lattice multiplication is SO COOL!

[mindygz]

I'd inadvertently downloaded a lattice multiplication app a couple weeks ago and thought "Huh?" when I looked at it. But yesterday I watched the Khan Academy video on lattice multiplication and now I'm sold! http://www.khanacademy.org/video/lattice-multiplication?playlist=Arithmetic

 

I'd never heard of it before, but I think it is a really nice way to do multiplication of multi-digits. Better than remembering the 0 in the standard way--so nice to do all the multiplying then all the adding. Plus it's kind of fun. :001_smile:

[heidip2p]

Wow, I have never seen anything like that. My dd really struggles with X. I wonder if this would help or hurt her? I am almost scared to teach her a totally different way. It looks so much easier though. If you worked these on graph paper it would be a breeze.

[duckymama]

Lattice multiplication is wonderful! My husband teaches lower level community college classes and recommends this to his students. Our kids are, of course, using it. :)

[mindygz]

We introduced it to DD9 last night (just as we were figuring it out ourselves), who hasn't done a lot of larger number multiplication yet. I am going to make a "battle" game out of it where we each roll dice and fill in boxes and see who can get the largest number (thus deciding which of her Littlest Pet Shop toys is the "winner"). I am hoping she will like it.

[EKS]

I'd inadvertently downloaded a lattice multiplication app a couple weeks ago and thought "Huh?" when I looked at it. But yesterday I watched the Khan Academy video on lattice multiplication and now I'm sold! http://www.khanacademy.org/video/lattice-multiplication?playlist=Arithmetic

 

I'd never heard of it before, but I think it is a really nice way to do multiplication of multi-digits. Better than remembering the 0 in the standard way--so nice to do all the multiplying then all the adding. Plus it's kind of fun. :001_smile:

 

I agree that lattice multiplication is kind of neat but what I really don't like about it is that it doesn't reinforce place value in an obvious way.

[Dana]

I strongly dislike lattice multiplication.

If you look ahead to multiplication of polynomials (algebra I), the traditional algorithm for multiplication can generalize to polynomial multiplication (thus reinforcing place value). You can't do that with lattice.

[kristinannie]

While I think that lattice multiplication is "cool" and the first time I saw it I thought it was neat, I also have a lot of concerns about it that PP have posted. You are likely to get some very negative responses since the much maligned Everyday Math uses lattice multiplication. :lol:

[ChandlerMom]

Lattice math is a cool parlor trick and fun for the advanced student to figure out WHY it works. But the fact that the why isn't obvious is why I HATE it being taught as a method to use. The trouble is, it is easier to DO, but harder to understand what the heck you ARE doing. I'm more interested in teaching my kids to understand math than to become human calculators.

 

Lattice math, as well as other problems in math education, are discussed here:

 

 

[Spy Car]

Neat "novelty act" but not a good teaching method.

 

Bill

[mom2scouts]

I'm not a fan of lattice multiplication. It's fun to try, but I would never teach it that way. My oldest son's girlfriend is a math teacher and her school taught the lattice method. It confused students and they didn't have any understanding of place value of why it was done that way.

[BatmansWife]

I've never heard of this before....I think it looks great. If you watch the next video, Why Lattice Multiplication Works, he explains why it works and explains the place value. Won't teaching that (the explanation) deal with the place value issue some are bringing up? The diagonals are the place value (the bottom diagonal is the the ones, the diagonal on top of that the 10's, etc). For some reason....it totally makes sense to me (not just the place value...but the entire process). What I really liked was at the end of the second video he said, "it allows you to do all your multiplication and then switch your brain to do the addition and carrying over". This would definitely be something that my son would benefit from. He still gets confused because of the constant switching around....mulitiply, carry over, multiply & add what you carried over, carry over again, etc. I will definitely show him these videos and practice this with him. It might be just what he needs. Thank you for posting this!

[i.love.lucy]

I've been doing it with dd for a few months now. She was already quite solid with place value and really does get multi-digit multiplication. It just takes too long and is too prone to mistakes. We started doing lattice and she is not making mistakes any longer. I plan to have her watch the "why it works" video several times and also practice the old way of doing multi-digit sometimes, so she remembers how to do it but doesn't have to do it all the time. For a kid that you already know is not heading into particularly high maths, this seems like a fine "parlor trick" to me.

[QuirkyKidAcademy]

Just one of the reasons I enjoy this board: the give and take, the discussion of how and why.

 

So now I know to make sure DS is solid in understanding long multiplication before introducing lattice as a fun trick.

 

Thanks, y'all!

[Roadrunner]

I didn't think the methods of much hated "new mathematics" would find popularity on this board. :lol:

[BatmansWife]

I showed this to my son last night (not the video yet...I just showed him an example on the white board). I explained about the place value...where the 1's were and the 10's and so on, and that in say....340 x 25, when you come to the 4 times the 2 it's really 40 x 20 and the answer is in the 100 diagonal column. He got all that, but doesn't care too much about knowing all the details. I worked a large problem and then gave him one. He did it without any help, he did it quickly, and got it perfect. This from a kid who would ask me nearly every.single.step of a regular multiplication problem. I have been like this when it comes to multiplication with him: :banghead: . "Parlor trick" or not....I think this is just what he needs. :thumbup:

 

Now.....is there something like this for long division????

[SorrelZG]

No I think some people are just biting their tongue (or in this case maybe their fingers). ;)

 

This is why I get so confused reading math threads. It appears that there are two entirely different groups of people on the forum and I can't keep track of who is in what group. At first I thought everyone (okay, majority) were united on the math issue so I figured some apparent conflict in various threads were just evidence that I have no understanding of what the math issues are and are not.

 

I'm still uncertain which is the case.

[Spy Car]

I didn't think the methods of much hated "new mathematics" would find popularity on this board. :lol:

 

"Reform Math" (aka "Fuzzy Math") is not the same as "New Math."

 

Just to be clear :tongue_smilie:

 

Bill

[Dana]

This is why I get so confused reading math threads. It appears that there are two entirely different groups of people on the forum and I can't keep track of who is in what group. At first I thought everyone (okay, majority) were united on the math issue so I figured some apparent conflict in various threads were just evidence that I have no understanding of what the math issues are and are not.

 

I'm still uncertain which is the case.

 

You didn't get the scorecard when you registered? :001_huh:

 

 

As you read, you get a feel for who thinks what. When there are some posters who you agree with & whose kids seem to match up with your kids, you "listen" for their posts & get advice.

 

As always, take what works for you & your family and discard (mostly) the rest. Do think about contrary opinions though. Are they things you should be doing (but aren't because it takes time) or do they just not fit your situation?

 

There isn't one right way.

[Ray]

nm

Edited November 7, 2011 by Ray

[Way2blessed]

I never have understood the draw of the Khan Academy. I have always found the presentations boring, but couldn't put my finger on a more specific reason of why I dislike the site. Now I have my reaason. :lol:

[Spy Car]

I think there are more than two groups. :D

 

Two basic groups I think, it's just that one is prone to internecine warfare :D

 

Bill

[Roadrunner]

This is the first time I saw anything positive about "reform" math (hope I got it right this time) :001_smile: on those boards.

There seems to be more than one group mainly along the lines of Saxon versus Singapore (or something like American traditional versus Asian math ?), but that isn't anything like this division (real math versus fuzzy math). Again, I haven't been on those boards for long enough and I am surprised.

[Lang Syne Boardie]

I think the main reason that we don't come out with pitchforks on a thread about lattice multiplication is because this single method isn't the enemy.

 

Parlor trick or public school math, it really does work! On its own, lattice multiplication poses no harm to the future of the country. Nobody needs to say anything against it.

 

Of course, many of us see a problem with lattice multiplication if the child is never taught what multiplication (or place value) means or how to use the traditional algorithm. On its own, lattice multiplication does not get the job done. But failure to teach concepts or more reliable methods for larger numbers doesn't have to go hand-in-hand with teaching lattice multiplication in the first place. They aren't mutually exclusive, except in my local public school which uses TERC Investigations. (there's your snark)

 

Now, if you want to have a generalized fight about new new math or TERC or Everyday Math, I'm sure we'd be up for that.

[Carpe]

I think there are more than two groups. :D

 

There's quite a few variables and each is a continuum.

Discovery --> Guided Discovery --> Instructed

True Mastery --> Mastery Light --> Spiral --> Incremental Spiral

Living Books --> --> --> Textbooks

Concrete --> --> --> Abstract instruction

All real word math --> --> --> All algorithms

Explicit "why"s --> Implied "why"s --> No "why"s

So that's what more than 700 combinations?

 

I think most of us feel the newest math things are very light on "why"s. This particular method especially. Yes it works and is really neat, but it's even harder to explain why it works (than the standard algorithm), and most programs are doing a very bad job of that explanation. It's not the method itself, it's the program it's been inserted into.

Edited November 6, 2011 by Carpe

[Spy Car]

This is the first time I saw anything positive about "reform" math (hope I got it right this time) :001_smile: on those boards.

 

You are a quick study :D

 

There seems to be more than one group mainly along the lines of Saxon versus Singapore (or something like American traditional versus Asian math ?), but that isn't anything like this division (real math versus fuzzy math). Again, I haven't been on those boards for long enough and I am surprised.

 

To oversimplify, I think there are still two "basic groups."

 

One that puts an emphasis on learning how to do basic arithmetic efficiently. Getting the "right answer" and doing so quickly and accurately are the prime objectives.

 

The other will tolerate (and even embrace) more circuitous routes if they feel it adds to a child's mathematical understanding over the long-haul.

 

So with Group One you will find two sub-sets:

 

a) Those who find lattice multiplication inefficient, slow, and error-prone, in addition to not teaching place-value well.

 

b) A much smaller subset who find that *for their children* the lattice method is more efficient than the standard algorithm.

 

In Group Two you have:

 

a) Those who might go along with learning lattice multiplication if they felt it advanced mathematical understanding—but they don't feel that it does, and therefore reject it. Except maybe as a "novelty."

 

b) A much smaller sub-set that feels the lattice method can be explained mathematically, and are therefore willing to include it as one alternative method.

 

Anyone buy that? :tongue_smilie:

 

Bill

Edited November 6, 2011 by Spy Car

[SorrelZG]

I believe I'm in Group 2b except that I would put off the teaching of it for quite some in the same way I'd put off calculators.

 

The video was the second time I've seen it done. The first time it looked like a jumbled mess. This time I thought about it as he did it (that the 2x8 was actually 20x8) and noticed that the 10s fell in one diagonal column, the 100s in another, etc. and it made sense .. just like the regular way without needing the zeros to line everything up right (I can't actually recall if I was taught why we use the zeros or if I just figured it out myself .. so, couldn't the regular way be taught badly and result in the same problems as the lattice method? .. either way, I won't be teaching either until the idea is fully grasped concretely).

[i.love.lucy]

I'm Group 2b. But also feel it's efficient, so might also be 1b within 2b. 2b + 1b = 3b :lol:

[BatmansWife]

I believe I'm in Group 2b except that I would put off the teaching of it for quite some in the same way I'd put off calculators.

 

The video was the second time I've seen it done. The first time it looked like a jumbled mess. This time I thought about it as he did it (that the 2x8 was actually 20x8) and noticed that the 10s fell in one diagonal column, the 100s in another, etc. and it made sense .. just like the regular way without needing the zeros to line everything up right (I can't actually recall if I was taught why we use the zeros or if I just figured it out myself .. so, couldn't the regular way be taught badly and result in the same problems as the lattice method? .. either way, I won't be teaching either until the idea is fully grasped concretely).

 

This is what the second video explains.

[5knights3maidens]

Wow! I'm sitting here making up my own math problems. :001_smile:

[Roadrunner]

I just watched it. Anybody who gets this is a genius in my book. No kidding.

[Ester Maria]

I just watched it. Anybody who gets this is a genius in my book. No kidding.

I was so confused when I first learnt of lattice multiplication. I did not understand why cannot they just use the standard algorithm with a clear explanation, not... this.

 

To this day, my confusion has not disappeared. :tongue_smilie:

[SorrelZG]

I wonder if it makes more sense to certain brain types .. you know, like how some people are grid people and some are box people when it comes to daily/weekly planning. Not really a genius thing, just an information processing thing.

[BatmansWife]

I just watched it. Anybody who gets this is a genius in my book. No kidding.

 

I'm gonna take that as a compliment. :lol:

[mindygz]

Well, who knew this would spark a new math world war.

 

I actually "get it" and like it. But honestly, I was good at math in school because I learned all the algorithms and could do them, not because I had a great understanding of what was happening. I was always a "do what works" student, and honestly didn't give a fig if I didn't understand as long as I was getting the right answer. I was a valedictorian at my school and went on to get a BS and a MS in zoology. But I couldn't have articulated the how/why of "borrowing/regrouping" until I went through MUS's lessons. It honestly hadn't occurred to me to truly understand it. (I like to think that I could have figured it out with any amount of thought on the issue...I just never cared.)

 

I hope for more for my kids, but know that they can get pretty far in life even if they don't understand the whys and hows of every little math operation. I think in words and understand the world verbally--give me a page of explanation rather than show me a single equation any day.

 

And with regard to the different "camps" on the Math issue, I must be in the third camp, where people who like things that work and make sense hang out but don't spend a lot of energy getting upset about people who prefer to chill in other camps. (Though chill is perhaps not the right word....) ;)

Edited November 6, 2011 by mindygz
clarify intent

[SorrelZG]

Oddly, the above post is the first I've read from anyone that didn't sound "chill".

[momma2boys]

I like it, too!

[ktgrok]

Also, it makes it REALLY easy to make simple mistakes. And hard to figure out where you made them. Oh, and the fact that parts are done left to right and parts are done right to left is a disaster waiting to happen as far as I'm concerned.

[BatmansWife]

Also, it makes it REALLY easy to make simple mistakes. And hard to figure out where you made them. Oh, and the fact that parts are done left to right and parts are done right to left is a disaster waiting to happen as far as I'm concerned.

 

I did a bunch of multiplication problems last night and a bunch today. Yeah....I was bored...so I wanted to really test this out. I found just the opposite to be the case with me. Every problem I did the lattice way I did without any errors and I could do it quickly. I worked the same problem the "normal" way and several times the answers didn't match. I'd look over each way and every.single.time my error was in the regular multiplication way, never in the lattice. Go figure (pun intended).

 

I'm not really sure what you mean by some parts are dont left to right and some right to left. I'm pretty sure it's all right to left.

[BatmansWife]

And with regard to the different "camps" on the Math issue, I must be in the third camp, where people who like things that work and make sense hang out but don't spend a lot of energy getting upset about people who prefer to chill in other camps. (Though chill is perhaps not the right word....) ;)

 

I'll join you in camp 3 Mindy! Let's have smores. :001_smile:

[SorrelZG]

I'm not really sure what you mean by some parts are dont left to right and some right to left. I'm pretty sure it's all right to left.

 

Perhaps he did the original multiplication left to right, starting with the 2(0). I don't recall specifically. With the lattice method it seems that you could start anywhere you wanted and it wouldn't matter.

[SorrelZG]

I also protest the presence of camp 3. :lol: The other camps alreadly didn't necessitate any expenditure of energy in getting upset over others "chilling" in other camps, unless SpyCar left some description of inherent animosity out of his definitions and I have been entirely overlooking.

[Haiku]

Math Mammoth starts kids with multi-digit multiplication by having them multiply each number and writing the complete product under the line, then adding all those products to get the total product. This teaches them why multi-digit multiplication works. They spend one lesson on it and then learn the standard algorithm, which is, of course, quicker.

 

I think lattice multiplication mucks things up and introduces more potential for error. I was visiting a friend in Chicago two years ago, and her daughter's book had lattice multiplication. I was astonished that someone would actually teach multiplication that way. My friend told me that the very first day her dd started learning lattice multiplication, she taught her the standard algorithm and refused to allow her to do the lattice. She even sent a note to the girl's teacher explaining that her dd would NOT be doing lattice multiplication and would complete her homework with the traditional algorithm.

 

Tara

[sagira]

It looks too complicated to me. I can see ds balking at all the extra writing and picture drawing, too. IMO, more potential for error.

[Tabrett]

I have taught low, middle school math classes and watched dc draw lattices all class long. Unfortunately, that was all they did- draw lattices. No math problems were ever inserted in the lattice. I had to take kids out in small groups and teach them the traditional way of multiplication. It was wonderful to see when they finally understood how to do multiplication.

 

I don't like teaching multiple strategies to young kids. I have seen (in PS) how dc never learn one particular way and start combining ways to multiply.

 

I would not teach lattice since it can't be used in algebra.

[BatmansWife]

Perhaps he did the original multiplication left to right, starting with the 2(0). I don't recall specifically. With the lattice method it seems that you could start anywhere you wanted and it wouldn't matter.

 

In the video he filled in each lattice by row...from right to left (right to left first row across, right to left 2nd row across, etc).

:iagree: with the bolded. You could start anywhere and it won't matter. A few times I went down in a column....if it was a simple quick fill-in like multiplying by 0's or 1's.