the chinese are coming the chinese are coming their six-year-olds can do math that not even our seven-year-olds could conceive of when i was a kid it was japan japan was the menacing asian threat to american hegemony into the future and this can't be true but in my.

Mind there was like a local news story on this thing called the japanese line method for multiplication and it was a similar angle to this video like oh my gosh look how fast the japanese can multiply two-digit numbers nothing can stop them now the idea is that you represent 12 and 14 with a series of lines so the 12 is going to be one line.

And then two and the 14 is going to be one line and then four and what you want to look at are the intersections for these lines top middle and bottom you can see there is just one intersection here at the top and that is the one of the 168 product you can see there are one two three four five six intersections in the middle and that's.

The six of our product and then down here where the two lines and the four lines cross of course we have eight intersections and that's the eight of our product the video obviously didn't show the lines but that is what's happening here with the one times one equals 1 the 2 plus 4 equals 6 and the 2 times 4 equals 8. the problem is this.

Method doesn't scale well it's very clever for smaller numbers in the teens and maybe even into the 20s but certainly as you get into higher two-digit numbers or for sure as you get into numbers larger than just two digits it's not particularly convenient there's also nothing particularly asian about it this isn't just a japanese method it's.

Not just a chinese method in fact there's an american method similar to this that we call the area model for multiplication although it's certainly true that we teach distribution in america i presume they teach it everywhere when students are younger they often learn about distribution through something called the area model.

For multiplication the area model for multiplication would represent this product 12 times 14 as a 10 plus a 2 and a 10 plus a 4 and rather than represent the different distributions we would just compute these partial products 10 times 10 is 100 10 times 2 is 20 10 times 4 is 40 and 4 times 2 is 8. it's the sum of these different boxes that.

Give us the product of 168. you can tell that the area model actually is the same as the line method but rather than count up some number of dots in an array we're just actually multiplying out the numbers as many people are fond of pointing out the area model also doesn't necessarily scale super well there are clever ways to use it but typically once.

We start multiplying larger and larger numbers number one we're just going to use a calculator but number two if we have to do it by hand for some reason we're probably just going to use the standard algorithm the standard algorithm itself is a further abstraction of counting up dots in an array or looking at the area of.

Rectangles in the area model so no i wouldn't worry too much about the chinese the chinese are coming anybody can do any of these forms of multiplication what's beautiful to me about math education is demonstrating all these different models and the connections that they have to each other.

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