How should we teach kids to multiply?
January 28, 2008 am31 6:15 am
Standard long multiplication algorithm? Partial products? Latice? Fingers? Calculators? Any way they come up with on their own?
You’ve got an opinion. Dave at Math Notations has a poll. (poll is on the upper right. explanation is in this post)
Go vote!
7 Comments
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JD2718 
WHich method is easier for students to Understand — not just do.
Look at the standard method. 24 x 612 means “24 groups of 612.”
That means, 4 groups of 612 and then 20 more groups of 612.
Thus, does multiplying 4 times 612 make sense?
When multiplying by 10, 20, 30, etc, one notices a pattern: the answer always ends in a 0 and a short cut is just multiply by the ten’s digit and add a 0 – e.g. 20 x 612 is 1224 and a 0 so 12240.
Make’s sense? Does the method for the standard algorithm make sense now? Is it easy to understand?
Look at the alternative. It shows 37 x 469. Does the display show 37 groups of 469 as clearly as the standard algorithm?
I don’t think so. Nevertheless, some students like the lattice method, especially if they have been improperly taught the standard one. They are eager to get the right answer, even if they don’t understand the method, as long as it works.
The lattice methods is an interesting method for students to e xperience. The should ask themselves: can I do it rather easily?
(usually yes). Can I understand “why” it makes sense? (Not really)
And hence appreciate the standard algorithm as doable but also understandable.
I’ve found that the lattice method is just as easily understood by students, perhaps more easily. There is a direct correspondence between the lattice grid and an area model for multiplication: split the width of one’s rectangle (corresponding to the image above) into the sum 400 + 60 + 9 and the height into 30 + 7; the “42” (i.e., 420) in the middle of the bottom row naturally corresponds to the area of a 60×7 box, etc….
One thing I especially like about the lattice method is that it naturally extends to polynomial multiplication, a topic most algebra texts make unnecessarily obscure by divesting the algorithm of any geometric intuition. Most students I’ve taught it to find it far simpler, and (I believe) have an easier time relating it to area than the so-called “traditional” algorithms. (“traditional” = “dominant in last-half of the 20th century US schoolbooks”)
how do you add the numbers to get the answer
its very easy but if we have 3*3 grids. it seems very difficult
Hello,
I think the standard long multiplication algorithm was very simple, and it was very understandable. This is something we can easily teach our kids about as long as we show them the exact way it was shown here. This was a great way in explaining it!
Information is power and now I’m a !@#$ing dictator.