NCTM Standards
Within the NCTM Principles and Standards, the concept of ratio falls
under the Number and Operations Standard. The document states that one
curricular focus at this level is "the proposed emphasis on proportionality as
an integrative theme in the middle-grades mathematics program. Facility with
proportionality develops through work in many areas of the curriculum,
including ratio and proportion, percent, similarity, scaling," and more.
Another focus identified for middle school is rational numbers, including
conceptual understanding, computation, and learning to "think flexibly about
relationships among fractions, decimals, and percents" (NCTM, 2000, p. 212).
Characteristically, the document emphasizes the deep understandings that
underlie the coursework. For example, to work proficiently with fractions,
decimals, and percents, a solid concept of rational number is needed. Many
students hold serious misconceptions about what a fraction is and how it
relates to a decimal or a percent. They can develop a clearer, more intuitive
understanding through "experiences with a variety of models" that "offer
students concrete representations of abstract ideas" (pp. 215-216).
The online resources in this unit offer several models for hands-on encounters
with ratio under some of its many guises: a rate, a scale factor, a percent, a
comparison of geometric dimensions. We hope that your students will enjoy their
encounters with ratios and deepen their understanding of this useful concept.
National Council of Teachers of Mathematics. (2000). Principles and standards
for school mathematics. Reston, VA: Author.
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Copyright
June 2006 — The Ohio State University. This material is based upon work
supported by the National Science Foundation under Grant No. 0424671. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views of
the National Science Foundation.
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