Lattice mulitiplication Vs. Traditional multiplication algorithm

Discussion in 'Elementary Education' started by Green_eyed_gal, May 31, 2008.

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May 31, 2008

I've been doing some research on lattice multiplication... I thought it was a cool way of doing multiplication, but I was trying to find more information about it... I didn't want to teach my kids something that I wasn't informed about.

I'm a new teacher and I want to do what is best for the kids.. Our school uses Scott Foresman Mathematics and we have TERC as supplemental material. I've never used TERC so I brought home some stuff to look over during the summer.

I was excited about finding lattice multiplication because double digit multiplication is a tough concept for a lot of kids. Well, after viewing the video above I'm not so sure anymore. I think that teaching the traditional algorithm is the only way to go even if I have to spend more time having the kids practice.

I'm just curious about other teacher's views on this.. Would it still be ok to teach the lattice method after the kids have mastered the traditional algorithm?

3. buck8teacherDevotee

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May 31, 2008

Lattice is kinda hard for me to follow. I tried it a few times with some of my struggling 4th graders when I student taught last year. I use Investigations (TERC) math as my main math program. Therefore, I'm all about letting the kids use the strategies that are best for them.

For two digit multplication, a lot of my kids perfer repeated addition. A lot of them like to break it up, for example:
32x6
We break up 32 into 30 and 2. Then they multiply 30 x 6 and 2 x6.
30x6=180
2x6=12
180+12=192
so 32x6=192.

Some of my kiddos like the traditional algorithm, while some don't. I think it's because we teach addition with regrouping (up and down) in the middle of the year, and they can't use it as a strategy until it's introduced. Therefore, a lot of my kids forget to add in the tens that they carried. They like breaking it down because it's more like how they are used to doing math.

Of course, I teach third and we don't double digit multplication. I did in 4th and they did it the same way, breaking it down.

I hope this helps!

4. EMonkeyConnoisseur

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May 31, 2008

The video appeared to be saying lattice and cluster are effective teaching tools but the everyday math and the other text book are lacking in the way multiplication and division are being taught. Basicly the video is cutting down the text books and incouraging teachers if you are useing the lattice method or the cluster method not to leave out the more common algorythm which those text books do.

I have used all of the methods in my class (when I taught fifth). the cluster method assists children in conceptual understanding. the lattice and the breaking the numbers up help children who feel stumped by the normal algorythm. They all help children who are doing well in math see the multitude of ways one can do a single problem.

5. Miss KirbyFanatic

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May 31, 2008

When I took a math class in undergrad she said to teach the traditional algorithm first. Then, when most of them have it, teach the other algorithms.

6. mdith4himCompanion

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I had to teach lattice multiplication and partial product multiplication to 3rd graders during my student teaching. I hated it. The traditional algorithms are so much simpler and efficient. Lattice and some of the other "reformed" math techniques are better at helping kids see why they are doing what they're doing to solve a problem, but can you seriously see an adult in a business meeting drawing a lattice table to solve a problem??

I say if it's not broken, don't fix it! Lattice and some of the other methods might be best saved to introduce to individual students who have trouble figuring out the traditional algorithm.

7. MrsCMultitudinous

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May 31, 2008

I like to introduce my students to a variety of methods and have them be able to use what works best for them. When introducing a concept (e.g. multiplication), I present a problem and have them come up with a variety of strategies to come up with a solution. Other methods are more awkward for us, because that isn't they way we are used to, but they are just as valid; many of the "reformed" methods are actually very old and are common in other cultures.

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May 31, 2008

I don't teach the lattice because it takes too long to make the thing if they are not premade for the kids, and anyone with any spatial difficulties is incredibly confused by this. It's just sort of a trick.

Instead, I teach partial products like buck8. We also use investigations. I have adapted it a bit though.

Say the problem is 27 x 34.

we do 27 x 4, and 27 x 3(0).. they solve for 27 x 3, and tack on the zero. Then they add the two products together.

The coolest thing with the partial products is after awhile, the kids automatically start to line them up the way we do the traditional algorithm because they get tired of writing the numbers over and over. I saw a kid doing this and asked him if his parents showed him how to line the numbers up that way. He said, "no, I just saw it was a shortcut so I didn't have to write the numbers so much." I was pretty darn impressed!

When I introduced the larger problems we spent time together trying to figure out the best way. They were initially confused by the traditional algorithm and we tried a few different ways. The kids were drawn to the partial products. I only have 7 kids in my 4th grade math group though, so we can do things like that together.

For my third graders, when we just multiply by 1 digit, I just taught the traditional algorithm.

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I currently teach the lattice method and it is great how the low kids GET IT! Our district has a lot of cool stuff on our website. Check out this website. It has a powerpoint explaining lattice. We actually did it for one of our first lessons on the smartboard! I hope it helps! http://www.cdschools.org/5422101251...5141221820/9.9_EDM_Lattice_Multiplication.ppt

If that doesn't go right through... go to this website:
http://www.cdschools.org/542210125141221820/cwp/view.asp?A=3&Q=298196&C=58088
and then scroll down to Unit 9 and click on 9.9 Lattice powerpoint lesson

Also check out our website for a lot of good ideas!

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I looooove lattice method! I wish they would have shown me that when I was in school!! I learned it in college and showed my 5th graders both ways. I tell them that I don't care which way way they do it as long as they get the right answer. I don't care if it takes them longer....as long as they're getting the right answer...their state tests are NOT timed so i'd rather teach them a way that they understand and can get the right answer than teach them something that they don't understand and won't be able to get the right answer.

11. 3SonsEnthusiast

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The lattice method seems to leave an incredible amount of room for careless error, and I'm not convinced it does anything to actually aid understanding.

I think every elementary teacher should at least investigate Singapore math. It successfully does what constructivist theorists are hoping to do but do not accomplish.

12. knitter63Groupie

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I had to teach lattice multiplication and partial product multiplication to 3rd graders during my student teaching. I hated it. The traditional algorithms are so much simpler and efficient. Lattice and some of the other "reformed" math techniques are better at helping kids see why they are doing what they're doing to solve a problem, but can you seriously see an adult in a business meeting drawing a lattice table to solve a problem??

Yes, I can see adults using this method-I do. We use Everyday Math, and we teach the lattice method. It is not difficult to teach, especially if you give it time, and provide lots of practice. My 5th graders have dramatically improved their multiplication skills because of this method. I am not the least bit embarrassed by using the lattice method myself. In fact, when I have in front of other non-teaching adults, most tell me they wish they had learned that when they were in school!

13. MrsCMultitudinous

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Actually, they would be most likely to whip out a calculator! :lol:

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The idea of these methods is to begin to understand how the problem works... I NEVER thought about the fact that you are actually multiplying ones, tens, and hundreds and multiplying each by each in a three-digit problem until I was an adult.

In the upcoming years of business, technology, etc. we don't have any idea WHAT people will be doing, calculator or otherwise... the old ways of memorizing and knowing rote facts may not be as useful as they were in the days of assembly line business and technology. We need to create a generation of people who can understand the WHY and HOW of things (not just math) because they will be the innovators. It's too easy to just use a calculator or go online.

I do teach the algorithm eventually to all my students, and I do have kids memorize their math facts, but in general, understanding WHY we do an algorithm the way we do is how we will continue to have inventors and engineers, etc. However, I will say, I was having this conversation with my grandpa who is a genius, graduated HS at 14 has about 5 degrees and is a nuclear engineer. He seemed puzzled about how anyone could NOT understand how multiplication works. He was shocked that I never thought about nor completely understood it until I became a teacher. I do think SOME people (and not just geniuses) get the traditional algorithm and what it really is without all the lattice and partial products and base ten blocks and all that. But for the people who don't get it, I think it's important.

For example, I was always told that you put the zeros in the second row of the multiplication problem because it's a "place holder". No one ever TOLD me that zero is actually there because you are multiplying by 50, not 5 and if I understood place value I MAY have understood this, but no one even told me. I couldn't multiply in my head, not even simple problems like 15 x 4. Now that I understand partial products, I can multiply in my head. I love to show off to the kids and have one with a calculator and one give me problems and I will solve three digit problems in a few seconds. I'm no genius, and I'm not even great at it, but I never could have done that before.

Ok, enough of my railing and raving!

15. MrsCMultitudinous

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Excellent points, MissFroggy. I think that when focussing only on being able to use the algorithm we are not ensuring that our students understand what they are doing. I was great at memorizing formulas and algorithms, but, like you, didn't have a deep understanding of what I was doing (for me, that understanding developed when I began teaching the concepts).

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I cannot tell you how many ah-ha moments I had while going through my education program.. During math classes I was constantly saying..."Oh, that's why you do that". I was taught to memorize algorithms and never knew "why" behind them and that's why I struggled with math. I don't want my kiddos to struggle!!

17. TeacherGroupieModerator

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(climbing laboriously up onto the soapbox)

It's hard to make that kind of useful and eye-opening connection without someone modeling the process.

And this, ladies and gentlemen, is why even kindergarten teachers need to KNOW math. And English. And history. And science. And PE. And the fine arts. And... you get the idea.

Froggy, MrsC, and Green-eyed, I wish for you many decades of connection-making aha! moments you just haven't gotten around to yet.

Remember: it's not the facts that you know but what you can understand with 'em that makes a real education.

(climbing laboriously down from the soapbox)

And, oh yeah: the play of ideas is the best play ever.

18. MrsCMultitudinous

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And I hope that my students don't have to wait until they are as old as I am before they have those moments!

I like to present a math problem and have the students work in groups to come up with as many ways of solving the problem as they can. We then spend time analyzing the wide variety of strategies that can be used to arrive at the same end. Almost invariably, I hear, "I never thought of doing it that way. I'm going to try it!"

19. TeacherGroupieModerator

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I trust, MrsC, that what you mean is not hoping that they're not having them at your age, but hoping that they don't wait till they're your age (whatever your age is) to start.

The age past which it's improper to have aha! moments doesn't exist.

Fortunately for me.

20. MrsCMultitudinous

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Exactly what I meant to say, TG. Providing my students with opportunities to have those "aha" moments is the whole purpose in what I do.

21. pwhatleyMaven

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I may be wrong, but here is the point that I think was being made by the woman in the video: The math curricula about which she was speaking only teach the lattice, partial product/quotient type of methods. They completely leave out the traditional algorithm, and totally dismiss the idea of SKILL MASTERY.

Here is what I think (for what it's worth, lol):

• There are traditional algorithms in mathematics for valid reasons -- they work. We use them to teach addition, subtraction, etc., so why not multiplication and division?
• The traditional algorithm should be taught first (IMHO). However, as part of teaching that method, students must be taught aspects of math such as place value, carrying, etc.
• The lattice method and others should be taught as secondary methods that will improve student understanding of how and why the traditional algorithm works.
• The same goes for division. More about that below.

Before anyone gets mad, here are my thoughts as to why I think this way.
• I was NOT a math whiz in school. I was reading books by age three, but hit a brick wall when I was introduced to division in 4th grade. It took months of tutoring for me to understand the basics. If my (wonderful and creative) math teacher had put any of these "nonstandard" or "nontraditional" methods in front of me, I would never have understood division at all.
• I tutored in two different university learning centers for a number of years. While I did not tutor math (I did English, SS, Humanities, Psych, Sociology, etc.), I had a front page seat to see the problems being encountered by the incoming students. They could not do simple multiplication and division problems without calculators! It was like breaking an addiction to get them to do the problems with pencil and paper.
• Despite my life-long love of learning (and possibly because of my efforts to instill such a love in her), my daughter did not complete high school. In fact, she attended a youth boot camp program of her own volition. A huge part of her problems in school was her mouth - she's a social butterfly who would rather talk than eat.
• However, probably the most serious problem began in 5th grade, when she began having problems in math. Prior to that, most things came easy to her. I tried everything that I could think of to help her (so did my husband). I honestly think if we could have afforded to take her to Sylvan or something it might have helped (mainly because it would have been SOMEONE ELSE tutoring her).
• Anyway, she is now fighting her way through studying for her GED. She has tested for it twice, and both times she missed passing it by 2 points on the math portion.
• Had I known more about the methods of math she was learning in school, I might have been able to help her more. I was one of those parents who had no idea what the textbook/workbook was talking about! (Estimation threw me for a loop, too - I couldn't figure out why you would want to estimate, when you could just solve the problem, lol.) I DID stay in contact with her teachers, but I was working an hourly position & couldn't take off during the week unless someone was dying (I got one day off for a miscarriage).

Anyway, those are my thoughts on the matter. I didn't write them out of self-pity or anger. I'm just trying to give a different point of view. Sorry it was so long - I can't help it - I'm just wordy by nature, lol.

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A lot of the reasons kids start to have problems in math in 4th and 5th grade, is because they do not have the conceptual understanding of NUMBER. They do not understand how to manipulate numbers, understand place value and so forth. Addition and subtraction should not be taught with the standard algorithm either, at least not at first in my opinion. Kids should have access to base ten blocks to learn to regroup, so they can SEE what they are doing- then they can learn to do it on paper.

Everything is built up step by step. The "tower of knowledge" crumbles in 4th or 5th grade because the foundation was not strong. Alternative methods for teaching math are necessary for some students to have a strong foundation, just like phonics is necessary for some students (but not all) to build a strong foundation in reading.

I absolutely believe kids need practice WITH THE STANDARD algorithm, and need this practice repeated until they are fluent in it. I don't think a week long chapter in multiplication will do it.

In my class, every morning begins with math problems. I present them in the standard algorithm, and they can solve them that way, or in the beginning use the base ten blocks, expanded notation, partial products, or whatever method they need to use. Eventually, day after day of this, they figure out the fastest way is the traditional way.

I do 5-7 problems a day.

At the beginning of the year, it was simple addition and subtraction problems, then fractions, multiplication, division, etc. Now the kids in my class can use the standard algorithm in most of these skills. But if they can't, we go back to the manipulatives and the alternative methods.

Even with 5 problems a day in the "old fashioned" way, I make sure everything is introduced and practiced repeatedly with the conceptual underpinnings (such as blocks and problem solving) before it is added to their arsenal of morning problems.

23. TayCompanion

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I haven't read through all the replies yet, but i'm interested to see what everyone says. During my student teaching I had to teach my third graders lattice and partial products algorithm with 2 digit numbers. They loooooooved the lattice. I had them challenge each other on the board and they had so much fun. In fact, when I told them we had free time and could either do a spelling activity, math challenges, or silent reading, they always picked the challenges.

When I taught the algorithm....they were extremely confused and mixed up their numbers. They weren't lining the numbers up right, not multiplying right. It was a mess and took much more practice.

Lots of luck with it!!!

24. pwhatleyMaven

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I have seen these problems as well. My solution for the place value (lining up) problems was to give them graph paper, project a graph paper page on the board (computer projector), and show them how to do it using the graph squares. Then I helped them do it in groups (and in color), then they did it themselves, then for homework. It worked for most of the students! The few it didn't work for needed extra help anyway.

MissFroggy: I totally agree that the students need practice with all facets of math, including manipulatives, puzzles, games, challenges - any way we can get them to thinking about the numbers and how they relate to each other. My only issue with the program she discussed (I believe it was Saxon?) was that it left the traditional algorithms out entirely and dismissed mastery as a valid student learning goal. To me, a huge part of mastery in ANY subject is the ability to logically think through what you are doing.

25. TeacherGroupieModerator

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(doing clumsy dance)

Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes! Yes!

26. TeacherGroupieModerator

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Huge hug to you and your kid, pwhatley. Let me lecture for a moment - you don't have to listen, I just have to get this out of my system.

Ahem, children. The standard algorithm for each of the operations (addition, subtraction, multiplication, division), or to be precise for situations when the numbers are such that we can't just wrangle 'em in our heads, was devised as a shortcut - an expedient. It exists not because it's insightful but because, in the days before ANYbody had calculators, it was fast and reliable... well, and learning to do the operation Just That Way marked the learner as an insider rather than an outsider. (For most of human history, education has been as much about keeping Some People out as it has been about letting Our People in. What changed in the 20th century is that the definition of Our People got broadened. And about time, too.)

(Side note: back before Hindu-Arabic numerals, it was fairly common for some of the brightest minds in human history to admit cheerfully that multiplication was quite beyond them. Then again, multiplication using Roman numerals is a fate I wouldn't wish on my worst enemy. Three cheers for the abacus!)

The big little secret of mathematics is that there may be Just One Right Answer, but there's almost always more than one way to get to it, and sometimes half a dozen or so ways, all of them perfectly defensible mathematically. For instance, if I'm calculating the total cost plus 7.5% sales tax of a \$200 suit,

- I can multiply the cost of the suit by the tax rate (7.5%(\$200) = \$15) and then add the result to the untaxed cost of the suit (\$200 + \$15 = \$215).

- I can add the tax rate to 100% (that's for the suit itself: 100% of the suit + 7.5% of the suit = 107.5%) and then multiply that sum by the cost of the suit (107.5%(\$200) = \$215).

- I can use mental math: 7.5% is half of 15%, and 15% = 10% + 5%, so I can find 10% of 200, which is 20, and half of that is 5% or 10, so 15% would be \$30 and half of 15% is 7.5% or \$15, and then I can add that to \$200 to get \$215. (This method is related to the method for calculating a tip followed by many of us who live in states with a 7.5% or so sales tax: if you believe that a 15% tip is reasonable, just double the sales tax on the meal.)

- Similarly, I can divide \$200 in half to get \$100, which is very easy to work with: the tax on \$100 would be \$7.50, so the tax on twice the cost has to be twice that much, or \$15.

And someone else is bound to come up with a bunch more possibilities.

I'm willing to wager, by the way, that your problem isn't that you learned everything else but the traditional algorithms. If you'd gotten the math teaching you should've gotten, the traditional algorithms would have made sense.

Now, then, pwhatley: You and your daughter might want to consider rummaging up Visual Math by Jessika Sobanski. It's been out under that title for years, and the chances are pretty good that your local library system has it. The publisher, LearningExpress, has recently reissued it under a different title that I don't now recall (and removed Sobanski's name from the cover - sheeeesh!), but it is still out there: you could check the Web site, http://www.learnatest.com, which also helpfully has online practice.

27. pwhatleyMaven

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As always, I bow to your genius, oh great sage.... Honestly, I never fail to enjoy and to learn from your so-called "lectures." Your posts are always written fairly and with fabulous grammar and wording! Can I borrow your brain sometime???

Thanks for the book tip (Visual Math). I actually found it on Amazon.com. I think I will order it tomorrow for my daughter (after I deposit my last check of the school year, heavy sigh). Do you have any thoughts on the book GED Preparation from learnatest.com? I'm considering that, too, because my DD lives across the state and has no internet connection at home, so a book will work much better for her. Parents of active 2 1/2-year old boys cannot concentrate well in the public library, lol.

28. TeacherGroupieModerator

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Jun 6, 2008

wincing slightly, and blushing

Ouch. Did I go too know-it-all again?

I would recommend not ordering ANYthing yet, pwhatley: I would recommend for your DD that she visit the books in the bookstore or in the library first, and that she look at some of the other books that are in the same place. The idea is for her to find things that will work with her learning style. Could be that a different one of LearningExpress's options would work for her - there's Practical Math Success in 20 Minutes a Day, and a number of other useful items in LearningExpress's Skill Builders series. Or she might be better served by one of the offerings from Princeton Review or Kaplan or Barron's or Cliffs or whoever... I happen to think that LearningExpress books are pretty good, by and large, but that doesn't mean they'll work for her, and that's the nature of things: there really is no such thing as The One Right Resource For Absolutely Everybody, any more than there's such a thing as The One Right Way To Eat Chicken. (Or, for that matter, The One Right Way To Compose an A to Z Post.)

29. MrsCMultitudinous

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I always makes my a little (okay, more than a little) sad when I read that there are teachers who must teach "only" certain things or in certain ways. The joy (and great challenge) of teaching is being able to find what works best for every student. I have specific curriculum expectations (standards) that must be addressed each year--the how and the resources used are totally up to me. (Sorry for the hijack!)

30. TayCompanion

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Jun 6, 2008

Thanks PW! That's a good idea. I just had them draw vertical lines to keep their place values. That seemed to help a little bit, but I think keeping all the numbers straight would be the best way to go. I will definitely use the graph paper next time!

31. paperheartGroupie

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Jun 6, 2008

I teach near the border of Mexico...the "traditional" algorithm for many of the regions in Mexico is the lattice method. Its a geographical/country thing.
Some of my students come in already knowing the lattice method so, of course, I encourage them to keep using it. Sometimes they will teach it to other students.
I started using the breakdown method for my 7th graders who are still having trouble with multiplication.

32. pwhatleyMaven

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No :lol:... I was just paying homage to your extensive (and appreciated) knowledge bank!

You are right again, of course. However, the problem with my daughter's situation is that she & hubby both are lacking their GEDs, so are both working pretty menial jobs for little money. She won't even walk into a bookstore right now, unless they have a huge sale on books for my grandson.

My husband and I have agreed to pay for their GED testing. We would pay for classes, too, but the closest ones to where they live is almost 100 miles away, so... I went to Amazon.com last night & found four books:
McGraw-Hill's GED book with a CD-ROM (This is for both of them to use -- they have a computer, but no internet access currently),
Steck-Vaughn's GED Math book (for my daughter),
Barron's GED Math Workbook (again for my daughter), and
The Best Test Prep for the GED Language Arts: Reading Section by Chesla (That is for my son-in-law).
I ordered them & they are being shipped to my daughter's house. We are hoping that they can both earn their GEDs by next Christmas. Right now all I can say is Thank God Amazon has free shipping!

33. mmath1212Rookie

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Jun 6, 2008

In this Math teacher's opinion

34. TeacherGroupieModerator

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Sounds like your daughter is feeling at least slightly burned by the process. Note, though, that my instruction was not for your daughter to go to a bookstore to BUY books, but to LOOK AT the books available and get some idea which book might be the most compatible.

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37. knitter63Groupie

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I just reread all the posts, and I have to correct myself. After working with the president of the National Council of Mathematics for two years, I have learned that the Lattice method is not method at all-it is a process to get the correct answer. (right on, Alice!)
With Common Core, the students must understand place value. They must know WHY multiplication works. We have stopped teaching lattice method to our students, even though we still use EDM.

38. applecoreDevotee

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Oct 4, 2012

We use Everyday Math curriculum in our district as well.

I hate lattice. And I normally do not toss that word around lightly.

I'm excited to NOT teach it this year because we're intergrating the CCS slowly this year in math. =]

39. HeatherYHabitué

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Oct 5, 2012

I agree- lattice is like a parlor trick. I call it "Math-a-magic."

40. foster_carerNew Member

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Oct 5, 2012

Hey Knitter63 & HeatherY

I have learnt at least fifty card tricks, but I only remember two, there is a third, but I need ten minutes to work out how to do it. LOL!

I totally agree with the concept of space and would extend this to high school work on the Nth value of a linear series of numbers. In the UK it is taught as follows:

For a series 8, 11, 14, to Nth, the common difference is 3, so it must be related to the 3 times table (3n)

The 3 times table is 3, 6, 9, etc.
and the sequence is 8, 11, 14, etc.

Every term in the sequence is 5 more than the corresponding term in the 3 times table, so the nth term is 3n + 5.

The lads I foster can follow the process on the day and get the homework correct. But a month later when tested they don’t have a clue, they are being taught a process, BUT this is not maths.

My action as a foster parent!

I get them to plot the values on a graph using n as the x axis, and then get them find the value of the intersection of the y axis (n1 - the common difference) here we are into fundamental maths, which they have already covered.

The equation is for Nth value is: V = A + Bn, where constant A is the offset and Bis the slope (or the difference of any points y/x)

This is a graphic learning experience easily visualised, and difficult to forget, the selection of signs is clear A is negative if below the x axis and B is negative if the plot slops down. All my lads quickly get the series really starts at n(zero) and the n(zero) value is the offset. I do encourage them when uncertain to do a quick freehand 15sec sketch to refresh the vision.

It also promotes the ability to revert to basics and rebuild, rather than rely on rusting processes that have become flawed; an ability that will help them across all aspects throughout their education and the rest of their lives.

Lattice is a proactive method that actively promotes failure of our children!!!!!!!!!!!