Yes, an intriguing problem…isn’t it?

At least we can take comfort in the fact that the problem is from a recreational math book and not a high school text book. Our children are still safe from this particular abomination.

I think it’s an orange of the variety they feed to lions in the Scottish Highlands, commonly known as a “MacGuffin”.

See, I’m not so sure we should be so quick to heap scorn upon this particular problem. If we were able to talk to its author, I’m quite certain that he/she would laugh at the idea that he/she intended it to be reflective of a “real-world” situation. It is merely a mathematical puzzle. It is also kind of silly. I don’t think the silliness takes away from the puzzle.

I agree with Z. Shiner, in that it would be more deserving of our scorn if it were a textbook’s attempt at “real-world” relevance. (I’m still resisting simply sending Dan a copy of the Geometry textbook my school is using…)

I find myself agreeing with both views in the comments. First of all, what a silly math problem. As if (Wayne’s World) anyone is going to have a burning desire to relate to this because of the guy, his favorite orange, or it’s eventual absurd weight.

But then I see the other point of view, and I find myself agreeing more strongly with this one. It’s just a puzzle, put into words about an orange and an obviously weird guy. But so what? When I see the problem I immediately see the unique word structure, the puzzle, and I want to solve it. However, that’s me. I do KenKen and Sudoku.

Which brings me to my resolution. It’s a horrible problem and a great problem. It’s horrible for the kids in my lower level classes who struggle, who we are trying to get to see that the angry wolverine isn’t so bad. It won’t capture their attention any more than two boats in a river will.

But it’s a great warm up for my algebra 2 kids. They’ll argue and come up with different ways to solve it, and they’ll laugh about a nine pound orange, and it will kick start my class in a positive way, and two hours later at lunch they’ll still be joking about it. Ain’t nothing wrong with all that.

I agree completely with #8 and #9. With the right “story” or funny presentation (I know some teachers who could pull this off, and some who couldn’t), and with the knowledge that students could solve it, this could be fun. Of course, why not pick an object that actually weighs 9 lb, and not tell them what it is, and have some more problems to guess its identity? Volume, surface area, molecular structure, etc.

I agree with Matt E: the problem is not intended to be a real world application. I interpret its intent to provoke an exploration into recursion without jumping right into jargon and notation.

Also, I believe this is a traditional style of problem carried down from ancient mathematicians. Without modern notation or structure, they relied upon carefully worded riddles.

So is this really in the same category as the Dog’s bandana?

I’m sorry — I think this problem is ridiculous. And stupid. And a waste of time — for the teacher to assign it; for the students to solve it. For the ink and paper that was wasted. A tree died for that problem…. (just sayin’)

I think what’s interesting here has nothing to do with oranges and probably putting it in a phony real-world context is likely to hide what I personally notice about the computation (yes, Virginia, we radical constructivist types DO like computation. . . just not for the sake of computation and deadening little minds). So I see no point in putting in giant rotting oranges or anything of the kind.

What I like is not seeing it algebraically, but simply as the fact that if 9/10ths of something + a given quantity equals the whole, then 10 times that given quantity must be the whole, since what was “missing” is 1/10th of the whole.

Doing this as mental arithmetic with of course the right initial observation seems particularly useful. Writing out the equation seems less sweet to me, personally, particularly if this shows up on some sort of timed test. Coming as I do out of the pre-calculator era, particularly the era before calculators were allowed on the SAT and ACT and the like, mental math and estimation are my by-words, along with process of elimination.

Big oranges are nice, but not here. And frankly, if you have a favorite orange. . .

While I agree that this is definitely pseudocontext, I think that the location of the problem at least partially excuses its unrealistic premise. I assume that someone who buys a book of mathematical brainteasers and puzzles has a different outlook on mathematics than a student who is being required to learn new mathematical concepts. I think that the type of person who solves problems from the book this problem is from wouldn’t mind the unrealistic nature of the problem as he would have an appreciation for mathematics beyond its applicability to real world situations. Would I give this puzzle to a student as an introduction to writing word problems as mathematical equations? No. Would I give this problem to a colleague as a challenge? Maybe.

I believe pseudocontext is a bad tool for teaching, but not necessarily a dark mark on all of mathematics. Remember, the Fibonacci Sequence was first derived by a very pseudocontextual problem involving rabbits mating on a monthly basis.

This reminds me of puzzle books I loved as a kid — they had mazes and logic puzzles and tricks with words and punctuation, and occasionally a light math problem like this. I think I like “my favorite orange” because it’s a good puzzle-book math problem, not necessarily because it’s a good math class math problem.

That said, I’ve got to appreciate that the word use is very economical and that there’s some dry humor to it. I imagine this as a problem in the style of my high school physics teacher, who would have us calculate the speed of (his favorite?) velociraptors chasing people.

To explain my earlier comment, the term “MacGuffin” was used by film director Alfred Hitchcock to refer to a plot element that is pivotal as the goal motivating the characters, but the particulars of which are of no importance to the plot. The audience does not need to know what the MacGuffin is to comprehend the plot or enjoy the film. It is characteristic of a MacGuffin that it could be replaced by something else without significantly altering the plot of the film.

Like the MacGuffin in a Hitchcock film, the orange in this problem could be replaced by an apple or an automobile or anything else without changing the mathematical solution. That is typical of math problems which are intended to test specific math skills. The “real-world” context in which the problem is framed is not really important because the math does not depend on it.

correction: […IN just one trip?]

My son (h.s. sophomore, in 2nd year algebra) mentioned to me apropos of his homework (and with no mention by me of My Favorite Orange or pseudocontextual problems) that he hates problems where you would never actually do the math to find the answer, e.g., your store receives 14 containers of eggs. If each container has 12 cartons of eggs and each carton holds 12 eggs, how many eggs did you receive? He said, “Wouldn’t you just check your order? Wouldn’t you probably KNOW how many eggs you needed when you placed your order?”

While the specifics he mentioned may not be exactly right, the general notion he had was dead on: blah, blah, blah. . . so what is Juan’s salary? Why not ask Juan?