How to help a 4th grader without intuitive number sense?

[JazzyMom]

My 4th grader (9 yo) is the 5th of 8 kids.  He seems to struggle with math quite a bit more than his older siblings.  I don’t know how to describe it, but he doesn’t seem to have much number sense.  He says math is his favorite subject.

He’s the only one of my kids who has had trouble learning his math facts. Today we were working on multiplication facts, and to solve 7 x 8, he did 7 x 4 =  28 and then added 28 plus 28.  Which works, but at first he did that math incorrectly, and it took him a long time.  And I wonder why he didn’t use skip counting, which is what we’ve been practicing.

I have him doing xtra math (online) to drill addition and subtraction.  I notice that he is still counting out the facts, not memorizing them.  He just counts it out very quickly, so he answers within the allotted time period.

I have used A Beka arithmetic with all of the kids until 6th grade, and I really don’t want to change that.  But are there some simple things I could do to help him?

[HomeAgain]

You can give him visual models, using sets of cuisenaire rods.  They're cheap, and easy to see the groupings.  The kids I work with now do similar (2x2x2 of a number to get 8x it), but my youngest came up with his own method of only working with half the multiplication facts.  He did up to 5 of a number.  For 7x8, for example, he would do 5x8 + 2x8, sorting the blocks physically, and then later mentally, into manageable groups.  5 of an even number is an set of tens, so he could add on easily after that.

I recommend the c-rods because they're inexpensive and there are a LOT of ways to use them with online materials like Education Unboxed.  There's a digital version from Dragonbox that uses different colors, but if he's more into using an app he might prefer that.

 

[forty-two]

12 minutes ago, JazzyMom said:

He’s the only one of my kids who has had trouble learning his math facts. Today we were working on multiplication facts, and to solve 7 x 8, he did 7 x 4 =  28 and then added 28 plus 28.  Which works, but at first he did that math incorrectly, and it took him a long time.  And I wonder why he didn’t use skip counting, which is what we’ve been practicing.

Actually, it sounds like he's got good math intuition - he saw a useful alternate way to solve it, and his instincts were spot on - he knew what he had to do.  It shows good understanding and flexible thinking 👍. It's just that his calculation skills weren't up to the task doing it correctly.  My oldest was this way: she saw the relationships well, knew how the numbers fit together, but had problems getting the calculations right. 

I agree with HomeAgain about using visual models - letting him work out the facts he doesn't know with manipulatives over and over (and over and over).  Let them keep proving it to themselves.  It's what I did with both of my girls when we were drilling mult facts.  If they couldn't remember what 6x8 was, for example, they'd pull out a bunch of counters (fake jewels, in our case), make 6 piles of 8, and then either skip count the piles, or put them together into piles of ten for easy counting, or whatever other way of making sense of them they wanted to try.  They got all anxious about being timed, so I didn't worry about speed as much as getting them able to figure it reliably enough to be able to see relationships at a glance in long division and in fractions (aka effective number sense).

You could also work on mental math techniques - our program emphasized "making tens" to add - when adding 7+8, for example, you think of it as "8 needs 2 more to make 10, which leaves 5 left over, which makes 15".  It's a super helpful technique and I use it myself a lot.  (It also meant that the only add/sub facts that needed to be memorized were those up to 10, which were a lot easier to learn.)  You can also combine it with RightStart's emphasis on 5s.  You can see quantities up to 5 at a glance, and then you think of 6 as 5&1, 7 as 5&2, etc. - more quantities you can see at a glance.  The program I used (Singapore Math) has set of supplemental mental math workbooks that you could do alongside your regular program: Level 1, Level 2.  I'd rec starting with Level 1 - it's below level for him, but it sets the foundation for the rest, and easy confidence building can be a plus.

[UHP]

4 hours ago, JazzyMom said:

Today we were working on multiplication facts, and to solve 7 x 8, he did 7 x 4 =  28 and then added 28 plus 28.

I think this is great! If he makes mistakes adding two-digit numbers that's something to work on but it doesn't show any misunderstanding of multiplication.

[PeterPan]

5 hours ago, JazzyMom said:

solve 7 x 8, he did 7 x 4 =  28 and then added 28 plus 28.

Not only does it work but it's BRILLIANT and reflects an accurate understanding of multiplication as *scaling*. If you look up Ronit Bird (British dyscalculia expert) scaling from known to unknown is exactly how she teaches multiplication. If he doesn't know 7X4, could he have scaled from what he did know (7X2)? Think about it. At that point, he would know 7X2X2X2 which you then point out is 7X2^3, a much more complex concept. 

If he has ADHD, poor working memory and low dopamine would hold back getting information from short term to long term memory. In that case, meds for the ADHD to raise dopamine, activities to build working memory (games), and working memory supports like you scribing his thoughts onto a whiteboard can help.

Fwiw, my dd's math ACT scores went up *dramatically* when she started ADHD meds. 

5 hours ago, JazzyMom said:

I wonder why he didn’t use skip counting,

Language and math store in different parts of the brain, so skip counting for math is illogical. Maybe try methods like visualization or organization based on scaling.

http://www.ronitbird.com/ebooks-for-learners-with-dyscalculia/ Link to Ronit Bird's ebook for multiplication. But if you've taught the facts conceptually and the issue is he's just not memorizing, odds are that's the dopamine/working memory/ADHD thing. Something to look into at least.

[PeterPan]

https://www.amazon.com/Multiplication-Facts-Seven-Days-Success/dp/1583242759  This little book is arranged very logically. It's good for working on memorizing once you've done the conceptual/visualization work. My ds has dyscalculia (number sense disability) and the ADHD and autism, so I have to do things a bunch of ways for anything to stick and be there when you change the manipulative, lol. 

I happen to really like the Fast Facts Math app btw. You can use it to narrow down which facts you're targeting and drill.

Edited June 19, 2021 by PeterPan

[JazzyMom]

Thanks, everyone!  I haven’t noticed any ADHD or attention issues, but we have not spent a lot of time playing with manipulatives, so I think that might help.  I have him working through a Kumon multiplication book this summer, so I’ll add manipulatives and see if that helps. 

Edited June 20, 2021 by JazzyMom

[Not_a_Number]

On 6/19/2021 at 1:01 PM, forty-two said:

Actually, it sounds like he's got good math intuition - he saw a useful alternate way to solve it, and his instincts were spot on - he knew what he had to do.  It shows good understanding and flexible thinking 👍.

Agreed. That's actually how I encouraged DD8 to do multiplication, because I wanted her to have a good feeling for it. 

[EKS]

On 6/19/2021 at 9:07 AM, JazzyMom said:

My 4th grader (9 yo) is the 5th of 8 kids.  He seems to struggle with math quite a bit more than his older siblings.  I don’t know how to describe it, but he doesn’t seem to have much number sense.  He says math is his favorite subject.

He’s the only one of my kids who has had trouble learning his math facts. Today we were working on multiplication facts, and to solve 7 x 8, he did 7 x 4 =  28 and then added 28 plus 28.

It sounds to me like he has great number sense.  It's the folks without number sense who resort to rote approaches to problem solving--like the skip counting they've been practicing.

Edited June 22, 2021 by EKS

[JazzyMom]

Skip counting helped my older children learn their math facts, and they’re all very strong math students.  If there are methods that would be better for this child, I’m open to suggestions, which is why I posted.  He’s currently spending a lot of time arriving at incorrect answers, and I’d like to help make it easier for him, if possible.

Number sense may not have been the best descriptor (or we may be defining it differently).  I am just trying to find a way to describe what I’m seeing, so I can help him.

Edited June 22, 2021 by JazzyMom

[HomeAgain]

@JazzyMomSo it sounds like what you're saying is that even though he knows HOW to get to the right answer in multiple ways, he doesn't have a strong math fact fluency - everything is shaky?

My comment about the c-rods still stand.  You can also drill in different ways, like I have sheets for my extra kids where they have multiple steps to do, like rolling a die, tripling the number and adding 2 to find a number to cover on their chart. 
BUT, my kiddos really get a lot out of the rods and the exercises found within different resources.  Making them look at the problem is really important for them to be able to do the problem.  Eight 7s could be seen as "two 7s less than ten 7s" or "Eight 5s and eight 2s" or "eight of the 3s less than eight 10s"

There are a lot of ways to see the problem, but they all require a fluency in addition bonds first, which is seen by measuring against a 10 rod.  Over and over and over.  Measure, prove, find ways to do it mentally.  Shift some over to make a ten.  Rearrange to make easier tens.  Visualize how many ways to make ten...

Edited June 22, 2021 by HomeAgain

[JazzyMom]

1 hour ago, HomeAgain said:

@JazzyMomSo it sounds like what you're saying is that even though he knows HOW to get to the right answer in multiple ways, he doesn't have a strong math fact fluency - everything is shaky?
 

Yes, this is it.  Everything is shaky.  There are some things he doesn’t seem to have internalized that are making things harder for him.  I’m using the summer to work with him on it, and what I’ve been doing just hasn’t been effective.  I do think you are right that he probably needs to actually see it over and over.  I have c-rods and counting bears and legos we can use.  I’ll look for some game ideas, too.

Edited June 22, 2021 by JazzyMom

[Not_a_Number]

2 hours ago, JazzyMom said:

Yes, this is it.  Everything is shaky.  There are some things he doesn’t seem to have internalized that are making things harder for him.  I’m using the summer to work with him on it, and what I’ve been doing just hasn’t been effective.  I do think you are right that he probably needs to actually see it over and over.  I have c-rods and counting bears and legos we can use.  I’ll look for some game ideas, too.

I think you’re going to be careful not to train him out of his intuitions. Breaking products up like that is excellent practice for later math like algebra.

When you say a kid is a strong math student, what does that mean? This student says he likes math a lot — do your other kids as well?

[HomeAgain]

3 hours ago, JazzyMom said:

Yes, this is it.  Everything is shaky.  There are some things he doesn’t seem to have internalized that are making things harder for him.  I’m using the summer to work with him on it, and what I’ve been doing just hasn’t been effective.  I do think you are right that he probably needs to actually see it over and over.  I have c-rods and counting bears and legos we can use.  I’ll look for some game ideas, too.

One thing I use for my kids is a process of making them defend their answer.  With the c-rods, that's easy.  So if he adds 28 and 28, and got the wrong answer, he would find that out in the next step of creating two lines, one of his eight 7s and one of what he thought the answer was. 
Or, once he starts getting to the point of grouping, I have place value stamps to start working through it with.  So it's a little more complicated, because it requires the first fact to be known cold: 4x7 is 28, and then making two groups of 2 tens and 8 units, making him compose a single ten from the units and trading it for that place value stamp.  You can start with any number, but it can be annoying to do this process with 8 groups of 7 units. The rods work a hundred times better when working with that.
 

Most of the kids I've worked with are visual learners, and I'm starting to think it's just a thing that a lot of kids benefit from.  It's also a thing that a lot of adults (like myself) benefit from. But, I think your son is well within the range of normal for 4th grade.  It can be difficult to keep the information for all four processes straight until there is a point of fluency again.

[JazzyMom]

2 hours ago, Not_a_Number said:

I think you’re going to be careful not to train him out of his intuitions. Breaking products up like that is excellent practice for later math like algebra.

When you say a kid is a strong math student, what does that mean? This student says he likes math a lot — do your other kids as well?

Just to clarify, I didn’t tell him not to solve the problem that way.  The original answer he gave was in the hundreds, so using his method, I walked him thru, okay what is 7x4?  Okay, now if we add 28+28, what’s that?  I didn’t say, wrong - do skip counting.  But it took him a while to get it right, and the goal I was trying to help him work toward was memorizing facts, so I wondered why he approached it that way.

By strong math students, I mean the oldest 2 had 95th percentile or above on math SAT, next line is a rising high school freshman and hasn’t taken the SAT, but passed the math portion of the community college entrance exam, next in line is probably best at math and does math puzzles for fun.  They all have varying interests but none of them have had trouble learning or complaints about math.  They also sometimes approached problems with their own methods.  They have not had any trouble learning algebra or advanced math.

Difficult to explain, and I don’t want to get into a debate about teaching methods, but my 4 older kids just seemed to have a better understanding.  I’d explain things once or twice (fractions, long division, or whatever), and they just got it.  They didn’t want or need tons of explanations or hands on work.  It just made sense to them.  So maybe they counted on fingers (manipulatives) or did skip counting (counting groups of numbers) for a short time, but we never really needed to do flash cards or computer drills or writing times tables or whatever.   

So I am seeing that this child is different and trying to figure out how to best help him.  Math facts aren’t the only area where I’ve noticed a difference.  He probably needs more visual/hands on work.

Edited June 22, 2021 by JazzyMom

[JazzyMom]

39 minutes ago, HomeAgain said:

Most of the kids I've worked with are visual learners, and I'm starting to think it's just a thing that a lot of kids benefit from.  It's also a thing that a lot of adults (like myself) benefit from. But, I think your son is well within the range of normal for 4th grade.  It can be difficult to keep the information for all four processes straight until there is a point of fluency again.

Yes, I do think he is within the range of normal.  I think this will help him.  Thanks for the suggestions! 

[Not_a_Number]

56 minutes ago, JazzyMom said:

Just to clarify, I didn’t tell him not to solve the problem that way.  The original answer he gave was in the hundreds, so using his method, I walked him thru, okay what is 7x4?  Okay, now if we add 28+28, what’s that?  I didn’t say, wrong - do skip counting.  But it took him a while to get it right, and the goal I was trying to help him work toward was memorizing facts, so I wondered why he approached it that way.

So from your perspective, does this seem like a worse way to approach it than by skip-counting? I'm genuinely curious -- why is that? It seems faster to me. 

 

56 minutes ago, JazzyMom said:

By strong math students, I mean the oldest 2 had 95th percentile or above on math SAT, next line is a rising high school freshman and hasn’t taken the SAT, but passed the math portion of the community college entrance exam, next in line is probably best at math and does math puzzles for fun.  They all have varying interests but none of them have had trouble learning or complaints about math.  They also sometimes approached problems with their own methods.  They have not had any trouble learning algebra or advanced math.

Difficult to explain, and I don’t want to get into a debate about teaching methods, but my 4 older kids just seemed to have a better understanding.  I’d explain things once or twice (fractions, long division, or whatever), and they just got it.  They didn’t want or need tons of explanations or hands on work.  It just made sense to them.  So maybe they counted on fingers (manipulatives) or did skip counting (counting groups of numbers) for a short time, but we never really needed to do flash cards or computer drills or writing times tables or whatever.   

I do believe he's having a harder time with things. But is it possible that it's because he needs to understand things more than the older ones? Because I've never once met a kid who immediately understood WHY fractions worked the way they did or WHY long division works. I have a really accelerated kid and it took her probably 6 months to fully get the hang of why fraction addition and multiplication work they way they do and what the formulas are. It's simply not obvious. 

Maybe I'm way off-base, but I was just struck by your description. As a math person, I really can't imagine discouraging kids from using the distributive and associative properties to do multiplication or finding that odd, I guess. It does sound like he needs fact drills more than your older kids, though, and maybe that'd be a good thing to work on. 

[JazzyMom]

36 minutes ago, Not_a_Number said:

So from your perspective, does this seem like a worse way to approach it than by skip-counting? I'm genuinely curious -- why is that? It seems faster to me. 

 

I do believe he's having a harder time with things. But is it possible that it's because he needs to understand things more than the older ones? Because I've never once met a kid who immediately understood WHY fractions worked the way they did or WHY long division works. I have a really accelerated kid and it took her probably 6 months to fully get the hang of why fraction addition and multiplication work they way they do and what the formulas are. It's simply not obvious. 

Maybe I'm way off-base, but I was just struck by your description. As a math person, I really can't imagine discouraging kids from using the distributive and associative properties to do multiplication or finding that odd, I guess. It does sound like he needs fact drills more than your older kids, though, and maybe that'd be a good thing to work on. 

I don’t remember saying I discouraged him or that skip counting was better.  I said that I helped him answer the problem using his method, but wondered why he approached it that way.  It could be a superior, faster method, but for him it was very slow and led to an incorrect answer.

For the past month we have been working through a Kumon multiplication workbook with the goal of memorizing multiplication facts, along with various other methods, skip counting, times tables, etc. So when I pointed to a problem he had accidentally skipped and saw his approach, I wondered why he approached it that way instead of using the methods we’d been practicing.  

I agree that he needs a better understanding.  Perhaps I incorrectly referred to it as “number sense,” but I posted looking for suggestions about how to help a kid who does not seem to have ”whatever it is” that made things easier for his siblings.

By posting here, I am already acknowledging that the things I thought would help him, weren’t helpful.  Fact drills have not been helpful.  That’s why I am asking for ideas.

[Janeway]

One thing that I have found that really really has helped was..print off a multiplication table and let them use it. By repeatedly looking up the answers on the chart, they not only see the patterns, but they also eventually remember the answers and stop looking. I freely have let my children use it and it has led to them memorizing without pain.

[Clemsondana]

Like others have said, he's showing great understanding and using a technique that will ultimately be more useful - breaking numbers apart like that lets you do all sorts of mental math with bigger numbers once you get the arithmetic correct.  Was his mistake with addition or the 7x4 multiplication?  I ask because some kids I tutored were much better at multiplying because they had memorized some of the facts, but they tended to make addition mistakes.  We used Singapore which was big on making tens for addition and subtraction.  We used blocks so that the kids could see 7+6 becoming 10+3, or 14-8 become 10-8+4.  It took longer to teach them than the 'count on your fingers' approach that I was taught in school, but their mental math skills were far better than mine by the time that we were done.  

I don't have any tricks for memorizing math facts other than repeition.  It's one of the few places that I let my kids use simple video games, although we also occasionally did minute drills to see how many they could get right in a minute.  My MIL would sometimes practice with one of my kids with flash cards, giving M&Ms every time they got a certain number right - it helped my kid who wasn't motivated.  I also had one who chanted the rhyme 'I ate and I ate 'til I fell on the floor...8x8 is 64' every time they came across that problem.  I think they learned it in a co-op class that used games to let kids practice their math facts.  

[Not_a_Number]

34 minutes ago, JazzyMom said:

I don’t remember saying I discouraged him or that skip counting was better.  I said that I helped him answer the problem using his method, but wondered why he approached it that way.  It could be a superior, faster method, but for him it was very slow and led to an incorrect answer.

So, for ME, as a math person, the reason he approached it that way would be that it probably made better sense to him? It sounds like making personal sense of things is important to him. 

 

34 minutes ago, JazzyMom said:

For the past month we have been working through a Kumon multiplication workbook with the goal of memorizing multiplication facts, along with various other methods, skip counting, times tables, etc. So when I pointed to a problem he had accidentally skipped and saw his approach, I wondered why he approached it that way instead of using the methods we’d been practicing.  

I agree that he needs a better understanding.  Perhaps I incorrectly referred to it as “number sense,” but I posted looking for suggestions about how to help a kid who does not seem to have ”whatever it is” that made things easier for his siblings.

By posting here, I am already acknowledging that the things I thought would help him, weren’t helpful.  Fact drills have not been helpful.  That’s why I am asking for ideas.

What I would do with him is let him use his sense to figure these things out and not insist on specific methods like skip counting. I'd also maybe try to figure out if the skip counting is making sense to him or not. Does he understand why that works? Is he able to skip count quickly to get that to be effective? How would HE personally do multiplication if left to his own devices? 

Since he doesn't have addition facts memorized, clearly, and he's obviously kind of struggling with place value if he's getting numbers in the hundreds, I'd start there. Does he have good addition strategies? Do you think some concentrated drill there first would help? 

[JazzyMom]

His mistake was with doing the addition in his head.

I think it’s likely there are a few things that don’t fully make sense to him, and it might help to go back to addition and move forward from there, working through things visually and maybe playing some games.  That will help me understand where he’s shaky and hopefully strengthen his understanding before working on facts again.  I like the idea of letting him have a chart handy once he starts the next book in his math program.

I appreciate all of the advice!

[Not_a_Number]

Just now, JazzyMom said:

His mistake was with doing the addition in his head.

Do you know what he did wrong in his head? Getting an answer in the hundreds is definitely not something that ought to sound reasonable to a kid with a robust understanding of place value, so that makes me more worried than the rest of the description. 

 

Just now, JazzyMom said:

I think it’s likely there are a few things that don’t fully make sense to him, and it might help to go back to addition and move forward from there, working through things visually and maybe playing some games.  That will help me understand where he’s shaky and hopefully strengthen his understanding before working on facts again.  I like the idea of letting him have a chart handy once he starts the next book in his math program.

That sounds like a great idea. 

 

[JazzyMom]

20 minutes ago, Not_a_Number said:

Do you know what he did wrong in his head? Getting an answer in the hundreds is definitely not something that ought to sound reasonable to a kid with a robust understanding of place value, so that makes me more worried than the rest of the description. 

 

That sounds like a great idea. 

 

Not sure where he went wrong that time, and he did it right the 2nd time, but he doesn’t seem to notice unreasonable answers.  I used math facts in my example because that’s what he’s been practicing, but there are other things that make it seem he doesn’t fully grasp everything.  It’s hard to describe.  He’s not terrible by any means, but he doesn’t fully grasp it. I feel like it could get very confusing for him once things get more complex, so I wanted to try another approach.

[JazzyMom]

On 6/19/2021 at 4:38 PM, PeterPan said:

http://www.ronitbird.com/ebooks-for-learners-with-dyscalculia/ Link to Ronit Bird's ebook for multiplication. But if you've taught the facts conceptually and the issue is he's just not memorizing, odds are that's the dopamine/working memory/ADHD thing. Something to look into at least.

Thank you! Thank you! Thank you!!!

I finally had a chance to look thru her website this morning, and she describes EVERYTHING - the random guesses, unreasonable answers, counting when doing drills (like I described in the OP), not noticing patterns, ability do algebra but not a simple multiplication fact.  

She even specifically mentions not having a feel for numbers and a lack of “number sense.”

He’s honestly not that far off the mark, but I had a feeling he was going to get very lost if we kept moving forward.  Now I have a game plan for actually helping him.

And you all were spot on about him needing to see things visually.

Thank you all so much!!!!!!!

Edited June 23, 2021 by JazzyMom

[Not_a_Number]

35 minutes ago, JazzyMom said:

Thank you! Thank you! Thank you!!!

I finally had a chance to look thru her website this morning, and she describes EVERYTHING - the random guesses, unreasonable answers, counting when doing drills (like I described in the OP), not noticing patterns, ability do algebra but not a simple multiplication fact.  

She even specifically mentions not having a feel for numbers and a lack of “number sense.”

He’s honestly not that far off the mark, but I had a feeling he was going to get very lost if we kept moving forward.  Now I have a game plan for actually helping him.

And you all were spot on about him needing to see things visually.

Thank you all so much!!!!!!!

Quick question: is his feel for numbers bad for smaller numbers as well? Like, does he have any sense for how big 3*5 should be? Or does he get just as lost there?

[Not_a_Number]

7 hours ago, JazzyMom said:

Not sure where he went wrong that time, and he did it right the 2nd time, but he doesn’t seem to notice unreasonable answers.  I used math facts in my example because that’s what he’s been practicing, but there are other things that make it seem he doesn’t fully grasp everything.  It’s hard to describe.  He’s not terrible by any means, but he doesn’t fully grasp it. I feel like it could get very confusing for him once things get more complex, so I wanted to try another approach.

Another example would be helpful, if you don't mind 🙂 . 

[JazzyMom]

1 hour ago, Not_a_Number said:

Quick question: is his feel for numbers bad for smaller numbers as well? Like, does he have any sense for how big 3*5 should be? Or does he get just as lost there?

He seems better with smaller numbers.  

1 hour ago, Not_a_Number said:

Another example would be helpful, if you don't mind 🙂 . 

For instance, if we are looking at a hundreds chart, and I point to the numbers and show how if you add 10 to 25, you get 35, and if you add 10 to 35, you get 45, and if you add 10 to 45, you get 55.  What do you get if you add 10 to 55?  He thinks for a very long time.  “58???” 

He does not detect the pattern, and his guesses seem very random.  And I know that, useful or not, this is something my 7 yo grasped with no problem.

I’m not saying he has dyscalculia, but her descriptions fit what I have been concerned about and confirm that there is a “something” my other kids have that he doesn’t have that is making things more difficult for him.  

I *think* he is within normal range, but when I thumbed thru the next level of his math book, I could see we needed to do some work before moving on.  It’s just that the things we have been working on haven’t been helping.

Edited June 23, 2021 by JazzyMom

[Not_a_Number]

8 minutes ago, JazzyMom said:

He seems better with smaller numbers.  

That's definitely a good thing! Does he know any of his addition facts, by the way? It sounds like he's been drilling them and that hasn't been sticking, right? Does he know quick tricks for any of them? 

 

8 minutes ago, JazzyMom said:

For instance, if we are looking at a hundreds chart, and I point to the numbers and show how if you add 10 to 25, you get 35, and if you add 10 to 35, you get 45, and if you add 10 to 45, you get 55? What do you get if you add 10 to 55?  He thinks for a very long time.  “58???” 

He does not detect the pattern, and his guesses seem very random.  And I know that, useful or not, this is something my 7 yo grasped with no problem.

Interesting. He does sound he's struggling and like he might need a more concrete approach. 

I'd definitely let him use some sorts of place value manipulatives. It sounds like things only make sense for him if he can figure them out himself using what he himself understands (hence the splitting up for 7*8, I'd guess), so probably being extra explicit with place value would help. (Honestly, it helps a lot of kids, but it sounds like he NEEDS in a way that your older kids did not.) 

I'd probably slow way down until he can get relatively consistent answers with what he's currently doing -- I'd agree that he's probably going to be confused if you move forward! 

[JazzyMom]

9 minutes ago, Not_a_Number said:

That's definitely a good thing! Does he know any of his addition facts, by the way? It sounds like he's been drilling them and that hasn't been sticking, right? Does he know quick tricks for any of them? 

He has the smaller addition facts memorized.  When it gets to adding 7, 8, or 9 to a number, he counts it.

So he can do double and triple digit addition, addition with carrying, subtraction with borrowing, multiplication by numbers up to 6.  But he does not have the facts memorized.  He has to figure them out.  We’ve been working on drills for a month without much progress.

He can “do” a lot of things with numbers, but he doesn’t really seem to “get” it. 

[Not_a_Number]

7 minutes ago, JazzyMom said:

He has the smaller addition facts memorized.  When it gets to adding 7, 8, or 9 to a number, he counts it.

Ah, so it's the bigger numbers giving him trouble. Perhaps teach him the "make 10" trick? That'll only seem intuitive to him once place value is totally clear to him, though. 

 

7 minutes ago, JazzyMom said:

So he can do double and triple digit addition, addition with carrying, subtraction with borrowing, multiplication by numbers up to 6.  But he does not have the facts memorized.  He has to figure them out.  We’ve been working on drills for a month without much progress.

But if he can't add 10 to a number with good understanding, then I assume he can do those purely algorithmically? 

 

7 minutes ago, JazzyMom said:

He can “do” a lot of things with numbers, but he doesn’t really seem to “get” it. 

It does sound like that. 

[JazzyMom]

Yes, I think he understands some things, but he’s doing a lot of it by rote.

Edited June 23, 2021 by JazzyMom

[Not_a_Number]

1 hour ago, JazzyMom said:

Yes, I think he understands some things, but he’s doing a lot of it by rote.

I think it's a great thing that you've noticed and are going to back up and make sure he's solid 🙂 . Some kids can learn by rote and gain understanding later (although that's never my preferred method), and some can't. Sounds like he's one of the latter type. 

[PeterPan]

10 hours ago, JazzyMom said:

I’m not saying he has dyscalculia, but her descriptions fit what I have been concerned about and confirm that there is a “something” my other kids have that he doesn’t have that is making things more difficult for him.  

You want evals to diagnose?

9 hours ago, JazzyMom said:

He has the smaller addition facts memorized.  When it gets to adding 7, 8, or 9 to a number, he counts it.

Ronit Birds stuff would help with this . She’s BRILLIANT

Sometimes you go back to go forward. You could do other (advanced) things while you review. Didax has great books for this.

Edited June 23, 2021 by PeterPan

[JazzyMom]

1 hour ago, PeterPan said:

You want evals to diagnose?

Ronit Birds stuff would help with this . She’s BRILLIANT

Sometimes you go back to go forward. You could do other (advanced) things while you review. Didax has great books for this.

I already ordered one of her books and a few of the things we need for the games.  I am thinking we’ll try that first before getting an eval.  I think he’ll make progress with the right tools and approach.
 

[Not_a_Number]

Personally, I'd concurrently work on developing his sense of multiplication (his instincts for that seem very good, as people have noted) and also intensively remediate place value via games and manipulatives as well as working on the addition facts (probably also via games and strategies.) 

[PeterPan]

22 minutes ago, JazzyMom said:

I already ordered one of her books and a few of the things we need for the games.  I am thinking we’ll try that first before getting an eval.  I think he’ll make progress with the right tools and approach.
 

The evals will still tell you quite a bit. Usually with SLDs there's going to be comorbid ADHD, processing speed low (relative to IQ), and maybe even some things you don't suspect that they'll catch. It will give you paper trail for accommodations. 

What you will learn varies with the psych obviously, because some are really basic and some dig in on extra things like narrative language, visual motor screenings, etc. But I'll just tell you, as water under the bridge thing, you're likely to learn things and that earlier is better.

Edited June 24, 2021 by PeterPan

[Not_a_Number]

Just now, PeterPan said:

The evals will still tell you quite a bit. Usually with SLDs there's going to be comorbid ADHD, processing speed low (relative to IQ), and maybe even some things you don't suspect that they'll catch. It will give you paper trail for accommodations. 

What you will learn varies with the psych obviously, because some are really basic and some dig in on extra things like narrative language, visual motor screenings, etc. But I'll just tell you, as water under the bridge for me, you're likely to learn things and that earlier is better.

It's all information, so may as well, right? But I think people do tend to feel reluctant... 

[PeterPan]

23 minutes ago, JazzyMom said:

ordered one of her books

Did you see her ebooks? They're like $10 and so great, open and go, with videos embedded. If he's counting for addition, honestly consider getting her Dots ebook. It won't take so long to run through, but it might be just the thing to snap that. With my ds, each lesson took a month, lol. Your ds is older, so he'll go much more quickly, like maybe one lesson every 2-3 days for perfect mastery. You'll love how open and go and easy it is to use.

You need an apple product for the ebooks, sigh. But if you have one, highly recommend.

[PeterPan]

1 minute ago, Not_a_Number said:

It's all information, so may as well, right? But I think people do tend to feel reluctant... 

Of course they feel reluctant. That's why I'm telling her straight my experience. If you go to some really basic psych who runs 2 hours of testing, you'll learn his processing speed and beyond that wonder why you bothered. But if you search around for someone who spends some time, you're likely to learn a lot. And getting things like ADHD, anxiety, etc. caught NOW can save a lot of grief. Nuts, just realizing his processing speed can make a huge difference in how you teach. And given that she has another thread currently on her 11 yo, she is probably in the market for a psych anyway. 

So shop around, find a gem, book some slots. The water under the bridge is what happens when you DON'T eval and you wait. And unless they mortgaged stuff and sold their cat to make it happen, most people are glad for the information they get. 

[PeterPan]

Adding: You have the *federal right* to free evals through the ps. Now some districts are less than helpful, but even then you have the right to dispute and compel them to pay for private evals. 

So if she's saying 8 kids, no funding, there's the ps. My ds has an IEP through the ps so I've btdt. I even had them do evals for my dd her senior year to get us paper trail. Evals are a good thing. Now sometimes you get crummy evals, somebody blowing you off, and it makes the situation worse. But that can happen whether you pay or go through the ps or whatever. Main thing is to take the leap, because these are situations that benefit from the info that comes from the evals. If she doesn't know what to do with the info, she can come hang on LC.

[JazzyMom]

 

@HomeAgain  Seems like maybe you’re a tutor?  When working strictly with hands on materials, do you think short sessions are better?  As long as the student wants to go?  How do you structure it?

Do you continue lots of repetition with the hands on materials even after it seems they have a strong understanding?

[Not_a_Number]

4 minutes ago, JazzyMom said:

 

@HomeAgain  Seems like maybe you’re a tutor?  When working strictly with hands on materials, do you think short sessions are better?  As long as the student wants to go?  How do you structure it?

Do you continue lots of repetition with the hands on materials even after it seems they have a strong understanding?

Do you want my opinion as well or no? I also tutor.

[JazzyMom]

Sure!  I thought I could tell from HomeAgain’s descriptions that she works with more kids than just her own, but I didn’t know you also tutored.

[HomeAgain]

21 minutes ago, JazzyMom said:

 

@HomeAgain  Seems like maybe you’re a tutor?  When working strictly with hands on materials, do you think short sessions are better?  As long as the student wants to go?  How do you structure it?

Do you continue lots of repetition with the hands on materials even after it seems they have a strong understanding?

I do tutor.  🙂 Right now I have my extras in a pattern of:
1. new or continued exploration.  This is our hands on portion and it's brain stretching.  We rotate through concepts, connecting to previous work as needed.  I try to max this out at half an hour, but it can run anywhere from 15-45 minutes.  There is usually a specific goal that I have in mind for the exercise, and I try to gauge whether we are going to meet that goal that day (or break it into two or more sessions) or whether we can go longer and stretch a little further/give more open exploration time.

2. Written work that is already mastered from hands on.  It's a good way to end our time, revisit concepts in a different way, make sure they're really understanding the principals behind the work and make the switch from visualizing to writing.  I have three kids at once, so I can rotate around and they can work individually or tell me what they're doing so I get feedback.

Every kid is different.  I've had ones that REALLY gravitate to hands on work and ones that think it's only for little kids, so our exploration time always has to be at a level where the manipulatives are incredibly necessary to understand the concept.  Or, conversely, has to bring the topic in with a more relevant or fun explanation. It also means balancing what they think age appropriate work is.

In a few minutes I'll edit this to post one of my kids' papers.  They did the exact same exercises last year when they were 8 & 9, but all hands on.  No written work.  The goal of this particular exercise was a few goals, actually:

1. reading a large math problem

2. understanding the order of operations when they are written

3. transitioning to written math.

4. take the multiplication skills they've been working on and apply them to division/fractions again, seeing the relationship.

 

Every problem was done, checked and proved with blocks.  But it had writing, which is what they wanted at the moment.  The second part of their work was much easier: addition in the hundreds, money math, and basic algebraic concepts (if A+B+C =6, and AxBxC = 6, what could A, B, and C stand for?)

 

Edited June 25, 2021 by HomeAgain

[HomeAgain]

When I say every part of that was done with blocks, I mean, one of my kids even made 14 over and over again with a 6 and an 8, double checking his work.  The others were taking a rod, cutting it into even parts, taking 2 or 4 or whatever of those parts, setting them on that part of the problem...

There's very little moving them strictly into a mental model.  Blocks, move to a new topic, review the old, touch on the new again, review...over and over and over.  If necessary, pictures for an interim.

I have one kid who seems to get it almost immediately, but can't work his way back through the steps or say why.

I have one kid who struggles with number sense.

I have one kid who, once he masters something, he has it, but it takes him a while to master it.

The hands on approach is working for all three of them:

One has to slow down and prove he knows it so he can work with bigger problems

One really needs the visual and tactile

One needs the repetition

 

[Not_a_Number]

31 minutes ago, JazzyMom said:

Sure!  I thought I could tell from HomeAgain’s descriptions that she works with more kids than just her own, but I didn’t know you also tutored.

I’ve been working with DD8’s peers for the last 2 years, and they have a wide range of abilities. I’ve also taught countless AoPS classes and many college kids. 

So yes, plenty of experience with other people’s kids. Will chime in shortly.

Edited June 25, 2021 by Not_a_Number

[Not_a_Number]

So what I generally do is make the manipulatives AVAILABLE and explain how to use them. 

I’m not a C-rod person, so all I provide for my kids are place value manipulatives. Our manipulatives for this are multicolored poker chips. Kids use them for all the operations they find useful. 

My weakest kid is still very reliant on the manipulatives. She’s been using them for every single operation for the whole year and is just now starting to tentatively do some additions and subtractions in her head, using a mixture of mental models and counting on. But the manipulatives are absolutely crucial for her forming a robust model. I’m sure she wouldn’t have been able to add 10 to 35 before spending a while using poker chips.

A few weeks ago, she did 210-106 in her head and also 55+65, so she’s doing MUCH better. But I’m sure she’ll need manipulatives basically for her entire elementary school career.

Some of my kids, on the other hand, are reluctant about manipulatives and will only use them when stuck. That’s fine by me as well, as long as they use them as needed!

Edited June 25, 2021 by Not_a_Number

[JazzyMom]

41 minutes ago, HomeAgain said:

I do tutor.  🙂 Right now I have my extras in a pattern of:
1. new or continued exploration.  This is our hands on portion and it's brain stretching.  We rotate through concepts, connecting to previous work as needed.  I try to max this out at half an hour, but it can run anywhere from 15-45 minutes.  There is usually a specific goal that I have in mind for the exercise, and I try to gauge whether we are going to meet that goal that day (or break it into two or more sessions) or whether we can go longer and stretch a little further/give more open exploration time.

2. Written work that is already mastered from hands on.  It's a good way to end our time, revisit concepts in a different way, make sure they're really understanding the principals behind the work and make the switch from visualizing to writing.  I have three kids at once, so I can rotate around and they can work individually or tell me what they're doing so I get feedback.

 

Would this be an okay length for daily work?

Glad you mentioned about the “little kids” aspect.  When I pulled out the c-rods two days ago, ds excitedly said, “Oh, I know about those!”  But when I told him we were going to use them, he said, “I don’t need those.  Those are for little kids.”  So I told him he could help me show his sister.  And he did show her some things.  
 

I also told him we were going to take a break from his Kumon book to do some games and stuff.  But he wants to continue his book, so we’ll do both.

Thanks for the detailed description.  Very helpful.  Also helpful to see the different needs of each of the kids and how you’re addressing them.

[Not_a_Number]

Just now, JazzyMom said:

Would this be an okay length for daily work?

Glad you mentioned about the “little kids” aspect.  When I pulled out the c-rods two days ago, ds excitedly said, “Oh, I know about those!”  But when I told him we were going to use them, he said, “I don’t need those.  Those are for little kids.”  So I told him he could help me show his sister.  And he did show her some things.  
 

I also told him we were going to take a break from his Kumon book to do some games and stuff.  But he wants to continue his book, so we’ll do both.

Thanks for the detailed description.  Very helpful.  Also helpful to see the different needs of each of the kids and how you’re addressing them.

Do you think he’d be more willing to use poker chips? Those are great for place value and have no “little kid” associations. They don’t help with facts, though, unless you arrange them in ten frames.