Q&A #4147

Understanding abbreviations

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Jun 13, 2000 at 00:00:27
Subject: Re: Understanding abbreviation

The teacher who wrote the previous response I spoke of has pointed me to the message, so I have copied it below. Notice that it also includes a third idea, the prime factorization, as part of the same approach, a powerful triunal concept. --------------------------------------------------------------------------- Jeanne wrote, in answer to Larry's question about factor trees: Hello Larry, I agree with Gail. The orientation of the tree/root system isn't as important as the information one obtains from them. Factor trees have a way of "growing" in such a way that my weaker students, especially those whose handwriting is messy, lose track of their factors. I teach my students factor trees and another graphic organizer which I'd like to share with you. For example, if my students want the prime factorization of 84, I have them write an "upside down long division symbol" and place 84 in it. )_84__ (Pretend the horizontal line continues under the 84.) Then I ask, "What prime number is a factor of 84?" The kids usually say "2." They record the 2 in front of the symbol and divide recording their quotient below the 84. 2)_84__ 42 Put another upside down division symbol around the 42. 2)_84__ )_42__ "What prime number is a factor of 42?" "2." Record the 2, divide and record the new quotient and upside down division symbol. 2)_84__ 2)_42__ )_21__ Repeat until 1 is your quotient. 2)_84__ 2)_42__ 7)_21__ 3)__3__ 1 The prime factorization of 84 in appears in a column on the left. The greatest common factor and least common multiple can be found using the same graphic organizer. I teach the concepts of GCF and LCM from a variety of perspectives. What I am about to share is simply a method to find them. Suppose we want to find the GCF of 12 and 18. Set up the upside down division symbol as follows: )_12__|__18__ "What factor (it doesn't have to be prime) is common to both?" "2" Record. 2)_12__|__18__ 6 9 "What factor is common to both 6 and 9?" "3" 2)_12__|__18__ 3)__6__|___9__ 2 3 "What factor is common to both 2 and 3?" "1" 2)_12__|__18__ 3)__6__|___9__ 1)__2__|___3__ 2 3 Conclusion: GCF of 12 and 18 is 2*3 or 6. Another conclusion: LCM of 12 and 18 is 2*3*1*2*3 or 36. My kids really like this way of keeping things organized! -Jeanne, for the Teacher2Teacher service ------------------------------------------------------------------- Hope this much better explanation helps. -Pat Ballew, for the Teacher2Teacher service

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