The trick looks impressive, so be prepared for jaw-drops when you show this to kids and adults. But can you figure out how it works? I’ll give you a hint: think about how to represent placeholders of powers of 10…


Ok, so now watch the video:
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Download Student Worksheet & Exercises


For the first example in the video, we represented the number 21 with a set of two lines and then with one line. Then we turned 90 degrees and added the number 13 on top by drawing one line followed by a set of three lines.


But what do the lines really mean? Remember my hint about placeholders? Well, the lines are really placeholders for the following multiplication:


21 x 13 = (2×10 + 1)(1×10 + 3)


Instead of writing out the numbers like the problem above, we simply draw lines to mean the same thing. If you were to cross-multiply that problem, we get a scary thing that looks like this when we group it in powers of ten:


(2×10 + 1)(1×10 + 3)= 2*102 + (2×3 +1)x10 + 3 = 273


The answer of 273 comes from figuring out there are 2 units of 100 (or 102), 7 units of 10, and 3 units of 1. Those are the intersection points of the lines we drew.


Exercises


  1. 23 x 45
  2. 56 x 72
  3. 52 x 26
  4. 62 x 49
  5. 67 x 92

For the following, write out the problems to solve and then solve them:


  1. graphical-6
  2. graphical-7
  3. graphical-8
  4. graphical-9
  5. graphical-10

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Comments

6 Responses to “Graphical Multiplication”

  1. Yes, you’ve hit on the limitation of this method. It does get cumbersome with large numbers, and zero isn’t able to be represented by a line. This is a fun experiment to share with kids learning math that need a visual to help them grasp the meaning of numbers.

  2. They are multiplying numbers using lines as a decimal placeholder instead of numbers. Cool, isn’t it?

  3. Hmmm… that’s not something I have an experiment for… I think you’re on your own!

  4. Julie Polanco says:

    ok so seriously WHAT R THEY DOING???????

  5. Julie Polanco says:

    oh, hi aurora? u got any ideas on how i can make my own love tester….u know to see if people like me…another person or watevr? plz!!!!!

  6. Fatima Shariff says:

    I love the way the multiplication is presented visually, I was just wondering how a number with a zero digit would be represented on the diagram? I also felt it was easier to multiply numbers with lower digits, once you get to digits above 5 it gets a bit tricky. I was also wondering about the history of this method, is it a method that was used in ancient times and is it a method that is still in use today?