Teacher2Teacher |
Q&A #19482 |
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Hi Linda, I think I see one way you could help them past this hurdle. You say they are considering multiplication as a short cut for addition. Well, I agree, up to a point. But when they consider the numbers being multiplied, they need to remember that one of the numbers names the amount in each group, and the other names the number of groups. So they can use that same thought when looking at fractions. You could guide them with a table, and help them look for patterns to make a generalization, like this: 2 x 4 = 8 2 x 1/2 = 2/2 or 1 1 x 4 = 4 1 x 1/2 = 1/2 1/2 x 4 = 2 1/2 x 1/2 = 1/4 1/4 x 4 = 1 1/4 x 1/2 = 1/8 Since you said they understand the idea of "half of", maybe they will see that each step uses half of the factor before it (2, 1, 1/2, 1,4), and the answers (products) are also one half of the preceding product. The first set just convinces them that there is a pattern, that they can predict. The second set establishes that the patterns involve both fractions and wholes. Now that they are certain it "works", perhaps you could return to the idea that 2 x 3 means 2 groups of 3, and that 1/2 x 1/3 means half of 1/3. When you find 2 x 3 you are really finding 2/1 x 3/1, but we just don't think about the wholes as fractions. We multiply those denominators. They just don't make a difference to the way the answer looks because of properties. I hope this gives you something to begin with. The patterns usually convince my students... :-) -Gail, for the T2T service
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