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4KookieKids

Can't grasp carrying more than one place?

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Has anyone ever had a kid who couldn't figure out the carrying rule about re-grouping with 9's until the end and then a 10 at the very end (e.g., when subtracting something like 598 from 1234)? We moved on when she got stuck on it last year, and she finished the rest of Singapore 3, but I tried revisiting it this week and she's still completely stuck on it. She can get there on her own by a series of regroupings (e.g., turn 1 into 0 and 2 into 12, then turn 12 into 11 and turn 3 into 13, then turn 13 into 12 and 4 into 14) but it seems like WAY more work (to ME!! lol). This is the only way she can do this that makes any sense to her. I've tried base 10 blocks, drawings, trading in money, etc. all to no avail, and I'm out of ideas. 

She does often forget to actually *add* the 10, as well, and frequently just replaces the number with 10 (i.e., instead of turning 1 into 0 and 2 into 12 in the first step above, she'll turn the 2 into a 10. And then she'll cross off the 10 and put a 9, and cross off the 3 in the tens column and replace it with 10.) When I ask her why you put the 10 there, she can fix it on her own half the time, or so. I feel like she *does* get the idea, but her EF skills and very low working memory are working against her here. How do I know when to move on or if I need to hit this until she's solid?

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I don't follow your explanation; but one technique used to help learning the algorithm is to use colored markers for each place.  So one color for ones place, another for tens,, another for hundreds, another for thousands.  Then do the actual  work with yet another color.

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You could go to youtube and find the Decimal Street video by Mr. Demme and see if that helps with the concept.

Personally, when doing that problem, I'd take 600 away and give back 2 so I could do it in my head. Singapore is into doing math the easy way (by making 10s and 100s), so I would have her do that. It's not often IRL that you'd need to regroup multiple times and not be able to do that IME--as long as you can "pull up" the knowledge that, say, 87 is 13 less than 100.

 

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The way I taught this to my kids is that we need to borrow from the neighbors.

1234 - 598

We don't have enough to subtract 4 - 8.  We can't do that, so we have to go borrow from the neighbors.

The neighbors had 3, they gave 1 to us.  Now they have 2 and we have 18.

Now the neighbors don't have enough to subtract 2 - 9.  Now they have to borrow from their neighbors...

 

For 1000 - 598

We don't have enough to subtract 0 - 8.  We have to go to the neighbors.

They don't have enough either.  We have to go farther down the street.

We finally find enough, and we leave some at each neighbor's house along the way.

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ETA:  I realized that I didn't address your question exactly.  With regard to your example of 1234 - 598, instead of doing a series of regroupings, what were you thinking she should do instead?  That one could be done mentally by subtracting 600 and adding 2.  Is that what you are thinking she should do? 

Original response:

I have two kids who learned this way:

Say you have 3007 - 2458

Instead of "borrowing" the ten from the adjacent zero, you borrow it from the 300.  So make the 300 into 299 (all at once), and put the one (ten) in front of the 7 to make 17.

So, 17 - 8 = 9

9 - 5 = 4

9 - 4 = 5

2 - 2 = 0

The answer is 549.Subtracting across zeros.jpg

Edited by EKS
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2 hours ago, EKS said:

I have two kids who learned this way:

Say you have 3007 - 2458

Instead of "borrowing" the ten from the adjacent zero, you borrow it from the 300.  So make the 300 into 299 (all at once), and put the one (ten) in front of the 7 to make 17.

So, 17 - 8 = 9

9 - 5 = 4

9 - 4 = 5

2 - 2 = 0

The answer is 549.

 

Subtracting across zeros.jpg

Yup, we sometimes do this as well, joking that 3007's nickname today is going to be two thousand nine hundred ninety-seventeen.

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On 5/15/2019 at 10:43 AM, EKS said:

ETA:  I realized that I didn't address your question exactly.  With regard to your example of 1234 - 598, instead of doing a series of regroupings, what were you thinking she should do instead?  That one could be done mentally by subtracting 600 and adding 2.  Is that what you are thinking she should do? 

Original response:

I have two kids who learned this way:

Say you have 3007 - 2458

Instead of "borrowing" the ten from the adjacent zero, you borrow it from the 300.  So make the 300 into 299 (all at once), and put the one (ten) in front of the 7 to make 17.

So, 17 - 8 = 9

9 - 5 = 4

9 - 4 = 5

2 - 2 = 0

The answer is 549.Subtracting across zeros.jpg

I like this one!! 

I’d let her do it however makes sense to her and revisit. And I’d make sure her understanding of place value is solid.

I personally don’t love the idea of borrowing from the neighbors since it makes it seem like we’re getting extra from somewhere instead of just decomposing the number into constituent bits.

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On May 14, 2019 at 11:52 AM, 4KookieKids said:

How do I know when to move on or if I need to hit this until she's solid?

Is this a dc who just got a more global diagnosis? And did she get an SLD diagnosis? In general, a certain amount of academic challenges are expected with certain global diagnoses (for instance ASD) even if they don't diagnose separately the SLDs. If the dc has a more global diagnosis or developmental delays, I would make sure you're generalizing and I would try to do it more ways. My ds, gifted IQ, only really got written addition/subtraction this year (age 10). We did lots and lots and lots of preparatory work on place value, understanding quantities lots of other ways. (money, manipulatives, blocks, abacus, etc.) 

The written math doesn't matter at all, because a calculator can do that. The underlying deficits of sense of quantity are going to affect her 2 digit mental math, and that's how most people do their everyday math (store, time, etc.). So it's more important to spend the time on sense of quantity, estimating, etc. than it is to move forward with computation. She will be able to do computation all the way (as many digits as you want) once it clicks.

Fwiw, when it was ready to click, I used this kit Hands-On Addition Regrouping Kit  It includes cards for 2 digit and multi-digit. We did 2 of each kind of per day, doing the 2 digit cards mentally and talking about what strategies we could have used, then doing the multi-digit with the hands-on until it clicked. Then we did the subtraction kits. Next we'll work through the multiplication and division kits when those are ready. 

We also used grids and we do subtraction the RightStart way, doing all the trades first. You can probably google and find a youtube of the RightStart subtraction method. It streamlines the steps. You may find it useful to work on working memory before going back at computation. Here, see if the RS subtraction is explained in this Advanced Subtraction Lessons - RightStart Mathrightstartmath.com/wp-content/uploads/.../RightStart-Mathematics-Subtraction.pdf

 

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Thank you all. Yes, we do a lot of the mental math stuff and talk about how it's easier to subtract a bigger number and add back in (she's doing Beast and Singapore concurrently, Beast a level behind Singapore). She's getting things a lot of different ways! 🙂 We do all the cheats out there! lol. I would just like this to be a tool in her arsenal as well, I guess.

 
28 minutes ago, PeterPan said:

Is this a dc who just got a more global diagnosis? And did she get an SLD diagnosis? In general, a certain amount of academic challenges are expected with certain global diagnoses (for instance ASD) even if they don't diagnose separately the SLDs. If the dc has a more global diagnosis or developmental delays, I would make sure you're generalizing and I would try to do it more ways. My ds, gifted IQ, only really got written addition/subtraction this year (age 10). We did lots and lots and lots of preparatory work on place value, understanding quantities lots of other ways. (money, manipulatives, blocks, abacus, etc.) 

The written math doesn't matter at all, because a calculator can do that. The underlying deficits of sense of quantity are going to affect her 2 digit mental math, and that's how most people do their everyday math (store, time, etc.). So it's more important to spend the time on sense of quantity, estimating, etc. than it is to move forward with computation. She will be able to do computation all the way (as many digits as you want) once it clicks.

Fwiw, when it was ready to click, I used this kit Hands-On Addition Regrouping Kit  It includes cards for 2 digit and multi-digit. We did 2 of each kind of per day, doing the 2 digit cards mentally and talking about what strategies we could have used, then doing the multi-digit with the hands-on until it clicked. Then we did the subtraction kits. Next we'll work through the multiplication and division kits when those are ready. 

We also used grids and we do subtraction the RightStart way, doing all the trades first. You can probably google and find a youtube of the RightStart subtraction method. It streamlines the steps. You may find it useful to work on working memory before going back at computation. Here, see if the RS subtraction is explained in this Advanced Subtraction Lessons - RightStart Mathrightstartmath.com/wp-content/uploads/.../RightStart-Mathematics-Subtraction.pdf

 

 

 

Yes, I suppose I'm not yet used to putting things into perspective with her new ASD diagnosis. She is profoundly dyslexic and we've known that for the last year, but all of her other language skills (expressive/receptive) where at or above expected. (caveat: it's not clear to me that "normal" is actually a good descriptor here, since she was also told she was reading "at or above grade level" last year before the SLP did actual phonological tests and found her profoundly dyslexic -- she's just a bright kid who compensates as best she can, you know?)  Would things like autism and dyslexia affect how she does arithmetic?

She has relatively good number sense and can subtract any two digit numbers, but she often has a hard time remembering the extra ten when she's trying to do something like make 100 (e.g., she almost always says that you need 65 to make 100 with 45 when she's doing it in her head. On paper, she can *always* do 100 - 45, because she's pretty much got the "carrying one place" procedure down -- though whether or not she has the concept down is a bit more fuzzy, despite it being emphasized/explained over and over and over again, since 130 - 40 is often gets regrouped as (0) (10) (0) on top, instead of (0), (13) (0) because she forgets to *add* 10, instead of just making the new number a 10.) She does have poor working memory, despite having exceptional processing speed (99.7th %ile).

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47 minutes ago, 4KookieKids said:

she often has a hard time remembering

that's the working memory and that can be improved by working on it. So if she understands the concepts and is just bogging down

-improve working memory and see if it comes together

-use grids (I even draw them on the whiteboard, don't work without grids) 

-do all the trades first like RS

-limit the number of problems you attempt so you don't wear her out

If she has low processing speed AND low working memory, then gross computation is just grunt work and torture. I ask my ds to do just enough to know he can, and then he gets a calculator for the rest of his life. There is zero benefit to turning a kid with low processing speed (which is a permanent disability) into a human calculator. Just saw her processing speed was good. Well cool. So up the working memory and see how much improves. I worked on it 4X a day with my ds when we were making our push. I've had posts. Go for multiple modalities, so visual, auditory, in motion, with distractions, with metronome, using language, lots of ways. 

47 minutes ago, 4KookieKids said:

can subtract any two digit numbers, but she often has a hard time remembering the extra ten when she's trying to do something like make 100 (e.g., she almost always says that you need 65 to make 100 with 45 when she's doing it in her head.

Have you played                                             Melon Rind Clumsy Thief Money Game - Adding to 100 Math Card Game for Elementary Students (Ages 8 and up)                                       It doesn't sound like she's solid on 2 digit mental math, because she should be able to do it every which way within 100 and over 100 mentally, with trades, without trades, backwards and forwards. I would go for that because it's a life skill. I personally wouldn't work on 4 digit written until she can do every 2 digit problem mentally with reasonable accuracy. So 97+23, 98+14. Doesn't have to be fast, but she should be able to tell you multiple strategies on how to get there and really be visualizing it. If she's not, she's screwed in real life.

Yes, we expect kids diagnosed with dyslexia to have crunchy math. I'll tell you though that SLD math (dyscalculia) has the LEAST scientific, least dependable diagnoses processes of all the SLDs. I've heard there's something they look at with coding in the IQ scores, I don't know. Dyscalculia is a number sense disability, and it's over in the language side of the brain (which is why it so commonly overlaps with dyslexia). Technically someone can be MATH GIFTED and have dyscalculia AT THE SAME TIME!!! I kid you not. I've known other people to say this and have the scores to back it up. My ds is considered in that boat. He's actually very bright at math, just struggles with number sense. 

So anyways, the diagnosis is crap as far as procedure and accuracy. Yes she could have dyscalculia and have it not be diagnosed. If she's gifted and the tester was only really looking for discrepancy in achievement, it might not be there. The tester actually has to use their heads and listen. There's a number sense test out of I forget where. Ronit Bird had a link to it. 

47 minutes ago, 4KookieKids said:

On paper, she can *always* do 100 - 45, because she's pretty much got the "carrying one place" procedure down -- though whether or not she has the concept down is a bit more fuzzy, despite it being emphasized/explained over and over and over again, since 130 - 40 is often gets regrouped as (0) (10) (0) on top, instead of (0), (13) (0) because she forgets to *add* 10, instead of just making the new number a 10.)

Why are you doing this? Sorry, I'm being blunt. 2 digit math should be done MENTALLY, always, always, always. It's a vestige of paper curriculum and doesn't reflect reality. It's basically teaching in a disability, because it's telling her there's one way to think through the math. Doing 2 digit math mentally is essential for life. So drop all written math that is 2 digit, do that mentally, and talk through strategies, problem solving together. I solved it this way, how did you solve it, could you have gotten there another way, now show me another. THEN, when she can do it that way, then start doing 4 digit using manipulatives and let her figure out the algorithm.

 

47 minutes ago, 4KookieKids said:

She has relatively good number sense and can subtract any two digit numbers, but she often has a hard time remembering the extra ten when she's trying to do something like make 100 (e.g., she almost always says that you need 65 to make 100 with 45 when she's doing it in her head.

Yeah, doesn't seem to fit. Her number sense is poor enough that to her 45+65 could =100. Something is glitchy. 

There is no substitute for foundation. Curriculum is crap worthless with my ds, and you wouldn't believe HOW MANY people with kids with ASD go well my kid did it for this curriculum but he can't DO it. The curriculum is pushing her through steps her brain hasn't taken yet, so she'll memorize, memorize it in that context, not have it in the next context, and not be able to be FLEXIBLE and do it other ways.

So the concepts are:

-2 digit mental math is a life skill

-anything larger can be done by a calculator and in fact is done with a calculator by most adults

When I work on a concept with my ds, I try to do it lots of ways. Like 

-measuring (linear and volumetric)

-money

-temperature

-dates (years, months, etc.)

-time

-decimals

-fractions

So think about how many of those naturally involve things that make 100 or slightly cross 100. 

If she has a gifted IQ and is struggling with 2 digit mental math at a 3rd grade age (hold old?) despite reasonable instruction, I would just *assume* she has dyscalculia and start reading about it and using techniques for it. It won't hurt and it might help. Dyscalculia plus autism is nasty, because you take all the difficulties of the dyscalculia and then compound them by someone who might compartmentalize their learning. They might learn it for the Singapore worksheet and not know it when you put a 100 table in front of them. I got a whole book of games that uses a 100 table. Ronit Bird has a few. And then she might have to learn it again with Clumsy Thief and again for money in the store. She might know it at the table in your kitchen and not in a different room or in the car. It can compartmentalize THAT MUCH.

That's why it's not adequate to use curriculum for some kids, because the curriculum makes it sound like if you could JUST GET them to get it in the workbook, they'd be fine.

Edited by PeterPan

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1 hour ago, 4KookieKids said:

despite having exceptional processing speed (99.7th %ile).

Total, total rabbit trail, but you might read Dyslexic Advantage and their explanations of some of the brain structures being seen in the MRIs and see what you think. Now personally I think their theories and observations are underdeveloped. My ds has a known gene for dyslexia and an ASD2 diagnosis. So it's hogwash to say they don't occur together. To me that just means their samples were too small and they didn't run genetics. But the idea of brain connectivity and the wiring and pruning and spacing of the mini-columns is really interesting.

I've just sort of grossly assumed that widely spaced mini-columns translate to lower processing speed and more closely-spaced translate to faster processing speed. i really don't *know* though if that's the case. But it's just interesting to ponder, kwim? Because then it takes it beyond are you normal or not (a setting on the washing machine) to how do you work, why do you process this way, how could we HARNESS this...

So for my dd, who has super low processing speed and presumably widely spaced mini-columns, we would harness those narrative strengths (that come as things bounce around diversely and try to make connections) in her math. We'd rabbit trail with the history of it and the stories. And then you might go kinda inverse, like what would really interest her about math and how could you use her brain structure to connect with her better? It's just interesting to ponder. Some kids only engage once you step up the intensity. Like you never know what might happen if you stopped doing computation and went and did something totally DIFFERENT. She might turn out to be crazy brilliant at it. 

I was strongly counseled by a psych to TEACH my ds like he's MATH GIFTED WITH A DISABILITY and not to ignore the gift. So we were doing +/- numbers in 1st grade and we've worked through tons with fractions. The hard things are very simple for him and the simple things (computation, number sense) are wicked hard. It's just another strategy. I try to divide my instruction into 1/3s and not get too stuck on any one area. Like I'm not obsessive about that, but I'm just saying in general I try to have something to move forward his gifted thinking side (something more advanced), something at instructional level (computation, whatever), and something that is sort of interventiony. So we might do all in the same day a middle school geometry program and a grade level daily word problems book and some Tang math sheets below grade level. And I focus on word problems instead of raw computation, because the language of the word problems is an issue with the ASD. Also word problems are real life. It gives us enough work on computation without getting stuck on something that isn't going to be a strength for him.

https://www.evan-moor.com/p/20048/evan-moor-daily-word-problems-grade-3  This is one of my favs. I like that it has been redone to fit Common Core. The gr 3 is mostly single step and the gr 4 goes to multi-step. Hits lots of areas, makes sure they're developing the language of math, has charming themes. It's just a winner. And I get that Singapore is great and all that. Whatever. I'm kinda snobbish and think it's unnecessary. People who are strong at math can do it anyway, without going through their program, and people who are weak at math go through it and still struggle. So to me, I'm like TEACH YOUR KID WHERE HE'S AT. That's my two cents. 

I'm using the grade 2 Tang math stuff with my ds. Yeah I'm out saying that in public, lol. But that's fine, because that's what he can do comfortably and stay calm. I always start him easy and work up. That's how we get to great places in our house. My ds really has issues with frustration tolerance, staying calming, needing to feel like it's working. So like to me, if the kid with ASD is in Singapore and they're just bogged down, cross the street, kwim? Go somewhere else, get math working again. My ds needs consistent small steps, a very dependable format, same thing every day, very predictable. It helps keep him calm and helps him achieve things he wouldn't have been able to do otherwise. The harder the task, the more we just have to break it down into those small steps that he can keep calm with till he can go ok, I've got this. That's why I use a lot of stuff that people might be like OH I WOULDN'T USE THAT... Fine, I get it, I get Evan Moor doesn't pass the swanky test, whatever. But I'm hitting language goals, keeping him calm, getting work done consistently, not getting bogged down. It's a lot of good stuff there beyond the math.

Think through your relationship and how you want math to feel each day, how you want it to flow. 

Edited by PeterPan

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