Whacky math homework problems

[Zep]

Okay, here's the next one:

Construct a rectangular prism with volume 36. The height is 4 units. How many can you construct?

Say what? How much time do they want the kids to spend on this problem?

~~ Paul

Unless the question specifically states whole number units, the answer is pretty much infinite.

 

[Hypocolius]

I saw a maths book a couple of years ago with a section on ratios etc. The example involved using a map to a scale of 1:100,000 or something. The question said (IIRC)

"Two cities are 80,000km apart, how far apart are they on the map?"

WTF, 80,000km? are they on f*ckin Jupiter or something?

 

[Zep]

I saw a maths book a couple of years ago with a section on ratios etc. The example involved using a map to a scale of 1:100,000 or something. The question said (IIRC)

"Two cities are 80,000km apart, how far apart are they on the map?"

WTF, 80,000km? are they on f*ckin Jupiter or something?

And how big was the freakin' map!!!

 

[Paul C. Anagnostopoulos]

T'ai said:
So you just have to list various (b,c) combinations such that bc = 9 as desired. I would also assume whole numbers, but maybe your son could list fractions in addition for some extra credit?

They have had plenty of problems with fractions, so I wouldn't assume the problems involves only integers. If it does, then the problem author should say so.

Jes said:
It seems to me that no matter how poorly worded the question is, if you word your answer appropriately, the teacher has to accept your answer. If you are really concerned about correctness, write every answer you can think of and explain your rationale for each. I can't imagine the teacher not giving credit even if you only gave one answer.

This is 5th grade, for Ed's sake. Where is the sheet of simple, graphical surface area problems? At least do that first. "Ooh, let's trick the poor kids. Our teachers did that to us in grade school, so nyah, nyah!"

Anyway, being the smartass I am, I answered the first one and put "Not possible" for the rest. Of course, I was right, but I was also the only one who answered the questions this way. Everyone else converted, for example, 16 in base-5 to 11 in base-10. I got full credit since I could back up my answers, and so did the other kids, even though they were dumber than me since they didn't really do anything "wrong".

And the teachers are probably still handing out that stupid problem. What?!, eliminate or edit a busted problem? Never heard of such a thing.

Hypocolius said:
WTF, 80,000km? are they on f*ckin Jupiter or something?

That's a riot. This kind of thing, along with the Feynmann quote, makes me wonder how many kids get turned off to math because (a) the problems are totally impractical; (b) the problems are tricky/confusing and lead the kid to think that's a fundamental attribute of math; (c) the teacher never bothers to relieve the kid of this belief by explaining that certain problems are wrong; (d) no one bothers to edit the problems.

~~ Paul

 

[Jaggy Bunnet]

They have had plenty of problems with fractions, so I wouldn't assume the problems involves only integers. If it does, then the problem author should say so.


This is 5th grade, for Ed's sake. Where is the sheet of simple, graphical surface area problems? At least do that first. "Ooh, let's trick the poor kids. Our teachers did that to us in grade school, so nyah, nyah!"


And the teachers are probably still handing out that stupid problem. What?!, eliminate or edit a busted problem? Never heard of such a thing.


That's a riot. This kind of thing, along with the Feynmann quote, makes me wonder how many kids get turned off to math because (a) the problems are totally impractical; (b) the problems are tricky/confusing and lead the kid to think that's a fundamental attribute of math; (c) the teacher never bothers to relieve the kid of this belief by explaining that certain problems are wrong; (d) no one bothers to edit the problems.

~~ Paul

To put the alternative spin, do you really want all the problems to be:

What is the volume of a box with sides of 6cm, 10cm and 20cm?
What is the total surface area of this box?
What would the volume be if the lengths of each side were doubled?
What would the surface area be now?
etc, etc.

where there is absolutely no room for anything other than mechanically producing the correct answer.

I think the wrapping paper is an excellent question as it encourages the child to actually think about practicalities. As long as there is time available to discuss the answers, not simply mark them right or wrong, then I suspect the child will learn a lot more from it than a simple calculation. If you get a calculation wrong because you don't know your 6 times table (or you pressed the wrong button on your calculator) then you learn very little.

On the other hand if you produce an answer (say based on surface area) that is correct and someone else produces a different answer (say on length of paper used) that is also correct, to me that is much more interesting.

 

[Paul C. Anagnostopoulos]

I agree with you in principle, Jaggy, but I have trouble with problems that are "trick questions," either purposely or because the person who wrote them was a dolt. I don't think people appreciate the degree to which a load of trick questions conditions a kid to think that math is one big trick.

Do we use trick questions in other disciplines?

Students, please read The Old Man and the Sea and write an essay about the old man's belief in mermaids as messengers of God.

Students, please mix together these highly volatile chemicals and write an essay about what happened. . . . I'm sorry, Mom, Johnny was supposed to figure out not to do it. It was a life lesson, don't you know?

I know I'm overreacting a bit.

~~ Paul

 

[Jaggy Bunnet]

I agree with you in principle, Jaggy, but I have trouble with problems that are "trick questions," either purposely or because the person who wrote them was a dolt. I don't think people appreciate the degree to which a load of trick questions conditions a kid to think that math is one big trick.

Do we use trick questions in other disciplines?

Students, please read The Old Man and the Sea and write an essay about the old man's belief in mermaids as messengers of God.

Students, please mix together these highly volatile chemicals and write an essay about what happened. . . . I'm sorry, Mom, Johnny was supposed to figure out not to do it. It was a life lesson, don't you know?

I know I'm overreacting a bit.

~~ Paul

I just don't see any "trick" in the question about wrapping, although I agree that the prism one is badly worded.

Is asking someone to write an essay about the causes of WW1 a trick question? It is certainly much more difficult to identify a "correct" answer than the wrapping problem.

 

[Hellbound]

I have to agree that, if worded a bit more clearly, the problem is excellent.

I've tutored several friends and, more recently, children of friends in mathematics. The biggest problem I find people having with math, specifically word problems and real-world applications, is figuring out what numbers to use. Word problems such as this, even if the 30 inches figure was completely irrelevant, are practice to develop these skills. It never ceased to amaze me how people would mix up numbers in their problems.

Me: "Okay, look at this one. 'There's a 100 ton train leaving Townsville travelling 60 mph towards Cityton. A 200 ton train leaves Cityton going towards Townsville at 45 mph. The two cities are 100 miles apart. Where do they meet?' Okay, what do we need to do to solve this one?"

Tutee: "Um, 100 times 200? Then divide by the distance and add the two speeds?"

Me: *smacks self in head with book*

Anyway, the questions are often poorly worded, which is a problem I had with these tests. I had the same trouble in other subjects, especially with True-False questions (ex: The angles of a triangle, when added together, always sum 180 degrees. True or False? Well, it depends on the surface your triangle is on). I don't think the problem is questions with red herring numbers or extra information. Those questions help prepare us for real life. The problem is unclear questions, that do not adequately expalin what they expect one to do.

 

[Soapy Sam]

Huntsman- "meet"? These trains are on the same track?
Is this a trick question?

 

[Paul C. Anagnostopoulos]

Jaggy said:
I just don't see any "trick" in the question about wrapping, although I agree that the prism one is badly worded.

The "trick" is that it's not clear, even with some good thinking, whether the 30" number is relevant. I'm afraid I can't get excited about the educational possibilities of first assuming it's irrelevant, then not, and giving multiple answers to the problem when assuming it is relevant, and so forth. This is 5th grade, for crying out loud. Address the fundamentals first.

Is asking someone to write an essay about the causes of WW1 a trick question? It is certainly much more difficult to identify a "correct" answer than the wrapping problem.

One is historical opinion, the other is math. Don't make kids think that math is nothing but confusing opinion!

Huntsman said:
I've tutored several friends and, more recently, children of friends in mathematics. The biggest problem I find people having with math, specifically word problems and real-world applications, is figuring out what numbers to use. Word problems such as this, even if the 30 inches figure was completely irrelevant, are practice to develop these skills. It never ceased to amaze me how people would mix up numbers in their problems.

Yes, that is an important skill, so give some homework about it! Stop trying to kill seven birds with one stone. The fact that kids play that guessing game is testimony to the difficulty of sorting out the problem's facts. Give kids a long while to learn how to sort without tossing in distractions.

I should point out that my son has a reading disability, which makes these issues more important for him. However, watching so many kids struggle with math leads me to think it is a general problem.

~~ Paul

 

[TillEulenspiegel]

I can see what the teacher is trying to accomplish. Rather then rote memorization and methodology, they are attempting to teach the concepts and applications of math. I however agree with Paul that this is not 5th grade material at least the way it's presented.

 

[T'ai Chi]

I saw a maths book a couple of years ago with a section on ratios etc. The example involved using a map to a scale of 1:100,000 or something. The question said (IIRC)

"Two cities are 80,000km apart, how far apart are they on the map?"

WTF, 80,000km? are they on f*ckin Jupiter or something?

I would imagine it is just poorly worded. I would think that the distance, say by road, is 80,000km, and they want the straight line distance "as the crow flies"??? I don't know.

For some reason it reminded me of an interesting problem: if you have a map, say that has 10 cities on it, it is easy to read the distances from every city to every other city. An interesting problem is given only a matrix of these distances, can you reconstruct the map?

 

[Torlack]

I agree with Curt, this is a good problem. It requires you to think about the problem. There is no extra data since the 30" width of the paper is what makes the problem a little more complex than just plugging in the numbers.

As far as the other stuff goes (tiling), that is just us over thinking the problem. It is actually a very simple problem.

 

[Paul C. Anagnostopoulos]

If you want treat the problem simply, then just calculate and compare the surface areas. But in that case, the 30" number is superfluous. So I'm not sure I get your point, Torlack.

~~ Paul

 

[Paul C. Anagnostopoulos]

It's been an amusing week for homework. Tonight my son was supposed to take a large plastic bottle, squeeze it, plug it with a wad of paper, and then reshape it to its original shape. Ta da! The wad of paper is sucked into the bottle.

No freaking way that was going to happen. So in the spirit of honest science, he wrote that it didn't happen and offered an explanation why not.

We did have fun popping the wad of paper out of the bottle.

~~ Paul

 

[Vorticity]

For some reason it reminded me of an interesting problem: if you have a map, say that has 10 cities on it, it is easy to read the distances from every city to every other city. An interesting problem is given only a matrix of these distances, can you reconstruct the map?

I've been trying to picture this in my mind, and I believe that the answer is yes, modulo arbitrary rotations of the entire map and mirror reflections about a line joining any two cities.

If we think of the cities as points on a featureless plane, we can imagine building up the map from nothing by putting one point at a time back onto the map, consistent with the known distances between that new point and the already existing points.

First point: just throw it down anywhere.

Second point: Just throw it down anywhere on the circle of the appropriate radius centered at the first point.

Third point: 3 lengths serve to uniquely define a triangle (modulo flips and rotations). There are 2 possible places you could put the third point.

Etc...

My intuition tells me that having put down the first 3 points, the positions of the remaining points are uniquely determined (except in the case of a few pathological configurations). But I may be wrong...

 

[T'ai Chi]

Originally posted by Hypocolius

I saw a maths book a couple of years ago with a section on ratios etc. The example involved using a map to a scale of 1:100,000 or something. The question said (IIRC)

"Two cities are 80,000km apart, how far apart are they on the map?"

WTF, 80,000km? are they on f*ckin Jupiter or something?

Oops, I didn't read this correctly when I responded to it the first time!

Yeah, 80000km is a tad large. 80000km is about 49700miles!

Maybe they meant 80000m, which is about 49.7 miles??

 

[T'ai Chi]

I've been trying to picture this in my mind, and I believe that the answer is yes, modulo arbitrary rotations of the entire map and mirror reflections about a line joining any two cities.

If we think of the cities as points on a featureless plane, we can imagine building up the map from nothing by putting one point at a time back onto the map, consistent with the known distances between that new point and the already existing points.

First point: just throw it down anywhere.

Second point: Just throw it down anywhere on the circle of the appropriate radius centered at the first point.

Third point: 3 lengths serve to uniquely define a triangle (modulo flips and rotations). There are 2 possible places you could put the third point.

Etc...

My intuition tells me that having put down the first 3 points, the positions of the remaining points are uniquely determined (except in the case of a few pathological configurations). But I may be wrong...

Check out 'multidimensional scaling'. It is a pretty neat topic. I haven't done much with it, only a few problems in a multivariate stats. class when I was in grad. school.

 

[Atlas]

For some reason it reminded me of an interesting problem: if you have a map, say that has 10 cities on it, it is easy to read the distances from every city to every other city. An interesting problem is given only a matrix of these distances, can you reconstruct the map?

This does seem strangely possible. The first city point is picked arbitrarily on a blank piece of paper. Then 9 circles of varying radii signifying the possible locations of the other 9 cities at the proper distance to city1.

Then arbitrarily choose a point for city2 somewhere on the appropriate circle drawn around city1, and draw 9 more circles with radii appropriate for the distances from city2 to the other 9 cities.

I'm trying to imagine if that is enough. Would the intersecting circles around City1 and City2 identify the locations of the other 8 cities? I think it would.

[edit] I just reread Vorticity's solution. There will be a choice of two points for each of the cities, won't there? But selecting the 3rd city's position arbitrarily from the 2 available choices and drawing 9 more circles should definitively give you the relative locations of all the cities. And my answer is the same as his, darn it! [/edit]

 

[Darat]

My son is studying volumes of solids. All his homework last week and this week is on that subject. In the middle of this evening's homework is this gem:

WTF? My first reaction was ...snip...Who makes up this stuff?

~~ Paul

WTF indeed! Why on earth was the question set using inches?