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melbotoast

Basic Multiplication Question (Miquon)

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If the problem is 2 x 3, does it really matter if you think of it as two threes or three twos? In the lab annotations (and in the workbooks) it is opposite from the way I think of it.

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You won't do any harm by viewing 2 x 3 as 2 + 2 + 2 rather than 3 + 3.

 

It's important to know that multiplication of real numbers is commutative, so 2 x 3 is the same as 3 x 2.

The model of addition for multiplication is where you start. Later you (ideally) see multiplication as a scaling operation (think of enlarging or shrinking by a percentage), because if you only see multiplication as addition it's a problem with expanding to fraction multiplication or decimal multiplication for instance.

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The main advantage I know to teaching it one way is that you can use the handy translation word "of". 2 x 3 = 2 of the 3's. This is a HUGE help in later fraction and percent problems. But of course, it's also important to recognize that multiplication is commutative, as Dana said, which means that for mental calculation you can choose whichever way seems easiest to you.

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Since Miquon teaches things like 1/2 x 4 really early using the "of" phrasing would seem to help. So 2 x 3 is 2 of the three's. And 1/2 x 4 is one half of the four.

 

ETA: From a practical, problem solving strategy, I think you have to encourage kids to do it the easiest way for them. I mean, no one is going to count by 8's if they're doing 10 x 8 is the same as 8 x 10 since counting by tens is obviously easier.

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We use of also...... 2 of 3. But I have taught my children to take the larges number, or the easiest one, no matter which is first. So they would have said 2 of 3 = 6. 5 X 7 would be to them 7 of 5, since fives is easier for them than adding 7's. What ever works, is my opinion.

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Thanks all! I figured there must be a reason for teaching it that way. I can see how thinking of it as "of" could be helpful.

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