Teacher2Teacher |
Q&A #750 |
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Hi, Crystal -- I think one reason it may be difficult for some students that age to learn the algorithm we present to them is that they really don't understand what it is they are doing when they multiply the two numbers. If they haven't a good idea of what the answer should be (i.e., a reasonable estimate of some sort) they probably don't have a good idea of what is happening with smaller multiplication problems either. When I present multiplying of these sorts of numbers to my upper elementary students, I give them concrete examples of what we are doing. We actually draw out the multiplication using rectangular arrays. For example, for the problem 17 X 23, one side of the rectangle measures 23 units, and the other side measures 17 units. Inside that large rectangle we find there are four smaller rectangles, a 3 X 7 rectangle, a 3 X 20 rectangle, a 10 X 3 rectangle, and a 10 X 20 rectangle. We look at all four, and determine where they are shown in the traditional algorithm. Some students continue drawing the rectangles for quite some time. They haven't made the concrete - to- abstract connection yet. Others discard the strategy almost immediately, because they have a mental image of what is happening. -Gail, for the Teacher2Teacher service
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