HUH??? I don’t think they ever tried to teach estimation when I was in school. I mean, what is the point when it is easy to figure out the exact answer.
I think I’ll pass this one on to my Dad just to make him simmer. He has a PHD in math and this is going to drive him nuts. 
This reminds me of a section of a Richard Fenyman book where he talks about a stint he did on the school book committee. Fenyman goes off about how utterly bad the books were. Apparently things haven’t changed.
Slee
Whew, Thanks I figured the solution to be 11/40 then I saw that and said to myself “holy crap I’ve forgoten how to do 7th grade math!”
[heart rate slowly goes back down to normal]
What the crap? When did kids start rounding fractions? When I did fractions, we had none of this rounding. I couldn’t solve that now (Math is NOT my forte), but I do remember hating fractions. No rounding was done!
Sigh.
It’s a typo. (:wally , directed at the athors/editors/publishers) You cannot subtract one positive number from another and get an answer that is GREATER in magnitude.
I quickly estimated 1/4, just like most everybody else.
I then took the 1.625 seconds to convert 3/8 and 1/10 into decimals and perform the subtraction.
The problem with the math problem is that it’s trying to teach kids to round off numbers to a scale that’s wholly inappropriate for the situation. The roundoff error thoroughly swamps the numbers in the problem. I don’t consider this to be good estimating; I consider this to be sloppy.
I prefer: “3/8 is small. 1/10 is much smaller. So subtract a bit from 3/8, and we should get something around 2/8, which is 1/4.” (Which happens to be pretty much how I worked the problem.)
Also, one of the key facets to estimation is this: Since you are introducing inaccuracy, you should try to have your innaccuracies oppose each other, rather than add.
With subtraction, you should try to round both up, or both down, or leave one the same, but not round one up and one down!
Some better esimations might be:
3/8 - 1/8 = 1/4 (error of .025)
or
1/4 - 0 = 1/4 (same)
or perhaps
3/10 - 1/10 = 2/10 (error of .075, getting worse)
3/10 - 0 = 3/10 (also error of .025)
or even
1/2 - 1/4 = 3/8 (.100 error, which is worse)
but not:
1/2 = 0 = 1/2 (.225 error, which is 81%!! [li])[/li]
Aieee! that’l teach me to do basic arithmetic after 9:00 pm. Good thing I have all those engineering calculus and differential equation courses :smack: :o
And my first multiple posting a triple one too…
[slinks away in embarassment…]
I am totally not a math person, so I went to 80ths: 30/80 - 8/80 = 22/80, or 11/40, or about 1/4.
No, the problem is that the context isn’t given, so there is no indication of how accurate an estimate is called for. If all you need is an order-of-magnitude estimate, 1/2 is a “correct” answer. If you need something accurate to 30% or so, you’d know that 3/8=1/2 is not an acceptable estimate, but 1/10=1/8 is acceptable. You’ll end up with 3/8-1/8=1/4.
Approximations and estimations are an important skill, and I’m rather happy to hear that it’s been taught in school.
I got 3/10, but only because I didn’t estimate – I put it in decimals, did the math, then rounded off the answer to the nearest tenth.
Perhaps the problem is being used to show why you’ve got to be flexible when estimating. In that case, it’s a good example: obviously, holding too strictly to the “round to the nearest half” rule gives stupid results some times.
If it’s not being used for that purpose, it’s an idiotic question, above all likely to make students conclude that math doesn’t make any sense.
Daniel
Absolutely. This example may seem trivial but as you step up in level the simple process becomes far more useful and important.
E.g. 12 47/83 * 3 19/131 = ?
Solving this precisely (~39.5) will take a number of calculations but by estimating, even to the nearest 1/2, the child can gain a quick and accurate approximation (~37.5).
====
Also a math major and on the subject of usefulness, I’ll go with the logic and proofs in geometry class as the best thing to learn (“especially if you’re going to post on internet msg boards”)
3/8 minus 1/10 = approx. 1/4 makes sense.
3/8 PLUS 1/10 = approx. 1/2 makes sense.
3/8 (which is already less than 1/2) minus 1/10 (which makes it smaller yet) = approx. 1/2 strikes me as, well, stupid.
I think that everyone agrees that estimation is a useful skill, (although it pales in comparison to ccwaterback’s cross-multiplying and solving for x) but the application of it in this case renders it meaningless. It teaches kids to use the rules no matter how stupid the result. I’d rather my daughter used her brain.
By that logic, 3/8 - 1/8 = 1/2, right? Round up the 3/8, round down the 1/8, you have your answer.
This also promotes the outrageously stupid and dangerous idea of rounding the inputs to an operation rather than the result. Too many times I’ve seen 1.4 rounded off to 1 before being multiplied by 1000. You CAN do this, but you have to be very careful about it or your answer is worthless.
The right way to estimate this is to replace the 1/10 with 1/8 and do the normal math. It requires thought and consideration to do it right, not a rote method. ugh.
What answer did Paris Hilton come up with?
She told me she loved me like a brother. She was from Arkansas, hence the Joy!
I don’t get this “estimating” thing at all. Why take 5 seconds to estimate when you can take 5 seconds to come up with the correct answer? In either case, you have to me up with a common denominator.
Why are we teaching our children to accept the incorrect answer?
PS - this has bugged the hell out of me at home, much to my daughters chagrin. I told her to screw the estimating and get the correct answer, and tell the teacher she won’t settle for doing things half-assed. She snuck off to estimate somewhere I couldn’t see her. Poor girl…
where did my “co” go? That’s “come up with a common denominator”…
Maybe I should work on my seventh-grade spelling?
Beelzebubba, I think there ARE times that estimating is useful. Perhaps I know that I’ve got $2,000 in the bank, and I want to put hardwood floor down in two rooms in my house, at $3.50 a square foot. One room is 18’ x 15’; the other is 14’ by 14’. If I round all the dimension off to 15, I get twice fifteen squared times $3.50, an easy problem to solve: twice $3.50 is $7, and $7 times 225 is a little over 1500. I know, therefore, that I easily have enough money in the bank to put down the hardwood, and can go ahead and work further on researching the project. (For those playing at home, “a little over $1500” equals $1631).
And this wasn’t a great example: what if the rooms were actually
15’ 3.75" by 17’ 9" or something like that?
Obviously, you can use a calculator in cases like this – but in real life, you don’t always have a calculator handy, and being able to estimate makes it much easier to do figures in your head.
Thing is, you gotta do it smart: you gotta realize that if you get a stupid result (as you do in the OP’s example), you’re doing something wrong. You should never discover that 2+2=5 for large values of 2.
Daniel
I have a couple mathematics degrees, FWIW.
Personally, I like the problem. Although, I hope that they’re also teaching a technique to get the answer correct.
That kind of mathematical thinking is probably going to serve you better than being able to calculate it to 11/40 (especially if you have to do that in your head, and invariably go through more work to come up with something like Trupa’s 9/40 – an easy mistake), or knowing logic and proofs.
However, I don’t like their answer. For so many tasks that require estimation-- housework, time management, gas, money, etc. – we can get by estimating things to the nearest quarter, and you should keep in mind that 3/8 is a little above a quarter, and you’re subtracting a small postive quantity from it. But if a kid answered 1/2 I wouldn’t rake him over the coals for it. I’d rather have him show up with too much cake than too little cake.
Maybe, but it seems to me we’re teaching the kids “Here’s the correct way to do it, but that’s hard. So we’re going to show you this shortcut that might get you in the general vicinity of the right answer.”
This is an academic setting - we have the time to teach them how to come up with the correct answer. If you know how to do it correctly, you can figure out estimating on your own pretty successfully.