multiplication and division

[meemee]

what are the different ways to do long multiplication and division>

i tried the traditional method of lining up but dd is struggling with that. i have to either make up a rhyme or song to help her remember the way long multiplication happens.

any ideas. i discovered the lattice method of multiplication which i will try tomorrow. it could work as she enjoys doing soduku.

dd is 7.

[LauraLoo]

I don't even know if this will help, but there are online demonstrations that may help. Here's one (and you can search for more in division, etc.)

http://khanexercises.appspot.com/video?v=8Ft5iHhauJ0

I'm also wondering if her struggles are somewhat developmental. I've heard of a number of kids having problems keeping things lined up, even if they are ready academically for the concept of long division.

[kathymuggle]

You could try partial product and quotient...we like it!

http://video.google.com/videoplay?do...0681203583203#

Turning lined paper sideways so there are columns on the paper, using graph paper, using different coloured pencils and writing big (on big paper or a whiteboard) often help kids keep stuff in line.

I suspect it is partly developmental...cognitive abilities outpace organisational one.

I would not be suprised if in general gifted kids were a little less organised than more neuorotypical peers. They do not have to pracitce organisation to get it the answer right...so they don't.

[itsmyturn]

My DD learned on our whiteboard. She has lots of room and can write big. I also wrote DMSB on top of the board until she could remember the order Divide, Multiply, Subtract, and Bringdown

[meemee]

kathy yup. its not just my child but a few others who suffer the same problem.

another child tries doing the problem in her head and then gets headaches from trying to keep track.

with dd its two fold. she is just being introduced to it. in fact it came in her homework packet. i dont think her 3rd grade teacher has introduced yet to the second graders who are in his class or he did it fairly recently so she hasnt got the hang of it yet. plus yes the organisational part is still there.

its just she is having a hard time remembering the order it is done. the khan academy one is an adult way of teaching which is not working for her right now. she learnt borrowing by making up many different kinds of stories.

i had forgotten. a white board and coloured pen might make the difference as seh IS a visual learner and partly kinesthetic too - so she needs both visual and whole body aids.

her teacher is also v. good with involving body movement and jokes as tricks to help remember the process itself.

i like the partial quotient way. i think that will help her remember the steps much easily than the traditional way.

i wonder what all the culturally different methods are. i remember the russian using all ten fingers way. i think it was the russian farmer way.

[moominmamma]

Sometimes all the little digits and regroupings can be tough to keep track of. For multi-digit multiplication try using graph paper or a grid of some sort to keep everything lined up and a different colour ink for each place value. Erasable pencil crayons work pretty well.

For division I taught my children "short division" for one-digit divisors first and they had no difficulty with long division for multi-digit divisors once that had become natural. We use partial quotients method as a short-cut, but I think kids need to know full long division too. My 7-year-old is now working with decimals and percents and partial quotients become very awkward and complex when you try to adapt them to working with decimals.

But I think it's important to understand what these algorithms are all about and why they work the way they do. Otherwise they're just memorized procedures, and if the memory gets fuzzy or the problems get more complex there's no way for the child to reground herself in the sense of them.

Does your dd fully understand that 35 x 1725 is the same as (30 x 1725) + (5 x 1725)? Does she realize that 30 x 1725 is the same as (3 x 1725) x 10? Does she understand that "carrying the two" is really just short-hand for regrouping two units of higher place value through addition as you multiply the next higher place value? Does she realize that this is what she's doing with the multidigit multiplication algorithm?

If she doesn't deeply understand the sense of those parts of the algorithm, I think it is doing a disservice to simply ask her to memorize it and execute it anyway. A child who is bright enough and advanced enough in mathematics to be several years "ahead" deserves to be given a very rich understanding of the basic place value relationships and sense of the operations.

Miranda

[meemee]

aaaaaaaaaaaah thank you miranda. i think you hit the nail right on the head.

yes dd does see the algorithm with smaller numbers. in fact that's how she does her multiplication. but when it gets to three or more numbers she cant keep it in her head. no one taught her that algorithm. she discovered it one day and i was there to see that light bulb come on. she was soo excited.

i think if i help her break it down just for her to see the pattern it will make sense to her. placeholders are the part she is struggling with. where it goes. line it up. the order. even though i use graph paper. mind you though i am writing this after sitting with her for 15 mins.

i'll see how confident she feels today.

[HeatherB]

Moving to Learning at Home...

[One_Girl]

The lattice method can be very nice for multiplication.

http://www.coolmath4kids.com/times-t...ication-3.html

I use this partiel quotient method for division when I don't feel like doing it the long way.
http://classic.sidwell.edu/LS_Math_A...lymathnews.htm

This is another method, but I didn't read through the whole thing.

http://www.merga.net.au/documents/RP382006.pdf

Some kids also just need a lot of guided practice as they work to remember all of the steps in division. It seems easy once you master it, but it can take a long time to get to that point. You may want to check out your library or the internet to see if you can find a division and multiplications video. Sometimes kids just need to hear someone else explaining things a little differently even if it is the same method.

[shoefairy3]

I have never seen that lattuce method. Clever!