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Q&A #1217 |
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Marylou gave you some terrific resources. As an introduction to the instruction, you may want to remind your students about what we are trying to find out when we divide. For example, if we were dividing 138 by four, we would be trying to find out how many groups of 4 there are in 138, or how many are in each group, for 4 equal groups, depending on the context of the problem we were doing the arithmetic for. (You have 138 pairs of sock to put in boxes, and four pairs will fit into each box. How many boxes will you need, vs. You have 138 pairs of socks to store in 4 boxes. How many should you put into each box, to evenly arrange them.) When we divide with fractions we are looking for the same sort of information. 1/2 divided by 1/4 is really asking, "if you have half a pie, how many fourths of a pie do you have." Since 2 fourths is equivalent to one half, the answer is two. It forces us to think about the fractions in relation to the whole. How about one-fourths divided by one half. That is asking how many halves there are in one fourth. If you draw a whole, and shade a fourth of it, you can see that half of a half is in a fourth. So the answer is one half. Here is where a pitfall enters. Some teachers have taught their students that when you divide you get a smaller answer. That is true for whole numbers, but not for fractions and decimals necessarily. When students divide one half by one fourth, and get the answer "two" it does not seem reasonable to them. Having them actually cut a half into fourths (fourths of the original whole, that is, not cutting a half into four equal pieces) will help them see what is happening when fractions are divided. -Gail, for the Teacher2Teacher service
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