This statement shows you don’t know what you are doing when you “borrow” in a subtraction problem. “Borrowing” one from the hundreds column and putting the 1 next to the tens column is “regrouping”, that is, stealing one group of 100 and making it be ten groups of 10, so you can subtract the group of tens in the bottom number from the augmented group of tens in the top number and avoid a negative result.
It’s not shocking you don’t remember this, because we tend to teach it at the start, but then simply turn it into an exercise in following an algorithm for solution without reminding students of why they are doing it. But as a student, this is usually emphasized by using things like various types of sticks to represent units, tens, hundreds, etc. Often, it can be done with popsicle sticks arranged in groups by being rubber-banded together. There are a number of other useful props to get the idea across.
As for the “problems” themselves (they aren’t really problems, but rather questions requiring solution using a pre-taught algorithm):
These sorts of poorly-worded questions accompany some sort of procedure taught during a class. The teacher will have used the terminology over and over again in a best-case scenario, so the student should simply be re-applying the same procedure demonstrated in the classroom. Of course, if that procedure isn’t reflected in her take-home math book, that can create a real problem.
The answer, as deduced elsewhere, is 3 and 13 in the first question. The second question has a number of possible answers I presume; I didn’t look closely to see how many can be used. Clearly, she’s being taught how to “regroup” powers of ten so she can “borrow” in subtraction.
She does pretty well, actually. Neither my wife and I are math-lovers. I was in advanced math as a kid, but only because my parents pushed me. I’m an English teacher now.
She learned “borrowing” in all of the subtraction HW I’ve done with her. Same as I learned as a kid.
I did too, but everyone else seems to think you should use all of them once. My daughter wasn’t sure either way.
Other parents are complaining too that their kids got the last one(#28) wrong as well after doing pretty good up to the test.
Yeah, my recollection was that we were doing multiplication tables at third grade, although now it seems they even start doing multiplication by second grade. I don’t recall being introduced to decimals quite that early, though (which the money problem would require some knowledge of, I think). But this type of subtraction involving regrouping/borrowing would certainly have been covered in second grade. I went to a pretty middle-of-the-road school; the math curriculum never got beyond arithmetic (no algebra whatsoever was offered at the time. No idea if they do so now.)
Not quite. (Though I’m not entirely sure, as this one I do think is poorly worded.)
You need to set it up so that the “tens” digit in the minuend is less than the “tens” digit in the subtrahend. The thrust is that (assuming you use the standard algorithm) that you MUST regroup (there’s that word again) from dollars to dimes. So $9.75 - $4.13 doesn’t qualify because regrouping is not needed: you have enough dimes already (7) to allow you to subtract the specified number (1).
The example given by pulykamell works because you need more dimes to carry out the subtraction. You get them by exchanging one of the dollars for ten dimes.
It did take me about five reads to figure out what I think the question is looking for. What I was wondering somewhat is if an answer like $5.34-$1.79 would be accepted since there is both regrouping a dime into ten pennies and fulfilling the question’s request to regroup a dollar into ten dimes. (Plus there is the ambiguity of whether digits can be reused. I assumed not, as six digits were given, but there’s nothing in the way it is written that definitively requires use of each of the six digits once.) Hopefully, a teacher would accept all variants of the answer due to the ambiguous wording.
Pretty sure he understands exactly what is happening when “borrowing” a 1. The problem is that people who immediately grasp a concept can get confused when the concept is broken down to unnecessarily small steps for them.
exactly, It is and has always been clear to me what is going on when such operations are carried out. The reason being that I was taught addition first and when we did that it was pointed out that adding together a 6 and 5 in the hundreds column means you end up with an extra ten hundreds (i.e. a thousand ) in the thousands column that then had to be included in that calculation. Subtractions merely reverse that thinking but if you’ve already grasped what is happening in addition then subtraction is not a problem.
My grasp of rudimentary maths is fine and I did say that this could well be and USA/UK style thing but I come back to the point that the wording is still crap, the context and point to the question is badly lacking, that’s the real issue. At age 7 or 8 (which I assume this is) I’d have been annoyed by having to piss around with rearranging numbers to no practical end.
The context is lacking for us, because Mahaloth hasn’t given us the context. We haven’t been sitting in his daughter’s classroom with a bunch of example problems exactly like this, and heard the teacher’s explanations of how this is useful in subtraction. And keep in mind that what looks to us like “unnecessary extra steps” probably aren’t unnecessary to the kids who are just starting to learn it.
were these math problems come up with by autistic savants? That one in particular is enraging. “Explain your thinking?” I wasn’t thinking anything until I read that question, and now all I’m thinking is “that’s a stupid question.”
Yes, to me “regroup […] for” is an odd way of expressing the idea. “Regroup […] into” would sound more natural. If it had said “regroup one of the hundreds into ten tens,” I might have grasped what the question wanted me to do. I don’t think British English speakers use “for” in that way. “Exchange x for y”, yes, but “regroup x for y”? No.
And it could have said “in the following equation, regroup <etc.>” rather than just putting a colon and leaving you to work out what the question actually is.
It doesn’t sound natural to this American English speaker. Actually, I was going to make the same point that the phrasing sounds strange.
It would be better if the question were phrased to write the numbers after you had regrouped.
I’ve been helping my third grade girl with her math homework and we’ve had to work on the same idea, although it’s called something different in Chinese.
I personally think that “Brownell’s crutch” which I learned abstracted the distance reality of subtraction and made it far more difficult to be successful in higher math.
The problems it was meant to solve (memorization) are gone in this era of calculators, but algebra, set theory and group theory are becoming a far more common need.
While it may be confusing for someone who learned using the above crutch “for” isn’t wrong from a math perspective.
Decimal is just a set of groups.
If call hundreds x and tens y, you are solving for y.
x/100 = y/10
“into” is commonly used to describe a set of all answer to a function like “f(x) = x^2”
To be sure, there are multiple algorithms for working out a subtraction problem, but what do injections and surjections have to do with it? Those concepts seem relevant to abstract set theory which may appear in New Math or in a course on category theory, but how do they facilitate basic arithmetic?
I tutor kids through a volunteer program. And I’m sure they’ve been taught - but not all of them have learned. The kids who picked up the concept right away are fine. It’s the ones who don’t have a handle on it yet.
In the local school district, they don’t have books, they just have worksheets (and usually just that day’s worksheets. All of the past worksheets have (according to the kids) been taken back by the teacher). So the kid I’m helping has no idea what regrouping is, and I wasn’t taught with the word “regrouping,” so I’m not sure what it means. And so I stare at this problem and guess that they want it to be understood that 438 is 4 hundreds, 3 tens, and 8 ones (which is a concept that needs to be learned - but not the concept that is being emphasized for this particular problem). But I don’t know that because I wasn’t in class with the kid.
For tutoring, I spend a lot of time trying to guess what they were supposed to have been taught “did your teacher use the word _____?” “do you remember any words they did use?” “did they draw a picture on the board?” “were the numbers up and down or sideways?” “did they draw x’s or circles anywhere?” but there’s often not enough information for someone other than the teacher to help. It’s great to have a deeper understanding of the problem and multiple methods of solving it, but there needs to be more.
So, my daughter told me they did discuss/learn this in class. However, none of the classwork has been graded and sent home, so we had not seen it at home. All HW we saw and assisted with did not do this. They borrowed, but re-grouping was not part of it.
Still, the teacher was not pulling this out of nowhere. But it was not practiced enough for a test in our opinion.
Think of it the other way, the problem that is targeted is not basic arithmetic but barriers to learning higher math.
Overloading terms that students will need to unlearn in the future. There is no reason to avoid the more accurate terms except that parents, who were limited by learning under the old method can’t intuitively understand it, because they learned under the old model.
