Any Math Wizards ready to solve this "4th" grade problem??

[happymomma]

I am reading a problem in a 4th grade book that I found really hard. We've been doing some extra math to enrich his understanding. This is for factors and multiples chapters. I wanted to see if others think this is beyond a 4th grader? I haven't been able to solve it even though I have the answer. Is this what a 4th grader should know? I asked my DS and he couldn't figure out. I can't believe I can't do a 4th grade math. To me this is more than a regular multiples and factors issue. Maybe my brain is fried.

Two men baked as many cakes as 3 women. If 6 men and 11 women baked 4400 cakes all together, how many cakes did each man bake?

[SnuggleBuggles]

That hurts my brain. I'm sure I could figure it out...I prefer not to. :)

[KrisM]

I think it's beyond. I asked DS1, who's I 4th grade and good in math, and he did not know. It's algebra, really.

I do not find it difficult myself, but I am a math person.

[Twoboos]

Oh no, is this what we're in for in 4th? I need a remedial class...

There is no way my DD could solve this.

[happymomma]

That's what I thought also. I felt really stupid when I couldn't figure it out. It seems so complex. DS is generally really good in math and they are no where teaching this. I was looking at one of the Singapore math books and this was one of the questions. I still can't figure out.

[Mommy2Two]

Well I don't think it is too bad. A friend is taking math enrichment and in 6th grade they are prepping for SATs.

[lil_acorn]

I think it's beyond 4th too. Was the answer 220?

[KrisM]

M stands for man
W stands for woman

2M = 3W
6M + 11W = 4400
Those were our 'givens'.

since 2M=3W, that means 6M=9W (multiply each by 3)
substitute into the 2nd equation:
9W + 11W = 4400
20 W = 4400
W = 220
So, each woman baked 220 cakes. Therefore, each man baked:
2M = 3*220
2M= 660
M= 330
Each man baked 330 cakes.

[mommy111]

The men bake 330 cakes each. It's simple algebra and entirely inappropriate for a 4th grader

[happymomma]

M stands for man
W stands for woman

2M = 3W
6M + 11W = 4400
Those were our 'givens'.

since 2M=3W, that means 6M=9W (multiply each by 3)
substitute into the 2nd equation:
9W + 11W = 4400
20 W = 4400
W = 220
So, each woman baked 220 cakes. Therefore, each man baked:
2M = 3*220
2M= 660
M= 330
Each man baked 330 cakes.


:bowdown::bowdown:

Kris--- You are a math wiz!!! That is correct. Thank you for setting it up for me to understand.

[mommy111]

Whoops, posted with the other poster....the problem is that they're teaching our kids to do contortions and get answers to pronems like these teaching them bad habits whereas they should just be teaching them simple algebra first and then giving these problems. Give a man a matchstick before asking him to light a fire

[hbridge]

X = Cakes baked by men

Y= Cakes baked by women

2X=3Y or X = 3/2 Y

and 6X +11Y = 4400

solve the system of equations

6 * (3/2 Y ) + 11 (Y) = 4400

Y = 220 (number baked by each woman)

X = 3/2 Y = 330 (number baked by each man)

Check... (6 * 330) + (11 * 220) = 4400

Therefore, each man baked 330 cakes.


Not sure this is actually 4th grade math. There is probably a better solution using factors...


Oops....Just saw Kris M's post... same concept but much cleaner solution :)

[happymomma]

I think it's beyond 4th too. Was the answer 220?

220 is the number of cakes that each woman makes. That is awesome. Did you do it in your head?

[ett]

I was able to solve it with algebraic equations but I agree that it is way too hard for 4th grade. I'm pretty sure my fifth grader would not be able to solve it. Though if the math levels are more advanced in Asia, then this may be an appropriate problem in the 4th grade Singapore Math book. Just not appropriate for 4th grade math in this country.

[KrisM]

:bowdown::bowdown:

Kris--- You are a math wiz!!! That is correct. Thank you for setting it up for me to understand.

You're welcome. I like math. I do it for fun. And, I did it in my head, until I wrote it out for you :). Math is cool.

[lil_acorn]

220 is the number of cakes that each woman makes. That is awesome. Did you do it in your head?

No, jotted it down but I confused the W with the M when I did my algebraic substitution.

[Indianamom2]

:dizzy: I am 100% certain that I didn't tackle anything like that until Algebra, which wasn't until jr. high at the earliest. There is no way that my DD would be able to do that next year (she's in 3rd right now).

And there's no way that I could have done that tonight. Problems like that are the perfect example of why I have always hated math. Some things never change!

[bisous]

I could answer this problem. My 4th grader would probably be frustrated. But then again, I'm often surprised by what he figures out. Stuff I think should be really hard for him isn't difficult at all. So it is tough to say... I suppose I could ask my 4th grader but really, I think it would be above his level!

[justlearning]

The men bake 330 cakes each. It's simple algebra and entirely inappropriate for a 4th grader

I agree. I called my DS over who's in 5th grade but taking 6th grade math in an advanced class and he said that there's no way that most 4th graders could solve this. He could solve it but it took him a few minutes.

[abh5e8]

well, it is algebra, but i'm not so sure about the "entirely inappropriate" part. the op said they were using some math books for enrichment work at home, not that this was the given problem in the childs homework that day. if the math system the problem came from had prepared a child up to that point to do that work, i dont' see why its inappropriate? most math curriculum is progressive, in that you start the child were they are and they work forward. some move through the material more quickly then others.

[happymomma]

This book went from 0 to 10 really fast in terms of difficulty. I know that DS understands factors and multiples pretty well. I was just so confused that they would ask something this hard when the previous page was finding common multiples of numbers.

I've been bummed recently because I really feel like DS' school's new curriculum is so easy. Our county enacted a new curriculum that was adopted by almost all the states (core curriculum). But it seems like the math has been dumb down to the lowest denominator. So I recently decided that they will do a few problems each day and I would teach them new materials so that they could learn something. Honestly DS' 4th grade class is still working on "place values". When I went to the parent teacher night, they were trying to impress us that the advanced kids were learning in the millions. I was just so shocked at how little they were doing. It took DS less than 5 minutes to do his actual school work. I guess I am really concerned that our county is going down the dumps with this new curriculum. But I don't want to teach him stuff that was way beyond either.

[KLD313]

I hate math, I always did poorly. However, I somehow figured this out really quickly in my head but didn't do it like Kris at all. Hmm, I wondering if it was dumb luck on my part. Lol. I agree it's difficult.

[egoldber]

Well, older DD's school used Hands on Equations to teach algebraic techniques in 4th grade. I don't think there's any reason a mathematically inclined 4th grader who had been taught how to break this problem down like KrisM did couldn't do it. Older DD did get problems like this in 5th and 6th grade. And I know many schools in our county do the same.

In general, I think we underestimate what kids can do and learn when given the right building blocks.

[o_mom]

I would explain it to a fourth grader like this....

The total number of cakes was 4400, made by 6 men and 11 women. The six men make as much as nine women, so it was like 20 women (9 + 11) had made them. The number of cakes the six men made was 9/20's of the total, or 1980 so each one made 330 (1980/6).

I would probably draw a picture to go with it showing the portion of cakes made by the men, giving the equivalent number of women and then how it was 9/20's of the total. If they had been given problems like this in the past with the techniques to solve it, it may be appropriate, but in general it is going to be more of a trial and error problem for most fourth graders.

[happymomma]

I would explain it to a fourth grader like this....

The total number of cakes was 4400, made by 6 men and 11 women. The six men make as much as nine women, so it was like 20 women (9 + 11) had made them. The number of cakes the six men made was 9/20's of the total, or 1980 so each one made 330 (1980/6).

I would probably draw a picture to go with it showing the portion of cakes made by the men, giving the equivalent number of women and then how it was 9/20's of the total. If they had been given problems like this in the past with the techniques to solve it, it may be appropriate, but in general it is going to be more of a trial and error problem for most fourth graders.

Thanks! This is something that I can explain to DS since he hasn't been taught algebra.

[bisous]

I would explain it to a fourth grader like this....

The total number of cakes was 4400, made by 6 men and 11 women. The six men make as much as nine women, so it was like 20 women (9 + 11) had made them. The number of cakes the six men made was 9/20's of the total, or 1980 so each one made 330 (1980/6).

I would probably draw a picture to go with it showing the portion of cakes made by the men, giving the equivalent number of women and then how it was 9/20's of the total. If they had been given problems like this in the past with the techniques to solve it, it may be appropriate, but in general it is going to be more of a trial and error problem for most fourth graders.

Awesome explanation!

[JMS]

My DD is in 4th grade and is in one of the higher/above grade math classes (out of 5) and they are doing nothing like this. I would be scared and I like math!

[MontrealMum]

It's basic algebra, but I don't know that this is what they're teaching 4th graders now. I'm in QC so our curriculum arc plays out differently than the US one does. I will say, though, that I have 8th graders who are *in* Algebra that would probably have trouble setting that one up!

I got the same answer Kris did, and in the same manner, so I know I was right...because she's an engineeer :)

[larig]

I would explain it to a fourth grader like this....

The total number of cakes was 4400, made by 6 men and 11 women. The six men make as much as nine women, so it was like 20 women (9 + 11) had made them. The number of cakes the six men made was 9/20's of the total, or 1980 so each one made 330 (1980/6).

I would probably draw a picture to go with it showing the portion of cakes made by the men, giving the equivalent number of women and then how it was 9/20's of the total. If they had been given problems like this in the past with the techniques to solve it, it may be appropriate, but in general it is going to be more of a trial and error problem for most fourth graders.

This is a really nice, elegant explanation.

Given you're talking about factors and multiples, you could emphasize this....6 men make what 3 times 2 men can make. So that's 3 times what 3 women can make (might help explain the 6 men make as much as nine women in terms of the concepts you're covering).

[mommy111]

Well, older DD's school used Hands on Equations to teach algebraic techniques in 4th grade. I don't think there's any reason a mathematically inclined 4th grader who had been taught how to break this problem down like KrisM did couldn't do it. Older DD did get problems like this in 5th and 6th grade. And I know many schools in our county do the same.

In general, I think we underestimate what kids can do and learn when given the right building blocks.
Wow! So our school is doing division in 4th grade. No algebra here.
However, in the absence of any algebraic instruction, my child constantly gets word problems that could easily be solved with algebra but that she then has to use 'logic' to solve. I find that whole approach destructive, because when there is a systematic way to solve things I don't feel like they should be encouraged to solve them in a haphazard and chaotic manner. I just find that teaching them bad habits. I can understand where simple algebra problems could be given to the kids to solve prior to learning algebra, so that they understand what algebra is all about. However to give them this level of difficulty without first teaching them how to do this in a systematic manner is setting them up for bad mathematical habits.
Of course I am particularly sensitive about my.daughters math curriculum (or lack thereof) with school back in session, so maybe this just hit a nerve

[crl]

Well, older DD's school used Hands on Equations to teach algebraic techniques in 4th grade. I don't think there's any reason a mathematically inclined 4th grader who had been taught how to break this problem down like KrisM did couldn't do it. Older DD did get problems like this in 5th and 6th grade. And I know many schools in our county do the same.

In general, I think we underestimate what kids can do and learn when given the right building blocks.


But your daughter is gifted, right? As in, tested gifted and in a special class full time. So not necessarily representative of typical kids. My fourth grader would not have been able to figure that out. He tests as slightly above standards on the CA standardized tests, but I think he is likely below average in figuring things out on his own.

Catherine

[larig]

Wow! So our school is doing division in 4th grade. No algebra here.
However, in the absence of any algebraic instruction, my child constantly gets word problems that could easily be solved with algebra but that she then has to use 'logic' to solve. I find that whole approach destructive, because when there is a systematic way to solve things I don't feel like they should be encouraged to solve them in a haphazard and chaotic manner. I just find that teaching them bad habits. I can understand where simple algebra problems could be given to the kids to solve prior to learning algebra, so that they understand what algebra is all about. However to give them this level of difficulty without first teaching them how to do this in a systematic manner is setting them up for bad mathematical habits.
Of course I am particularly sensitive about my.daughters math curriculum (or lack thereof) with school back in session, so maybe this just hit a nerve

It is just a difference in educational philosophy. Curricula that emphasize the approach above are constructivist. As a h.s. mathematics teacher, I find this approach and philosophy most in-line with my own, so I am very comfortable with some messing around with math like this. The OP gave the clue about multiples and factors, so that signaled to me that we should be able to do that using those concepts. Sure, using a system of linear equations and is one way to do it, but it's certainly not the only systematic way.

[crayonblue]

At the risk of sounding like a braggart (is that a word?), my 4th grade DD could figure this out. DH could figure it out in about 15 seconds and DD has his math mind. I LOVED math in high school and college and could figure this out but not without paper and pencil and a bit of time.

ETA: OP, this is NOT what I would expect for 4th grade though.

[mommy111]

It is just a difference in educational philosophy. Curricula that emphasize the approach above are constructivist. As a h.s. mathematics teacher, I find this approach and philosophy most in-line with my own, so I am very comfortable with some messing around with math like this. The OP gave the clue about multiples and factors, so that signaled to me that we should be able to do that using those concepts. Sure, using a system of linear equations and is one way to do it, but it's certainly not the only systematic way.
Larig, I would Love some references about this approach to teaching math. I am very uncomfortable with it, but that may be due to the fact that I am unfamiliar and do not understand what this is trying to do. Maybe if I could educate myself on the constructivist approach, I would actually feel more comfortable with the curriculum that my DD's school is using. Thank you so much for this explanation, no one ever explained to me before that this is just a difference in approach off teaching math and not just them randomly proceeding in a disorganized manner. I should probably hang my head in shame at this confession, but there it is. You must be a great math teacher!!

[hellokitty]

My fourth grader wouldn't be able to do that problem. The second set of larger digits of the men and women would have thrown him off. Kris, you did a great job showing how it works. My algebra is rusty, but your equation joggled my brain.

Sent from my SPH-L720 using Tapatalk 4

[trales]

The sad thing is that I put a very similar problem up on the board yesterday for my 32 college students who are taking high school replacement chem for institutional and not college credit to fill in gaps in their education. About 3 in the class were able to solve it, the rest could not. Most of these students are taking a pre-algebra course also right now. We get a lot of students who must spend two years basically re-doing high school in an attempt to fill in the major gaps in their education, they get no college credit for it and pay full college tuition. However, without this opportunity they would not be able to eventually take college courses and get a degree.

My perspective is to keep enriching your childs education with math, it can only help them in the long run.

[westwoodmom04]

Well, older DD's school used Hands on Equations to teach algebraic techniques in 4th grade. I don't think there's any reason a mathematically inclined 4th grader who had been taught how to break this problem down like KrisM did couldn't do it. Older DD did get problems like this in 5th and 6th grade. And I know many schools in our county do the same.

In general, I think we underestimate what kids can do and learn when given the right building blocks.

I a hundred percent agree with this, and often complain that even the G&T math could be more. That said, I do think whether a fourth grader could solve the problem is mostly a question of exposure to algebra in their school's curriculum. Our district starts giving basic algebra problems in first/second grade in a very limited manner, and it increases each year.

[brittone2]

Singapore Math has word problems like that. The Challenging Word Problems book for 4th and 5th grade often has problems in there similar or more difficult to things I remember being on the SAT.

[happymomma]

I a hundred percent agree with this, and often complain that even the G&T math could be more. That said, I do think whether a fourth grader could solve the problem is mostly a question of exposure to algebra in their school's curriculum. Our district starts giving basic algebra problems in first/second grade in a very limited manner, and it increases each year.


Thanks everyone for the many advice. I really think that our school system has not been doing a good job of teaching math. This is coming from a top 10 county in the US. They changed the curriculum about 2 years ago and it really impacted him. In first grade he was taught 2nd grade math and then they changed the curriculum that in 2nd grade he was taught only 2nd grade math. But it was even easier than the previous year so he literally didn't learn one new concept. I feel bad that I didn't do anything the past 2 years but decided that I really should. So for the past few weeks we've been supplemented a little. Last night's problems was the first time that he was truly interested and fascinated with math. It was amazing. We literally stayed up till 9:15 (usual bedtime is 8:30) because he was talking about the new problems. I think he felt really challenged and was fascinated to try to figure out the answer. I just couldn't figure out how to direct him. Based upon the non algebra way of explaining, he was sort of on the right path.
I am thinking that having some challenging questions is a good idea to cultivate his curiosity.

[brittone2]

If he enjoys puzzling through things, by all means, continue to encourage that! It also is really valuable to work on perseverance to slog through a challenging problem for a kid who can tolerate that. If you can help frame it as fun, discovery, etc. then it may shape his perspective on those challenging problems long term.

[egoldber]

But your daughter is gifted, right? As in, tested gifted and in a special class full time. So not necessarily representative of typical kids.

Technically her curriculum was one grade ahead. In 4th they did 5th grade math, in 5th they did the 6th grade math curriculum, and in 6th the 7th grade curriculum. They enriched it with things like Hands on Equations, which was not in the regular text.

While she was in the full time gifted classroom, there were at least 2 other classes in the "base" school who were else getting what they call the advanced or compacted math curriculum. But like a PP mentioned, they had integrated algebraic concepts into the curriculum from an early grade, so all the students should have been getting those concepts as part of the curriculum.

So it may not be typical 4th grade math curriculum, but I think that many 4th graders and certainly 5th and 6th graders are capable of doing that type of work when given the proper foundation.

I can remember being bored with math throughout elementary school. I would have loved to have been given that type of problem in those grades!

OTOH, to trales comments above, many students are either not being exposed to those concepts or are not being taught in a way that reaches them. When I taught college introductory stats classes in grad school, the students who struggled were those who didn't understand basic algebra concepts: how to set up an equation, how to solve for an (single) unknown, order of operations, etc. Frankly, some of them struggled with basic fractions and division. I don't know what the answer is to problems like that.

[westwoodmom04]

Duplicate, not sure how that happened.

[carolinacool]

X = Cakes baked by men

Y= Cakes baked by women

2X=3Y or X = 3/2 Y

and 6X +11Y = 4400

solve the system of equations

6 * (3/2 Y ) + 11 (Y) = 4400

Y = 220 (number baked by each woman)

X = 3/2 Y = 330 (number baked by each man)

Check... (6 * 330) + (11 * 220) = 4400

Therefore, each man baked 330 cakes.


Not sure this is actually 4th grade math. There is probably a better solution using factors...

This is why I majored in journalism. :ROTFLMAO:

[squimp]

This is good. I solved it with "two equations, two unknowns" but this is simpler. Also, 11*2/3 is not a whole number, so that is totally unfair! Lol

[VClute]

My *first* though upon reading this? Why would you want a 4th grader to get the idea that men are more productive than women? Hmph.

[sariana]

My *first* though upon reading this? Why would you want a 4th grader to get the idea that men are more productive than women? Hmph.

I had that thought too, but then I thought since it was about baking, they probably were trying NOT to be sexist.

Has anyone tried to use drawings to work toward a solution? I recognize it as a fairly straightforward algebra problem, but the is not how I would approach it with my 4th-grade son. I do think itnwouldnhave made more sense for the total number of cakes to be 4000 or another number (more) easily divided by 200. Why make it even more complicated by making the arithmetic more challenging? For an algebra class, yes, but for a 4th-grade introduction to the algebraic CONCEPTS, keep the numbers simple.

[o_mom]

I had that thought too, but then I thought since it was about baking, they probably were trying NOT to be sexist.

Has anyone tried to use drawings to work toward a solution? I recognize it as a fairly straightforward algebra problem, but the is not how I would approach it with my 4th-grade son. I do think itnwouldnhave made more sense for the total number of cakes to be 4000 or another number (more) easily divided by 200. Why make it even more complicated by making the arithmetic more challenging? For an algebra class, yes, but for a 4th-grade introduction to the algebraic CONCEPTS, keep the numbers simple.


Yes - This is what I would draw (all I have is Paint).

http://i125.photobucket.com/albums/p58/o_mom2/problem.png

[brittone2]

That's why I have grown to love the Singapore bar diagrams. When I first started teaching those, it was hard for me to set problems up using a bar diagram, even at the third grade CWP level (but those are pretty challenging in my defense ;) ). I would default to algebra and then have to figure out how Singapore wanted me to do it. Once I mastered the bar diagram, I found myself wishing I had been taught that way.

[oneplustwo]

Yes - This is what I would draw (all I have is Paint).

http://i125.photobucket.com/albums/p58/o_mom2/problem.png

While I think our town's school district could do better with math education, at least they introduce various approaches to solving problems including using visuals like this in middle school.

[happymomma]

Yes - This is what I would draw (all I have is Paint).

http://i125.photobucket.com/albums/p58/o_mom2/problem.png

This is awesome!! I can totally use this visual to help him understand.

Thanks!

[buttercup]

Singapore Math has word problems like that. The Challenging Word Problems book for 4th and 5th grade often has problems in there similar or more difficult to things I remember being on the SAT.

Yes, and even more so in Intensive Practice. We use this program but my 4th grader is not able to solve a two equations, two unknowns yet: we have just started working with these. So he would most certainly miss this problem right now. Perhaps by the end of 4th grade he would be able to get it, but I don't know.

[squimp]

My husband and I thought the same thing. He said the men's pies probably would taste 2x as bad. LOL

[YouAreTheFocus]

I would explain it to a fourth grader like this....

The total number of cakes was 4400, made by 6 men and 11 women. The six men make as much as nine women, so it was like 20 women (9 + 11) had made them. The number of cakes the six men made was 9/20's of the total, or 1980 so each one made 330 (1980/6).

I would probably draw a picture to go with it showing the portion of cakes made by the men, giving the equivalent number of women and then how it was 9/20's of the total. If they had been given problems like this in the past with the techniques to solve it, it may be appropriate, but in general it is going to be more of a trial and error problem for most fourth graders.

Thank you so much for sharing this approach! Love it (and your diagram)!

[larig]

Larig, I would Love some references about this approach to teaching math. I am very uncomfortable with it, but that may be due to the fact that I am unfamiliar and do not understand what this is trying to do. Maybe if I could educate myself on the constructivist approach, I would actually feel more comfortable with the curriculum that my DD's school is using. Thank you so much for this explanation, no one ever explained to me before that this is just a difference in approach off teaching math and not just them randomly proceeding in a disorganized manner. I should probably hang my head in shame at this confession, but there it is. You must be a great math teacher!!

You are too kind. I am itching to get back into the classroom--just have to get certified for our new home state!

Education is just like any other field, people come at it from an ideological perspective (mostly informed by what they believe about how people learn) and that shapes the way they write curricula. Wikipedia's definition is one I think does a fair job explaining it succinctly. I find that when people understand the standpoint from which the curricula is written it helps them "get" what is trying to be accomplished.


Constructivist teaching is based on constructivist learning theory. Constructivist teaching is based on the belief that learning occurs as learners are actively involved in a process of meaning and knowledge construction as opposed to passively receiving information. Learners are the makers of meaning and knowledge. Constructivist teaching fosters critical thinking, and creates motivated and independent learners. This theoretical framework holds that learning always builds upon knowledge that a student already knows; this prior knowledge is called a schema. Because all learning is filtered through pre-existing schemata, constructivists suggest that learning is more effective when a student is actively engaged in the learning process rather than attempting to receive knowledge passively. A wide variety of methods claim to be based on constructivist learning theory. Most of these methods rely on some form of guided discovery where the teacher avoids most direct instruction and attempts to lead the student through questions and activities to discover, discuss, appreciate, and verbalize the new knowledge.

I will find some links to some stuff constructivism in education generally and some math ed constructivism too.

And I agree with the other posters who said that the question could have been written with some more friendly numbers. And kudos to o_mom for her rockin' explanations and diagrams!

[SnuggleBuggles]

My good 6th grade mathematician could not do it. Their school let them down wrt multiplication and that rocky foundation is a big concern. But, word problems appear to overwhelm him too.

[mommy111]

You are too kind. I am itching to get back into the classroom--just have to get certified for our new home state!

Education is just like any other field, people come at it from an ideological perspective (mostly informed by what they believe about how people learn) and that shapes the way they write curricula. Wikipedia's definition is one I think does a fair job explaining it succinctly. I find that when people understand the standpoint from which the curricula is written it helps them "get" what is trying to be accomplished.



I will find some links to some stuff constructivism in education generally and some math ed constructivism too.

And I agree with the other posters who said that the question could have been written with some more friendly numbers. And kudos to o_mom for her rockin' explanations and diagrams!
Thanks so much for that, I'm looking around some more too!

[Pyrodjm]

I would explain it to a fourth grader like this....

The total number of cakes was 4400, made by 6 men and 11 women. The six men make as much as nine women, so it was like 20 women (9 + 11) had made them. The number of cakes the six men made was 9/20's of the total, or 1980 so each one made 330 (1980/6).



This is how I solved ti. I remember doing basic algebra like this in 4th grade. I have major trouble with math especially number facts and order of operations and have always had to use pictures, stories and "nontraditional" techniques to solve these types of problem.

[bisous]

I think that kids that can muddle their way through problems like this understand the principles behind what is happening. Since many problems on the SAT (at least that I remember and it has been awhile!) are in nontraditional formats, I find that this kind of understanding is really, really helpful to good success on that important test. What's more, it is just generally useful for problem solving.