I’m not quite sure what the appropriate forum for this is. It’s kind of a poll. Feel free to move it as needed.
My daughter’s 7th grade math book poses the following problem:
Using estimation , what is 3/8 - 1/10?
Ready for the answer?
[spoiler]1/2
Their reasoning: 3/8 should be rounded up to 1/2. 1/10 should be rounded down to 0. 1/2 - 0 = 1/2.[/spoiler]
I’m not sure what useful skill this is supposed to teach but I’m pretty sure my daughter doesn’t need it.
What book are you using? That makes no sense whatsoever.
Why estimate it when it can be solved in about three seconds? Ten seconds if you have to use pencil and paper. This is seventh grade? I don’t remember for sure when I learned to add and subtract fractions, but I know it was way before seventh grade. How ridiculous.
Oh, and my “estimate” would have been 1/4. Figuring that subtracting a small amount off 3/8 would have got it somewhere in that neighborhood.
Yeah, since the answer is a lot closer to 1/4 (.275) than 1/2. :dubious:
I saw an independent review of several math books for students that age, and they were all rated horrible at best.
My daughter thinks the name of it is “Mathematics Today”. She doesn’t have it with her tonight. If it turns out to be something else, I’ll let you know.
I’ve been simmering over this for several days. My wife thinks that I need to let it go. I remain righteously incredulous.
Help me understand you better,** KRM**, what is it about this problem that bugs you so? Do you feel it is:
-too easy / below 7th grade level
-too hard / above 7th grade level
-bad because the answer is way off?
-a complete waste of time (estimating, that is) since she should have been able to solve it accurately in 10 seconds in grade 5? (my own reaction, in case it didn’t come accross…)
Grade 7, hmmm, shouldn’t they be starting single variable basic algebra by then?
If you feel that all this emphasis on estimating is a waste, pehaps you can make it a game with her to "reverse-engineer"the question by:
-figuring out the exact answer
-rounding out to a simpler fraction, eg in your problem:
3 - 1
8 10
common denominator:
15 - 4 = 9
40 40 40
9/40 is almost 10/40 which is 1/4, so say 1/4 as your “approximation”
But I’m not sure where you’re coming from on this, so I may be way off base… 
Help me understand you better,** KRM**, what is it about this problem that bugs you so? Do you feel it is:
-too easy / below 7th grade level
-too hard / above 7th grade level
-bad because the answer is way off?
-a complete waste of time (estimating, that is) since she should have been able to solve it accurately in 10 seconds in grade 5? (my own reaction, in case it didn’t come accross…)
Grade 7, hmmm, shouldn’t they be starting single variable basic algebra by then?
If you feel that all this emphasis on estimating is a waste, pehaps you can make it a game with her to "reverse-engineer"the question by:
-figuring out the exact answer
-rounding out to a simpler fraction, eg in your problem:
3 - 1
8 10
common denominator:
15 - 4 = 9
40 40 40
9/40 is almost 10/40 which is 1/4, so say 1/4 as your “approximation”
But I’m not sure where you’re coming from on this, so I may be way off base…
Help me understand you better,** KRM**, what is it about this problem that bugs you so? Do you feel it is:
-too easy / below 7th grade level
-too hard / above 7th grade level
-bad because the answer is way off?
-a complete waste of time (estimating, that is) since she should have been able to solve it accurately in 10 seconds in grade 5? (my own reaction, in case it didn’t come accross…)
Grade 7, hmmm, shouldn’t they be starting single variable basic algebra by then?
If you feel that all this emphasis on estimating is a waste, pehaps you can make it a game with her to "reverse-engineer"the question by:
-figuring out the exact answer
-rounding out to a simpler fraction, eg in your problem:
3 - 1
8 10
common denominator:
15 - 4 = 9
40 40 40
9/40 is almost 10/40 which is 1/4, so say 1/4 as your “approximation”
But I’m not sure where you’re coming from on this, so I may be way off base…
Trupa, three times you are wrong. 15 - 4 is 11, not 9.
Trupa, three times you are wrong. 15 - 4 is 11, not 9.
Trupa, three times you are wrong. 15 - 4 is 11, not 9.
I think the “method” they are trying to teach here is OK, it’s just a very poor example.
Perhaps a better example would be:
Using estimation what is 99 / 4?
Answer: 25.
I’ll take a guess that they’re trying to teach the kids to estimate and they’ve given them a very strict definition of “estimation” for this section, something like “to estimate means to round off to the nearest one-half.” And so they would stress using estimation in the problem’s phrasing; the kids aren’t estimating the way those of us who’ve gone through all our high school and college math courses would, but instead practicing this one specific skill.
Personally, I’ll give the kids the benefit of the doubt to recognize that 3/8 != 1/10, and think they’re probably getting the point here. (Isn’t “!=” the board’s convention for “does not equal”?)
I recall when I was in third grade and we were introduced to the concept of the equation; apparently someone decided the word “equation” was big and scary, and so they called it a “number sentence” because it works like a sentence constructed of words. I got what a number sentence was, and it was useful to have that concept in my mind as I learned some of the higher stuff we moved on to later, even though I never used it again.
Of course, I could be wrong, and the creators of the textbook could be total idiots. But that’s my guess.
The issue is that the answer given for the an estimate between the difference in two numbers is greater than either number. It’s clearly ridiculous.
!= is standard for “not equals”, and comes from several programming languages.
[soap box]
I think the number one most important thing for people to learn in math is ratios.
(I was a math major, statistics emphasis).
Using ratios pops up over, and over, and over again in practical applications.
If 27 things weigh 32 units, how much does 11 things weigh?
27 / 32 = 11 / x
27x = (32 * 11)
x = (32 * 11) / 27
If a car gets 21mpg and a gallon weighs 7.6 pounds, how far can you travel on 3 pounds?
21 / 7.6 = x / 3
(21 * 3) = 7.6x
x = (21 * 3) / 7.6
Learn this method, it will serve you well.
[/soap box]
I was just curious about the text. I was homeschooled and went through several different math books - I’ve seen some really weird crap.
It seems that in my younger sister’s books, the emphasis on estimation has increased. It used to be a minor topic in mine, but
I see a lot more problems like the one in the OP where the focus is one little aspect that isn’t going to be very useful outside class. Like jackalope said, maybe they were just given a super-strict definition of “estimating.” I just don’t think that is going to help them out much later.
The book’s answer is totally counterintuitive.
All it takes is a glance at the numbers. The first thing to note is that three-eights is clearly less than one-half. The second thing to note is, you’re subtracting something from it. I don’t care what planet you’re from, if you have a number below one-half and you subtract from it, one-half is NOT a good estimate!
For a different spin, if I had to estimate that quickly, I would try this:
Changing the denominator by +/- 1 doesn’t change the value of the fraction by much. So 3/8 - 1/10 becomes 3/9 - 1/9 = 2/9. Which is .222.
I came up with 1/4 too.
I agree totally with ccwater. That was THE most useful thing I learnt in maths.
I also got 1/4.
(Thought process–> 3/8 is 1/8 bigger than 1/4. 1/10 is almost 1/8…ergo 3/8-1/10 ~= 1/4)