Do you remember that old days when you were struggling to memorize the multiplication table? What if I told you that you didn’t need to memorize the whole table? 😀
While I was watching an online course on edX called “Effective Thinking through Mathematics” Professor Michael Starbird introduced an effective way to do multiplication operations. Suppose that you have a 5*5 grid as the following:
Then I asked you to make that squared grid a 4*6 rectangular grid by simply removing the grid’s top row and concatenating it as a new column, which will result in the following:
How many squares should we get rid off to obtain the correct 4*6 rectangular grid? Simply the one which is colored above!
Alright. Then I asked you again, starting from the 5*5 grid, to obtain a 3*7 rectangular grid from that squared grid by removing the top two rows and concatenating them as two new columns. The result will be:
Now, how many squares should we get rid off to obtain the correct 3*7 grid? Again, the four colored squares.
Have you realized what’s going on? We are removing a^2 squares each time we’re converting the n-squared grid to a (n-a)*(n+a) rectangular grid.
You are now probably wondering what’s the relation between those grids and multiplication. The answer is that if you want to do the following operation: x*y, where x<y, you can can calculate the number n as (x+y)/2 and the number a as (n-x) and do your operation by subtracting a^2 from n^2, which means that you only need to memorize the squares of the numbers not the whole multiplication table!
Will that method be valid if the sum of x and y is odd? YES! For example, if we are multiplying 6*7, then n equals 6.5 and a equals 0.5, by applying our method: (6.5)^2 – (0.5)^2 = (42.25)-(0.25) = 42 = 6*7!
I am feeling sorry for your suffer while you were a kid (and for myself too :D), but you can still save another kids from what we went through :D.
I’ll be happy to read your positive or negative feedback!