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What kind of mindbending insanity is this problem??


ktgrok
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4 minutes ago, Not_a_Number said:

I think it is every two years, isn't it? 

No, homeschoolers NEVER have to take a NY state test. You have to use a standardized test every other year starting in 4th (then yearly in high school) but there is a list- most people use the CAT ordered from Seton testing & they give it at home.

I would never, ever send my kid to school for the state testing weeks if they hadn’t been a school student- the tests the state gives are their own thing and there’s prep to “pass” that sort of test
Trust me, just use the CAT 🙂

Edited by Hilltopmom
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1 minute ago, Hilltopmom said:

No, homeschoolers NEVER have to take a NY state test. You have to use a standardized test every other year starting in 4th (then yearly in high school) but there is a list- most people use the CAT ordered from Seton testing & they give it at home.

Yes, jinx, I thought of that after I posted! 

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1 hour 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!!!

It'll probably be on most tests these days but you could just take it as a loss. I'm sure your DDs will do well enough without it. I'd go nuts if I tried to teach to some test unrelated to what I'm trying to teach!

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5 minutes ago, Paige said:

It'll probably be on most tests these days but you could just take it as a loss. I'm sure your DDs will do well enough without it. I'd go nuts if I tried to teach to some test unrelated to what I'm trying to teach!

DD9 isn't a very visual kid, either. She never wanted to visualize multiplication like this in the least -- that's more DD5's cup of tea. 

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1 hour ago, Indigo Blue said:

 

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……

 

 

 

YUP! Friend woudl say they couldn't even help with their kids homework, how could they homeschool? I kept saying, because you have the teacher's manual!

Edited by ktgrok
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I'm a little late to the conversation here, but this is basically how DD does multiplication and division in her head. She struggled with the traditional long division algorithm in 2nd grade and never really got it until polynomial long division. She wrote a scholarship essay that touched on her method, with the primary point being that students should be presented with more than one method of problem solving because different people learn differently.

When I saw the OP's post, I sent DD a screen shot right away and asked her, "Isn't this how you multiply/divide?" She does not actually picture it with the boxes but she does the method of subtracting out a multiple of 10, etc. It is fascinating to me since I was so bewildered by her struggle with long division. I was homeschooling her at that point and using Singapore Math, which was otherwise a really great fit for her. She never struggled with anything else in that same way, and went on to have a 35 ACT and lots of AP credits, so clearly grasping the traditional long division algorithm is not a prerequisite for overall academic success 🙂

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22 minutes ago, Longtime Lurker said:

When I saw the OP's post, I sent DD a screen shot right away and asked her, "Isn't this how you multiply/divide?" She does not actually picture it with the boxes but she does the method of subtracting out a multiple of 10, etc.

That's how I teach long division, too 🙂 . But I don't like the confusing visual or where the numbers go in it. 

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18 minutes ago, Not_a_Number said:

That's how I teach long division, too 🙂 . But I don't like the confusing visual or where the numbers go in it. 

Yes, I agree that the placement of the numbers is very confusing. The diagram reminds me of the area model of multiplication, but makes much less sense.

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10 hours ago, Not_a_Number said:

That's how I teach long division, too 🙂 . But I don't like the confusing visual or where the numbers go in it. 

Exactly. Once I saw the actual explanation (which was NOT confusing) I saw how it could sometimes help. But that version I posted was insane. 

9 hours ago, Longtime Lurker said:

Yes, I agree that the placement of the numbers is very confusing. The diagram reminds me of the area model of multiplication, but makes much less sense.

Yup - like they took a few good ideas and then twisted them together to be terrible. 

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34 minutes ago, gstharr said:

Every Day Math  from University of Chicago is very popular at competitive private k-6 schools.  It is why I took over my son's math edicuation.  here are examples of concepts:  https://www.nychold.com/em-arith.html

Some of this looks familiar from when younger ds was in elementary, before we took him out. I remember the lattice method, especially.

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46 minutes ago, gstharr said:

Every Day Math  from University of Chicago is very popular at competitive private k-6 schools.  It is why I took over my son's math edicuation.  here are examples of concepts:  https://www.nychold.com/em-arith.html

The thing about all these methods isn't that they are BAD... it's that for lots of kids, they wind up JUST as algorithmic as anything else. 

I had a kid in my homeschooling class who skip counted for all her multiplication. I think skip counting was introduced as a way to make sure kids weren't simply memorizing, which is good! But this kid didn't understand WHY she was skip counting, as was evidenced by the fact that she kept asking me "where to start, at 0 or at 1 copy of the number." So then it just became a longer, more onerous algorithm for her. 

Edited by Not_a_Number
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6 minutes ago, Not_a_Number said:

The thing about all these methods isn't that they are BAD... it's that for lots of kids, they wind up JUST as algorithmic as anything else. 

I had a kid in my homeschooling class who skip counted for all her multiplication. I think skip counting was introduced as a way to make sure kids weren't simply memorizing, which is good! But this kid didn't understand WHY she was skip counting, as was evidenced by the fact that she kept asking me "where to start, at 0 or at 1 copy of the number." So then it just became a longer, more onerous algorithm for her. 

Exactly. DD figured this method out for herself when the traditional algorithm was confusing to her. So she really understood what she was doing. If I could go back in time, I could explain it to her in a way she could understand and then show her how her method corresponded to the traditional method. We actually had a in-depth discussion about this when we were reviewing together for the SAT and came across polynomial long division problems. She understands all the methods now and how they relate to one another so that should be helpful to her future students.

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9 hours ago, gstharr said:

Every Day Math  from University of Chicago is very popular at competitive private k-6 schools.  It is why I took over my son's math edicuation.  here are examples of concepts:  https://www.nychold.com/em-arith.html

Everyday Math is the reason, when my kids were in school, that I told the teachers that reading was the only "homework" allowed in my house. I refused to fight the math fight anymore. 
 

Shortly after that, we began homeschooling.

Edited by fraidycat
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5 minutes ago, fraidycat said:

Everyday Math is the reason, when my kids were in school, that I told the teachers that reading was the only "homework" allowed in my house. I refused to fight the math fight anymore. 
 

Shortly after that, we began homeschooling.

What happened when you tried to fight the fight? How did your kids feel about the math? 

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34 minutes ago, Not_a_Number said:

What happened when you tried to fight the fight? How did your kids feel about the math? 

It was only my DD who actually had to do "Chicago Math", as DS was only in pre-school at the time. This was grade 2, but much like the original problem in this thread, the homework problems were very convoluted and just didn't make sense. What happened at homework time was tears and frustration on DD's part, and me phoning every teacher friend I knew asking them WTH is this even asking!?! Unfortunately for me, but fortunately for my teacher friends in other states and another country, they were NOT using this curriculum and didn't have a clue.

Between that and "teaching to the test"/standardized test prep, it got to the point that DD was in tears every morning, not wanting to go to school.

Homeschooling was much easier, compared to that.

 

 

 

Edited by fraidycat
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On 9/21/2021 at 8:36 PM, 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. 

DH still complains about his teacher who graded their spelling in math class. He could do math; he couldn't spell (still can't). So, all that accomplished was making him struggle in math class (and hate the teacher).

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3 minutes ago, historically accurate said:

DH still complains about his teacher who graded their spelling in math class. He could do math; he couldn't spell (still can't). So, all that accomplished was making him struggle in math class (and hate the teacher).

Hahahaha, this is weirdly reminding me of my Ph.D thesis, where my advisor didn't read any of the math I wrote, really, but did remove every instance of the word "we" and request me to put it in the passive voice... 

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In defense of Everyday Math - and I promise, I don't say it that often - it's shown to have good results in one highly specific situation:

When the kids have been doing it all along since kindy, the teachers are extremely confident and secure in their math skills, the parents buy in to it, and they can afford to spend more than an hour of class time every day on it.

Of course, you'll be lucky to meet even one of those conditions in the average classroom, and then it'll probably only be the first one.

Edited by Tanaqui
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So I subbed today in a district that teaches long division with the traditional algorithm. There is not a bit of that particular formatting of laying out your work that is intuitive or obvious.  It only seems that way to people who’ve been using it for years.
 

These kids had learned it last year and were being introduced to decimal division, but over half of them were still not solid on whole number division.  They knew that they were supposed to look at the “underneath number” starting from the left and use only as many of the digits as they needed to fit the “outside number” into it.  Most, but not all of them knew that you put “how many times” it fits on top.  Most, but not all of those remembered that if you’re using multiple digits of the “underneath number” you have to line up your “how many times” number with the rightmost digit that you’re using.  After that it got messy.  Everyone remembered that you have to do something with the number you just wrote on top, but they didn’t all remember if you were supposed to multiply, add, subtract, or divide with it and which other number you were supposed to do it with.  
 

 

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2 minutes ago, Danae said:

So I subbed today in a district that teaches long division with the traditional algorithm. There is not a bit of that particular formatting of laying out your work that is intuitive or obvious.  It only seems that way to people who’ve been using it for years.
 

These kids had learned it last year and were being introduced to decimal division, but over half of them were still not solid on whole number division.  They knew that they were supposed to look at the “underneath number” starting from the left and use only as many of the digits as they needed to fit the “outside number” into it.  Most, but not all of them knew that you put “how many times” it fits on top.  Most, but not all of those remembered that if you’re using multiple digits of the “underneath number” you have to line up your “how many times” number with the rightmost digit that you’re using.  After that it got messy.  Everyone remembered that you have to do something with the number you just wrote on top, but they didn’t all remember if you were supposed to multiply, add, subtract, or divide with it and which other number you were supposed to do it with.  
 

 

We kept a chart up with the steps for a while when first learning it and used this mnemonic

image.png.fd08f715dad7495d12726ed7c83124bc.png

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20 minutes ago, ktgrok said:

We kept a chart up with the steps for a while when first learning it and used this mnemonic

image.png.fd08f715dad7495d12726ed7c83124bc.png

Okay, but how is that any less ridiculous than the model in the opening post?  Is having to remember a phrase about stinky monkeys more mathematically serious than putting your intermediate calculations inside a box?

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1 minute ago, Danae said:

Okay, but how is that any less ridiculous than the model in the opening post?  Is having to remember a phrase about stinky monkeys more mathematically serious than putting your intermediate calculations inside a box?

well, I don't care how serious it is, lol. 

I actually see no issue with the box method that was linked somewhere in the thread - that made sense and the way it was written was clear. This particular problem/method was not that - they put numbers in places that MEAN things in other area of math. Putting the numbers along the outside meaning one thing in one place, but totally different thing on the other side, etc is super confusing. Heck, calling it an area model but not having it model area (the way it was laid out) was confusing. That they didn't use easy numbers as intermediaries was confusing - since that is the whole point of the box method. It was a bad problem, and writing it the way they did leads to confusing, in my opinion. 

Had it been the actual box method shown in the other link I'd never have posted about it - and in fact might use it. 

(now, don't get me started on lattice multiplication -HATE that stupid thing because it goes right to left and left to right in the same problem!)

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1 hour ago, Danae said:

So I subbed today in a district that teaches long division with the traditional algorithm. There is not a bit of that particular formatting of laying out your work that is intuitive or obvious.  It only seems that way to people who’ve been using it for years.

Pros to the traditional long division algorithm:
(using 2718/14 as an example)

- It is efficient and compact. No boxes. No direct copying of whole numbers from one place to another.

- It utilizes standard place value. In 2718/14, when we start by asking ourselves how many times 14 goes into "27", that is shorthand for how many times 14 goes into 2700. And the answer, "1", is written in the hundreds place and is shorthand for 100.

- To anyone who truly understands place value and division, it is then entirely intuitive that you need to subtract to find how much of your dividend is still left to divide up. Your 1 in the quotient stands for 100, specifically 100 14s which is 1400. People who are fluent with the algorithm can skip writing the zeros (that is the whole point of an algorithm), and just subtract 14 from 27.

- You are then left asking yourself how many times 14 goes in to "13" meaning 1300. Now clearly, the answer is almost a hundred times, but the beauty of the algorithm is how efficiently you can realize that the hundreds place of your quotient is set in stone, and therefore you should reframe the calculation into "tens": how many times does 14 go into 131 tens?

- The box/area model is just partial quotients - which is fine, but quite inefficient...and drawing a bunch of boxes makes it even more so. My kids use partial quotients. I start them very young physically dividing piles of manipulatives, and eventually they figure out that it makes sense to repeatedly subtract multiples of the divisor. Once they completely, fully, intuitively understand why that is the basis of long division, then I show them how to notate the partial quotient method. I make it look as much like the standard algorithm as possible to ease the transition...plus that way we don't have to keep rewriting the results of our subtraction at the top of a new box, we can just keep subtracting vertically.

- Using the standard algorithm is a good test of whether kids actually understand how long division works. I have never taught a mantra or mnemonic to help them memorize the steps. If you truly know how long division works at its core, then the rules are perfectly intuitive...and they are actually more like guidelines. For example, in the problem 1328 divided by 12, you could certainly follow the algorithm precisely and say that 12 goes into "13" (hundreds) 1 time. But it is actually more efficient to stray from the algorithm and immediately say that 12 goes into "132" (tens) 11 times. No subtraction required - just throw an "11" (tens) in the quotient and immediately move on to dealing with the 8 ones.

- Which brings me to my last pro. Using the standard algorithm, the steps remain exactly the same to divide dividends with decimals or quotients that extend into decimals. The box method seems mostly suited for finding "remainders", which isn't nearly as useful in the real world as precise decimal answers.

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2 hours ago, Danae said:

So I subbed today in a district that teaches long division with the traditional algorithm. There is not a bit of that particular formatting of laying out your work that is intuitive or obvious.  It only seems that way to people who’ve been using it for years.
 

These kids had learned it last year and were being introduced to decimal division, but over half of them were still not solid on whole number division.  They knew that they were supposed to look at the “underneath number” starting from the left and use only as many of the digits as they needed to fit the “outside number” into it.  Most, but not all of them knew that you put “how many times” it fits on top.  Most, but not all of those remembered that if you’re using multiple digits of the “underneath number” you have to line up your “how many times” number with the rightmost digit that you’re using.  After that it got messy.  Everyone remembered that you have to do something with the number you just wrote on top, but they didn’t all remember if you were supposed to multiply, add, subtract, or divide with it and which other number you were supposed to do it with. 

Yeah, this is why I don't teach long division until kids are incredibly solid on the concept. It's a LONG algorithm. 

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22 minutes ago, wendyroo said:

Pros to the traditional long division algorithm:
(using 2718/14 as an example)

- It is efficient and compact. No boxes. No direct copying of whole numbers from one place to another.

- It utilizes standard place value. In 2718/14, when we start by asking ourselves how many times 14 goes into "27", that is shorthand for how many times 14 goes into 2700. And the answer, "1", is written in the hundreds place and is shorthand for 100.

- To anyone who truly understands place value and division, it is then entirely intuitive that you need to subtract to find how much of your dividend is still left to divide up. Your 1 in the quotient stands for 100, specifically 100 14s which is 1400. People who are fluent with the algorithm can skip writing the zeros (that is the whole point of an algorithm), and just subtract 14 from 27.

- You are then left asking yourself how many times 14 goes in to "13" meaning 1300. Now clearly, the answer is almost a hundred times, but the beauty of the algorithm is how efficiently you can realize that the hundreds place of your quotient is set in stone, and therefore you should reframe the calculation into "tens": how many times does 14 go into 131 tens?

- The box/area model is just partial quotients - which is fine, but quite inefficient...and drawing a bunch of boxes makes it even more so. My kids use partial quotients. I start them very young physically dividing piles of manipulatives, and eventually they figure out that it makes sense to repeatedly subtract multiples of the divisor. Once they completely, fully, intuitively understand why that is the basis of long division, then I show them how to notate the partial quotient method. I make it look as much like the standard algorithm as possible to ease the transition...plus that way we don't have to keep rewriting the results of our subtraction at the top of a new box, we can just keep subtracting vertically.

- Using the standard algorithm is a good test of whether kids actually understand how long division works. I have never taught a mantra or mnemonic to help them memorize the steps. If you truly know how long division works at its core, then the rules are perfectly intuitive...and they are actually more like guidelines. For example, in the problem 1328 divided by 12, you could certainly follow the algorithm precisely and say that 12 goes into "13" (hundreds) 1 time. But it is actually more efficient to stray from the algorithm and immediately say that 12 goes into "132" (tens) 11 times. No subtraction required - just throw an "11" (tens) in the quotient and immediately move on to dealing with the 8 ones.

- Which brings me to my last pro. Using the standard algorithm, the steps remain exactly the same to divide dividends with decimals or quotients that extend into decimals. The box method seems mostly suited for finding "remainders", which isn't nearly as useful in the real world as precise decimal answers.

Sure.  But my point is that all the new-fangled multiple ways of teaching division that people love to complain about are trying to get kids to the point where they “truly understand place value and division” so that the algorithm is a useful, compact way of writing what they’re doing rather than a god-awful monkey butt series of memorized steps.

The fact that they’re often taught by rote and thus become another series of stinky monkey butt hoops to jump through is a problem, though.  
 

 

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Just now, Danae said:

Sure.  But my point is that all the new-fangled multiple ways of teaching division that people love to complain about are trying to get kids to the point where they “truly understand place value and division” so that the algorithm is a useful, compact way of writing what they’re doing rather than a god-awful monkey butt series of memorized steps.

The fact that they’re often taught by rote and thus become another series of stinky monkey butt hoops to jump through is a problem, though.  

Agreed and agreed. 

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