Gifted Issues Discussion homepage Forums General Discussion The Ultimate Bad Homework Question Thread!

Yet another bad question shows up:

Envision a figure showing four types of pizza sold in one month: 10 anchovy, 70 mushroom, etc. The figure tells you how many of each pizza were sold. This is the sum total of information given.

1. What was the total number of pizzas sold in the month? Answer = 320. Okay, fine.

2. What was the median number of pizzas sold in the month?

DD just brought home a giant packet of graded work (happens every few weeks). They are doing multidigit multiplication problems, which she is finding easy. Worksheet after worksheet of what basically adds up to 465 x 56 (some are word problems). Except they like to throw in one per page like this:

X county has 5,678 citizens. Y county has about 8 times as many citizens as X county. About how many people live in Y county?

DD (who just did 15 other problems along the lines of "What is 3676 x 14?"): 45,424 citizens.

WRONG!

(The answer is 48,000 citizens, of course. "ABOUT how many people." Get it? Yeah, I almost feel like they put these in just to ding the kids who are zipping through.)

There must have been 4 worksheets like this; every problem was straight-ahead nonestimation multiplication except for one or two questions where they threw in an "about." DD got every single "about" one wrong, having done the actual problem (correctly). Now, I get that reading carefully is important. But meh.

The bigger problem here is the author's incorrect assumption that only citizens live in a place.

Even setting that aside, if they're going to teach estimation, they should at least teach it responsibly. Rounding is only helpful if you're rounding to a useful degree of precision. In this case, it's far more useful to round up to 5700 than to 6000.

I mean, yeah, I could just round up all my monthly bills to the nearest hundred instead of the nearest tens. That'd sure make budgeting for movie night a lot more exciting.

In what universe is the more accurate answer wrong? Reading carefully so that you see the word "about" doesn't make the answer *wrong*. If they want the kids to practice estimation, they should say "use estimation." But even then it's unclear what would be the "right" answer. Estimating can be to varying degrees of precision. 45,600 would be a reasonable estimate.

Sheesh, I swear this stuff comes from some Bizarro Totalitarian Alternate Reality, where "words mean what I say they do, because I'm in charge."

The detailed answer was wrong because of significant figures: when multiplying, your answer can only have as many significant figures as the least accurate number you start with. So when the problem said "about 8" it was throwing out ONE significant figure. Ergo, the answer cannot include more than ONE significant figure.

This means that the math book was also wrong. The correct answer is 50,000. 5,678*8=45,424. You round up to 50,000, which has only one significant figure (the 5).

And I have no idea where "48,000" came from (please tell me it was a typo). Did they just pull that out of the air? ETA: Oh, I get it now. They rounded FIRST, and then multiplied, and failed to account for sig. figs. This is painful. The rule is: multiply first with whatever you have, then round. Ouch. This really hurts.

I wouldn't expect someone learning multiplication to understand significant figures. But the people who wrote the book should, and they should have specified the necessary information, such as "round to the nearest x." You still have to read the problem to get that information and yet putting it there also removes the need to guess.



Agreed.

"About" is such a culturally and context-specific word as to be virtually meaningless wihout further elaboration.

My dad was a fighter pilot, and I'm reminded of a story he told me about a German-born colleague describing his commute to work in the event of an emergency call. (I think I was fuming at a "wrong" answer like the one described!) The Canadians all rounded transit time to the nearest 5 minutes, while the German pilot said something like, "The trip takes me approximately 11 minutes and 40 seconds in average conditions." In an emergency, that precision would be valuable!

To be fair: I don't actually know for sure what the expected answer was, because the teacher did not write it in. (Yay! She never does.) It could be 50,000. However, based on oodles of prior experience AND the fact that she was not told what to round to, I am pretty darn sure the answer was 48,000. Yes, I TOTALLY AGREE that this doesn't make any sense.

I should collect the other 5 problems like this she got wrong on otherwise completely perfect math papers.

Yes, DS has missed a significant number (ha) of math problems lately involving rounding and the casual use of the word "about". I tied myself in knots trying to figure out what was wrong with his answers when he brought home papers marked wrong, and everything I could see was right! Finally I checked the book to see what he was supposed to be doing, and discovered we were estimating. To the nearest god knows what, because "about" is not helpful.

I would have estimated your problem at 45,600 myself. Although, with the "citizens" question, and depending on where these counties are located, and what time of year it is, it's probably more like 100,000. But only 253 of them vote.

I can't actually post any of these because they are assessment items, but SHEEEEEEESH....

my daughter's AP Physics class is using assessment practices from somewhere hot and sulfurous, I'm pretty sure.

This is the third exam in a row where she's had about 40% problems which are completely novel-- not just novel in terms of the particulars, which I'd be totally okay with, but novel in terms of the conceptual APPROACH to the problems, as well. As in, they've never seen anything like it, had no instruction in how to approach a problem like it, and there are NO examples in their course or text to support solving them. They have to remember material from three or four units back, (or from a previous course, even), and SYNTHESIZE it with new material, in order to have any hope of solving the problems.

Oh-- and they have to make a bunch of assumptions. But not others, obviously. Because making those assumptions would be wrong. Only the ones intended are the correct assumptions. Apparently.

(Seriously, DH and I have both looked these exams over in the context of the course instruction and frankly, most college sophomores would be sinking under these expectations.)

It's completely surreal. She really knows the material well, can explain it well, can do the math well, can set problems up, etc... but she's routinely earning ~70% on these exams. Yikes.

Oh-- and just to make it more interesting, many of the problems include the multiple choice "trickster" answers which are basically "gotchas" for arithmetic/algebraic errors, and occasionally they throw in an answer which IS completely correct... but only if you define the coordinate system in an unconventional manner. Which, (drumroll please)... yes, that's right, my out-of-the-box kid has a penchant for. DH and I are both trying to figure out how they can omit telling students HOW to conventionally define things... but then PUNISH them for not figuring this out themselves, evidently.

:head. desk: