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“3.NF.3. b. Recognize and generate simple equivalent fractions, e.g., 1/2 =
2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by
using a visual fraction model.”“In Grade 4, instructional time should focus on three critical areas: […]
developing an understanding of fraction
equivalence,”
“Because the equations 28/4=7 and 36/4=9 tell us that
28=4*7 and 36=4*9, this is the fundamental fact in disguise:
(4*7)/(4*9)=7/9
It is possible to over-emphasize the importance of simplifying fractions in this way. There is no mathematical reason why fractions must be written in simplified form, although it may be convenient to do so in some cases.”
http://commoncoretools.files.wordpress.com/2012/02/ccss_progression_nf_35_2011_08_12.pdf?#page=4
You can get some answers by searching the forums for “simplif”. All quotes are from Bill McCallum. I think it’s helpful to see all these together because they address the general theme of simplifying in the same way.
Re simplifying polynomials:
. . . the standards do indeed quite consciously avoid the word “simplify”, the point being that different forms of expressions are useful for different purposes, and there is often no mathematical reason to call one of those forms the simplest. This is in accord with MP7, Look for and make use of structure. Students are expected to be able to make strategic choices about what manipulation they perform for the purpose at hand, rather than respond mechanically to commands like “simplify”. http://commoncoretools.me/forums/topic/simplifying-polynomials/#post-675
Re simplifying radicals:
Note the emphasis is on rewriting rather than simplifying, however. Indeed, it’s not at all clear which of √18 and 3√2 [hoping this pastes correctly–CK] is simpler, and each might be useful in different contexts. http://commoncoretools.me/forums/topic/simplifying-radicals/
Re simplifying fractions:
. . . the Standards do not require simplifying fractions into lowest terms, since it is not a mathematically important topic. To quote the Fractions Progression, “It is possible to over-emphasise the importance of reducing fractions …. There is no mathematical reason why fractions must be written in reduced form, although it may be convenient to do so in simple cases.” http://commoncoretools.me/forums/topic/mixed-numbers-in-grades-4-and-5/#post-954
As Jim and Cathy point out, this has been extensively discussed on the blog (thanks for the quick followups). Just to be clear, since this point is often misunderstood, understanding fraction equivalence and being able to produce equivalent fractions are both very important in the standards (see 4.NF.1). What’s gone is the insistence on reducing to least terms as a matter of course.
Just to be clear, if the thinking is that reducing fractions is considered unnecessary, then we have to be prepared to accept whole number-equvalent results expressed in the following form, without the student necessarily recognizing that they are looking at a whole number result:
32/8
5/1
-27/3
As a computational math person, I’m all for this new freedom in numeric formats. I just want to make sure educators and assessment folks are on the same page.
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