To: Teacher2Teacher Public Discussion
Subject: Re: Division and Reciprocals
Hi, Jennifer, How you define a reciprocal depends upon how old, or how mathematically mature your student is. A reciprocal of a number is itself a number so thatthe product of the reciprocal and the number is one. Younger students will understand a reciprocal of a number # as 1 over # or 1/number. Sometimes students view a reciprocal as the number turned upside down. For example if the # is 2/3, then 1/# is 1/(2/3) or 3/2. Why do we use reciprocals? Again this depends upon the maturity of the student. Think about addition. When we wish to "undo" addition we subtract which is the opposite of addition. When we multiply we are doing repetitive addition. That is, 3 x 4 is adding 4 three times or 4 + 4 + 4. If we divide 4 by 3 we are looking for three number # so that when the number is added three times we arrive at 4. Therefore, # + # + # = 4. Since the numbers are all equal the # is 4/3 or one and one-third. Think of taking 1/3 of 4. Is this not dividing it into three equal parts so that the sum is 4? I think it makes sense to teach division by teaching multiplication; for example, what is 3 x 4 to get twelve and then asking the children to divide 12 into 3 groups where each group has the same number in it. Do your students know their time-tables? Knowing them makes division much easier. A teaching example for dividing 4 by 3 is to have four rectangles of equalsize. To divide these into three piles with the same amount of area in each requires that one rectangle goes into each of the three piles and then the fourth rectangle be cut into thirds. A nice example for dividing 3 by 4 is to take three rectangles. One way is to take 1/4 off of each rectangle so that each of the four piles has the same amount of area. A second way is to cut each of the rectangles into 1/4 of the area. You will then have twelve pieces, each of which is of the size "1/4." The twelve pieces can be placed three in each of the four piles. Each pile has 3 "1/4" or 3/4. I hope that these ideas have helped you.
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