At Crewton Ramone's House of Math we don't just get multiplication through 9x9 down, we go all the way out to 20X20. Notice I say "get it down" not just memorize. Manipulatives make multiplication easy, so easy, ans so fast that it will look like they have it memorized even if they have to do a little calculation in their heads...with enough practice they will memorize their multiplication facts but instead of it being difficult and hard we make it fun and easy. In this lesson they learn and practice several things at once.
If you watch the video below you can see why I spend so much time on addends. Addends are important. This lets them practice their addends WHILE they do multiplication like the big kids. No worksheets. No symbols to start with, just play with blocks and have fun, let them build the problems. Don't tell the youngest kid but I was teasing him a little bit by telling him this stuff was "too hard" for him. SO of course he wants to show everybody he can do it too...and he does. (Proper motivation works wonders. You need to be smarter than your six year old.) Any little kid can do math especially if they speak English. On this blog and on my website I try to show you their best use.
The seven year old kept confusing multiplication with addition and wasn't always sure which numbers to add when he was just looking at the symbols. He was also over thinking it and getting ahead of me because he knew there were more than just 3 tens in (17)(3) = 51 and that there were 5 tens not just 3. But I was asking him to count the blue ten bars not the ones "hiding" in there with the sevens. Note how the younger boy wasn't even thinking about the tens hiding with the sevens he just saw the 3 tens, and the oldest boy knew what I meant. He understood I was going thru the problem in parts.
If you listen you can hear the development differences between the three boys. They also get different problems for their skill level but the basic concept is the same throughout. Don't lose track of the idea that the concept remains the same the numbers just change. I use smaller numbers that require less counting for the younger boys and bigger problems for the older boy, but very soon they all can do any problem...they just need more practice with single digit multiplication but it doesn't stop them from doing this in fact this teaches them that. I also want to point out we are practice skill sets not drilling. There is a difference.
We also talked about multiplication being addition...you just do it over and over again.
They get to practice and learn their multiplication AND addends, I try to make this blatantly obvious during the video. Again: one teaches the other and visa-versa: you don't have to have all your addends memorized before you can do this this will help you leran them, neither do you need to have all your single digit multiplication facts memorized before you can do this, this will help you learn those too...especially when you are playing with the blocks. It also just makes it natural to see you are adding the tens plus whatever the units are. Basically just adding two rectangles, in the case of (17)(3) = 51 you are adding 30 plus 21 they can SEE it.
Also note that even though you can't see them it sounds like they are having fun, because they are. Laughter should be a part of math, it's fun when you get it right, it feels good. I see so many math classes where they are forced to do worksheets in silence. Or where they are expected to learn in SILENCE. Why not make math fun?
Notice that pretty soon we are just using symbols, no blocks but after the lesson on vid we went back to using blocks, this was just a demonstration for YOU the viewer.
We've gotten so poor at teaching math public schools can barely get them to memorize the 9x9 matrix, that's only 81 facts, we are on our way to memorizing 20X20, that's 400 facts. Addends are not just "kinda important", they are crucial. Same with multiplication. Addends make multiplication easy and multiplication makes ALL the math easy because it allows you to count quickly, see patterns, find common factors and more. I can't stress enough how important it is.
There are those who say we don't need to learn our multiplication tables because calculators are so ubiquitous...the problem with that is kids hit 7x6 when they mean 7x9 because the six is right under the nine and it's easy to miss or "fat finger it" and they don't even notice. There's a big difference between 42 and 63, but they don't have the number sense to catch the mistake.
All of that can be avoided and it doesn't take hard work, tons of work sheets, or drudgery. Multiplication tables have their place but early introduction and playing are much more fun and effective than handing them a multiplication table and saying here memorize this. If you only click one link on this page click that one. And of course once you are done playing with multiplication it's time to to play with division. Then again it should be hard to do one without the other...
Can you think of the reason we count the tens first other than that it makes it easier?
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"You save an old man and you save a unit; but save a boy, and you save a multiplication table."
"Time neither subtracts nor divides, but adds at such a pace it seems like multiplication."