Equivalent Fractions, use in middle school & high school

Discussion in 'General Education' started by SportsFanTr, Apr 22, 2012.

  1. SportsFanTr

    SportsFanTr Companion

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    Apr 22, 2012

    I am writing a grant application for K-6 Math teachers that is due in about a week. The written part is approximately 15 pages :)dizzy:) which I haven't done in several years. My chosen topic is in a unit equivalent fractions, and the specific topic is of generating equivalent fractions (4th grade). I have my lesson plan ready for the video portion and about half of the written pages completed. However, there is one part I could use help with from middle school or high-school math teachers.

    The question states: "Explain why this topic or concept is important for students to learn and how it relates to more complex concepts that students will encounter in subsequent lessons, grades, or courses," and here is what I have so far:

    a) when adding or subtracting fractions, you must make sure both have the same denominator which requires equivalent fractions
    b) converting from fractions to decimals and percents, will require the fraction to be converted into one with a denominator in base 10 (is it proper to say base 10 here, or is there a better way of saying it?)
    c)extending a pizza or food for when more people unexpectedly show up.

    I'm trying to remember Algebra/Trig/Calculus and when this concept shows up, but I'm really drawing a blank...any help would be appreciated!

    :thanks:
     
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  3. Aliceacc

    Aliceacc Multitudinous

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    Apr 22, 2012

    Well, to add or subtract algebraic fractions, you need those same equivalent fractions. (Only these ones usually require factoring.)

    Many times when you have to prove a trig identity, you need to add or subtract those algebraic fractions, this time with trig functions.

    Many times, it's simply easier to reduce a fraction and use the equivalent form. For example, last week my Geometry kids covered length of arc and area of a sector. One side of both formulas is "n/360" where n is the central angle. I uniformly reduce my fractions to make the calculations easier.


    Ooops, gotta run. That may get you started.

    OK, I'm back. As a consumer, unit pricing is all about equvalent fractions.

    In calculus, related rates are based on the same ideas.
     
  4. mopar

    mopar Multitudinous

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    Proportions and ratios and rates.
     
  5. SportsFanTr

    SportsFanTr Companion

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    Apr 22, 2012

    Thank you both, those will help a lot. Alice I actually thought of unit prices too right before I came here and saw your updated answer!
     
  6. Aliceacc

    Aliceacc Multitudinous

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    Also, how about currency conversions?
     
  7. Upsadaisy

    Upsadaisy Moderator

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    How about stock market quotes, mortgage rates?
     
  8. mmswm

    mmswm Moderator

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    Apr 22, 2012

    Beyond the direct implications and uses of equivalent fractions, being able to manipulate numbers, and understand why you're doing so, forms the foundation for the type of logic required for advanced, theoretical mathematics. If a child understands how two different numbers are really the same thing, I can draw on that to teach them how two different formulations of the same theorem are saying the same thing, and using the same logic I use with the fractions, I can walk them through a more abstract proof.

    Math isn't all about numbers. It's also about logic and ideas, however, before we can get to those ideas, we have to teach our students how to think logically. We can't, however, just start with the abstract ideas. We have to start with something concrete. All of these methods, procedures and algorithms we teach in primary and secondary school can be used to bridge students from computational mathematics to the science of mathematical ideas.
     
  9. mopar

    mopar Multitudinous

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    Converting units of measure as well.

    mm---good point. Also showing that two equations are equal, especially when talking about the distributive property.
     
  10. Aliceacc

    Aliceacc Multitudinous

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    To build off what mm said, related rates in Calculus are a spin off of the idea of equal fractions. (In case you've forgotten what they are, they're problems like: "if the radius of a balloon increases at the rate of 1cm/sec, find the rate of increase of its volume"

    Not exactly equivalent fractions, since it's not a straight proportion. But it builds off the idea that one rate can be related to another.
     

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