What kind of mindbending insanity is this problem??

[BlsdMama]

1 hour ago, Carol in Cal. said:

By analogy, the answer is C.

But the problem itself is way into trick question territory.  AND FOR WHAT?  REALLY, FOR WHAT?

I’m with you, KTGROK.  This is BS.

This is what I was thinking too. 
 

Good heavens, I didn’t even like math before seeing this. 

[Jann in TX]

This method is purposefully designed to lead into the 'box' method of polynomial multiplication -- also followed by the box method of polynomial factoring.  The latter came first THEN someone came along and developed the 'younger student version' we see here.

I have tutored students using the box method--but I do not teach the beast. 

...Just to think the 'box method' all started with a simple multiplication chart (basic fact model) that almost all of used in grade school.

There are TONS of youtube videos on how to use the box method...  I like my traditional methods-- they are based in MATH and work, in most cases, in a more simplistic manner.

[EKS]

What program is this?

[Clarita]

I'm utterly lost. Granted I have no idea what the methodology they are trying to teach is, there is a part of me that feels no matter what method they are teaching the kids about adding, multiplying, dividing, multivariable calculus, etc. shouldn't the problem look something like something they might encounter in real life (even if it means they have to be rocket scientist or mathematician before they encounter such a problem).

Of course aside from SAHM my other career was electrical engineering so I'm fully in the math is a tool for doing fun stuff, and not math is fun in and of itself.

[Melissa Louise]

One of my kids has mild dyscalculia. Just the way this looks on the page would have made it impossible for her to focus on it. 

[ktgrok]

3 minutes ago, EKS said:

What program is this?

I don't know..something used by Orange County Public Schools. 5th grade. 

[ScoutTN]

This kind if stuff is part of why I am glad we have homeschooled. Ds is in school now and has a plain, old-fashioned, pre-common core math book. Love this choice.

[ktgrok]

Oh, and last time I saw this child's homework, two years ago so 3rd grade, it was all writing paragraphs about how to add numbers together. So for EACH problem 2 digit addition they had to write out every step, in complete sentences. Needless to say, that left time and space for not many problems. In fact I counted - six problems. 

I'm sorry, but you do NOT get fluent with addition doing six problems a day, even if you write out all the steps in complete sentences. Not to mention how now kids who have dysgraphia or dyslexia are going to struggle in math as well as language arts! So ridiculous. 

[vonfirmath]

1 hour ago, regentrude said:

But how do they represent the areas when they are not proportional and when both rectangles have the same size?
How is a long side representing "10" and a much shorter side representing "42" any help?

Btw, I just showed the problem to my DH. Theoretical physicists, researcher, does math all day. He read the words and said he doesn't even understand what the sentence is supposed to mean.

ET: teachers, pretty please, teach the kids to actually do division. In a way that translates to algebraic expression.

When kids draw rectangles to put numbers around, it doesn't matter if they are proportional.

The numbers matter. Not the relative size of the pictures.

[ktgrok]

5 minutes ago, vonfirmath said:

When kids draw rectangles to put numbers around, it doesn't matter if they are proportional.

The numbers matter. Not the relative size of the pictures.

if they were a bit off, fine. But when you purposely have one side WAY longer than the other, and then put the smaller number there, that's confusing! And then, putting the "answer" at the bottom makes it look like those numbers are the length of those sides, just like the numbers at the top. But they aren't. 

[EKS]

Here is an explanation of the technique.  Maybe someone has posted this already.  I'm not sure why it's called the area method.  

https://shelleygrayteaching.com/box-area-method-alternative-traditional-long-division/

[ScoutTN]

6 minutes ago, EKS said:

Here is an explanation of the technique.  Maybe someone has posted this already.  I'm not sure why it's called the area method.  

https://shelleygrayteaching.com/box-area-method-alternative-traditional-long-division/

Why bother with this, except as an alternative for kids who need a different approach than regular old long division? Is this the primary way a teacher/curriculum/school system is teaching division? 

[ktgrok]

Y'all, long division is NOT hard to teach. It is boring, and long (hence the name) but it isn't confusing or hard. Just annoying. That said, her box model explanation makes way more sense than the explanation given by the curriculum the problem was from. 

[regentrude]

35 minutes ago, EKS said:

Here is an explanation of the technique.  Maybe someone has posted this already.  I'm not sure why it's called the area method.  

https://shelleygrayteaching.com/box-area-method-alternative-traditional-long-division/

What purpose does drawing the boxes serve and why is this supposed to be "easier" than the simple standard algorithm? It certainly is a lot slower.

I have been teaching for twenty years and have been observing a steady decline in the math abilities of my students. It appears that whatever "new" methods are taught nowadays are inferior to the "old fashioned" ones. Unless the desired outcome is no longer that students can actually perform calculations proficiently.

ETA: A big general problem with math curriculum development is that the people involved are not people who are actually using math in their work. 

Edited September 22, 2021 by regentrude

[*****]

35 minutes ago, vonfirmath said:

When kids draw rectangles to put numbers around, it doesn't matter if they are proportional.

The numbers matter. Not the relative size of the pictures.

The publisher is assuming all 5th graders at this point are at the representational level, but some kids still need the concrete level. Common sense tells us to at least show a larger area for the part that should be larger, even if it isn't proportional. These are children, don't you remember what it was like at age 11? Publishers just don't seem to remember what it was like to be a child. 

It is just teaching that it is ok to be lazy, just get close. So why should the kid learn to spell 'piece' for example when 'peice' is close enough? It's  about the same...yes, I am being facetious. But for those kids where math doesn't come naturally, or they are visual learners, not using some sort of proportion just boggles the mind. I can only imagine what this does to the kid who notices these kinds of things, and just can't move on because the picture doesn't make sense to him, yes our Asperger kids for example. 

And I don't see how problems such as these helps the kind of kids who were already struggling with the old method. This would take so much more time to have to teach.  I love what regentrude said: Of course this is a good way to achieve equity. If nobody can do division, then no child is left behind.

 

[Murphy101]

Crap like this is why I just used the paper to make an airplane bookmark for my Dragonlance book in elementary school.

Why do people keeping thinking if they just make it more convoluted the kids will understand better?

No wonder most kids by end of 4th grade have decided they hate math and science and just “aren’t good at math”.

[Danae]

The actual method here is just a different way of writing down the steps of the regular long division that we all learned in school.  The thing that makes the problem funky is that instead of asking the student to do the division problem they have it written out with one intermediate step missing. Which is a function of making multiple choice tests for things that should be graded problems.  It would be like giving the attached and asking what subtraction problem belongs in the space.

 

Edited September 22, 2021 by Danae

[SanDiegoMom]

1 hour ago, regentrude said:

I have been teaching for twenty years and have been observing a steady decline in the math abilities of my students. It appears that whatever "new" methods are taught nowadays are inferior to the "old fashioned" ones. Unless the desired outcome is no longer that students can actually perform calculations proficiently.

 

I agree.  Yesterday at the hair salon the (much younger) clerk complimented on how good I was at math when I quickly figured out 20 percent for the tip.   I just took the first two numbers and doubled it. It made me wonder if everyone else was having to get out the calculator to figure out what 20 percent was? 

 

[Tap]

I understand where they are going with this style of math, but honestly it is so cumbersome to some people, that I feel it is a hinderance instead of a benefit. 

 

I can add groups of numbers really fast using my own method of counting, regrouping, using multiples and subtraction. But when I walk through  a problem verbally to try to explain my math to other people, their eyes roll back and they start rapidly blinking, much like an old computer saying Error! Error! Error!  LOL 

[debi21]

The way the Common Core reads, students are to be able to divide at all in 4th grade (with multiplication facts, e.g. 63/7=9), use these techniques such as area model in 5th grade (but not even introduce the standard algorithm), and "fluently divide with the standard algorithm" in 6th grade. I think a bigger issue is students are not gaining fluency in 6th grade (not enough time for mastery), it is not reinforced in 7th grade, and by 8th grade almost everyone allows the use of calculators.

[Bootsie]

2 hours ago, SanDiegoMom said:

I agree.  Yesterday at the hair salon the (much younger) clerk complimented on how good I was at math when I quickly figured out 20 percent for the tip.   I just took the first two numbers and doubled it. It made me wonder if everyone else was having to get out the calculator to figure out what 20 percent was? 

 

The probably are--and some may not be able to do it correctly with a calculator. I recently had a college junior using her calculator to multiply by 1 and could not figure out how to divide by 6%--she was very confused why it wasn't 0.6.  Many of my college students cannot multiply by 10%--20% would really through them.

[SKL]

I understood it, probably because it hasn't been that long since my kids had to deal with elementary school math.

For some reason, math curricula have always treated division as if it has to be taken apart and put back together in some weird way.

They did that when I was in 3rd or 4th grade, but it looked different from this.  And some other way when my kids learned it.  But because I knew what it was trying to accomplish, it wasn't hard for me to figure it out.

Thank goodness my kids are past that stage.  😛

[SKL]

When my class learned "long division," I had been out sick, and when I came back, it made no sense to me.  So I went home and asked my brother, who was one year ahead in school.  He taught me "short division," which I understood quickly.  I did all my homework and turned it in.  The teacher gave me a zero because I had used short instead of long division (but the answers were right).  I struggled and struggled to understand the cumbersome "long division," and the day after I finally mastered it, our teacher taught us short division.

I think that might have been the beginning of my distrust of teachers and schools.  😛

[Carrie12345]

Setting this specific example aside, I do think it’s good that it’s finally recognized that not all kids “get” math the way it was taught for ages. Yay, neurodiversity!  
My issue has always been with the concept of “different kids do better with different methods, so let’s base everyone’s GRADES on all of those methods combined!”  
As a former honors math student, I probably would have been a poor to mediocre one on paper. I still do most long-ish division by hand because it’s quicker for me than pulling out my phone and finding my calculator app.
 

I do give my homeschooled kids some basic alternative methods, but they get to use the ones that make the most sense to them for “grades”. Isn’t that supposed to be the real purpose?

[DawnM]

I am not smarter than a 5th Grader.

[Bambam]

I've wondered at the tendency of workbooks and tests to ask questions on intermediate steps of math problems, or to set up the problem, or various aspects of that VS just asking for the solution. I can totally see having the worksheet have you do the first step, then the second step, then the third step for arithmetic problems (for example, adding two fractions with different denominators - having each step laid out could be helpful vs. just writing the problem yourself), but I don't understand the advantage for standardized tests to ask intermediate steps math problem questions vs. solutions. What am I missing? 

[Farrar]

That blog post helped me understand what they were going for, but I don't understand how it helps understand long division and it's not faster. We did start long division by pulling out the Cuisenaire rods and base ten blocks and building large models - like, for a day or two. And we also did partial quotients, which I understand now this was modeling. But to me, partial quotients is useful for mental math and as a method of introducing ways to think about long division. This is turning that into an algorithm of its own with lots of extra steps and I don't get that at all. It's one thing to break up a number for the purposes of mental math. But this is like a whole other level. Even after reading all the things people have said here, I do not understand the purpose.

[ktgrok]

Oh, and when my sister messaged the teacher to ask about the answer/solution, even the teacher said the kids prefer long division to this! So...what on earth is the point? Maybe to torture them so that long division seems easy by comparison, lol?

My favorite long division teaching thing is to model it with money first. I found an amazing video using play money to show the steps of long division in a concrete way and that was awesome. We did the steps of the long division on paper as we did the money division. That's to show what the concept is...but it isn't how you freaking DO it. I didn't make her break out monopoly money to do each problem, that's silly. The point of the algorithm is it makes it fast and streamlined. 

Teaching kids division with this crud is like teaching home ec students to cook by making them build a fire each time, then milk the cow for the milk, raise a chicken for the eggs, etc. 

[Not_a_Number]

7 minutes ago, Farrar said:

This is turning that into an algorithm of its own with lots of extra steps and I don't get that at all. I

Exactly. This doesn't even feel less algorithmic than long division! I doubt it's helping them develop a model. 

[Not_a_Number]

4 minutes ago, ktgrok said:

e did the steps of the long division on paper as we did the money division. That's to show what the concept is...but it isn't how you freaking DO it. I didn't make her break out monopoly money to do each problem, that's silly. The point of the algorithm is it makes it fast and streamlined. 

I mean, I do actually make kids DO things with place value for a while before teaching any algorithm, which is why I don't actually TEACH any algorithms -- I show them as shorthand for things they already get. So I don't really agree with that. 

[vonfirmath]

3 hours ago, Carrie12345 said:

Setting this specific example aside, I do think it’s good that it’s finally recognized that not all kids “get” math the way it was taught for ages. Yay, neurodiversity!  
My issue has always been with the concept of “different kids do better with different methods, so let’s base everyone’s GRADES on all of those methods combined!”  
As a former honors math student, I probably would have been a poor to mediocre one on paper. I still do most long-ish division by hand because it’s quicker for me than pulling out my phone and finding my calculator app.
 

I do give my homeschooled kids some basic alternative methods, but they get to use the ones that make the most sense to them for “grades”. Isn’t that supposed to be the real purpose?

This is how my kids' teachers have mostly handled it. Using problems like this one to be sure you are listening to learn the different methods. But when it comes to actually doing division, as long as you show your work, get to the answer the way that works best for you.  (My son had difficulties with the showing work.  Even if you can look at a problem and "know" the answer, you had to use SOME method to show the teacher how you got there on paper)

 

Edited September 22, 2021 by vonfirmath

[cintinative]

This quote came to me as I was perusing this thread. From Jurassic Park

Dr. Ian Malcolm:
Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.

[cintinative]

DP sigh

Edited September 22, 2021 by cintinative

[cintinative]

DP

Edited September 22, 2021 by cintinative

[Jann in TX]

16 hours ago, Faith-manor said:

I would hope. But, I don't have a lot of confidence. Our district spends so much of the school day on standardized test prep, and guessing probable answers not actually solving problems. I think they believe filling in bubble sheets is a hot commodity skill in the future.

Standardized tests are typically NOT created by teachers--- these types of problems are FREQUENTING standardized tests at the 5th grade level (and all others too)-- so teachers, in turn, MUST 'teach' them to students or the teachers may get bad marks because of low student scores...

This really has NOTHING to do with actual learning so you can do/understand higher maths.

[Faith-manor]

19 minutes ago, Jann in TX said:

Standardized tests are typically NOT created by teachers--- these types of problems are FREQUENTING standardized tests at the 5th grade level (and all others too)-- so teachers, in turn, MUST 'teach' them to students or the teachers may get bad marks because of low student scores...

This really has NOTHING to do with actual learning so you can do/understand higher maths.

I agree. Sadly, standardized prep questions are a the bulk of the focus of our local district. It is just souring more and more students and teachers on education.

[TravelingChris]

17 hours ago, regentrude said:

This seems to be the most convoluted way to teach division.
I have a PhD in theoretical physics and this made my brain hurt. 
This is why my students cannot do math.

Exactly.   When there is a simple way to do it- why complicate the matter?

[Farrar]

I think "can the vast majority of mathematicians look at your teaching model and understand why it's useful and how to do it within a minute or so" is probably a good checkpoint for elementary math. It shouldn't be the only one (that's how we got the version of new math that so many teachers struggled to understand themselves back in the 60's) and there are times that spending time on conceptual concepts that simply help kids build the model of understanding are worth time, even if those visualizations and models were unnecessary to adults who become successful with math. But this is just silly.

[TravelingChris]

15 hours ago, ktgrok said:

Oh, and last time I saw this child's homework, two years ago so 3rd grade, it was all writing paragraphs about how to add numbers together. So for EACH problem 2 digit addition they had to write out every step, in complete sentences. Needless to say, that left time and space for not many problems. In fact I counted - six problems. 

I'm sorry, but you do NOT get fluent with addition doing six problems a day, even if you write out all the steps in complete sentences. Not to mention how now kids who have dysgraphia or dyslexia are going to struggle in math as well as language arts! So ridiculous. 

That would have been a sure way to discourage me from liking math.  And I ended up getting math centered degree- economics for my undergrad and while criminal justice may seem to not be math centered, there was no way we could become criminologists without a good understanding of statistics and how to use them.

[Farrar]

24 minutes ago, Jann in TX said:

Standardized tests are typically NOT created by teachers--- these types of problems are FREQUENTING standardized tests at the 5th grade level (and all others too)-- so teachers, in turn, MUST 'teach' them to students or the teachers may get bad marks because of low student scores...

This really has NOTHING to do with actual learning so you can do/understand higher maths.

I think a lot of the testing models are about weeding kids out and selling the textbooks. Corporate Education Company INC creates the test. If it's too understandable and accessible to all, then it will be called too easy. Or it will be good and they'll never be paid to change it and "improve" it. If you can do the test with any textbook, no one will buy Corporate Education Company INC's textbook series. So they put these problems into as convoluted a model as they can get away with so they can sell more books and expensive computer learning problems. Then they have to tweak the tests enough every year to make sure everyone has to keep paying for everything.

[ktgrok]

1 hour ago, cintinative said:

This quote came to me as I was perusing this thread. From Jurassic Park

Dr. Ian Malcolm:
Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.

I thought of the same quote!!!! But didn't send it to my sister cause I think she regretted awaking the beast in me regarding this topic, lol. 

I'm so glad I have you guys! We can share in the frustration. Dh couldn't get why I was still muttering about it at midnight, lol. 

[ktgrok]

7 minutes ago, Farrar said:

I think a lot of the testing models are about weeding kids out and selling the textbooks. Corporate Education Company INC creates the test. If it's too understandable and accessible to all, then it will be called too easy. Or it will be good and they'll never be paid to change it and "improve" it. If you can do the test with any textbook, no one will buy Corporate Education Company INC's textbook series. So they put these problems into as convoluted a model as they can get away with so they can sell more books and expensive computer learning problems. Then they have to tweak the tests enough every year to make sure everyone has to keep paying for everything.

This is it EXACTLY. None of it is about teaching kids. It is 100% about money. 

[Hilltopmom]

This is the “box method” and NY state requires we teach it on public school in grades 4 & 5 a d it’s a big part of the state test. I don’t teach it that way because I want to piss off parents- I’m required to by my job 

[Paige]

It looks like Everyday Math. This is one of the main reasons I continued to homeschool after moving to a new district when my kids were young. They'd been homeschooled but we heard the new district was good. My daughters had asinine problems like this in 3rd grade and they were also required to use calculators for basic calculations. There were test questions such as "what do I press next on the calculator?" I flipped through the rest of the 3rd grade book and my son's 5th grade book. It was terrible all the way through. You could say they were teaching "conceptually" so they wouldn't be robots, but the facts were that my homeschooled kids could do math and my then 5th grader was a solid 2 years ahead of his peers when he wasn't ahead at all in my book or according to Math Mammoth. DS was multiplying and dividing any whole number at that point, and probably some fractions. The class was drawing circles to do 4x7. He got points off for not drawing the circles. I had no idea how these kids were going to transition from that to algebra or prealgebra in 6th grade!

My daughters already struggled with math, so I thought they'd have no hope with this type of curricula, and DS was bored out of his mind, so I pulled all of them except the kindergartener. I let her go to K because it seemed harmless, but the school introduced calculators in 1st grade, so there was no way I was going to let her stay past kindergarten! The teachers were apologetic and encouraged me to complain. My son's said she tried to do her own thing as much as possible, but they could only do so much to make it better. I don't blame them. I blame whoever purchases this stuff and forces it on the kids and teachers.

Edited September 22, 2021 by Paige

[wendyroo]

44 minutes ago, Paige said:

It was terrible all the way through. You could say they were teaching "conceptually" so they wouldn't be robots, but the facts were that my homeschooled kids could do math and my then 5th grader was a solid 2 years ahead of his peers when he wasn't ahead at all in my book or according to Math Mammoth. DS was multiplying and dividing any whole number at that point, and probably some fractions. The class was drawing circles to do 4x7. He got points off for not drawing the circles. I had no idea how these kids were going to transition from that to algebra or prealgebra in 6th grade!

My son started in public school 5th grade this year. They had him do the iReady to assess his math skills; his diagnostic - according to their assessment - showed that he was at a late 7th/early 8th grade level. So...they have him working on multiplying numbers by factors of 10...and not conceptually at all (not that he needs conceptual instruction in that at this point), but rather in a "100 has two zeros, so you add two zeros to the number you are multiplying! Magic!!" way.

I think there is a good likelihood that they will manage to lower his iReady score by the end of the year. 😒

[ktgrok]

7 minutes ago, wendyroo said:

My son started in public school 5th grade this year. They had him do the iReady to assess his math skills; his diagnostic - according to their assessment - showed that he was at a late 7th/early 8th grade level. So...they have him working on multiplying numbers by factors of 10...and not conceptually at all (not that he needs conceptual instruction in that at this point), but rather in a "100 has two zeros, so you add two zeros to the number you are multiplying! Magic!!" way.

I think there is a good likelihood that they will manage to lower his iReady score by the end of the year. 😒

Yup, my son switched school districts when we moved here and the school was so bad he went backward in several subjects. 

[Jann in TX]

3 hours ago, Paige said:

... The class was drawing circles to do 4x7. He got points off for not drawing the circles. I had no idea how these kids were going to transition from that to algebra or prealgebra in 6th grade!  ...

The 'box' method continues into Algebra 1- I've even seen it in Algebra 2.  Students usually stop using it when they start using calculators for the basic (arithmetic) problems.  The box method of polynomial multiplication and division is very popular...

My youngest is in an 'applied' calculus 3 class (one specifically for bio-science majors).  Last week she taught her class how to factor polynomials (using my method) because the majority of the students could not remember how the 'box thing' worked.  This dd was public schooled-- she KNOWS the box methods... but she just rolls her eyes at them now that it is her choice and works problems the traditional way.  Her instructor commented on her organization (compared to the mess the box method students had on their papers!).

I DID use an 'area model' today in my Geometry class.  It was a quickie review of the area of a rectangle and I made a quick 4x2 area model just to emphasize that area has 'square units' because we are counting SQUARES...  basically I did this to remind students that area units are to the 2nd power...  Point took about 1 minute to go over.

[Not_a_Number]

4 hours ago, Hilltopmom said:

This is the “box method” and NY state requires we teach it on public school in grades 4 & 5 a d it’s a big part of the state test. I don’t teach it that way because I want to piss off parents- I’m required to by my job 

Sigh. You're saying I'll have to teach this nonsense to DD9 when she takes the state test? Cause she's been able to multiply anything by anything for years now, but I doubt she'll have any clue what this is saying!!!

[Indigo Blue]

11 year old me would have sat staring at that problem wondering why the lengths of the boxes were disproportionate to the number labels. If everyone else started writing things, I would have just talked myself into believing it was me and not the ridiculous problem. I would have then been too afraid to raise my hand to ask, especially if the teacher wasn’t friendly. A lot of them were not. And there I would be.

When my older son was in school, there was a lot of instructions sent home on organizing research papers, completing projects, math instructions, etc. Vague, convoluted, nonsensical instructions.

I have an especially strong dislike for this sort of thing. When I first began browsing through home school curriculum, I was in absolute heaven. Everything seemed academically challenging but lesson plans, math, everything was laid out as clear as the water in Bora Bora.

There’s just no sense in having to endure such. Sorry. This does really bug me……

 

 

 

[Hilltopmom]

40 minutes ago, Not_a_Number said:

Sigh. You're saying I'll have to teach this nonsense to DD9 when she takes the state test? Cause she's been able to multiply anything by anything for years now, but I doubt she'll have any clue what this is saying!!!

Yeah but if she’s not in school why would you have her take the state test? It’s not required for homeschoolers.