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  #51  
Old 02-18-2018, 07:59 AM
TokyoBayer TokyoBayer is offline
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Originally Posted by Ximenean View Post
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.
  #52  
Old 02-18-2018, 08:41 AM
Chefguy Chefguy is online now
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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.
Perhaps it's the method that's changed, or the terms or something. The 3rd grade for me was a very long time ago.
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  #53  
Old 02-18-2018, 02:36 PM
rat avatar rat avatar is offline
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Some people may find this history interesting, although it doesn't seem to be recent enough to cover the methods used in common core.

It appears that "Brownell’s crutch" which is a name given for the "borrow" or "carry" method markings that most of us older Americans remember.

Quote:
It is interesting to note how quickly and thoroughly
Brownell’s crutch, used in the decomposition algorithm,
became the primary algorithm used for subtraction. This
could possibly be because of the ease with which the crutch
could be modeled using manipulatives, or because of the
decreased emphasis on memorization. It is not clear why
the crutch caught on so quickly. Almost every textbook
seen after his report used the altered decomposition algorithm.
The equal additions algorithm and the Austrian
algorithm all but disappeared from textbooks.
http://math.coe.uga.edu/tme/issues/v08n1/1ross.pdf


The images on this page will make regroup make more sense.

https://www.homeschoolmath.net/teach...g_addition.php

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"

Quote:
adjective
Mathematics:
pertaining to a function or map from one set to another set, the range of which is a proper subset of the second set, as the function f, from the set of all integers into the set of all perfect squares where f (x) = x 2 for every integer.


You solve for x to get a value.
You solve into f(x) to get a set.

This is not absolute or universal but just another way of thinking about it.

Last edited by rat avatar; 02-18-2018 at 02:37 PM.
  #54  
Old 02-18-2018, 02:55 PM
rat avatar rat avatar is offline
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To clarify a bit more on my last post.

"onto" is "surjection"
"into" or "one-to-one" is "injection"

https://en.wikipedia.org/wiki/Biject...and_surjection

IMHO it is far better to not overload terms when learning arithmetic if possible.

Last edited by rat avatar; 02-18-2018 at 02:56 PM.
  #55  
Old 02-18-2018, 05:15 PM
simster simster is offline
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Well, thanks to this thread I learned something this weekend - thanks.

I saw 're-group' and simply thought they wanted to know how many 'groups' of each kind there was - never dawned on me it was a subtraction question.
  #56  
Old 02-18-2018, 05:27 PM
DPRK DPRK is offline
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Originally Posted by rat avatar View Post
To clarify a bit more on my last post.

"onto" is "surjection"
"into" or "one-to-one" is "injection"

https://en.wikipedia.org/wiki/Biject...and_surjection

IMHO it is far better to not overload terms when learning arithmetic if possible.
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?
  #57  
Old 02-18-2018, 05:51 PM
amarinth amarinth is offline
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Originally Posted by Thudlow Boink View Post
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.
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.
  #58  
Old 02-18-2018, 07:15 PM
Mahaloth Mahaloth is offline
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Update:

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.
  #59  
Old 02-19-2018, 02:15 PM
Dains Dains is offline
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Originally Posted by Mahaloth View Post
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 check-marks are how she marks them wrong, not that she checked them and they are right.
Better instructions:

Write the missing numbers after regrouping 1 of the hundreds into 10 tens:

438 = ____ hundreds ______ tens 8 ones.

Even I can do that now
  #60  
Old 02-19-2018, 03:12 PM
rat avatar rat avatar is offline
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Originally Posted by DPRK View Post
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?
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.
  #61  
Old 02-19-2018, 08:55 PM
Leo Bloom Leo Bloom is online now
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Fascinating thread. I too never heard the word regrouping, and thus skipped the intro to the question and got what OP daughter had; and the cavils on "borrowing" and "carrying" are amusing actually, as if they were problems in machine learning and semantics.

But of course with the concept as explained is perfectly clear and does flesh out what us older folks did, and its virtue, (over my dim distant education, perhaps) is nicely summarized by Ulf in #38.

The kids see "regroup" and it makes sense. Hell, I saw it, and I started puzzling on the set theory as part of 12-tone music theory.

Tell me, I've always heard the expression, including in this thread: is this an example of New Math? I realize it's a huge topic and don't want to go off-thread.

Last edited by Leo Bloom; 02-19-2018 at 08:59 PM.
  #62  
Old 02-19-2018, 09:13 PM
Leo Bloom Leo Bloom is online now
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Originally Posted by rat avatar View Post
Some people may find this history interesting, although it doesn't seem to be recent enough to cover the methods used in common core.

It appears that "Brownell’s crutch" which is a name given for the "borrow" or "carry" method markings that most of us older Americans remember.



....

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.

....
Brilliant cite on history of concepts of subtraction. Makes this thread make more sense. Also we can throw in "renaming" for the whole shebang of carrying/grouping/re-contextualizing numerals in different orders.

If I asked nice, could you tell me what you're getting at with "distance reality?"

FWIW, now, following your comment on Brownell's crutch, I have a handy excuse for why I suck at math.
  #63  
Old 02-19-2018, 09:56 PM
Chronos Chronos is offline
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"New Math" is what kids were taught starting in the 70s. In other words, unless you're a lot older than I think you are, it's what you call just "math".
  #64  
Old 02-19-2018, 10:01 PM
Leo Bloom Leo Bloom is online now
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If I were older (or was older, speaking contemporaneously relative to the 10:56 PM event) what would I call it (or would have)? PS: I learned how to subtract in 1962-63 I think.

Last edited by Leo Bloom; 02-19-2018 at 10:05 PM.
  #65  
Old 02-19-2018, 10:37 PM
pulykamell pulykamell is online now
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Originally Posted by Chronos View Post
"New Math" is what kids were taught starting in the 70s. In other words, unless you're a lot older than I think you are, it's what you call just "math".
Tom Lehrer’s song is from 1965, so I suspect it was beginning to be taught earlier than the 70s. It also appears in a Peanuts strip of the same year.
  #66  
Old 02-20-2018, 08:14 AM
Thudlow Boink Thudlow Boink is online now
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Staff Report: What exactly was the “new math”?
  #67  
Old 02-20-2018, 09:16 AM
SciFiSam SciFiSam is offline
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Originally Posted by Chronos View Post
"New Math" is what kids were taught starting in the 70s. In other words, unless you're a lot older than I think you are, it's what you call just "math".
These terms still aren't used in the UK now. Maths teaching has changed here but not in the same way. So the original question meant absolutely nothing to me at all. It's been educational
  #68  
Old 02-20-2018, 09:26 AM
Chronos Chronos is offline
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Yeah, and the terms "gasoline", "truck", and "cookie" also aren't used in the UK now. I'm pretty sure the actual methods are still the same, though we'd need to compare textbooks for 8-year-olds from both sides of the Pond to be sure (do you guys even use the same grade-numbering terminology as us?)
  #69  
Old 02-20-2018, 09:48 AM
SciFiSam SciFiSam is offline
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Originally Posted by Chronos View Post
Yeah, and the terms "gasoline", "truck", and "cookie" also aren't used in the UK now. I'm pretty sure the actual methods are still the same, though we'd need to compare textbooks for 8-year-olds from both sides of the Pond to be sure (do you guys even use the same grade-numbering terminology as us?)
No need to be snarky. I'm just pointing out that you don't have to be ancient to not understand this maths question. At first I thought it was just me being stupid (I'm great at arithmetic, not so great at more advanced maths) but no, it's a language issue. I'm not complaining - like I said, it's been educational.

I'm not sure if the methods are all the same, tbh, because that would require more knowledge of US maths than I have. Kids use numberlines a lot here these days.

Grades are different, yeah. For a kid who turns eight in that school year that'd be called year 3 (it goes nursery at age 3-4, reception, then 1, 2, 3 etc).
  #70  
Old 02-20-2018, 10:00 AM
Chronos Chronos is offline
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Sorry, didn't mean to come across as snarky, there.

And I guess the year numbering is more similar than I thought: The year of kids who were 5 at the start of the school year, we call "kindergarten", and we say "grade" instead of "year", and not everyone goes to nursery school, but other than that, it sounds basically the same.

What about Harry Potter being in "year one" at 11 years old? Do you re-start the numbering at secondary school, or was that a break from the usual British usage?
  #71  
Old 02-20-2018, 10:20 AM
SciFiSam SciFiSam is offline
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Sorry, didn't mean to come across as snarky, there.

And I guess the year numbering is more similar than I thought: The year of kids who were 5 at the start of the school year, we call "kindergarten", and we say "grade" instead of "year", and not everyone goes to nursery school, but other than that, it sounds basically the same.

What about Harry Potter being in "year one" at 11 years old? Do you re-start the numbering at secondary school, or was that a break from the usual British usage?
Essentially, yes, though you don't say year one (you say first year or first form) and it's outdated.

The numbering system changed in 1990, before the first Harry Potter book was published but possibly after she started planning it, and I don't think private schools all changed over. Before the 90s it was year 1, 2, 3 for ages 4, 5 and 6, then 1, 2, 3, 4 for ages 7, 8, 9, 10, then 1st, 2nd, 3rd, 4th, 5th, and 6th form (which went on for two years) for ages 11 to 17 (all by the age they'd start the year at). You'd make it clear by adding infants, juniors or seniors.

Last edited by SciFiSam; 02-20-2018 at 10:21 AM.
  #72  
Old 02-20-2018, 11:01 AM
Chronos Chronos is offline
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Huh, around here, "infants" is roughly synonymous with "babies", and ends somewhere at around two years (at which point you're instead a "toddler"). No eight-year-old would stand for being called an "infant".
  #73  
Old 02-20-2018, 11:23 AM
Inner Stickler Inner Stickler is offline
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If I understand Scifisam correctly, an 8 year old would be a Year 2 Junior.
  #74  
Old 02-20-2018, 12:27 PM
Chronos Chronos is offline
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Ah, right. Well, six-year-olds wouldn't stand for it, either.
  #75  
Old 02-20-2018, 02:06 PM
Leo Bloom Leo Bloom is online now
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Quote:
Originally Posted by Chronos View Post
"New Math" is what kids were taught starting in the 70s. In other words, unless you're a lot older than I think you are, it's what you call just "math".

Quote:
Originally Posted by Leo Bloom View Post
If I were older (or was older, speaking contemporaneously relative to the 10:56 PM event) what would I call it (or would have)? PS: I learned how to subtract in 1962-63 I think.
My question, with grammatically correct present and past counterfactual goofing around) was wondering: you meant "younger," right?

Last edited by Leo Bloom; 02-20-2018 at 02:07 PM.
  #76  
Old 02-20-2018, 02:10 PM
Leo Bloom Leo Bloom is online now
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SciFiSam, you want real snark? How 'bout jeez you guys don't even say "math" right. "New Maths." Makes it even stranger....

Last edited by Leo Bloom; 02-20-2018 at 02:12 PM.
  #77  
Old 02-20-2018, 04:52 PM
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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.
That pre-dates me as well, but I /think/ that

(a) some people were taught to rewrite the 10's column when borrowing from it ("cross out the 3 and replace it with 2), and

(b) some people were taught to add -1 to the 10's column when borrowing from it.

I /think/ that part of the new math was that you never re-write the numbers.

The genesis of New Math was that teachers thought math shouldn't be taught: they'd never used it, and children should be discovering things, not being taught useless facts. The mathematicians reacted that children should be taught math in a form that formed the basis for understanding and further study, not a bunch of rote learned rules that just confused the issue. The military thought children should be taught enough math to be soldiers and scientists (to keep up with the Russians). The parents thought math should be taught the way they learned, and the press thought it didn't matter what the argument was as long as there was an argument.
  #78  
Old 02-20-2018, 05:06 PM
MacLir MacLir is offline
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Originally Posted by Novelty Bobble View Post
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.
You probably call it "carrying"

♫You can't take three from two
Two is less than three
So you look at the four in the tens place
Now that's really four tens
So you make it three tens
Regroup, and you change a ten to ten ones
And you add 'em to the two and get twelve
And you take away three, that's nine
Is that clear?♫
"New Math" - Tom Lehrer
  #79  
Old 02-20-2018, 05:34 PM
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Originally Posted by rat avatar View Post
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.
Honestly, until your explanation I had no idea that the question was meant to be a subtraction problem. I've never heard of regrouping before, and it doesn't seem like how I was taught borrowing, either.
  #80  
Old 05-15-2018, 07:31 AM
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A test that serves as a test on how to take tests is poorly written.
I think the teacher took the questions from the text book written for TEACHERS to read.
They were testing that the teacher fully understood what regrouping was. Not intending that the teacher test the students understanding of english grammar and the meaning of the word for unusual uses of "regrouping" with the same ontological question.

Last edited by Isilder; 05-15-2018 at 07:32 AM.
  #81  
Old 05-15-2018, 09:21 AM
Mahaloth Mahaloth is offline
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I think the teacher took the questions from the text book written for TEACHERS to read.
They were testing that the teacher fully understood what regrouping was. Not intending that the teacher test the students understanding of english grammar and the meaning of the word for unusual uses of "regrouping" with the same ontological question.
No, but I think it was more of a formative assessment than something actually testing them. Perhaps grading it was not so wise. I tend to "check for understanding" and see if I have reached 80% class-comprehension before a big test. I'm guessing class-comprehension was quite low at the point this was given.
  #82  
Old 05-15-2018, 09:43 AM
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From what I saw growing up in the North American educational system in the 60's and early 70's:

The "new math" ("maths"?) seems to have been the same artsy-fartsy stuff that you get from anyone who sets out to "fix" something that ain't broke. Some academics decided that children were precious flowers who need to learn by having everything presented to them and then they discover it for themselves. So they studied for example, how children learned to read and do math and came up with better and totally radical ways to do these. Of course, if you're making your name as an academic theorist, you can't study the problem and say "the method that has evolved over hundreds of years is pretty good and only needs a few minor tweaks...". Instead, they had to come up with something that said "you've been doing t all wrong and we need to teach using a completely different method that we've just discovered". As a bonus, it had the effect of saying to parents "we're the teaching professionals, you amateurs obviously can't teach this or even understand it; so we need you to stand back and leave the teaching to the degreed professionals." You would think if "new" math were so self-evident that it is easy to learn, parents would be able to pick it up too. But instead, one of the goals of the designers (subconsciously, I hope) was to make it too confusing for parents.
  #83  
Old 05-15-2018, 09:54 AM
md2000 md2000 is offline
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"Borrow" was the word I learned starting in the early 60's. I don't think I ever was concerned by the concept that borrow meant had to return... I think most 7-year-olds understand the idea that sometimes borrowed items don't get returned to you. (Or more logically, the "return" was in the answer number...)

Whereas somewhere around grade 6 they tried to teach us some "new math" including groups, sets, and rings... perhaps that was interesting, but all it did was guarantee that the average parent was completely unable to help with math.

Last edited by md2000; 05-15-2018 at 09:56 AM.
  #84  
Old 05-15-2018, 10:18 AM
davidm davidm is offline
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I recall learning, in K through 12, about sets, number lines, and the concept of bases (base 10, binary, etc.). This was all foreign to my parents, but was invaluable to me when I started learning about computers. I entered my computer science classes in college pre-armed with a lot of the required basic knowledge.

Understanding why we do certain things, as opposed to learning rote procedures, can be very valuable.

It doesn't seem obvious to me that these new methods are better than the way I learned but the experts apparently think so. I do recall that a lot of my classmates struggled with things like algebra. Maybe these new methods have been found to help those kids.

Things change. knowledge progresses. That includes knowledge about how we learn.
  #85  
Old 05-15-2018, 05:29 PM
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Since this has been rezzed, I'll give my opinion:

The problem I see is that the instructions have you leave out a step. You first need to group everything into hundreds, tens, and ones, and THEN regroup. If it had been written that way, it would have been much clearer exactly what was desired, as well as encouraging the kid to write all the steps.
  #86  
Old 05-15-2018, 11:11 PM
Monimonika Monimonika is offline
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Originally Posted by Mahaloth View Post
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
Got an answer for this one!

$4.59 - $3.71 = $0.88

Explanation:
$4.59 would be 4 dollars + 2 quarters + 1 nickel + 4 pennies
It's not possible to take just $3.71 as-is from the cash/coins available.
But if 1 dollar is traded for 10 dimes, I can then take: 3 dollars + 2 quarters + 2 dimes + 1 penny
This will leave me with: 8 dimes + 1 nickel + 3 pennies = $0.88
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