Here’s a fun little math trick to show the kids.
Polish hand magic is named after a hand trick that someone posted on the internet years ago that they had supposedly learned from a Polish friend.
It is basically a way to multiply larger numbers using your fingers.
You use your fist and fingers to represent the numbers 5-10 and can multiply numbers like 8X7 by first adding the fingers up (for the tens place) and then multiplying the fingers turned down (for the ones place).
In some cases, you may have to carry or regroup, but the trick still works. For instance, when multiplying 6×7, you get a 12 for the ones place (4 fingers down times 3 fingers down). Kids should understand that 12 is the same as one ten and two ones, so the ten becomes another in the tens place (see the example above).
If kids want to understand more of why it works, it’s basically algebra.
Saturday Morning Breakfast Cereal posted about it back in 2010 and gave this formula:
As part of one long comic about it.
Scientific American also posted about it, twenty years ago in their Parents’ Corner. They explained.
As with many number tricks, you can understand it using simple algebra. The following explanation should be within reach for a 14-year-old.
Suppose you are multiplying Y by Z. For Y, the number of fingers up is Y – 5 and the number of fingers down is 10 – Y. Similarly, for Z the number of fingers up is Z – 5 and the number of fingers down is 10 – Z.
We sum the up fingers and use that result for the ten’s place:
(10(Y-5)) + (10(Z-5)) = 10Y – 50 + 10Z – 50 = 10Y + 10Z – 100
Now we multiply the down fingers:
(10 – Y)(10 – Z) = 100 – 10Y – 10Z + (Y)(Z).
When we add those two results together, we get:
10Y + 10 Z – 100 + 100 – 10Y – 10Z + (Y)(Z).
All the terms cancel except (Y)(Z). So the method gives us the product of Y and Z.
