Appendix of State Standards
The standards listed here are for Algebra 1 (containing "A1"), Algebra 2 (…"A2"), or grouped parallel sets of Algebra 1 and Algebra 2 standards for Pennsylvania, circa January 29, 2011. This relatively brief list does not touch on all standards to which fractions might apply. My comments reflect how I view each as highly applicable.
2.1.A1.C - Use ratio and proportion to model relationships between quantities: This basic hallmark of Algebra 1 is the most general notion of my strategies for relating patterns in number sequences to fractional reasoning.
2.1.A1.F. - Extend the concept and use of inverse operations to determine unknown quantities in linear and polynomial equations: As I illustrated above, understanding the fraction as division is essential to algebra students in applying inverse operations.
2.1.A2.D. - Use exponential notation to represent any rational number: Student use of this advanced notation in Algebra 2 is reliant upon comprehension of rational numbers.
2.3.A1.C. - Find missing quantities in measurement formulas by applying equation solving techniques/2.3.A2.C. - Solve a formula for a given variable using algebraic processes: As emphasized at the beginning of my strategies section, I most particularly wish to target issues with fractions as they arise in the central algebraic skill sets that students might otherwise find more success with, e.g. solving for unknown variables.
2.5.A1.B/2.5.A2.B: Use symbols, mathematical terminology, standard notation, mathematical rules, graphing, and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas, and results: The wording of this standard is identical for both Algebra 1 & 2. I hope that I have addressed to some degree the codependence between managing fractions and the central rules, notation, and terms, as well as multiple representations, in algebra studies.
2.6.A1.A. - Design and conduct an experiment using random sampling: If it is not too extraordinary to say such a thing, I am particularly fond of this standard. What is more, it exemplifies how implicit and taken for granted proportional reasoning is, as any numerically based experiment using samples will produce fractions and percentages as measurements that must be carefully and critically analyzed.
2.7.A2.C. – Compare odds and probability: This content of Algebra 2 relies on students having some sophistication in working with both part-to-whole and part-to-part reasoning simultaneously, while making valid observations of these two fraction types.
2.11.A1.B. – Describe rates of change as modeled by linear equations: The magic word is "slope."
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