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Comparing fractions
Old 01-03-2008, 02:27 PM
 
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I teach 5th grade and my students are having a hard time with comparing fractions. I taught them to find the greatest common denomenator, find the equivalent fractions, then compare. They just don't get it. Well I had a student that showed me another way that his dad showed him. I tried it on several problems and it seems to work. I am just afraid to show my students if I'm not sure. What his dad said to do was to multiply the denomenators, cross multiply, then compare. The only problem is that they have to simplify at the end. Does this sound right to you math wizards? I will admit that my math skills are not the best. Any help would be great!


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Old 01-03-2008, 03:57 PM
 
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I'm not sure about multiplying the denominators but cross multiplication works but they will have to simplify if needed. Cross multplying is like using the product of both denominators as the LCM.
18 20
3 5
4 6 Since 18 < 20 then 3/4 < 5/6.

It would be the same as saying that the lowest common denominator is 24 because you would be multiplying 3x6 and 5x4. It's hard to explain in written form.

Hope this helps.
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Old 01-04-2008, 05:21 PM
 
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My 7th graders prefer this method, too. If they can't see an obvious relationship between the 2 denominators (x/5 and y/20) where they can just multiply the numerator, then they cross multiply. The important thing is remembering that you go from bottom and cross up. So if it were 4/7 and 5/6, you'd multiply the 7 up to the 5, then that product stays on the right. You multiply the 6 up to the 4, and it stays on the left side. With 24 on the left, and 35 on the right, you can compare the fractions.

As mathtch said, it's essentially just finding a common denominator by multiplying the numbers times each other. But it's faster for comparing 2 individual fractions than going through the steps for an LCD.
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cross mult.
Old 01-04-2008, 06:28 PM
 
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The cross mult. method


3 5
4 6 works every time. In this example 6x3=18 &
4x5=20. The 18 (ends up on left side) is less than the 20 on the right, so 3/4<5/6. This method gives kids a fighting chance when comparing fractions.

Last edited by roo; 01-04-2008 at 06:28 PM.. Reason: clarification
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Procedural vs. Conceptual
Old 01-05-2008, 10:15 AM
 
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I teach 5th grade as well. I think you need to allow your students to explore a variety of approaches, starting with a conceptual approach. Have you tried drawing/using visual models of different fraction amounts when comparing? In my opinion, students should not solely be taught a procedure and expected to memorize steps and/or any "short cuts", like cross multiplying, without first having a good understanding of the actual concept or skill. There will be those students who prefer a procedural approach and will do well with it, but we shouldn't expect all students to use one method. We need to show kids a variety of "tools" or methods they can use when approaching a problem. Then we can guide towards evaluating different methods and reasoning why one method may be a "better" method (more time-efficient, etc) for solving a problem.


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both concepts
Old 01-05-2008, 06:34 PM
 
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I agree with post right before this one...yound students need to be taught what they are doing...I think as you did to begin with...then show them the cross multiplication...that is what our middle school kids use but they need to understand what you are doing is really finding a common denominator...so I show them the mult across...then I say how would we have done it showing them how it would be if we made the equivalent fractions they seem to "get it" then
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cross multiplying
Old 01-13-2008, 06:50 AM
 
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definitely works. The only thing is that they CONCEPTUALLY still do not get the reason why a certain fraction is greater than the other. I use fraction strips, finding the common denominator...if they understand I show them the cross multiplying short cut. This is fourth grade so I don't want to mess them up for next year's teacher if I show them something that isn't in our curriculum.
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