Distributive Method for multiplication Q (from Beast Academy in this case)

[tammyw]

DS9 has learned long multiplication a while ago - I taught him my "old school" method (example below):

 

      141

    x  22

________

    282

+2820

________

  3102

 

 

However, we are in Beast Academy 4A and it's teaching us this method:

 

And he doesn't like it! (and honestly, I don't really either!) And he's frustrated by this section of the book!

 

Is there a reason why I should make him do it their way? If so, I really need to understand why :)

 

TIA!!

[regentrude]

Yes, he needs to understand the distributive property. It will be absolutely vital later in prealgebra and algebra  when the things that are multiplied are not simple numbers but expressions that contain variables - the traditional algorithm will be of absolutely no help there,

He does not have to work all his multiplication problems by using the distributive property; the traditional algorithm is a very efficient shortcut - but it does not replace the conceptual understanding.

 

ETA: Maybe I misunderstand your question. The example you call "old school" is really doing several steps at once and only works if you don't have to carry and the numbers are not too large. He needs to master both the traditional algorithm and the distributive property. How, with "your" example, would you multiply numbers that contain larger digits, like the one in the BA example 97*63?

Expecting the student to do 97*60 mentally is error prone and slower, and it gets really problematic if the numbers have more digits.

[Penelope]

Because this is what you are really doing when you use the algorithm. The reason to teach that way is for conceptual understanding rather than just rote; it tells the "why" of why you either put zeros as place holders or move over one place for each row in the algorithm.

 

I think it also builds a facility for mental math. If you understand what you are doing, then you don't have to write down every problem and work it out with the algorithm on paper. Some problems can be done in your head or without writing everything out.

 

And then of course, later in algebraic problems where you have to use the distributive property, you already have some familiarity.

[Tanaqui]

There are people in this world who think the traditional algorithm for multiplication is kinda like magic. They have NO idea why it works, and if they get it wrong they often don't know exactly what they did to screw up.

 

This holds them back, math-wise, because they lack the understanding to go further ahead.

 

So, yes, teaching partial products like this is, imo, an important step in learning mathematics. Yes, your son no doubt prefers the traditional algorithm. It doesn't take up as much space, and anyway, he's used to it. He should still do the work to make sure he knows why it works.

[tammyw]

Ok - just to clarify I agree that he needs to understand the distributive property (and he does) he just prefers doing long multiplication this way. But I understand what you are saying about doing it to even further facilitate his understanding.

He also know how to carry when multiplying larger numbers. Was that one of the questions asked of me?

 

I read your answers to him and he also wanted to add a clarification :) He is doing pre-algebra and algebra (on his own through Khan Academy mostly) and he says he uses the distributive property all the time with variables and is very comfortable doing so. He understand WHAT he is multiplying. He just wanted to understand if he really had to fill out every single step the way they did it. Bottom line - he is very advanced in math (spends HOURS every day doing it on his own) but I still work through Beast Academy with him to make sure there are no gaps. I think because he's so far ahead in many areas, he just doesn't want to do the basic stuff that he already understands very well. Not sure if that makes sense to my original question though :)

[Tanaqui]

Meh, if he understands it and can demonstrate that he understands it, there's no need to belabor the point. I thought you were asking if he needs to learn it, not if he needs to keep on doing it.

[tammyw]

Meh, if he understands it and can demonstrate that he understands it, there's no need to belabor the point. I thought you were asking if he needs to learn it, not if he needs to keep on doing it.

 

Lol, the problem is becoming much better at math than I am :)

 

No, mostly I just wanted to understand if this was the "new way" of doing long multiplication, that everyone now considers the "right" way. I don't recall doing it this way in Singapore. I don't fully know all the ins and outs of Common Core Math, so I wanted to make sure that doing it "his way" wasn't going to be a problem down the road. Probably a silly question in the first place :)

[Tanaqui]

I think the way we all consider the "right way" in higher mathematics is just "so long as it consistently gets you the right answer". If he's working on algebra, he's no longer being judged on exactly what steps he takes, is he? By the time I was doing algebra, they let us use calculators on all the gruntwork!

[tammyw]

Okay, I think we're good then :) Thanks all!

[Tsuga]

DS9 has learned long multiplication a while ago - I taught him my "old school" method (example below):

 

141

x 22

________

282

+2820

________

3102

 

 

However, we are in Beast Academy 4A and it's teaching us this method:

 

And he doesn't like it! (and honestly, I don't really either!) And he's frustrated by this section of the book!

 

Is there a reason why I should make him do it their way? If so, I really need to understand why :)

 

TIA!!

I'm floored. The BA method is the one I learned in school.

 

Isn't that the proper algorithm?

 

Apparently, we had it going on in the 1980s.

 

OP I cannot answer your question but this has been enlightening for me. My daughter isn't at 4A but she already knows that algorithm. She learned it to calculate costs and savings plans. I find it interesting that they introduce it so late.

[tammyw]

I'm floored. The BA method is the one I learned in school.

 

Isn't that the proper algorithm?

 

Apparently, we had it going on in the 1980s.

 

OP I cannot answer your question but this has been enlightening for me. My daughter isn't at 4A but she already knows that algorithm. She learned it to calculate costs and savings plans. I find it interesting that they introduce it so late.

 

Actually, I believe they may have introduced this a bit in Beast Academy 3 as well...

[Farrar]

I think that's the worst BA chapter by far. By this point in their math education, the vast majority of kids who are doing an advanced math program like BA will have already learned the combination of steps method in Tammy's first example. For them, doing the longer method feels like a punishment and like they're being asked to take baby steps when they're ready for a marathon with this topic. The chapter does go on to do some deeper work more typical if Beast and it is good to keep taking kids back to that distributive property to check understanding, but I think this chapter was uncharacteristic of Beast overall.

 

And, yeah, skip their method if you're confident in his understanding.

[tammyw]

I think that's the worst BA chapter by far. By this point in their math education, the vast majority of kids who are doing an advanced math program like BA will have already learned the combination of steps method in Tammy's first example. For them, doing the longer method feels like a punishment and like they're being asked to take baby steps when they're ready for a marathon with this topic. The chapter does go on to do some deeper work more typical if Beast and it is good to keep taking kids back to that distributive property to check understanding, but I think this chapter was uncharacteristic of Beast overall.

 

And, yeah, skip their method if you're confident in his understanding.

 

That makes me feel a HECK of a lot better, Farrar!  And YES! It seemed like punishment to him. Exactly!!! His thought was "why do I need to do in ten steps what I can do in one?" Especially because he clearly gets it all. And a lot of this stuff, he's gotten to the point of doing it in his head, even the tougher problems.

 

In all honesty, most of the time I have no idea what he's talking about with math, because it's like he's in a deep love affair with it. It's so different from dd, who did it to get it done, but never really enjoyed it, where as he plays with math for fun. He is constantly "proving" things, designing airplanes based on some scale, coming up with algorithms, etc. I sometimes wonder if I'm holding him back, but I figure we do BA to make sure nothing gets missed and he goes crazy with Khan for everything else. At the moment he's satisfied with that.

 

Looking at his Khan stats, I see the following (and he just created his account one month ago):

 

Geometry: 28% progress

Precalculus: 21% progress

Differential calculus: 2% progress

Geometry: 90% finished

Trigonometry: 11% progress

Integral calculus: 3% progress

 

I don't even know what integral calculus is!!! (I never took calculus). Needless to say, the student is outgrowing the teacher, ha!

 

[EndOfOrdinary]

I would not go by Khan stats. In fact, for many advanced kids, Khan can be a killer. It asks for no understanding and mainly number crunching. If your son gets the longer algorithm, that's great. He is very much going to need to take it about ten steps past what Khan asks for in AoPS if he is going to continue using the program.

 

Most all the students who were advanced that I taught math to thought they were very hot stuff due to Khan academy. Only when they had to actually *use* the math on theory or real problems they disintegrated. Even more, they were mentally annihilated because they had considered themselves so smart. That might not your kid, but be leary of Khan learning as a benchmark.

[tammyw]

I would not go by Khan stats. In fact, for many advanced kids, Khan can be a killer. It asks for no understanding and mainly number crunching. If your son gets the longer algorithm, that's great. He is very much going to need to take it about ten steps past what Khan asks for in AoPS if he is going to continue using the program.

 

Most all the students who were advanced that I taught math to thought they were very hot stuff due to Khan academy. Only when they had to actually *use* the math on theory or real problems they disintegrated. Even more, they were mentally annihilated because they had considered themselves so smart. That might not your kid, but be leary of Khan learning as a benchmark.

Huh. Well I certainly wasn't thinking he was excelling in all those areas - just giving him good *exposure* in a subject he very much loves. On the other hand, I didn't realize that khan was bad either and would make him "too big for his britches", so not really sure what to do with that. He loves math. He loves learning it, studying it, playing with it. I can't spend hours every day just doing math with him, so he pursues it in his free time via khan, dragonbox, and just playing around in his notebook. I have been advised many times (because of his passion for math) to encourage him playing on khan, but now I'm wondering if it's really the right thing?

 

ETA: I hope my original post didn't come off as though I think he's some genius in math. My reason for posting the khan stats were simply to show how much he loves math by how many lessons he's gone through. I couldn't have paid my daughter to do lessons on khan. mostly I just want to support his passion, even though I know it's going to become difficult for me because I never took calculus or more advanced math.

[EndOfOrdinary]

Khan is not bad. It is just not a measure of understanding, knowledge or much by way of learning. You know that. You openly just called it exposure. He is 9. Make sure he knows that. Let him be geeked out on integral calculus, but then give him an actual story problem evy once in a while to show him what those words mean. Let him play for hours - I did. I was grounded from my math book "to make friends."

 

Using BA to make sure there are no holes is a really good idea, but perhaps run AoPS PreA along side. Instead of Khan, Zacarros Real World Algebra is great. Universe and the Tea Cup is an awesome book. Fractals are really cool. Combinatorics are mind melting and addictive. Struggling is not a bad thing. It is very important. Once the struggle is gone, then the brain stops stretching. In my experience Khan is fantastic for exposure, but very few people - almost no kids - realize that is all it is. The problem is not with the program, but more with how it is used.

 

 

I do not think you are feeling your kid is a genius. Be sure your kid doesn't feel like one :). Confident. Intelligent. Mathematical. Not a genius ;)

[tammyw]

Thanks for the recommendations. I will look into all of them! And I will definitely discuss the limitations of khan with and ensure he understands what it is and isn't :)

[EndOfOrdinary]

Netflix has a really cool Great Course called Understanding World's Greatest Structures. It is a very neat blend of geography, physics, and math. He might like it.

[tammyw]

Khan is not bad. It is just not a measure of understanding, knowledge or much by way of learning. You know that. You openly just called it exposure. He is 9. Make sure he knows that. Let him be geeked out on integral calculus, but then give him an actual story problem evy once in a while to show him what those words mean. Let him play for hours - I did. I was grounded from my math book "to make friends."

 

Using BA to make sure there are no holes is a really good idea, but perhaps run AoPS PreA along side. Instead of Khan, Zacarros Real World Algebra is great. Universe and the Tea Cup is an awesome book. Fractals are really cool. Combinatorics are mind melting and addictive. Struggling is not a bad thing. It is very important. Once the struggle is gone, then the brain stops stretching. In my experience Khan is fantastic for exposure, but very few people - almost no kids - realize that is all it is. The problem is not with the program, but more with how it is used.

 

 

I do not think you are feeling your kid is a genius. Be sure your kid doesn't feel like one :). Confident. Intelligent. Mathematical. Not a genius ;)

I spoke with him this morning. He definitely doesn't think he's a genius :laugh:  He says he loves that he can get better at it by going on Khan, and that he can go out and use it in other things. But we talked about how it's a great thing because it will help him when we / he really digs deep into those subjects, because he will already have been exposed to it.

 

I did buy the AOPS PreA, but haven't really dug into it yet. I have given him random problems from his sister's Dolciani PreA book, and he always surprises me by being able to actually get the right answer (without me going through the lesson). I think DragonBox really helped him with that kind of stuff. He's also helped his sister with her PreA homework and sometimes pointed out errors she's made (sometimes she's good with this, sometimes it just irritates her).

 

I will definitely look at adding that Zaccaro booko (we have an early book of his, but never really did much with it). I also have living math books for him, as another option.

 

Can you tell me more about Combinatorics and Fractals? What kind of resource should I be looking for?

 

Netflix has a really cool Great Course called Understanding World's Greatest Structures. It is a very neat blend of geography, physics, and math. He might like it.

 

I just added that to our streaming account. Thanks!