Math for an accelerated learner who’s hitting a wall

[NormaElle]

My son is 8 (2nd grade) and about to finish Math Mammoth 3. I’m noticing he’s slowing down as we are doing division. He’s still doing very well but I can’t see starting MM4 right now. But I don’t know what to do now. 

A different curriculum to review and practice all the 1-3 skills? Games and puzzles to practice? Other ideas?

He loves math and will be annoyed to stop going forward, so I want to take that into account too. 

Thoughts? Thanks in advance!

[SoCal_Bear]

I used Singapore Math and Beast Academy (physical books) a year behind. I used the extras in Singapore as well. You could consider using the Singapore Intensive Practice or the Challenging Word Problems books to go deeper. Beast Academy would do that as well.  Some people prefer to use the Fan Math Process Skills in Problem Solving for Singapore style word problems because it has explicit instruction and is a stand alone series that does not have to be used with SM. CWP does not have explicit instruction as it is meant as supplemental to SM curriculum. Fan Math also has Speed Math Strategies which focuses on mental math skills. 

Zaccaro Primary Grade Challenge Math could be used as well.

Edited December 25, 2020 by calbear

[Not_a_Number]

What’s he having trouble with in division?

[EKS]

You can run division alongside of whatever is being introduced in MM 4A.  I glanced through the TOC, and it looks like that would work fine.  Division comes back around again at the beginning of 4B.  That said, the last section in 3B is fractions, and division and fractions are interrelated.  Even so, it's possible that learning about fractions will help him to understand division better.

As long as you continue to work with him one on one, it's ok to move forward even if things haven't entirely gelled.  

[Not_a_Number]

32 minutes ago, EKS said:

As long as you continue to work with him one on one, it's ok to move forward even if things haven't entirely gelled.  

That's a really good point. Especially if one of the things that hasn't gelled is an algorithm, because sometimes, an algorithm doesn't JUST need to gel -- it requires components that haven't been processed to be understood first. So, for example, if there's any shakiness on division as the opposite of multiplication, that would trip you up with the long division algorithm, even if a child understood division as "splitting between people" and had good mental techniques for doing it that way. 

I'm a big fan of introducing new concepts early in an unpressured way. I did multiplication and division way back in kindergarten or first grade with DD8, and we worked on it alongside with addition and subtraction, because otherwise we got bored. We learned a LOT about how all the operations work together, even though we weren't anywhere ready to either memorize multiplication tables or to learn algorithms. 

By the way, OP, knowing how the operations work together is EXTREMELY helpful in algebra. DD8 could expand out a(b+c) before she could do long division 😉 . 

[Porridge]

Agree with @EKS and @Not_a_Number. DD didn’t “get” the division algorithm, but when we circled back to it a year or two later, it clicked right away.  My DS gets bored or discouraged if we stall too long on one topic. If my child is having more trouble with one topic, I give one or two problems every day as a “review” (until they seem to have mastered the topic), while moving on with the rest of the curriculum. Like @calbear, I’m also a big fan of Singapore’s Intensive Practice - I use that for the “review.” 

[lewelma]

You also don't have to go in order of the standard curriculum. My older boy was still learning his subtraction facts while doing AoPS Intro Algebra. You can run a stream for memory and algorithmic skills, and then you can run a separate, concurrent stream for problem solving and abstraction skills. They do not need to go in lockstep, nor would you expect them to in accelerated kids.

[Not_a_Number]

12 minutes ago, lewelma said:

You also don't have to go in order of the standard curriculum. My older boy was still learning his subtraction facts while doing AoPS Intro Algebra. You can run a stream for memory and algorithmic skills, and then you can run a separate, concurrent stream for problem solving and abstraction skills. They do not need to go in lockstep, nor would you expect them to in accelerated kids.

Yeah, DD8 learned how to add two-digit numbers quickly while learning to express numbers in binary... otherwise, she would have been extremely bored. 

[GracieJane]

My DS (1st grade) is accelerated in math, and we take weeklong „breaks“ with Beast Academy. BA is a practice of problem-solving and the format forces children to approach problems from novel perspectives, which is extremely helpful when they hit academic „walls“ (in any subject, actually). AOPS is my absolute favorite curriculum for bright kids, because it requires thinking more than following rote process. I promise I’m not a paid advertiser but I love them! 🙂

[Not_a_Number]

3 minutes ago, GracieJane said:

My DS (1st grade) is accelerated in math, and we take weeklong „breaks“ with Beast Academy. BA is a practice of problem-solving and the format forces children to approach problems from novel perspectives, which is extremely helpful when they hit academic „walls“ (in any subject, actually). AOPS is my absolute favorite curriculum for bright kids, because it requires thinking more than following rote process. I promise I’m not a paid advertiser but I love them! 🙂

I'd be the paid advertiser, lol -- I teach their online classes. (Although really, I wind up being contrarian about them 😄 ) 

[NormaElle]

Thank you everyone for all this feedback!

My son has just flown through math until now, figuring out novel ways to add, subtract, and do basic multiplication. He gets division, but I’ve noticed that he’s not getting it quite as quickly. But I suppose I can always move forward and see how he does, supplementing on topics as necessary. 

[Not_a_Number]

19 minutes ago, NormaElle said:

Thank you everyone for all this feedback!

My son has just flown through math until now, figuring out novel ways to add, subtract, and do basic multiplication. He gets division, but I’ve noticed that he’s not getting it quite as quickly. But I suppose I can always move forward and see how he does, supplementing on topics as necessary. 

What are his division strategies? 🙂 

[GracieJane]

27 minutes ago, Not_a_Number said:

I'd be the paid advertiser, lol -- I teach their online classes. (Although really, I wind up being contrarian about them 😄 ) 

Oh neat! We have never done their online classes, just the BA books. I love AOPS so much I even looked into their LA approach but...I think their math is just better.

Edited December 27, 2020 by GracieJane

[NormaElle]

Right now, he’s doing a combination of dividing chocolate chips into piles and using multiplication (aka backward division). 

[Not_a_Number]

Just now, GracieJane said:

Oh neat! We have never done their online classes, just the BA books. I love AOPS so much I even looked into their LA approach but...I think their math is just  better.

We've done a bit of BA -- they are fun 🙂. 

Yeah, I wouldn't follow them on LA -- they are definitely all math people 🙂 . 

[Not_a_Number]

Just now, NormaElle said:

Right now, he’s doing a combination of dividing chocolate chips into piles and using multiplication (aka backward division). 

Sounds great to me. 

Have you ever shown him partial quotients? 

[NormaElle]

2 hours ago, Not_a_Number said:

Sounds great to me. 

Have you ever shown him partial quotients? 

I just looked this up; this will work great for the way he thinks! I think they introduce this later in MM, but it’ll even work for him now. 

[Not_a_Number]

10 hours ago, NormaElle said:

I just looked this up; this will work great for the way he thinks! I think they introduce this later in MM, but it’ll even work for him now. 

It’s a great technique 🙂 . We used it as scaffolding for long division — if you restrict what easy multiples you’re allowed to subtract to powers of 10 times a digit, you basically get long division.

DD8 used this for a while and was not willing to restrict herself to specific multiples, and I didn’t push. Eventually, she was ready to make her “search” more efficient, and then we jumped into long division 🙂 . It took only a few days to learn.

[drjuliadc]

On 12/25/2020 at 6:55 PM, Not_a_Number said:

I'm a big fan of introducing new concepts early in an unpressured way.

Billion dollar statement. I couldn’t agree with this more. I like that YOU don’t get resistance to this concept on this board. Or maybe you do and I didn’t notice it.

It is a false idea that introducing things early = developmentally inappropriate. There is a way to do it that is inappropriate and that is where the resistance comes from, but there are LOTS of ways to do it that are delightful and joyful and engaging and will just light a kid up. Those “lit up” kids are so much fun.

 

[Not_a_Number]

On 1/8/2021 at 5:05 AM, drjuliadc said:

Billion dollar statement. I couldn’t agree with this more. I like that YOU don’t get resistance to this concept on this board. Or maybe you do and I didn’t notice it.

I do sometimes 😉. Depends on the audience. Doesn't stop me, though. 

[Jackie]

DD just finished the AOPS Intro Algebra book, enjoys math competitions and Epsilon Camp, and she *still* can’t remember the long division algorithm. I’ve decided to ignore the issue, and we’re both happier for it. It is extremely rare that she needs it as the vast majority of the time she can use other strategies. I think 2-3 times during the second half of the Algebra book, the algorithm would have come in handy and she asked permission to use a calculator to check her work before hitting the submit button on Alcumus.

I assume she’ll learn it eventually, but thought I’d reassure you that it turns out to be a lot less necessary than one might think.

[daijobu]

2 hours ago, Jackie said:

DD just finished the AOPS Intro Algebra book, enjoys math competitions and Epsilon Camp, and she *still* can’t remember the long division algorithm. I’ve decided to ignore the issue, and we’re both happier for it.

I also don't care for the standard long division algorithm and I was tutoring a bright student who also could not memorize the steps to save her life.  She did better with partial quotients which is explained in BA and elsewhere online.  If you ever decide to try again, you might consider partial quotients, if only so you can tell the story of the pirates dividing up the pile of gold coins.  

[Jackie]

30 minutes ago, daijobu said:

I also don't care for the standard long division algorithm and I was tutoring a bright student who also could not memorize the steps to save her life.  She did better with partial quotients which is explained in BA and elsewhere online.  If you ever decide to try again, you might consider partial quotients, if only so you can tell the story of the pirates dividing up the pile of gold coins.  

For the longest time, she could only do division when I took the written problem and turned it into a word problem. She’d been doing real-life division for years before encountering it in a math book, so I was really surprised when she had this issue.

She can work her way through when she needs to; it’s only when it doesn’t divide evenly that it hurts her. She had a problem that reduced to something like 23/7 and needed the answer rounded to the nearest something-or-other, stuff like that. Otherwise, she vastly prefers to think of all division as fractions, reduce as much as possible, then use partial quotients to finish. It works; it’s just slower. And, honestly, even though I find it likely she ends up in a math-heavy career, that type of division can be done by a calculator at that point, even if I don’t allow for the use of one now. 🙂

[Not_a_Number]

9 minutes ago, Jackie said:

For the longest time, she could only do division when I took the written problem and turned it into a word problem. She’d been doing real-life division for years before encountering it in a math book, so I was really surprised when she had this issue.

She can work her way through when she needs to; it’s only when it doesn’t divide evenly that it hurts her. She had a problem that reduced to something like 23/7 and needed the answer rounded to the nearest something-or-other, stuff like that. Otherwise, she vastly prefers to think of all division as fractions, reduce as much as possible, then use partial quotients to finish. It works; it’s just slower. And, honestly, even though I find it likely she ends up in a math-heavy career, that type of division can be done by a calculator at that point, even if I don’t allow for the use of one now. 🙂

I wonder if her model of division is a bit fuzzy? 

I've always thought that the jumping around we do between division with remainders and fractions was very confusing for kids. Like, what does 23/7 even MEAN? Does it mean you're splitting 23 cookies between 7 kids? Are you allowed to split cookies? What's happening here, basically? 

I didn't do remainders with DD8 at all for this reason. I've decided I don't believe in remainders, lol. 

[Jackie]

1 hour ago, Not_a_Number said:

I wonder if her model of division is a bit fuzzy? 

I've always thought that the jumping around we do between division with remainders and fractions was very confusing for kids. Like, what does 23/7 even MEAN? Does it mean you're splitting 23 cookies between 7 kids? Are you allowed to split cookies? What's happening here, basically? 

I didn't do remainders with DD8 at all for this reason. I've decided I don't believe in remainders, lol. 

I don’t think it’s fuzzy. She could easily tell you that there are two cookies left over. Or that everyone would get 3 2/7 of a cookie, even though she’d then go off in a tangent about how ridiculous it would be to attempt to divide the cookies into sevenths. And when she absolutely has to, she can even use whatever method she is using to convert that 2/7 to a certain amount of tenths, hundredths, etc. It’s just slow and painful. And she can glance at the fraction and *know* that it’s going to be slow and painful, which makes her drag her feet even more, making it slower and more painful than it needs to be. 

Meanwhile, I could whip out the algorithm and do it quickly. It’s about the only time she ever sees value in the algorithm, but still not nearly enough value to bother learning it.

[Cake and Pi]

20 hours ago, Jackie said:

I assume she’ll learn it eventually, but thought I’d reassure you that it turns out to be a lot less necessary than one might think.

Or... perhaps she'll just keep trucking along, unencumbered by the unlearned long division algorithm, get all the way through engineering college without ever needing it, and then years later she'll be homeschooling her oldest kid and have to look up the long division algorithm to teach said kid 4th grade math... 😅

 

[Cake and Pi]

17 hours ago, Not_a_Number said:

I didn't do remainders with DD8 at all for this reason. I've decided I don't believe in remainders, lol.

See, and I have a kid who is all about those remainders. He's not interested in dividing out those last little bits. He'd be like Jackie's kid, arguing the absurdity of dividing extra cookies into 7ths. He'd say they just need to do rock-paper-scissors for the last few cookies or divvy them out to the hungriest/ hardest working/ most deserving member(s) of the party (which would be him, btw, if we were talking real life, lol).

[Not_a_Number]

45 minutes ago, Cake and Pi said:

See, and I have a kid who is all about those remainders. He's not interested in dividing out those last little bits. He'd be like Jackie's kid, arguing the absurdity of dividing extra cookies into 7ths. He'd say they just need to do rock-paper-scissors for the last few cookies or divvy them out to the hungriest/ hardest working/ most deserving member(s) of the party (which would be him, btw, if we were talking real life, lol).

I never gave that option, lol. I mean, you can't really just decide that, or 1/3 makes no sense. 

But we only did division without remainders for a long time, in order to avoid the problem 😉 . 

[Not_a_Number]

17 hours ago, Jackie said:

I don’t think it’s fuzzy. She could easily tell you that there are two cookies left over. Or that everyone would get 3 2/7 of a cookie, even though she’d then go off in a tangent about how ridiculous it would be to attempt to divide the cookies into sevenths. And when she absolutely has to, she can even use whatever method she is using to convert that 2/7 to a certain amount of tenths, hundredths, etc. It’s just slow and painful. And she can glance at the fraction and *know* that it’s going to be slow and painful, which makes her drag her feet even more, making it slower and more painful than it needs to be. 

Meanwhile, I could whip out the algorithm and do it quickly. It’s about the only time she ever sees value in the algorithm, but still not nearly enough value to bother learning it.

Right, but those are TWO different understandings of division. One is with remainders and one is without. That's why I'm wondering if the model is a bit fuzzy: like, she doesn't quite know which one is really division, so then long division is a bit confusing, especially if it goes into the decimals. 

I'm not saying there's anything wrong with her understanding 🙂 . In my experience, having slightly fuzzy models where you can't quite put things into words is a very common state of things. But then it makes certain other things harder to learn because it's hard to build on top of fuzzy models.