Beast Academy Multiplication

[momacacia]

Okay, multiplication is driving me nuts. We're in BA 4A (after completing MM4A and doing MM multiplication). I think that DH and I learned what MM calls "the easy way," and after DH showed DD this (and I think MM teaches it) she seems to prefer it.

 

BA, however, seems to teach "only" (granted we're not that far in BA) the "add up method' with no carrying between multiplied numbers. Hopefully that makes sense. This is not the way that DH and I learned it, though it is an excellent way to explain the multi-digit multiplication concept! I told DH that this is the "common core math" that is making all the parents crazy. :lol:  (And, I'm a little curious if it actually is.)

 

But is this the new way to do multiplication. I can certainly see it reducing computational errors---all adding is left until all multiplication is completed, so only one operation is in the mind at a time. But it is a lot more writing. Is that the way we're going to do it from here on out, so do students eventually go back to the "old way" that we learned it (in which case I'll just have DD start computing that way now, because she understands the multiplication concepts).

 

Someone who is further along, please clue me in on multiplication. :hat:

[go_go_gadget]

I don't remember and don't have the book in front of me, but I can say that if it did end up teaching the carrying, I would have my kids skip that part. Sure, it's a bit more vertical space, but it doesn't actually take any more *time*, because you write something somewhere either way. I've seen too many kids who forgot what ''carrying'' meant and then mixed up what the procedure ought to be, and can see no advantage to doing it that way. 

[momacacia]

So you are saying that you would use this method (which seems to be the BA way, at least in 4A):

 

     56

   x78

  ******

     48

   400

   420

+3500

********

  4368

 

Am I understanding correctly that that's the method you'd go with? Just want to be sure I'm clear.

[Roadrunner]

It's called partial products method. We learned it, but also learned the old fashioned way from SM.

 

Corrected!

[go_go_gadget]

So you are saying that you would use this method (which seems to be the BA way, at least in 4A):

 

     56

   x78

  ******

     48

   400

   420

+3500

********

  4368

 

Am I understanding correctly that that's the method you'd go with? Just want to be sure I'm clear.

 

Exactly. Math programs don't have students multiplying huge, cumbersome numbers, and in real life you use calculators for those. This method keeps the concepts clear and grounded by the distributive property; there's no procedure to mix up or forget.

 

I think Roadrunner meant ''partial products method'', not ''quotients''.

 

ETA: I just checked the books, and BA does leave it at that. According to their FB page, the topic won't be revisited in the fifth grade level, either, so it seems safe to conclude that the authors prefer this method.

[momacacia]

Okay, I just emailed Beast Academy (duh!). I'll post back what they say. I just want to stick with something and move on! :)

[EndOfOrdinary]

AoPS - from everything I have seen - never teaches the standard algorithm.  This is mainly due to the curriculum being conceptual.  The conceptual way actually greatly increases mental math and mathematical accuracy (for the reasons you listed), as well as encouraging students to group and regroup the numbers which is later what you do all the way up into Calculus.  It seems slower as a person who spent years doing rote algorithms, but I would argue it is much faster once a student has their facts down and understands the base ten system.

 

To some degree, yes, this is Common Core math.  All Common Core is actually asking for is that the student understands the concepts about what they are doing.  The partial products method does not allow for anything but complete understanding because you are required to break the numbers into expanded form and use the distributive property.  That seems lengthier (and it is initially), but only because the adult has significant experience using the algorithm.

 

Ask most adults to explain why multi-digit multiplication works and how it relates to the base ten number system and you will get blank stares.  They can compute, but not explain.  Common Core requires explaining and thus adults are upset since they do not want to feel like 1) they do not know the answers to their third graders homework and 2) they get defensive that somehow their education wasn't "right."

[Kerileanne99]

It's called partial quotients method. We learned it, but also learned the old fashioned way from SM.

Partial products method, I think you meant. Similar setup for division is partial quotients method.

 

But I agree...we learned it as well as regular SM method. Always useful to have multiple tools, but it always seemed to be more work to me:)

[EndOfOrdinary]

Okay, I just emailed Beast Academy (duh!). I'll post back what they say. I just want to stick with something and move on! :)

 

You can teach your child both.  There is no reason not to.  It will not confuse the issue if they actually understand.  If they do not understand, you should not move on anyway.  Being able to translate the algorithm into partial products just shows that they really are getting that multiplication and addition are commutative and that the distributive property illustrates the ability for all commutative numbers to be grouped and regrouped in various ways ad-infinitum.

[SparklyUnicorn]

whoa...never was taught add up method

 

I kinda like it....

 

 

[Kerileanne99]

You can teach your child both. There is no reason not to. It will not confuse the issue if they actually understand. If they do not understand, you should not move on anyway. Being able to translate the algorithm into partial products just shows that they really are getting that multiplication and addition are commutative and that the distributive property illustrates the ability for all commutative numbers to be grouped and regrouped in various ways ad-infinitum.

ITA:)

Although I don't ask my dd to do it via partial products method, I did teach it and it served a very useful tool: by having her do it and talk me through it I was absolutely positive that she fully understood not only the multiplication part, but place value/ expanded form, distributive property, and had the ability to construct/deconstruct large numbers using their properties. If they CAN do it this way they do fully understand what they are doing and which method they ultimately choose to use everyday doesn't really matter at that point.

[zarabellesmom]

We did it the BA way. ;)

 

Once I knew she had it down, I taught her the"old-fashioned" way. (Suddenly feeling quite old.) I also let her watch the Kahn academy video that teaches the standard algorithm. I then let her choose which to use. She picked the standard algorithm. I've been working through the AoPS pre algebra book. There's a lot of multiplying going on with some fairly large numbers and they assume 0 calculator use. If I only had partial products in my tool box...I think I'd fling the book across the room.

[SparklyUnicorn]

I have shown my kids why the old fashioned way works using the add up method.  Just never thought to do it that way regularly.

 

 

[73349]

My 9th-grade teacher taught us how to do that with polynomials (putting them into boxes), and I wondered why on Earth no one had showed me that before. I think it's a great way to multiply.

[wapiti]

I'm confused and perhaps need a little coffee here... The MM "easy way" (e.g. MM 4A p. 131-133) is the exact same as the BA way described above.  MM teaches this for concept understanding before moving on to the standard algorithm.  And, it sounds like BA never gets to the standard algorithm (I don't have time to look right now).  If you want to teach the standard algorithm, then just use the lesson(s) on that in MM.

[momacacia]

Wapiti,

 

Yes, MM shows both ways. We have switched, or should I say are trying out the switch, to BA as our main math curriculum, so I'd like to stick with something and go with it. She did both in MM. I feel like she's almost getting confused and it's slowing us down. Anyhoo....

[momacacia]

The kind people at BA just confirmed to me what a poster said above. The multiplication algorithm isn't revisited in 5th, and they like the algorithm they present in 4A because it uses the distributive property which will be important later on and gives kids a more intuitive understanding of the multiply concepts. I've gotta agree on that. I think it might also help dd's accuracy!

 

Then he said something "funny" to me (humanities girl that I am) that "the mathematicians" in their office couldn't remember ever multiplying two 4-digit numbers after 4th grade or so. They either estimated or did a quick compute in their heads, or used a calculator for an exact number when necessary. Clearly they were on a different math track than I was. :lol:

 

Anyway, it's fascinating! I love math. Not that you'll find me doing it in my spare time and not that I'll ever be good at it, but there is a beauty and order to it that I can appreciate almost as much as I appreciate Baroque music. :coolgleamA:

 

 

[go_go_gadget]

We did it the BA way. ;)

 

Once I knew she had it down, I taught her the"old-fashioned" way. (Suddenly feeling quite old.) I also let her watch the Kahn academy video that teaches the standard algorithm. I then let her choose which to use. She picked the standard algorithm. I've been working through the AoPS pre algebra book. There's a lot of multiplying going on with some fairly large numbers and they assume 0 calculator use. If I only had partial products in my tool box...I think I'd fling the book across the room.

 

Which chapters? My son's using their Pre-A, and whenever he's started trying to multiply large numbers, it was always because he'd missed something. Perhaps he hasn't reached those parts yet.

[Tsuga]

I learned add-up and carrying in school. There are many, many algorithms for multiplying numbers bigger than ten!

 

I must have been in some experimental generation. My daughter is doing 3B which seems to review the concepts my daughter learned from her German books, so nothing new there.

 

To me the key is using the row/column algorithm from the German method we have:

 

100 dot matrix image.jpeg

 

When you move to numbers greater than ten, you can actually use that to make a much bigger matrix re-arranging the numbers. So like, 12*12= (10+2)*(10+2)= 10*10 + 10*2 + 10*2 + 2*2. Then you end up with a matrix of 100, two matrices of 10x2, and then one matrix of 2x2. You can re-arrange these dots into the base ten (ten rows) arrangement to find how many you have.

 

Even when you have 35 x 81, you really have 35 rows and 81 columns. So use the 100-dot matrices and stack until you get that. Then break it into base 10 (10x10 dot matrices) to count by tens to your solution.

 

This really lays it out in two dimensions conceptually.

 

Computationally, if a child can do this I never do anything more than four digits. How often do you buy more than three things that cost over $99.99 at one time?

 

 

 

They either estimated or did a quick compute in their heads, or used a calculator for an exact number when necessary. Clearly they were on a different math track than I was...Not that you'll find me doing it in my spare time and not that I'll ever be good at it

 

:( They were taught how to do mathematics rather than arithmetic computation.

 

It is criminal that some of our nation's best math talent is not allowed to learn math concepts until they never mess up their 2s and 5s. I never stopped mixing them up... I only got ahead because I tested high on the gifted test, so they stopped having me do arithmetic. Funnily enough, a number of people I know who work in stats and physics are equally absentminded with respect to arithmetic. Not that we don't get it, we just don't have that copying down.

 

That's why I'll teach my own kids math no matter what. They will never think that getting distracted from single-digit numerals means they aren't good at math.

[zarabellesmom]

Which chapters? My son's using their Pre-A, and whenever he's started trying to multiply large numbers, it was always because he'd missed something. Perhaps he hasn't reached those parts yet.

It's probably because I missed something. ;)

[blondeviolin]

I taught my oldest partial products and then showed her the standard algorithm. She was actually very reticent to use the standard algorithm. But after some practice, she decided it was quicker.

[wapiti]

 I've been working through the AoPS pre algebra book. There's a lot of multiplying going on with some fairly large numbers and they assume 0 calculator use. If I only had partial products in my tool box...I think I'd fling the book across the room.

 

Which chapters? My son's using their Pre-A, and whenever he's started trying to multiply large numbers, it was always because he'd missed something. Perhaps he hasn't reached those parts yet.

 

Yes.  The Prealgebra text is always looking for the use of math concepts (a.k.a. the "easy" way or "smart" way, as RR would say) rather than lots of computation.  One of my kids would prefer the long way rather than to think, but that's typically not what AoPS is looking for in the particular problem.  If the computations are getting tedious, there's probably a mistake someplace.

 

With regard to the Prealgebra text, I have often told my kids:  when in doubt, see if you can use prime factorization :)

[SparklyUnicorn]

Did you know I wasn't even taught place value in school.  We memorized math facts.  Calculations felt more like memorizing steps which were promptly forgotten and I had no fat chance in remembering since I didn't understand the concept behind it.

Now, I know how it works and I don't forget. 

[go_go_gadget]

Yes.  The Prealgebra text is always looking for the use of math concepts (a.k.a. the "easy" way or "smart" way, as RR would say) rather than lots of computation.  One of my kids would prefer the long way rather than to think, but that's typically not what AoPS is looking for in the particular problem.  If the computations are getting tedious, there's probably a mistake someplace.

 

With regard to the Prealgebra text, I have often told my kids:  when in doubt, see if you can use prime factorization :)

 

My son knows now that whenever he's about to do an annoying computation, something's wrong. He always says ''Hey Mom, I was about brute-force this one. I forgot to brain!''

[EndOfOrdinary]

It is actually kind of nice as a way to check yourself.  My son favored brute force quite regularly until PreA knocked him out of it.  We now have the slogan, "Don't go bigger to go smaller."  It helps him look for ways to simplify before he gets stuck going down the brute force path.

[kiana]

FWIW, I agree with the BA people. I see it as a good setup for doing problems like (x+3)(x^2 - 3x + 2) in algebra, because the procedure for algebra will be the same as the procedure for arithmetic was.

[Chrysalis Academy]

It's so freaking brilliant.  We are finishing up the Perfect Squares chapter in 3B, and today's lesson was called "Clever Computations."  If anyone had told me a few years ago that my 8 year old, who just learned her times tables, would figure out a quick and easy way to multiply 6x7x8x9 using the distributive property, I never would have believed it.  BA is rocking my world.  I'm sad that my big girl is too big for it.  The little one is learning to "think math" like I never did.  Well, I guess we're learning together!  :D

[texasmama]

Yes.  The Prealgebra text is always looking for the use of math concepts (a.k.a. the "easy" way or "smart" way, as RR would say) rather than lots of computation.  One of my kids would prefer the long way rather than to think, but that's typically not what AoPS is looking for in the particular problem.  If the computations are getting tedious, there's probably a mistake someplace.

 

With regard to the Prealgebra text, I have often told my kids:  when in doubt, see if you can use prime factorization :)

I've pretty much decided that prime factorization is the key to all the world's problems.  Who knew?  (And it's simple.)

[ikslo]

I just started DS in 3A, and I can't tell you all how much I appreciate this thread.  I am 100% certain I would have been questioning the Way of the Beasts come 4A. 

 

They were taught how to do mathematics rather than arithmetic computation.

 

This was my biggest downfall in high school Calculus, and why I went from feeling like I was a good math student, to feeling like I would be happy to just pass.  (The 4 I got on the AP exam surprised me more than my teacher - and he was shocked.)  I was only doing arithmetic computation most of the time. 

 

[Roadrunner]

When I first looked at partial products method, my head spinned. However my little one, having disliked the standard method thought in SM, rejoiced. He was so happy telling me that's how he does it in his head. Finally what he did mentally and on the paper were one and the same. :)

And yes, the perfect squares chapter was our favorite!

 

 

[FairProspects]

I've pretty much decided that prime factorization is the key to all the world's problems.  Who knew?  (And it's simple.)

 

Well geez, we are set then. That is one of ds's favorite actions to attempt in math. He loves seeing those trees.

[scbusf]

We are also finishing up the Perfect Squares chapter in 3B.

 

I have a master's degree in math and I teach college math. BA is seriously rocking my world. I just love it!

[texasmama]

Well geez, we are set then. That is one of ds's favorite actions to attempt in math. He loves seeing those trees.

Even non mathy people like me can make trees. :)

[sweetpea3829]

 

Anyway, it's fascinating! I love math. Not that you'll find me doing it in my spare time and not that I'll ever be good at it, but there is a beauty and order to it that I can appreciate almost as much as I appreciate Baroque music. :coolgleamA:

 

LOL, I could have written this exact thing....except for the Barogue music part.  ;-)  

[sweetpea3829]

I really enjoyed that Perfect Squares chapter, too.  But I have to say, DS has forgotten pretty much ALL of what he learned in that chapter.  Not having a way to review it, other than going back and redoing it, he's lost most of what he learned.

 

Which is why I so wish Beast had some kind of online gamey type review thing. 

 

I think I will ask DS to redo that chapter once we finish Singapore for this year.  He won't be happy about it ("MOM, I already DID this chapter!") but I'm pretty sure the review would be good for him.  And me.