quote wikipedia:
I submit that the results allegedly obtained by Eva are ridiculous, and should all be rounded off to 2 decimal places. What’s more, in the real world, they would probably be expressed in centimeters (i.e., whole numbers) rather than decimal fractions of a meter, unless she has enormous old-growth sequoias and redwoods in her yard, which I strongly doubt. For one thing, despite what Wikipedia says, trees NEVER have cross-sections that are exact circles. Secondly, anybody who says they can get the circumference of a tree to an accuracy better than one centimeter is deluding himself/herself. But even if we pretend that Eva did so, and then divided by pi to get the diameters, watch what happens when we work backwards. Tree #1 supposedly has a width, which I guess means diameter, of 0.5091 meters. If we multiply this by the approximation 3.14 for pi, we get a circumference of 1.59874 m. Now, that is obviously impossible, because nobody can measure anything that accurately with just a flexible tape measure. So, shall we assume that she measured the circumference to the nearest centimeter? That would be 1.60 meters, or 160 centimeters, or 1 meter 60 cm. Now, let’s go forwards and divide that by 3.14. If I do, I get 0.50955414, which Eva should have rounded off to 0.5096, not 0.5091. If I use a calculator’s built-in approximation for pi, something lik3 3.141592653589 instead, I will get slightly different answers, but the bottom line remains the same: her answer are probably impossible. Perhaps Eva really got a girth (circumference) of 1.59 cm instead? In that case, her reported thickness (diameter) should have been 0.506369… which would round off to 0.5064, not what she allegedly wrote according to the writers of this stupid question. Yeah, I know that my nit-picking won't change what the correct answer is (which I shall leave as an exercise for you, dear reader), but my point is this: when the writers of tests make up contexts for these problems, shouldn't the contexts actually make sense? (I actually do have to measure things to 4 decimal places when measuring stuff for grinding and polishing telescope mirrors. And you know what? It's extremely difficult, and takes very specialized and accurate tools, and a fair amount of knowledge, skill, understanding of sources of error, and old-fashioned experience to measure accurately to 4 decimal places. A bit more understanding, knowledge, experience and skill than is demonstrated by the writers of this worthless test, on which the fate of so many DCPS staff members will ride. And a test which does virtually NOTHING to help teachers decide what needs to be taught, because the questions are so poorly written.) Another remark: This question is a bit like a person saying that the sign that gives the age of the moon rocks on display at the local science museum is all wrong. The person reasons like this: 'The sign says they are 4,000,000,000 years old (that's four Billion years), but they were brought back to the Earth in 1971, and that was 39 years ago, so the sign should really say 4,000,000,039.' They don't realize that "four billion years" is merely an estimate made by some geologists based on the best evidence that they could find at the time, and is likely to be changed by many millions of years (but probably not by Billions) as better evidence comes in; what's more, the first group of geologists probably gave their estimate of the age with a range of error. In other words, they probably said that their answer is ‘give or take 10%', which would mean they would not be surprised at all if their date was off by 400,000,000 years either way. That’s plus or minus somewhere near FOUR HUNDRED MILLION YEARS!!! In comparison with that, 39 years is way less than the blink of an eye. A foolish quest for spurious precision is the hobgoblin of little minds. — G. F. Brandenburg |
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