Help solve
Monday, Dec 11, 2006
I figured I wouldn’t have to start buying the forbidden-on-Ebay teacher manuals until at least fourth grade. Yes, fourth grade seems about right because I don’t want to work each long division problem myself. But this one stumped me:
Two ducks watch the wheels of the cars that pass. The first duck said she counted 24 wheels. The second duck said he counted only 22. Which was correct and why?
Naturally, whichever duckie was paying closer attention is correct. We can’t always assume that it’s the female, you know. But I assume there is a more logical answer to this one.
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Actually, they could *both* be correct. The author of the question assumed only four wheel vehicles. There are plenty of vehicles, however, that have 2 wheels, or 6 or more (think “18-wheeler”).
Assuming only standard 4-wheel passenger cars, of course, “24″ is the correct answer because it’s the only one that is divisibly by 4.
The second duck probably got distracted by the detailing of one of the cars.
Of course, again, they could *both* be wrong. What ought to be asked is, “Which is more likely to be correct?”
Comment by Evers (December 11, 2006 @ 2:34 pm )
This is my take on it. Cars have four wheels, so the number must be divisible by 4 . . . thus 24 must be the answer. HTH!
another homeschooling mama
Comment by blessedwith5 (December 11, 2006 @ 2:39 pm )
The other unstated (and likely erroneous) assumption seems to be that the ducks could see all the wheels of each car. However, one would have to be an astute observer to see the wheels on the far side of the vehicle as they pass by.
Comment by JFC (December 11, 2006 @ 2:41 pm )
Evers and blessedwith5,
The fact that 24 is divisible by 4 seems to be what they’re looking for. I didn’t think of that. The chapter we’re on is division, so that answer would make sense.
The wording on this problem is why I don’t like SAT analogies because an intelligent person can think of ways that each answer could be correct.
I was thinking along the lines of JFC—that perhaps one duck saw the wheels on the other side of the last car in a long parade of cars.
Comment by Amy Scott (December 11, 2006 @ 2:45 pm )
Greg emailed with his thoughts:
“Well, I could think of several different answers depending on the context.
For example: where one duck was standing, one car passed directly behind another - but the other duck had a different angle and therefore saw all the wheels.
Another: The ducks started counting when there was one car in transition between them - therefore, the car had already passed the one duck who counted 22.”
Comment by Amy Scott (December 11, 2006 @ 2:57 pm )
I think the answer is obvious. The second duck counted 22 before the final car slammed on his brakes but, too late, ran him over. The duck never saw the last set of wheels because, at the time they passed over his inert body, he was already in a coma.
Comment by Tim Challies (December 11, 2006 @ 3:08 pm )
And people ask why I don’t homeschool-if I can’t figure this out,how could I be ever be teaching Allison geometry!!
Word problems are the worst!!
Comment by Tammy (December 11, 2006 @ 3:36 pm )
Besides the car running over the second one (which would have bee an answer counted correct for creativity at my house!)
My thought was that they are on a corner and had different numbers of cars pass depending on where they were standing. But then again, I only passed high school math due to my creativity… so don’t listen to me !
Comment by petersonclan (December 11, 2006 @ 4:10 pm )
I want to know why duck are counting the tires on cars anyway.
Comment by Claire Weaver (December 11, 2006 @ 4:16 pm )
The answer is too logical…ducks can’t count. (I foresee a very interesting time with these kinds of math questions when we get to fourth grade
Comment by Stephanie (December 11, 2006 @ 4:46 pm )
I’m just curious. Which math curriculum are you using?
Comment by Kendra Vita (December 11, 2006 @ 5:13 pm )
Not only can ducks not count, they can’t talk, either.
All that aside, 18-wheelers were not mentioned in the problem, so we have to reason that 24 is the correct answer, unless, of course, they were positioned differently and one saw all 4 wheels of each car and the other one kept moving around and seeing the cars from various angles. Oy…..I think I would just delete that problem from the book and move on (or transfer it to a lesson on logic).
Comment by Susan in Elk Grove CA (December 11, 2006 @ 7:21 pm )
MCP (Modern Curriculum Press) after a daily drill of addition facts (1 - 18) and multiplication facts (we’re up to 7’s). Kid #1 uses Book C. Kid #2 uses Book B. Kid #3 does Bob Jones K.
Comment by Amy Scott (December 11, 2006 @ 10:10 pm )
Operating under the assumption that there are talking ducks that can count:
The first duck was probably correct in saying she counted 24 wheels. The second duck was probably correct in saying he counted 22 wheels. How many wheels actually passed is irrelevant to how many were counted, and the ducks are giving how many they counted, not claiming that’s how many there actually were. It never states that either duck was counting all wheels, or that they were supposed to be doing so.
Comment by Jeff (December 11, 2006 @ 10:42 pm )
obviously the first duck is correct. because she is the girl duck!!
Comment by Heidi (December 11, 2006 @ 11:10 pm )
Jeff - this is a homeschool curriculum which, being stuck in modernity as we Christian homeschoolers are, demands a single right answer.
Tim - too easy - try again.
Heidi - ding ding! (But the second duck still knows that he is right, even if he has to give in to her)
What I want to know is were the tires moving past the ducks or were the ducks moving past the tires, thereby rendering the question moot? (Alas, too much time in modern physics way back in college).
Comment by Greg (December 12, 2006 @ 12:57 am )
The problem with the problem is that it fails to provide one important piece of info, that is how many cars went past. If 11 cars passed and the duck was standng on the side of the road, as he should be for safety sake, then he could only see 2 wheels of each car and he would be correct in that he only observed 22 wheels.( 11/2 ) On the other hand, if he was in the middle of the road when the first car ran over him he could observe all four wheels on each car. If his answer was 22 then he probably died before the rear wheels of the 6th car were counted. ( 22/4=5 plus 2 ) The same is true of the other duck. However, this presents another problem in that they couldn’t report if they were run over. In either case both ducks could be correct or wrong depending on their perspective. A lesson we might want to teach our children along with the math.
Comment by KING CHARLES (December 12, 2006 @ 1:37 am )
This kind of question is one reason we ignored home ed curriculum altogether until the teenage years (and, in retrospect, should probably have continued not using any). Too many maths books assume just one correct answer to each problem, and children who think in only one narrow way. Part of the reason we home educated was to encourage creativity and questions, and any formal word problem such as the one you described would have led to a discussion much like the very enjoyable comments thread above
Of course it’s kind of fun brainstorming around word problems like that!
Division is much easier to learn using lego bricks and/or a calculator! I did a maths degree and worked for four years as a computer programmer when I was younger, and never, since my high school days, have I had to use long division…
Comment by Sue (December 12, 2006 @ 11:48 am )
What is scary is that my thoughts were the same as Greg…Silly engineers all think a like.
Comment by Todd (December 12, 2006 @ 1:00 pm )
I think you should teach the ducks to stay away from the road. They could get hurt! And perhaps the second duck actually saw a motorcycle. Ducks are little, and so might not have been able to take in the scope of the entire vehicle. Or perhaps the 2nd duck saw one of those big pickups with two sets of wheels in the back.
I always loved analogies, and did really well on that section of the SATs!
Comment by Ashley (December 12, 2006 @ 1:26 pm )
I agree with Amanda
You take one and I’ll take the other.
Comment by Another Heather (December 12, 2006 @ 11:26 pm )
21. Because it’s a Pairodux!
Comment by Pooka (December 13, 2006 @ 2:11 am )
I’m sure the “correct” answer is “cars have 4 tires….” but creative and alert people have to observe that there are 3-tired cars and that ducks don’t talk and that lying on the road is (a) dangerous and (b) a position from which it’s unreliable to see all tires anyway. Try explaining all that on IQ tests or SATs.
What I’ve learned from this is that, gratifying from one point of view but disappointing from another, apparently homeschooling doesn’t prevent ridiculous questions to which there is no good answer in a standardized setting.
Comment by anne (December 14, 2006 @ 12:01 am )
Hmmm…What about spare tires hanging on the back of the vehicles, like a Jeep? That could account for odd numbered sightings as well. The more important question than the correct number of tires sighted is: How do the ducks FEEL about the tires? Isn’t that all that matters in education today?
Comment by Kimberly (December 14, 2006 @ 1:21 am )
According to Challies (comment #6), Kimberly, the second duck doesn’t FEEL real keen about tires right now.
Comment by Greg (December 14, 2006 @ 8:23 am )
Sue - I agree with you. I would take one look at that question and my eyes would cross permanently.
I’ve tried 2 curriculums in 1.5 years and I’m done - mostly due to crazy questions just like this one..
Comment by sonja renee (December 14, 2006 @ 4:12 pm )
This is a terrible math question! Are the ducks watching the same street? At the same time? Are they on the same side of the street? Can they see all 4 wheels of the car, or only 2 as it passes? I’m not actually understanding the question… which duck is correct, i.e., which duck knows how many he counted, or what? If I say I counted 24 cookies on the rack, and my husband says he counted 22, we’re both correct assuming that we can count! It doesn’t ask how many there actually are.
What if one car was parked, and the first duck counted those wheels (the 2 he could see); but the second duck only counted moving wheels?
Make up your own question instead.
BTW
Comment by Milehimama (December 16, 2006 @ 12:10 pm )
I am not sure it is a math problem, as much as it serves to provoke thought and conversation. It seems the human intellect begs us to explore far beyond the obvious intention of the question, which requires us to question the very nature of the question. I think this is productive, but we should use this skill to perhaps tackle some more meaningful topics, like PEACE, GLOBAL WARMING, HEALTHCARE and CHOCOLATE CHIP MINT ICE CREAM. The Marx brothers once asked “VHY A DUCK ?” “VHY NOT A CHICKEN ?” I want to know what the chickens were doing while these ducks were counting. They obviously were engaged in road crossing and the reason they were crossing the road may have something to do with this duck counting. Did you ever think of the conspiracy angle, perhaps this was FOWL PLAY, and worthy of investigation?
Comment by Gerry (December 20, 2006 @ 5:53 am )
Too funny, everyone. I’m glad I asked!
Comment by Amy Scott (December 20, 2006 @ 7:41 pm )