A number of people have gotten in touch with me recently about Appendix A, so I wanted to clarify something about its role. States who adopted the standards did not thereby adopt Appendix A. The high school standards were intentionally not arranged into courses in order to allow flexibility in designing high school courses, and many states and curriculum writers have taken advantage of that flexibility. There was a thread about this on my blog 3 years ago, and there is a forum on the topic here.

Appendix A was provided as a proof of concept, showing one possible way of arranging the high school standards into courses. Indeed, on page 2 of the appendix it says:

The pathways and courses are models, not mandates. They illustrate possible approaches to organizing the content of the CCSS into coherent and rigorous courses that lead to college and career readiness. States and districts are not expected to adopt these courses as is; rather, they are encouraged to use these pathways and courses as a starting point for developing their own.

States will of course be constrained by their assessments. But Smarter Balanced consortium does not have end of course assessments in high school, leaving states and districts free to arrange high school as they choose. And although PARCC does have end of course assessments, they do not follow Appendix A exactly. See the footnote on page 39 of the PARCC Model Content Framework , which says

Note that the courses outlined in the Model Content Frameworks were informed by, but are not identical to, previous drafts of this document and Appendix A of the Common Core State Standards.

Furthermore, there are plenty of states not using either the PARCC of SMARTER Balanced assessments.

I hope this helps clear things up.

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## About Bill McCallum

I was born in Australia and came to the United States to pursue a Ph. D. in mathematics at Harvard University, met my wife, and never went back. I am a professor at the University of Arizona, working in number theory and mathematics education.

We are in a state using PARCC. I am speaking specifically for geometry. The Problem Based Assessment assumes particular concepts are covered within the first 75% of the course . It appears they did use Appendix A as a guideline as can be seen in the sample PBA provided at http://parcc.pearson.com/practice-tests/math/. The End of Year assumes other concepts are covered within the 90% of the course and adds Unit 5 from http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf page 28 as can be seen in the sample EOY provided.

From Al Cuoco:

While a longtime Common Core enthusiast, I’ve always thought that Appendix A missed the mark. I’ve talked with the authors of App A about this, and I understand that it was a rapid prototype, just to show that one could create three courses that meet all the (non +) standards.

But some of the ways things are split between courses don’t make mathematical sense. For example, adding and multiplying two polynomials is the same (and requires the same skills) no matter what the degrees of the polynomials are. Yet these skills are divided between algebra~1 and algebra~2; algebra~1 is restricted to linear and quadratic expressions (so, multiplying a linear expression by a quadratic is off limits, it seems, in A1).

It makes much more sense to split the subject of polynomial algebra by operations rather than degree, so that addition and multiplication are part of A1 and division with remainder, the factor and remainder theorems, and composition are reserved for A2.

There are other examples: That the graph of an equation in two variables often forms a curve (which could be a line) is a statement about *any* equation, regardless of its type or special characteristics. An A1 student who understands this idea should, given the graph of an equation in x and y, be able to sketch the graph of the equation resulting from replacing x by x-3 and y by y+2.

General principles need to be illustrated in special cases, but the generality of the principles should not be hidden or tied to the specific examples.

The PARCC content frameworks takes a more sensible approach to how the standards split between elementary and advanced algebra.