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#1




What is the correct answer to my daughter's math homework? Third grade.
You can see her homework and answer here.
Regroup 1 hundred for 10 tens: 438 = ____ hundreds ______ tens 8 ones. Write the missing numbers. My daughter answered "4 hundreds" and "3 tens". Is this not right or do I not get this Q at all? Note: Those red checkmarks are how she marks them wrong, not that she checked them and they are right. Last edited by Mahaloth; 02172018 at 11:26 AM. 
#2




maybe she wanted 0 and 43 ?
If you're daughter is wrong, then I am wrong as well. 
#3




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#4




Sorry to be a pain, but we can't solve this one either. My daughter has left it blank after a few attempts.
https://imgur.com/a/KkWnK Last edited by Mahaloth; 02172018 at 11:37 AM. 


#5




Yeah, that's a confusing phrasing. Is there anything from the context of other problems in the homework that could help?
(At least it wasn't this question.) (eta that was for the first questionthe second one seems to reinforce the interpretation that the answer to the first might be 3 and 13.) Last edited by Darren Garrison; 02172018 at 11:44 AM. 
#6




My friend from facebook, an accountant, has said this:
#17: " 3 and 13. Normally [little Mahaloth] would be right saying 4 and 3 but you are regrouping 1 of the hundreds for 10 more tens, which gives you 3 and 13." #28: " There might be multiple solutions for this one, but right of the top of my head use $3.49 and $1.57. When you subtract 1.57 from 3.49 you have to trade (regroup) one of the dollars for 10 dimes. Basically the regrouping happens when subtracting the dime position. The answer would then be $1.92." I think she has it, right? 
#7




I could not say why the questions are phrased in that manner, but the subject does indeed seem to be subtraction and the reference to money is a bit of a red herring, so she just needs to make up an exercise like $4.57  $3.91

#8




4 hundreds and 3 10s is just a grouping, not a regrouping. But it says to regroup one of our hundreds into 10 tens, so that leaves 3 hundreds and 13 tens.
The second one is the same idea: If you have some number of dollar bills, dimes, and other coins, there are some amounts of money you can't subtract from that. But if you trade in one of those dollars for ten dimes, then maybe you can now do the subtraction. The question is looking for such an example. 
#9




How does she mark them right or wrong if she is not absolutely sure what the answer is?
[ETA little Mahaloth would make her Mahalath (as in daughter of Ishmael)?] Last edited by DPRK; 02172018 at 12:04 PM. 


#10




The question, as worded, is incomprehensible. That said, 4 and 3 are the only possible answers. I say this ex cathedra.

#11




A test that serves as a test on how to take tests is poorly written.
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#12




The obvious critical analysis is that the author of the module wanted to avoid a page full of identicallooking arithmetic exercises, and therefore tried to mix it up with some word problems. Maybe it is not such a bad idea to force the student to think (though Darren Garrison's example seems rather perverse).

#13




Who said the teacher does not know? I'm sure the teacher knows.

#14




That is a shocking piece of questions writing.
I'd get your daughter to put a big red line cross through the whole question and write in green pen "incomprehensible question setting, 0/10 please see me!"
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#15




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I can see an interpretation of this leading to 0 and 43. Also 1 and 33. This test serves no function, apart from an early lesson that the world is full of idiots who cannot clearly express ideas, and that you're going to have to get used to that. 
#16




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Oh, and the question that Darren Garrison linked is also a perfectly good question, to which the correct answer is "I don't know", or "not enough information", or the like. Any attempt at a mathematical answer shows the teacher that the student doesn't understand the math being taught, and that's a really important thing for the teacher to know. 
#17




Or you're regrouping 1 hundred for 10 tens, and doing it four times.
When I first read the OP, I took "regroup 1 hundred for 10 tens" to be describing an equivalence. One dollar is equivalent to ten dimes, regroup 1 foot for 12 inches, that sort of thing; handy conversions to know under the right circumstances. My first thought was 0 hundreds and 43 tens. Once I parsed the question a little bit more, taking "regroup..." as a specific instruction, I figured out what the teacher was probably after. To me, having not sat in this teacher's classroom all term, it's rather poorly worded. Oddly, "0 and 43" would probably work in any situation where "3 and 13" would be useful. Suppose you're subtracting 438  80; regroup into 0 hundreds and 43 tens, subtract 8 tens and get 35 tens, regroup back to 3 hundreds and 5 tens. 
#18




I’m guessing 0 hundreds, 43 tens, 8 ones. I think it’s confusing that a space was given for the 100s, but I guess the kids were suppose to see the 100s can be regrouped as 10s. I think a 2 step problem would’ve been clearer. First rename with 100s, 10s, and 1s and then rename with just 10s and 1s.

#19




After a few seconds headscratching and a reread, I assumed this was an example of this new common core stuff I've heard about and started thinking outside of the box to quickly arrive at 3/13 which is clearly what they were looking for.
I was always a good testtaker and would have loved tests more like this. 


#20




The wording is not one I’ve encountered before, but I got 3 and 13. The only reason I got this is that’s the only answer I see that makes sense given that the 4 and 3 answer is wrong. Otherwise, I would have glossed over that first part of the question.

#21




Maybe this is a UK/USA thing what the hell is "regrouping" anyway? and why would it be relevant for any maths problem?
It isn't something I've ever come across and my wife is a teacher specialising in maths and she shook her head and couldn't see the point either.
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#22




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#23




I think 3 and 13 is right. And the purpose of it is probably as a setup for big subtraction, ie 438292
3 100's 13 10's 8 1's minus 2 100's 9 10's 2 1's equals 1 100 4 10's 6 1's ie 146 I remember having to do pages of these in primary school  only we did them in columns rather all that wordy crap they like these days, which made it more obviously a sensible maths exercise. I also remember that after a while I started getting bored and started doing groupings like: 1 hundred, 30 tens, 38 ones ..which fit the criteria but have no earthly use for mathematics. Teacher marked me right anyway. Good times!
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I don't think I'm being unreasonable if I suggest that the number of inferences required to extrapolate the cause of Chinese population growth from your hairdresser's experience puts a burden on fundamental logic fair greater than it can reasonably bear.  RNATB Last edited by Aspidistra; 02172018 at 03:43 PM. 
#24




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Code:
52  19  Code:
4 Last edited by pulykamell; 02172018 at 03:52 PM. 


#25




Yeah, most complaints about "new math" are from people who never knew anything other than new math.
Novelty Bobble, if you don't do regrouping, how do you do subtraction? 
#26




what does that mean?
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#27




I learned subtraction in the same way pulykamell describes, but never have heard the term "regrouping" to describe it, and didn't jump to that association until pulykamell's post. I don't remember the term that was usedprobably "borrow." (Is there a different term than "carry" for adding numbers to the next column in multiplication, or is that more universal?)

#28




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(but then as I said, this may be specific to the USA educational system and not the UK one. Lord knows I see enough of my wife's mandated mathematical tickbox teaching methods here that make me roll my eyes so I'm not about to heap criticism elsewhere. If it works for your kids then great) How old are third grade kids in the USA anyway?
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#29




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And I've never heard anyone use any word except "carry" for adding a value to the next placevalue over in addition and multiplication. It's even what computer hardware designers and assembly language programmers use, with the bit to indicate integer overflow typically called the "carry bit". But we all know that if the adults have forgotten something, it must be new and innovative and, therefore, something to thunder against.
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#30




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#31




Parents are unhappy with new math because they cant understand their children’s homework, the intent of the new math is to give people the tools to learn math that they don't know through rote memorization.
Regrouping is another term for carrying or borrowing. In this case they give your a (value) (place) to carry to a (value) (place) So regroup 1 hundred or 100 to 10 tens So 3 and 13 would be the answer. 438 100  338 pull off the 3 as your first answer and then: 38 +100 (10 x 10 or 10 tens)  138 Pull off the 8 and you are left with 13 which is the second answer in the question from the OP. This is actually a very important skill in math and should help people understand why they are doing operations vs just memorizing how to do them. Last edited by rat avatar; 02172018 at 05:12 PM. 
#32




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#33




What the makers of that question (and similar ones) are saying is the the methods that most of us learned in school and called "borrowing" and "carrying" can be thought of as regrouping the numbers in the columns. So consider the following example:
Addition: 56869213 22829438 ________ 79698651 You can think of this (as you learned to do) as 3 and 8 summing to 11 and the 1 being carried over to the next column, which makes it the sum equal 5 instead of 4, and then 9 and 9 summing to 18 and the 1 being carried over to the next column, which makes it the sum equal 9 instead of 8. and then 8 and 8 summing to 16 and the 1 being carried over to the next column, which makes it the sum equal 9 instead of 8. Or you can think of 3 and 8 ones equaling 11 ones, which are regrouped to 1 ten and 1 one, and then 9 and 9 thousands equaling 18 thousands, which are regrouped to 1 ten thousand and 8 thousands, and then 8 and 8 hundred thousands equaling 16 hundred thousands, which are regrouped to 1 million and 6 hundred thousands. The same is true of subtraction, where you can think of borrowing as regrouping. As long as you learn to do the arithmetic correctly, who cares what you call it? 
#34




The question is presumably asking the student to rewrite 430 = 4 * 100 + 3 * 10 as 3 * 100 + (10 + 3) * 10, though it's expressed in an needlessly awkward way.
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#35




This is a chapter test, by the way. She was given it marked and told to redo the Q's missed.
Thing is, we check her homework and help her with it. I haven't seen anything like problem 17 or 28 on it. It's like the test comes from a different workbook/source than the HW has come from. And I am a teacher, so I know about these kinds of things at least a little bit. Anyway, we got 17. Am I right, then, that any subtraction problem will work for #28 as long as we make the subtrahend smaller than the minuend? Assuming we know enough to use all 6 assigned digits. 
#36




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When my kids were in school I ran into several things like this. The lingo may have changed from what I was taught, but if the teacher is on the ball, they were talking about "regrouping" for a few lectures before the chapter test came around. One teacher let me borrow the teacher's guide and I was quite intrigued by the multiple ways they teach children to solve arithmetic these daysit seems to have a more practical feel. They teach arithmetic from multiple problem solving angles. They are doing things like estimating, as a means of doing a quick sanity check once the real answer has been worked out. We never did such useful things when we were kids. If anything, the real challenge my kids faced was that they would offer too many ways to do, say, multiplication, and that would overwhelm the kids. Sometimes it's nice to be told one single rigid recipe to follow for a particular problem. 
#37




I'm shocked that this is a question for a 3rd grader. When did kids start learning this level of math that early?
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#38




Elementary school math specialist here (US). So I've taught third grade math for about 15 years, and worked with third (and second and fourth...) grade teachers who teach this stuff as well. Before that I taight second grade fo ten years. So that's 25 years of teaching subtraction (and addition) strategies and algorithms.
I also have taught math methods on the college level. And I have worked on a ton of textbooks, many of them math textbooks for grades 24. So I have my finger in a lot of edcational pies. So to speak. Yes, the correct answer, as many people have surmised, is 3 hundreds 13 tens. You are being asked to take 1 of the hundreds and essentially "break" it into 10 tens: 100 is equal to 10 tens or 10 x 10, so you are not changing the value by taking this step. Why take the step? As many again have pointed out, this enables you to use the standard US algorithm to subtract. If you wanted to solve 438  164, you'd need more tens in the top number and you'd get them by changing 4 hundreds 3 tens to 3 hundreds 13 tens. So understanding that 4 hundreds 3 tens is equal to 3 hundreds 13 tens is an importsnt prerequisite for actually carrying out (and understanding!) the procedure. A couple of points: 1) The use of the word "regroup" is absolutely standard in US textbooks these days (and has been for a while) to describe the process above. There are a few holdouts, I'm suremaybe Saxon still relies on older terminology, maybe Kumon, maybe a couple of others, but every program I've worked on for quite some time uses "regroup." 2) We used to use "borrow" and "carry," yes, and some people still do: I have a couple of teachers who have a very hard time not using these words. BUT: 2a) The term "borrow" is inexact and misleading. "Borrow" implies "giving back eventually" and in the standard algorithm you never give it back. This confuses more kids than you might think. 2b) Both "borrow" and "carry" mask what's really going on in the algorithm. You do not take a "1" from the hundreds. You are taking 100 from the hundreds. You do not "carry the 1" from the ones to the tens place when you are adding; you are taking ten ones and making them a ten. It is a subtle difference, but it does matter. As an example: If you are simply "carrying a 1" from the ones place there is no particular reason why you should "carry" it to the tens place instead of to the hundreds, or even the thousands, except that the teacher says you do it this way. That encourages rote learning and taking what's said on faith. If you "regroup" ten ones as a ten, then it's obvious (if you understand place value at all) where they go. 3) Regardless of whether people in their thirties, or fities, or seventies find this question confusing, I assure you it should not be confusing to a US third grader. We've had threads like this before and this is the most important takeaway. I'll repeat it: Just because you don't understand the question does not imply that a kid can't possibly understand it. The reason is that (ideally), kids have seen a dozen problems like this one before they are tested on it. They have (ideally) used the term "regrouping" for weeks or even months before being asked to be responsible for it on a test. Because this is how the material (should have been) taught. What a sixtyfiveyearold remembers from elementary school has no bearing on the subject. 3a) Unfortunately, the ideal is not always the real. I do not intend to imply that the OP's daughter has paid no attention in class (though I will say that kids who are very strong in math do forget things or misinterpret things or DON'T BOTHER TO READ THE DIRECTIONS). It's quite possible that the teacher DIDN'T prepare the kids well enough for the question, DIDN'T use the vocab consistently, DIDN'T make the directions as clear as possible. So it's reasonable to wonder whether the kids were adequately prepped for this question, especially given the OP's later comments. And I suppose it's conceivable that the school is using one of the increasingly rare programs that doesn't talk about regrouping, in which case the question is unfair. But there is nothing inherently wrong or unfair about the questionit is completely standard in form and concept as well as in vocabulary for American third graders, TLR 3 hundreds 13 tens. According to the conventions of American school mathematics, this is unambiguous, and should be answerable by pretty much any well prepared third grader. 
#39




Chefguy, when did you learn subtraction? It doesn't seem very advanced to me.
And Mahaloth, I interpreted the instructions for that second problem as meaning "use only these digits", not "use all of these digits". It's a bit of a silly extra requirement, but I think it might be meant to prevent the student from just reusing one of the example problems, or making a slight tweak to one of them. 


#40




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ETA: Oh, sorry, I didn't realize this has already been answered. But my interpretation was to use all of the digits. Last edited by pulykamell; 02172018 at 10:11 PM. 
#41




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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 rubberbanded 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 pretaught algorithm): These sorts of poorlyworded questions accompany some sort of procedure taught during a class. The teacher will have used the terminology over and over again in a bestcase scenario, so the student should simply be reapplying the same procedure demonstrated in the classroom. Of course, if that procedure isn't reflected in her takehome 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. 
#42




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She does pretty well, actually. Neither my wife and I are mathlovers. 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. Quote:
Other parents are complaining too that their kids got the last one(#28) wrong as well after doing pretty good up to the test. I personally find both questions hard to parse. 
#43




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 middleoftheroad school; the math curriculum never got beyond arithmetic (no algebra whatsoever was offered at the time. No idea if they do so now.)

#44




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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. Does that make sense? 


#45




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.

#46




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#47




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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.
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#48




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.

#49




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#50




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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. 
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