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.
They’re trying to get students to think, not be human calculators.
I think 3 and 13 is right. And the purpose of it is probably as a setup for big subtraction, ie 438-292
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!
“Regrouping” has been something I grew up with in the 80s in the context of subtraction. For example, when I was taught how to do the following problem:
52
- 19
-----
You were taught that you couldn’t take 9 from 2, so you borrowed a ten from the tens place, regroup (so the 5 becomes a 4 and the 2 becomes a 12]:
4
[del]5[/del][sup]1[/sup]2
- 19
----
33
And here it is set to song by Tom Lehrer, the same sort of complaints back in the 50s (or whenever this was). The song itself starts at 1:18, but that’s exactly the way everybody I know does subtraction. I have no idea what this “old method” he outlined in the beginning was. “Three from two is nine” WTF is that?! Three from two is negative one. (Yes, yes, I can figure out how it works, but it makes no sense the way I was taught.) Also note that the complaint back then was “in the new approach, as you know, the important thing is to understand what you’re doing, rather than to get the right answer.” So same old bullshit complaints back then as now.
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?
what does that mean?
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 used–probably “borrow.” (Is there a different term than “carry” for adding numbers to the next column in multiplication, or is that more universal?)
just as pulykamell said, you borrow one from the next column as required. Never came across the concept or term “regrouping” though and the question as stated is not placed in the context of any type of sum at all so I don’t see how it helps. Unless it is just an exercise in getting the the kids to see that the “one” they borrow has a specific value in which case…it still reads like a crap question, more likely to annoy than enlighten.
(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 tick-box 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?
I learned “borrow” as well, and I turn 34 this year, which might bracket it.
And I’ve never heard anyone use any word except “carry” for adding a value to the next place-value 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.
Maybe you’re unfamiliar with the word regrouping. I think it’s reasonable to assume that the kids in this class have been taught what “regrouping” means.
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.
338
pull off the 3 as your first answer and then:
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.
Well, we did use the word “borrow,” (I use it in my explanation) but I also recall “regroup” being thrown in there as well, just as it is in the Tom Lehrer song. That said, it’s possible that I’m conflating the song (since I’ve been familiar with it since about 6th grade) with how I was taught to subtract.
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?
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.
Right. The point is that unlike most problems of the same vague shape, that question is not asking you to add the two numbers 26 and 10 that appear in it. There’s an annoying tendency among even undergrads to treat math problems as pattern-matching rather than actually understanding the material; this question is about that.
This is a chapter test, by the way. She was given it marked and told to re-do 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.
This.
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 days–it 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.
I’m shocked that this is a question for a 3rd grader. When did kids start learning this level of math that early?
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 2-4. 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:
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 sure–maybe 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.”
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.
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 question–it is completely standard in form and concept as well as in vocabulary for American third graders,
TL:DR 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.
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 re-using one of the example problems, or making a slight tweak to one of them.
$5.39 - $1.74? You can’t take 7 from 3, so you have to trade one dollar for ten dimes to get 13-7. (Other answers are possible.)
ETA: Oh, sorry, I didn’t realize this has already been answered. But my interpretation was to use all of the digits.