Have you ever wondered why the Oriental Soroban abacus has 4 separate beads? It is in base 10, not 4 or 5, so why organize it that way?

In response to yesterday’s post Hand tricks! Alexander Bogomolny linked his page explaining finger math. As I looked at that neat way of counting to 99 on your two hands, I finally understood Soroban! The four beads stand for the four fingers on your hand, and the separate bead for the thumb.

With Alexander’s photos of hands, and screenshots from an online Soroban abacus, I can show the idea. It works the best if you count along. First, use the four fingers of your right hand to count 1, 2, 3, 4. This corresponds to the four beads in the first row of Soroban, shown yellow.

Then things become slightly more abstract. The thumb stands for 5, all by itself, just like the lonely yellow bead does. We move from direct counting to symbols:

You add fingers to the thumb to count 6, 7, 8, 9. Imagine a young child playing traditional finger counting games with parents. Kids can instantly recognize (subitize) quantities from 1 to 4, but the Western finger counting goes all the way to 10 – well beyond the subitizing range. Unlike the Western finger counting, this system introduces groups and symbols (the thumb stands for 5), as well as addition, as soon as you leave the subitizing range.  In other words, the system follows the way children’s minds work.

What happens when you arrive at 10? Something very rewarding and exciting! You get to use your other hand, which stands for the new place value – and the new row of beads on the abacus. The digits, the beads, and the fingers all fit together like hand in glove.

Here is another difference of this system from just counting your 10 fingers. You can count all the way to 99 on your two hands!

And if you join forces with a friend, you can show even bigger numbers.

Here is a video showing how to count all the way from 1 to 99:

Using one’s hands is practically intuitive in the math world. Counting on one’s fingers is the most basic mathematical practice one could think of. But there is other more complex math you and your kid can do with your hands!

Images from Wikipedia.org

For example, you are hardly limited to counting to 10. If you bring the binary system into the equation, your kid can count all the way to 1,023 using their hands. It’s pretty simple: 0 is your right fist, 1 is your right thumb, 2 is your right index finger, and 4 is your right middle finger. Do you see a pattern? Each finger number is the double of the one before it. So, if you want to count 6, you hold up your index and middle finger (2 and 4). A more thorough explanation is in comic form at Instructables.

From Teacher Blog Spot

In addition to counting on your hands, you can also use them as multiplication tables. Ms. K at Teacher Blog Spot explains how your kid can divide each finger into sections of 3 or 4 and multiply by the number of fingers, with a maximum of either 15 or 20.

A similar method of multiplying on your fingers is called finger reckoning. Finger reckoning has been used since at least the 15th century, when merchants would use it to calculate numbers out of the sight of competitors eyes. While Ms. K’s method is based primarily on counting, finger reckoning uses multiples of ten. It is more complex but you get the answer faster and more efficiently. You can read more about finger reckoning in our blog post about it.

There’s no need to limit you or your kid to computing multiplication and addition, however. An easy and useful trick for remembering how many days are in each month is to count out the months on your knuckles and the spaces in between. Make sure to remember that each knuckle is 31 days and each space is 30 days, except February, which is 28 or 29.

From Krokotak

Hand tricks aren’t limited to computation either. One of the most common practices in kid art is tracing hands for drawings, and that can be used to teach symmetry. While we didn’t come up with this particular example, the Moebius Noodles book has a symmetry game called Double Doodle Zoo which demonstrates how one shape (like the hands) can turn into another (the heart).

An easy three-dimensional example of a hand shape is getting a few people together and having them recreate a fibonacci spiral with their hands. This is a great example of shapes in math and how they can transcend two dimensions.

You can do even more geometry with your body than making a Fibonacci spiral with your hands. In this video, mathemetician James Tanton explains how to do the National Math Salute. Using knot theory, you create a simple knot with your hands and undo it. The hand salute also uses elements of topology: the study of insides and outsides, and the orientation of surfaces. It’s simple to watch, but it’s easy to do it wrong. See if you and your kid can figure it out!