Here’s a fun way for kids to play with math — teach them how to do Japanese multiplication. This visual math trick lets kids use lines and their intersections to see how math works, and helps show that math and numbers can be fun.
To multiply with this method, you simply draw diagonal lines to show the tens and ones place (or higher) of each digit you are multiplying. Then you count each intersection of lines in each section. The sums will be the first, second and third (or higher) digits in the answer.
Math Fun Facts explains how it works:
The method works because the number of lines are like placeholders (at powers of 10: 1, 10, 100, etc.), and the number of dots at each intersection is a product of the number of lines. You are then summing up all the products that are coefficients of the same power of 10.
You can find more detailed explanations of how this method works at Teaching Math with Technology.
In order to further show why this works, you could also simply write each number as an expression of ones, tens, hundreds and so on, and then add them. For instance, in the video he multiplies 14 x 23 and he has to carry twice, since two of the sections get answers above 9 (12 for the far right total and 11 for the middle total). If kids wrote the numbers as what they’re truly representing, then you could simply do the exercise from left to right: 200 (2 intersections in the hundreds place) + 110 (11 intersections in the tens place) + 12 (12 intersections in the ones place), and then add them = 322. Either way works, and this one may seem even more complicated to younger children but can also help explain what’s really happening and why this works. It’s another way to get kids thinking about the mechanics behind the “trick.” The more they think about these things, the better they will be at actually understanding how math works instead of just knowing how to plug in formulas.
Note this is not intended to replace teaching convention means of multiplication. Of course children should also know the traditional multiplication methods taught here in the United States. They should also know how to simply use a calculator, along with the many ways that they can use mental math tricks to get the answers more quickly. The more they learn alternate ways of doing math and the more they are encouraged to think about why these other methods work, the more they will become actually fluent in mathematical thinking, though. Many of the adults who complain these days when kids are taught extra ways of doing math are the same ones who say they hate math and are bad at it. The more we teach kids to play with numbers and learn different ways of getting the answer (and think about why it works), the more we help create kids who truly understand math and excel at it.
For more great math exercises, see Math fun: Kids can easily multiply large numbers with peasant math trick and Short division makes math easy.