Teacher2Teacher 
Q&A #522 
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From: Don To: Teacher2Teacher Public Discussion Date: 2004011416:31:03 Subject: Re: borrowing in subtraction Before a child can really understand the rule or algorithm of borrowing, they need to understand what the borrowing represents. Base 10 manipulatives and a base 10 mat are really good for this. You can see the materials at http://www.shnta.com/Product/Mathematics/Manipulatives/SR0750.htm If they work with questions with the manipulatives where they don't have to borrow and get used to what the numbers actually mean, they can discover the difficulty when they are given problems where they do have to borrow. Children can frequently come up with the idea that they need to borrow themselves using these materials. They should also use the blocvks to add to get used to the concepts. You can see the base 10 mat at http://www.didaxinc.com/shop/productdetails.cfm/ItemNo/314292.htm You don't need to have commercial materials for this. Popsicle sticks gathered into hundreds and tens can work. You could also just cut out base 10 materials, there's templates at: http://math.about.com/gi/dynamic/offsite.htm?site=http%3A%2F%2Fmason.gmu.edu%2F%257Emmankus%2Fwhole%2Fbase10%2Fbaseten.htm There's also a program at http://matti.usu.edu/nlvm/nav/frames_asid_155_g_2_t_1.html which is very well done. Doing it by hand is probably better because you actually take away they blocks when you subtract, not cancel a blue on with a red one as in the program. The basics of all this is that the student has to visually see that when they cross out and borrow, they're really changing a ten for 10 ones. There's some more info at http://www.michigan.gov/scope/0,1607,715513481_13482_1348476410,00.html which should help.
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