Japanese Multiplication

One of my students showed me something new.  She’d seen it on Youtube and chose to share it with me.  It was interesting. It’s called the Japanese multiplication method also known as Chinese multiplication, or the stick method.  Apparently, it's been around a while. I've used it and it reminds me a bit of the box method without the box.

It uses parallel lines that run diagonally and when the line cross, they form intersections and it is the intersections that provide the multiplication. I've done a problem showing each step so you can see how it works. I'm using the problem 24 x 13.

For 24, I've got two parallel lines in green with a space and then four more that are dotted. 13 is represented by one red line and then 3 more a bit a way. It is easy to see the 24 and 13.

The line are supposed to cross at 90 degree angles or be perpendicular. Usually the lines are running along the y = x or y = -x pathways.

The next step is to place dots on the intersections so they are so much easier to see.

These dots are what provides us with the product for each step of the multiplication.

The intersections at the middle left represent the hundreds, the group at the top and bottom represent the tens, and the group to the right represent the ones.

So based on the last photo, we have 200 from the left, 60 plus 40 from the middle and 12 from the bottom. Each of these represents one number from the standard multiplication algorithm.  When you follow the standard multiplication algorithm you would go 3 x 4 = 12, 3 x 20 = 60, 10 x 4 = 40 and 10 x 20 = 200 so when you add all the numbers up, you get 312 using either method.

There are problems when trying to use this method with larger numbers.  For instance, if you multiply 8 x 9 you'll have 8 lines crossing 9 which gives you 72 intersections to count.  Or if you so something like 599 x 798, you end up with lots of lines which can be quite confusing but when children are learning to multiply, they tend to use small numbers so this system works well.

I am glad to know about this as it gives me one more method I can use with students who struggle with multiplication.  In fact, I have a couple of students who do not know their multiplication tables so I want to show them this method.  It might help them so they are not as reliant on a calculator. Let me know what you think, I'd love to hear.  Have a great day.