Week 2 – Mastering Mental Multiplication

Total Time – The full 5 hours

Total Cost – None

The inspiration for this weeks challenge came from a video I saw on children in Japan who used a “Mental Abacus” to perform advanced math in their heads. These kids were so familiar with the abacus that they didn’t even need one in front of them to use it – they moved their fingers around in the air as they pictured an abacus in their mind.

Unable to multiply 2 digit numbers together in my head, I decided to set the goal for this project to 3 by 3 digit mental multiplication. It took me every minute of the 5 hours to be able to do it, but I’m happy to report that I’m now able to multiply 3 digit numbers together without anything but by brain and some nifty tricks. I’m counting this project a victory, but in truth I’m only about 80-90% accurate with 3 by 3 digit multiplication as I write these words. I feel very confident that I could get that number up to 99% with another week or two of regular practice, but that time would be falling outside the 5 hour restriction of 5 and 50. You can watch me do 3 by 3 digit multiplication in the video below:

Having never used an Abacus before, my quest began by watching videos on how to use the Soroban, the Japanese equivalent of the Abacus. The Soroban is a very simple device to grasp, each column of beads is there so you can quickly represent and manipulate single digits during math operations. Before learning how it worked I assumed that the Soroban enabled you to do some nifty tricks and shortcuts when multiplying large numbers together, but I quickly found out that device was more of a replacement for pen and paper than it was for a calculator.

The true beauty of the Soroban was the process it uses for multiplication, which can you see in the video below:

It breaks down the multiplication of any 2 numbers into a sequence of two basic operations – 1 by 1 digit multiplication (remember your “times tables” from 2nd grade?) and 2 digit addition. Using the Soroban method for multiplication the actual math required to multiply 2 and 3 digit numbers together is trivially easy at each individual step.
I started the timer for this challenge when I finished learning how to use the Soroban to multiply and was ready to attempt my first 2 by 2 digit multiplication. I closed my eyes, tried my hardest to picture a Soroban, and moved my fingers in the air to move the beads in my mind like those kids in the video did.
Picturing the Soroban and manipulating the beads was a real challenge for me, presumably because I’d never used a physical Abacus or Soroban before attempting to picture one in my head. I continued attempting to use the mental Soroban for the first hour of the project before I noticed something strange. At one point or another my brain had stopped storing the digits on the beads of my mental Soroban but I was starting to get the right answers anyways. I was correctly executing the Soroban process for multiplication but I was remembering each number in my mind as I would any other number, and not by using the mental image of a Soroban.
At this point I gave up on trying to picture an ancient device in my head and instead focused on alternative methods for keeping track of four to six single digit numbers. What I found worked best for me was using the fingers on my left hand to picture each individual digit while using my right hand to keep track of where I needed to be performing the next addition. At an hour and a half into the project I was using this new method to crush 2 by 2 digit multiplication and was ready to move on to the next step – 2 by 3 digit multiplication.
My first few attempts at 2 by 3 were a little overwhelming. I found that it wasn’t very challenging to keep track of a few 2 digit numbers while performing basic addition and multiplication, but remembering a 2 digit and 3 digit number was notably harder for me. I was getting wildly wrong answers for the first fifteen minutes or so, but after some practice the pieces eventually fell into place. At the 2 hour and thirty mark (half way through the project) I was feeling comfortable with 2 by 3 digit multiplication and was ready to take on 3 by 3.
Here’s where things get a little weird. A 3 by 3 digit multiplication requires 9 total 1 by 1 digit multiplications and 8 additions to complete, which are tricky to keep track of as-is. Managing these 17 operations while simultaneously storing the 3 digit numbers you need to multiply together was simply too much for me process. I needed to try something new.
Having recently read an article on how to quickly memorize a deck of cards (perhaps a future 5 and 50?) I decided to try out a memory technique the article discussed for keeping track of 52 cards at once.
I created a table with three columns – one column for the first digit, one for the second digit, and one for the third digit. The first digit of each 3 digit number was assigned to a memorable person, the second digit became a strange action or object, and the third digit became the location that the person was performing the action in. My table ending up looking like this:
I tried to have there be a relationship between the sound of each number and the image it was corresponding to, which you can see in bold. The key here is to try to think of things that are as strange, disgusting, and memorable as possible. It might be easy to forget the mental image of your neighbor Karl mowing the lawn, but you probably aren’t going to forget the image of Adolf Hitler waving a sex toy around while skydiving. Choose celebrities or fictional characters that are very distinct, actions that will easily stick out in your memory, and locations that you can place yourself in. You can see that I chose “ro”, the Korean word for street to represent my third digit 0. As I currently live in Korea, it is very easy for me to picture one of the narrow and busy Korean streets near my apartment. I can smell the smells, hear the sounds, and see the brightly colored signs on all the buildings. Try to chose locations where you can do the same thing.
This technique might seem strange, but it totally works. I’ve never once had a problem recalling the 3 digit numbers I was multiplying together. All in all it took me 45 minutes to construct and memorize the table, which I did during my lunch break at work. If you use my table as a starting point for your own you might be able to do it even faster.
With this new memory tool in hand I was eager to work on 3 by 3 digit multiplication. I really enjoyed the challenge of this project and was eager to come home and see if I could master the final step of the project. I predictably struggled at first, but as the memory table became second nature to me I started to get the occasional answer correct. As I got more and more practice with 3 by 3 digit multiplication I started to get more and more answers correct, and by the time that my 5 hours were up I was feeling great about what I had learned. As mentioned above I’m certainly not 100% accurate at 3 by 3 digit multiplication, but seeing as my response to “whats 857 times 494?” a week ago was “fuck you”, I’m very happy with where I left things off.
Here are my tips for mastering mental multiplication faster and better than I was able to:
  • Unless you’re extremely familiar with the Abacus/Soroban, don’t screw around with trying to picture one in your head. I probably wasted 30 minutes or more on trying to do this.
  • Its much easier to multiply 2 and 3 digit numbers when you can see the numbers you’re multiplying together written down in front of you. Though it might be tempting to start out by having the numbers written down in front of you, I recommend learning 2 by 2 digit multiplication entirely in your head. It will seem tricky at first but I promise you can do it if I can – my memory skills are below average at best. You’ll need to learn how to do it without paper eventually, and I think its better to start that process sooner than later.
  • In 2 by 3 and 3 by 3 digit multiplication, start out by looking at the numbers you’re multiplying together before moving on to doing it in your head. Essentially, do the opposite of what I said to do in the previous step. You dont want to get bogged down in the added complexity of the additional digits to remember and operations to keep track of, so make sure you master the process first.
  • If you have a better way of keeping track of the digits in your head than picturing them on your fingers, go for it! The finger method was what worked for me but everyone’s mind works differently. I’m a kinesthetic learner (movement or action based learning), but you might be a visual or auditory learner. Use whatever method works best for you.

That’s all for now! For week three of “New Skills Month” I’ll be looking to lighten things up a little bit by attempting to learn something a little less serious. I’ve always been jealous of people who can raise one eyebrow like an evil villain, especially Stephen Colbert:

I have huge, Greek, bushy eyebrows, but completely lack the ability to use them nefarious expressions. NO LONGER!!!

See you next week,

Aleco Pors

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