Jean in Newcastle Posted September 29, 2011 Share Posted September 29, 2011 Does it matter when I'm teaching my dd about multiplication what order she puts the numbers? Ie. We put out 3 plates with 2 cookies on a plate. Does it matter if she has 3 x 2 or if it is 2 x 3. I know that multiplication is commutative. I'm just wondering if it's also important to know that 3 x 2 means 3 groups of 2. Quote Link to comment Share on other sites More sharing options...
WiseOwlKnits Posted September 29, 2011 Share Posted September 29, 2011 :bigear: I'm curious to hear what others say. Here's what I'm doing: We just started multiplication. I'm teaching her that 2 x 3 = 6 is a sentence in mathematical language. So we read it as 2 groups of 3 = 6. I also stressed that it's the same answer as 3 x 2 = 6, but it doesn't mean the same thing since it's 3 groups of 2. Quote Link to comment Share on other sites More sharing options...
Trilliums Posted September 29, 2011 Share Posted September 29, 2011 One of my kids' favorite math programs was a visual based one that used square math tiles. 3x2 was represented by a square composed of 3 tiles up and 2 across. Then they could re-arrange it into 2x3 (2 tiles up and 3 across). Using those tiles also really helped them to get square roots too, but that's another subject. The program focused a lot on the kids' finding connections on their own, so I think it is ok to mix up the groupings and see if they catch onto it themselves. And since I love links, here it is: http://www.mathlearningcenter.org/approach http://www.mathlearningcenter.org/media/MathMindEye_Gr5-10_Samples/MathMindsEye_UnitII_Activity_1.pdf It is aimed at schools, but they also have several fun samples there. Quote Link to comment Share on other sites More sharing options...
Jean in Newcastle Posted September 29, 2011 Author Share Posted September 29, 2011 Bill! I want to hear your opinion too! Quote Link to comment Share on other sites More sharing options...
joannqn Posted September 29, 2011 Share Posted September 29, 2011 I personally don't think it matters, but I teach my kids to write them in the order that makes for the easiest problem: 342 x 5 is easier to solve than 5 x 342 Quote Link to comment Share on other sites More sharing options...
Spy Car Posted September 29, 2011 Share Posted September 29, 2011 Bill! I want to hear your opinion too! No, it does not matter. It is the Commutative Law of Multiplication. a x b= b x a Bill Quote Link to comment Share on other sites More sharing options...
Jean in Newcastle Posted September 29, 2011 Author Share Posted September 29, 2011 One of my kids' favorite math programs was a visual based one that used square math tiles. 3x2 was represented by a square composed of 3 tiles up and 2 across. Then they could re-arrange it into 2x3 (2 tiles up and 3 across). Using those tiles also really helped them to get square roots too, but that's another subject. The program focused a lot on the kids' finding connections on their own, so I think it is ok to mix up the groupings and see if they catch onto it themselves. And since I love links, here it is: http://www.mathlearningcenter.org/approach http://www.mathlearningcenter.org/media/MathMindEye_Gr5-10_Samples/MathMindsEye_UnitII_Activity_1.pdf It is aimed at schools, but they also have several fun samples there. Thank you for the links. They look interesting! Quote Link to comment Share on other sites More sharing options...
Jean in Newcastle Posted September 29, 2011 Author Share Posted September 29, 2011 I personally don't think it matters, but I teach my kids to write them in the order that makes for the easiest problem: 342 x 5 is easier to solve than 5 x 342 Good point. Quote Link to comment Share on other sites More sharing options...
WishboneDawn Posted September 29, 2011 Share Posted September 29, 2011 I think I would arrange the cookies so that she could see 2 groups of 3 and 3 groups of 2 were the same. And in an array and let her decide what 2x3 and 3x2 could mean visually. I'd play with it for awhile so that she understood it didn't matter with the cookies and then take it to the paper with the equations. Once she firmly understood then no, I don't think it would matter how it was written. Quote Link to comment Share on other sites More sharing options...
Jean in Newcastle Posted September 29, 2011 Author Share Posted September 29, 2011 No, it does not matter. It is the Commutative Law of Multiplication. a x b= b x a Bill I knew it was commutative but the books seem to spend a lot of time teaching them to write 3 (groups of) 2 before they ever get to teaching the commutative law, so I wasn't sure if I could just skip to the end or not. Quote Link to comment Share on other sites More sharing options...
Spy Car Posted September 30, 2011 Share Posted September 30, 2011 I knew it was commutative but the books seem to spend a lot of time teaching them to write 3 (groups of) 2 before they ever get to teaching the commutative law, so I wasn't sure if I could just skip to the end or not. At this point Jean I think it goes more towards "following directions" skills than it has anything to do with fundamental math skills. Following directions can be an important skill to develop, I'm a bit challenged in that department myself :D Bill Quote Link to comment Share on other sites More sharing options...
Crimson Wife Posted September 30, 2011 Share Posted September 30, 2011 I've had arguments with my DD over the convention of putting the larger number on top when writing a vertical multiplication problem. She's right that it doesn't change the answer but it just *LOOKS* wrong to me to see her write: 18 X 97 ----- 126 1620 ----- 1746 instead of 97 X 18 ----- 776 970 ----- 1746 Quote Link to comment Share on other sites More sharing options...
ChristusG Posted September 30, 2011 Share Posted September 30, 2011 I tell my DD to put it whichever way is easier to solve. Even I switch it up in my head that way when I'm solving something. Quote Link to comment Share on other sites More sharing options...
Jean in Newcastle Posted September 30, 2011 Author Share Posted September 30, 2011 I tell my DD to put it whichever way is easier to solve. Even I switch it up in my head that way when I'm solving something. OK - I was doing that but then I wondered if I was forgetting some deep reason why it had to be done in the precise steps taught by the math book;) Quote Link to comment Share on other sites More sharing options...
Unicorn. Posted September 30, 2011 Share Posted September 30, 2011 I think knowing that it is 3 groups of 2 helps them when it comes to figuring out word problems, but then as a pp said, 342 is easier to multiply by 5 than vice versa. So as long as they understand that when doing the actual equation, order doesn't matter. Quote Link to comment Share on other sites More sharing options...
Kirch Posted September 30, 2011 Share Posted September 30, 2011 OK - I was doing that but then I wondered if I was forgetting some deep reason why it had to be done in the precise steps taught by the math book;) I think maybe it's only really important when they're figuring out what multiplication *is* (or are struggling with the concept). I think it's kind of funny--Horizons (if this poster is using Horizons as listed in her siggy) reads "2 x 3 = 6" as 2 groups of 3 = 6. We just started multiplication. I'm teaching her that 2 x 3 = 6 is a sentence in mathematical language. So we read it as 2 groups of 3 = 6. I also stressed that it's the same answer as 3 x 2 = 6, but it doesn't mean the same thing since it's 3 groups of 2. But RightStart expresses it as "2 taken 3 times = 6," which is 2 in a group with 3 groups, meaning 3 groups of 2. So exactly the reverse of the interpretation in the pp's curriculum. So I'd guess it doesn't really matter, as long as they understand what it means! Quote Link to comment Share on other sites More sharing options...
Wildiris Posted September 30, 2011 Share Posted September 30, 2011 I think knowing that it is 3 groups of 2 helps them when it comes to figuring out word problems, but then as a pp said, 342 is easier to multiply by 5 than vice versa. So as long as they understand that when doing the actual equation, order doesn't matter. 3 groups of 2 --3x2 xx xx xx 2 groups of 3--2x3 xxx xxx This might help when making grids or arrays. Quote Link to comment Share on other sites More sharing options...
chepyl Posted September 30, 2011 Share Posted September 30, 2011 We demonstrated it by taking 3 two blocks and 2 three blocks. We lined them up, one beneath the other. The lines were equal. Then he understood he could write it either way. Quote Link to comment Share on other sites More sharing options...
WishboneDawn Posted September 30, 2011 Share Posted September 30, 2011 I've had arguments with my DD over the convention of putting the larger number on top when writing a vertical multiplication problem. She's right that it doesn't change the answer but it just *LOOKS* wrong to me to see her write:... I generally have the kids put the larger number on top but it's just because I think it's a good habit when they're still shaky on their math facts. If they do it for addition and multiplication they'll do it for subtraction as well. Quote Link to comment Share on other sites More sharing options...
Jean in Newcastle Posted September 30, 2011 Author Share Posted September 30, 2011 I've had arguments with my DD over the convention of putting the larger number on top when writing a vertical multiplication problem. She's right that it doesn't change the answer but it just *LOOKS* wrong to me to see her write: 18 X 97 ----- 126 1620 ----- 1746 instead of 97 X 18 ----- 776 970 ----- 1746 I thought that was a good idea simply because of place value. It can be easy to get messed up if you have a smaller number (esp. in terms of digits) on the bottom. Quote Link to comment Share on other sites More sharing options...
catz Posted September 30, 2011 Share Posted September 30, 2011 I think in terms of longer multiplication problems it's good to demonstrate how it's easier to set up once they really understand the concepts of early multiplication and why "long" multiplication works. Although, in that case it's still good to demo how it would work either way. But in terms of showing a child with manipulatives how multiplication works conceptually early on, I think it's great to lay out 3 plates with 2 cookies on each plate and show how it would work with 2 plates with 3 cookies on each plate. A child who really "gets" that is going to be in a much better position later on IMHO. From a math major who is OCD about this kind of thing. :D Quote Link to comment Share on other sites More sharing options...
Jean in Newcastle Posted September 30, 2011 Author Share Posted September 30, 2011 I think in terms of longer multiplication problems it's good to demonstrate how it's easier to set up once they really understand the concepts of early multiplication and why "long" multiplication works. Although, in that case it's still good to demo how it would work either way. But in terms of showing a child with manipulatives how multiplication works conceptually early on, I think it's great to lay out 3 plates with 2 cookies on each plate and show how it would work with 2 plates with 3 cookies on each plate. A child who really "gets" that is going to be in a much better position later on IMHO. From a math major who is OCD about this kind of thing. :D Hmmm. If I do this, could we eat the cookies? Or would that be corrupting the lesson by introducing subtraction?:D Quote Link to comment Share on other sites More sharing options...
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