Thursday, November 12, 2009

Teaching Multiplication Facts for Mastery

Ever had the thought cross your mind of, "I wish I could teach my students the multiplication facts once, and they would always remember them."

Well guess what! You can! It's all about the method in how you teach it. And a couple rules too!

It starts by remembering this first rule: DON'T RUSH IT!!!!!

As recommended by NCTM, students should learn the multiplication facts, 0-12, over the course of 3rd and 4th grade. That's two grades folks. Not one grade. Not one quarter. Not one month. Not one week. TWO GRADES!

See what I mean by don't rush it?

Think about it. If you really want to remember something, say 10 lines for a play, how long do you practice? A long time if you really want to remember it. You take maybe 1-2 lines, and practice those until you know them by heart, then you add another, and keep going until you've committed it all to memory. Hopefully you would know better than to start practicing the day, or even the week before the play, and then expect to get up on stage and recite all 10 lines perfectly.

That's probably not the best analogy, but that's all I could think of at this moment, so just play along, will ya?

Second thing to remember, never, ever, ever, point out or "teach" the patterns. You'll see what I'm talking about in a minute, but just remember that. If your kids figure out the pattern on their own, they will remember it. If you tell it to them, take a stab at how many times you'll be asked to remind them of that pattern over the course of the next month.

Okay, so remembering to go slow, and not spoiling the surprise of patterns, let's get started.

(Do note: your students (or children) should already have some background knowledge with multiplication and how it works. This is not teaching multiplication. This is teaching the basic, standard facts.)

Start with the ones and the tens facts. Make a chart with two columns, one labeled "Ones Facts" the other "Tens Facts." Start asking your kids to list all the ones facts (1x1, 1x2, 1x3, etc.). Again, do not spoil the element of surprise and tell them that anything times one equals itself. Because guess what, pretty quickly, they are going to notice that it does indeed equal its self. And ta da! They now got it.

Let that process in their little brains for a couple days, and let them practice and experiment with it. Ask questions like, "Does any number times one always equal itself?" I darn bet you, they will want to know. So let them play around with manipulatives and calculators, etc. Pretty soon, they are going to realize, that no matter how big the number, it will always equal it self when multiplied by one.

Now it's time to move on to the second column on your chart, the tens column. Start listing the facts with your class's assistance by letting them punch the facts into a calculator. And oh my gosh, pretty so someone is going to realize, that when muliplying by ten, all it does to the number is add a zero, and that the tens facts, is also like counting by tens, something your students are already so familiar with and know the pattern of.
Now your kids have the tens facts figured out. Again let them think about it, experiement, play games with them, and so on and so forth.

When they have fully mastered, and I mean fully, meaning every kid being able to spit the facts out with no hesitation, it's time to move on the the fives. Again, make a chart, but this time, only make one column. Again, give your students calculators, and start listing. Guess what pattern they are going to see this time? Yup, all it is is counting by fives, again, something they know oh so well by now. They should also see that it is half of the tens.

After that comes the twos facts. This time make a three columned chart. Again, with your students' assistance, list the facts. Does anyone notice that it's just counting by twos? And it's also numbers doubled (i.e. 6x2 is the same as saying 6+6). Again, pattern noticed, facts mastered.

After the twos are mastered, let's move on the fours. Why? Because the fours are all double of the twos. Woah, baby! Bet you had no idea that there were so many patterns. I know I didn't! Anyone want to take a stab at what comes next? That's right, the eights, because they are the doubles of the fours.

By now, it's probably late in 3rd grade, and your students should be very well versed in the facts. And if they understand the commuitive property (that 2x5 is the same as 5x2), they already have master a large portion of the facts, even if you have yet to focus on certain fact families yet.

So now it's time to move on to the threes, sixes, and twelves. Again, using the three columned chart like with the twos, fours, and sixes. Anybody want to guess the pattern here? Go try it. I mean it!

What do you see? Hey.... doubles again!

Guess what, by now, it's 4th grade, and the only facts your students have left to learn are 7x7, 7x9, and 9x9, thanks to the communitive property. The elevens are quite simple, like the ones and the tens, and can be thrown in when you would like. The nines, because of their neat patterns, can also be thrown in wherever you like.

The key is, that because your students see and understand the innerelationship and patterns between the facts, they are more likely to remember then, and also use other facts to quickly and accuratly figure out facts they don't know or can't remember. If they cannot remember 3x6, but remember that 3x3 is 9, and know that the sixes are the threes doubled, they know that 3x6 must be 18.

Do you see what a powerful tool you have just given them? And why you will never have to teach your students the muliplication facts again?

Even if you have older students, take the time, maybe over the period of a month, to help them discover all the patterns. Obviously, you aren't going to take it as slow, and nor are you going to want to, but if you find them still struggling, consider taking the time to give them this tool. They will thank you!

Happy Muliplying!

1 comment:

Sandy said...

Thank you for the reminder!