Multi-digit multiplication - ProTeacher Community


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Multi-digit multiplication
Old 10-03-2008, 06:55 PM
 
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Hi all...

I would love some help in how to best teach my kids multi-digit multiplication. I'm planning on showing them the lattice method, and partial products, but I'm having trouble figuring out how to teach them the old-fashioned algorithm without confusing them.

Ideas??

Thanks!!

Lori


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Multiplication
Old 10-04-2008, 02:30 AM
 
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Lori, I would never teach them the lattice method. It is not based on any underlying mathematical principles or place value. It is confusing for many kinds and does not require them to rely on their number sense. Our district has told us not to teach it, even though it's in the Everyday Math series, which we use.

I would really focus on partial products. For those students who get it completely, I'd show them the traditional algorithm and just have them practice it (I have no real teaching method to share; I think you just have to show them.).

When I teach partial products, I make boxes to keep it clear. I have attached what I mean.
Good luck!
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File Type: doc Partial_products_boxes.doc (19.5 KB, 567 views)
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Multi-digit Multiplication (long)
Old 10-04-2008, 04:41 AM
 
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I would suggest using a partial products method to get to the traditional algorithm. The aha moment came for a few of my students this year when I suggested that rather than multiplying each individual digit by each other individual digit in the other number that they use their understanding of single digit multiplication with a multi-digit number. Say that the multiplication problem is 496 x 32. Using the distributive property, this can be rewritten as 496 x 30 + 496 x 2. It was easy to show 496*2= 992 -- Connect it to the sum of the 1st 3 numbers in a more detailed Partial Products Problem. 12 + 180 + 800 = 992. Then do the same process with the 30 and explain that it can be shown as 496*3 = 1488 with a zero on the end because 30 = 3*10 -- 496*30 = 14880, same as 180 + 2700 + 12000. Then you add the products of 496 *2 and 496*30 to get the same answer as if you added all six products in the partial products method. I still have some who break it apart, but there is a lot less chance of error because there are fewer steps.


I disagree with the PP about Lattice though. Lattice is actually a form of partial products you just need to connect it by identifying the different diagonal lines with the correct place value. For example the digit in the bottom right corner is alone and represents the ones place. The next diagonal is the 10's place, the next the 100's place and so on.
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Working problems on a white board
Old 10-04-2008, 05:07 AM
 
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One thing that helps: write the problem with a black marker. Multiply by the one's digit with blue, multiply by the ten's digit with red, add to get the total and write it in black.

Obviously the exact colors don't matter, but using different ones really helps. Also, as the pp said, using boxes for the digits of the partial product helps.

They can check their problems by reversing the top and bottom numbers and multiplying again. Students can work in pairs - each work the problem and then compare answers.
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Thanks!!
Old 10-04-2008, 09:26 AM
 
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Thanks for all of the great answers!

Funnygirl: Actually, some of my kids seem to know the lattice method, although I had no idea what they were trying to show me. I do see where it could get confusing because of the diagonal lines, and trying to keep things straight.

janiebird19: Thanks for the sample document. Our new math program, enVision, shows that as an introductory activity. I could see where it would help some of the kids visualize partial products. Many of my kids have trouble keeping things lined up, and the box method would probably help them work their way up to the traditional algorithm.

Phyllis: I really like your idea of using different colors for each of the steps. I'm going to use that on Monday, along with the other ideas.

Many thanks!!
Lori


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Annenberg Media
Old 10-05-2008, 10:50 AM
 
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... has an interesting approach in Learning Math: Number and Operations Video 4. Meanings and Models for Operations. Multi-digit multiplication is shown using blocks. The multiplication segment is short and starts about 12 minutes from the beginning of the video. It can be viewed at http://www.learner.org/resources/series171.html. Registration is required, but it's free. Rather than tell you what I like about this, I'll let you decide for yourself. If you don't have blocks, check with your department and colleagues. Grid paper works too, but is not quite as appealing or effective with those kinesthetic learners.
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Boxes
Old 10-05-2008, 03:26 PM
 
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Lori, I'm the one who attached the box method!
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I teach 3 methods
Old 12-01-2009, 03:34 PM
 
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I use three methods: break apart, then traditional, then lattice. I usually teach one method per day, so they can practice it before getting a new method. After that, I let them decide which method to use on their daily work (whichever one is best for them).

When I do the first two methods, I use a multiplication cheer to help them know which numbers to multiply. It goes like this...

"Up and over"
(students raise right arm up, then diagonal to the left)
"Down with the zero"
(students squat down)
"Over and up"
(students raise left arm up, then diagonal to the right)
"Add, baby, add!"
(clap, clap, clap)

I'm attaching a colored mini-poster of the cheer that I made, and a student copy that they can keep and color. Feel free to share this!

When I teach lattice multiplication, the following website is very useful and kid-friendly. It teaches them step by step how to do it. http://www.coolmath4kids.com/times-t...ication-1.html
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File Type: doc Mult Cheer.doc (183.0 KB, 192 views)
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