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Another great trick is using diagonal lines to calculate multiplication [1]. It's a neat little trick that really helps drive home an understanding of what 'mul
by NamTaf 14y ago
Another great trick is using diagonal lines to calculate multiplication [1]. It's a neat little trick that really helps drive home an understanding of what 'multiplication' actually is, since it's just like the OP's grid of boxes but turned on its side and contracted down to points. The trick is getting 45 degree lines so they line up more easily.
The advantage of lines is that you can spew out multiplication in the double-digit by double-digit range quite quickly. 51x23 for example is super easy to calculate - 10 100's + 17 10's + 3 1's. You're essentially just doing 50x20 + 503 + 201 + 1*3, but with lines to track everything.
Show it to a kid, and watch it blow their mind.
[1] http://lifehacker.com/5975917/quickly-multiply-big-numbers-the-japanese-way http://lifehacker.com/5975917/quickly-multiply-big-numbers-t...
- brazzy 14y agoHow painful then to see it called "magic" and read "I don't know how or why this works [...] wonder why we don't teach math the way" That doesn't sound like any kind of understanding is involved...
- Sunlis 14y agoWith a method like that it is very easy to accept the answer you get as magic, because there is no understanding involved. The method shown by OP is not practical to use for anything other than teaching concepts, but it is at least easily expandable and actually describes multiplication. This line thing is more of a trick than anything else. I sincerely hope that if this is used to teach children, they also properly explain multiplication rather than simply pulling a rabbit from a hat.
- mturmon 14y agoI purposefully didn't mention the line-crossing algorithm, because I think (like other nearby commenters) that it's more of a mysterious trick than a visualization that promotes deeper understanding. Maybe as they get older, it would be fun to present the line-crossing algorithm, and then ask them if they can explain why it works. My 7-year-old would not be able to do this, but she can easily relate to the multiplication-by-area analogy and its generalizations.