Mental Math

Very often, I'm amazed at what my kids can't do. The fact that they can't do any sort of mental math has astonished me over and over again, as I wait on things like 30 divided by two or 46 divided by 10. Only today did I realize that even skills like these need to be taught.

I started thinking about a week ago about what I do when I divide something in my head. For example, if I wanted to divide 68 by 2, I first divide the sixty by 2, to get thirty, then divide the 8 by two, to get 4, and add to get 34. Pretty standard, I thought. But today after school, as I watched FM labor through the same problem using long division, I realized it might not be the standard thought process for my kids. So I stopped him and told him how I did it. Oh yeah, he said. That's so much easier. That does make sense. Hopefully, it is a little more intutive for him. FM has become my mental math experiment. A few days ago I caught him laboring over a multiplication problem where he had to multiply something by five. Just take half of it, I told him, and put a zero on the end. Works anytime you have to multiply by 5. That astounded him. And when I explained why, it was like a little light went off. It made sense.

Today, FM stayed after school along with DB. (DB was in my class for a few months in the fall before he got moved to pre-algebra. He is the sweetest kid in the world, and would kill to be back in my class. That's why he stays after school.) Anyway, DB was showing off his solving equations skills, while FM was solving some quadratics. FM was simplifying a square root, trying to make a factor tree for some number, and asked me what went into it. So I decided to tell them about how you can tell if three goes into a number. I told them any number they gave me, I could tell them if three went into it 5 seconds or less. They gave me some horrendous numbers, 5 and digits, and were amazed when I told them yes, three is a factor or no, three isn't a factor as soon as they had finished writing. Finally, after about five minutes of them giving me bigger and nastier numbers, I told them the trick, which had them holding their heads and laughing and generally being amazed at math. As they walked out the door, DB told me he was going to go right home and show that to his mom. FM said he was going to show it to his friends tomorrow. I need to think of some other "tricks" to have ready for them next time. I also need to decide what to do with the last month of the school year. Three weeks for seniors. Oh man.