Teaching Math Shortcuts

This past week, while I was working in Math period, I started helping a young man about 17 years old,  for the first time.  I have been at this school for 4 weeks, but hadn't worked with this boy yet.  He was a quiet one, usually keeping his down and not interacting with any of the other children.  Realizing he was one of the students that I hadn't connected with, I honed in on him at the beginning of class.  I told him that I hadn't worked with him before and asked him if he needed help with his math.  He said that he didn't know how to do a certain problem, so that was my chance to start helping him.  Usually, I get down on my knees, but this time I grabbed the closest chair and sat next to him.  We started going over his math.  I saw that he had made a mistake on subtracting a "9" from a larger two digit number.  With enthusiasm, I told him that I had a shortcut for subtracting a nine from other numbers.  I asked him if he knew how to subtract a "10" from a number.  He said he did.  So, I gave him some numbers, like, 17, 34, 48, 56 and 74.  I asked him if you had 17 and subtracted 10, what would you have.  He would say 7.  I would say that is right, so now you add 1 more to the number and you have the answer.  It went like this:
Me:  O.K.... 56 minus 10... what do you get?
Boy:  46. 
Me:  Yeah, now add one
Boy: 47
Me:  That's right! You have the answer!  56 minus 9 is 47...

I did this with a whole lot of numbers and then told him that it only worked with 9's.  Then I realized that it worked with 8's also, you just have to add 2, after you subtracted the 10.
Then he chimed in and said, "Then for 7's you would subtract 10 and then add three?"
I replied with a yes.  His eyes lit up and he smiled the biggest smile! 

After learning that shortcut for subtracting 9's, 8's, and 7's, I asked him if he knew his 9 multiplication facts.  He said that he didn't.  I smiled and told him that I had a shortcut for the 9's too.  So, I went on to tell him the shortcut.

Me:  Nine times two... Say, the number one less than two...
Boy:  One
Me:  Yeah, that's the first digit to the answer.  Now, one plus what number is nine?
Boy:  Eight
Me: Yeah, that's the second digit.  So, nine times two is eighteen.
Me:  Now, we will try nine times three.  Say the number before three...
Boy: Two
Me:  Yeah, now, two plus what number equals nine?
Boy: Seven
Me:  Yeah, that's the answer... nine times three is twenty-seven.
We did this all the way to nine times nine.  He was quite amazed at his accomplishment of learning the nines that quickly.  I was so happy to see his smiles and to see how he felt good about himself.  I then showed him the second way of learning the nine facts by using his 10 fingers.  He smiled on that one two.

Events like these make my day!