# 3X5 or 5X3

## Recommended Posts

My boy currently is learning multiplication and he memorizes the table of multiplication.

Currently I am using miguon math and singapore math to teach him. Both materials teach multiplication operation in the expression as follows:

5+5+5 =3X5

My boy, however, always does the multiplication operation in a reverse way:

5+5+5 = 5X3. He follows this logic and already gets right answers in the end when dealing with multiplication related questions.

I have tried very hard to correct him but it seems that his method is deep rooted in his brain and it is very hard for him to change.

Actually his way is exactly the same way I learned multiplication operation while I was a kid. And this way did not stop me from becoming an engineer.

I am just afraid that if his way will create conflict with how school will teach him. Should I be concerned about this? Or It is really not a big deal?

##### Share on other sites

My ds had a similar problem in that he would reverse 3 x 5 for 5 x 3 willy nilly. I didn't see a problem with that until we got to those sections in Miquon and MM that explain that "x" means "of" in math. So even though the answer is the same, "3 of 5" (as in 3 groups of 5 things) is a different sort of problem than 5 of 3. It took some drilling to get in the habit of seeing that x means of. So with the c-rods, I would do something like lay out 3 groups of the yellow 5 rods, and he would have to tell me if it's 3 or 5, or 5 of 3. I'm not sure that it makes any difference in the long term outcome but for me, I wanted him to understand that multiplication is really just a way of saying means "of" in math and to be able to figure out problems by understanding that.

##### Share on other sites

My boy currently is learning multiplication and he memorizes the table of multiplication.

Currently I am using miguon math and singapore math to teach him. Both materials teach multiplication operation in the expression as follows:

5+5+5 =3X5

My boy, however, always does the multiplication operation in a reverse way:

5+5+5 = 5X3. He follows this logic and already gets right answers in the end when dealing with multiplication related questions.

I have tried very hard to correct him but it seems that his method is deep rooted in his brain and it is very hard for him to change.

Actually his way is exactly the same way I learned multiplication operation while I was a kid. And this way did not stop me from becoming an engineer.

I am just afraid that if his way will create any conflict with how school will teach him. Should I be concerned about this? Or It is really not a big deal?

I don't know that it's really reverse....maybe just reverse of how Miquon and Singapore teach it. It's really the same thing. I would think that the math you are using is trying to say...."three 5's"; thus 3x5. But when I look at 5+5+5=, I would write it like your son 5x3...which to me is saying "five three times". I can't imagine it would matter...but maybe someone else can explain if it does.

##### Share on other sites

My boy currently is learning multiplication and he memorizes the table of multiplication.

Currently I am using miguon math and singapore math to teach him. Both materials teach multiplication operation in the expression as follows:

5+5+5 =3X5

My boy, however, always does the multiplication operation in a reverse way:

5+5+5 = 5X3. He follows this logic and already gets right answers in the end when dealing with multiplication related questions.

I have tried very hard to correct him but it seems that his method is deep rooted in his brain and it is very hard for him to change.

Actually his way is exactly the same way I learned multiplication operation while I was a kid. And this way did not stop me from becoming an engineer.

I am just afraid that if his way will create any conflict with how school will teach him. Should I be concerned about this? Or It is really not a big deal?

Due to the commutative property of multiplication, does it really matter? 5+5+5 DOES equal 5 X 3. One is 15 and the other is 15. But if you're concerned about fractions later on where knowing that 1/2 OF 2 means to multiply 1/2 X 2 then I would use those words. 5 plus 5 plus 5 equals 3 groups of 5.

##### Share on other sites

I don't think it's a problem. I have always thought of 5 x 3 as "5, three times" and I have never had a problem (and I made it through trig and college-level statistics).

I think the idea of "how many groups of how many" is more of a teaching tool.

Tara

##### Share on other sites

But if you're concerned about fractions later on where knowing that 1/2 OF 2 means to multiply 1/2 X 2 then I would use those words. 5 plus 5 plus 5 equals 3 groups of 5.

That's a good point, I hadn't thought of that. Maybe that's why multiplying fractions came easily to my ds, because by then he was in the habit of seeing that 1/2 x 2 is just 1/2 of 2.

##### Share on other sites

I don't know that it's really reverse....maybe just reverse of how Miquon and Singapore teach it. It's really the same thing. I would think that the math you are using is trying to say...."three 5's"; thus 3x5. But when I look at 5+5+5=, I would write it like your son 5x3...which to me is saying "five three times". I can't imagine it would matter...but maybe someone else can explain if it does.

This is exactly what my son's logic... 5+5+5 is "five three times"..

The way he memorize the multiplicationt table is

5x1=5 (5)

5x2=10 (5+5)

5x3=15 (5+5+5)

5x4=20 (5+5+5+5)

....

....

5X10=50 (5+5.......+5)

Once, he even told that 5X15=75, which I never taught him before. I asked him how he did it...he simply explained that, "5x10=50 and then 50 + "five five times" is 75". Right at that moment, I figured that it is almost impossible for him to change his thinking. He got all his logic imprinted in his brain. Currently he is 4 and half years old. I just taught him multiplication table for fun. I neither expected him to memorize nor understand it. I just wish his logic of "five three times" will not create any trouble in the future.

IF there are really negative effects, please your thoughts. I hope it is not too late for me to correct him.

##### Share on other sites

3x5 = 3+3+3+3+3= 15

5x3=. 5+5+5 =15

I found this http://www.st-yuki.net/blog/008.html link when looking for a demo of the above property.

HTH

##### Share on other sites

Quoting the commutative property of multiplication, I don't see anything wrong with what his thought process is.

##### Share on other sites

The more I've thought about it, it wouldn't even matter in fractions. 1/2 of (a group of) 2 equals 1. 2 (groups) of 1/2 equals 1. I can think of no way his "mixing them up" could be harmful as long as he can justify how he came by his answer.

##### Share on other sites

I suppose it might matter if you ever had to identify the multiplicand and the multiplier. But until this week I didn't know the word "multiplicand" existed so I assume the issue doesn't come up often. ;)

##### Share on other sites

I tend to do it that way but with as we usually do X groups of Y.

##### Share on other sites

I think the bigger problem would be failing to see that 3x5 and 5x3 result in the same numeric product, and that is clearly not an issue.

I do make something of a big deal of it when doing word problems. The idea in that case is that the multiplicand and the product should be the same object. So 5 chairs in 3 rows will be 15 chairs and not 15 rows. Mentally I don't care how the 15 is calculated, but I do care how it is written out in a word problem.

##### Share on other sites

Currently he is 4 and half years old. I just taught him multiplication table for fun. I neither expected him to memorize nor understand it. I just wish his logic of "five three times" will not create any trouble in the future.

I don't think you have anything to worry about at all.

##### Share on other sites

The only thing you have to worry about is finding challenging math materials to feed this boy's furtive mind.

Fortunately, such materials exist.

When a child figures out how to employ the Distributive Law to solve multiplication problems on their own (my son did the same) it is a very good sign!

Enjoy the ride.

Bill

##### Share on other sites

This is exactly what my son's logic... 5+5+5 is "five three times"..

The way he memorize the multiplicationt table is

5x1=5 (5)

5x2=10 (5+5)

5x3=15 (5+5+5)

5x4=20 (5+5+5+5)

....

....

5X10=50 (5+5.......+5)

Once, he even told that 5X15=75, which I never taught him before. I asked him how he did it...he simply explained that, "5x10=50 and then 50 + "five five times" is 75". Right at that moment, I figured that it is almost impossible for him to change his thinking. He got all his logic imprinted in his brain. Currently he is 4 and half years old. I just taught him multiplication table for fun. I neither expected him to memorize nor understand it. I just wish his logic of "five three times" will not create any trouble in the future.

IF there are really negative effects, please your thoughts. I hope it is not too late for me to correct him.

:ohmy: Wow....that is awesome that at such a young age he can do this. My 17 year old struggles with knowing multiplication and my 9 year old is just beginning!

##### Share on other sites

I really really really really really don't think this is an issue.

Whether he writes 3x5 or 5x3 he will get the same answer in the end. This is the commutative property of multiplication.

##### Share on other sites

I really really really really really don't think this is an issue.

Whether he writes 3x5 or 5x3 he will get the same answer in the end. This is the commutative property of multiplication.

This. I really don't think you need to correct him.

##### Share on other sites

My son did the same thing. I didn't worry about it. He's almost done with Singapore 5B, and it has never caused any problems.

##### Share on other sites

I think the bigger problem would be failing to see that 3x5 and 5x3 result in the same numeric product, and that is clearly not an issue.

I do make something of a big deal of it when doing word problems. The idea in that case is that the multiplicand and the product should be the same object. So 5 chairs in 3 rows will be 15 chairs and not 15 rows. Mentally I don't care how the 15 is calculated, but I do care how it is written out in a word problem.

But if you are going to be picky about how it is written out, then the multiplicand and the product DO NOT have the same units. The multiplicand is actually a this-per-that unit, in the example you give "5 chairs per row". This is not very important in elementary school, but being picky about units will become very important in (for example) high school chemistry.

##### Share on other sites

I think I'd use this as a good opportunity to "show" him the commutative property. I'd get some blocks out and make 3 rows of 5 blocks in a rectangle shape and have him count them all. Show him along the sides of the blocks that it's 3x5. Then you take the same blocks, rearrange them into 5 rows of 3 blocks....look at the sides, it's 5x3. It's the same answer, 15. And, really you've just turned your rectangle. He might think this is fun.

##### Share on other sites

I follow the example of the AoPS folks and don't worry about "multiplicand and multiplier" and instead favor "factors."

3 and 5 are both "factors" in the multiplication problem 3x5 whose product is 15. It does not matter mathematically which factor comes first. Worrying about it is a waste of brain-cells IMO.

I do know that Crewton Ramone, in his own inimitable style, thinks it is important. But he reverses the Miquon/Singapore order (and understanding of the syntax) to put the "multiplicand" first and the multiplier second, and is very insistent on the point. You can't win :D

http://www.crewtonramoneshouseofmath.com/multiplicand-and-multiplier.html

Bill

##### Share on other sites

But if you are going to be picky about how it is written out, then the multiplicand and the product DO NOT have the same units. The multiplicand is actually a this-per-that unit, in the example you give "5 chairs per row". This is not very important in elementary school, but being picky about units will become very important in (for example) high school chemistry.

Yeah, it'd really be:

5 chairs/row x 3 rows = 15 chairs*row/row = 15 chairs

The "rows" cancel out.

##### Share on other sites

Mostly, it doesn't matter. The program we use sometimes employs calculators for games and competitions, and with the calculator, it does matter. For example, if I want to program the calculator to multiply whatever I input times 3, then I have to enter "3x=". (But if I were to program it to add three, I would enter "+3=".) But when you are doing math on paper, it doesn't matter, so long as the child understands that 3x5 = 5x3, i.e., that he is using the commutative property.

##### Share on other sites

Yeah, it'd really be:

5 chairs/row x 3 rows = 15 chairs*row/row = 15 chairs

The "rows" cancel out.

Or it could easily be (3 rows)(5 chairs/row) = 15 chairs*row/row = 15 chairs.