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You are correct that it is not explicit, but I think it is very much suggested. The standard
S-ID.A.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
suggests an act of choice to me, and more generally the phrase “Summarize, represent, and interpret …” in the cluster headings S-ID.A and S-ID.B includes both choosing a data display (in order to represent) and detecting possible misinterprations from one that is misleading. Bear in mind also that all the Statistics and Probability standards in high school carry the modeling star and therefore link to the description of modeling on pages 72–73, including the sentence
Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions.
The term “cone” in
8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
refers to a cone on any sort of base (at least any sort of base for which the area can be computed), so it includes pyramids.
Problems about surface area should generally be handled by seeing how the surface of the figure can be decomposed into elementary figures (rectangles, triangles, circles) whose area is computable. The idea is to know a few basic formulas and then use those to calculate volumes and surface areas of more complicated figures through decomposition.
Whichever reading you take, surface area of pyramids is fair game in Grade 7 since it was introduced in Grade 6. I see your point that it falls through the cracks of this particular standard if you take the first reading. With the second reading there is still some reason to keep cubes and right prisms in the wording, however, in that it indicates what sorts of volume problems are appropriate. In Grade 7 students might be computing surface areas of pyramids, but they are not yet computing the volumes of pyramids as a matter of course.
I’ve indicated elsewhere that I don’t feel comfortable commenting on various acceleration and tracking schemes without knowing what’s in the curriculum, and without knowing the particular circumstances of the school district in question. But I’ll just make one general remark here: there is plenty of mathematics in the CCSS Grades 6–8. It is completely different from the wasteland of repetitive curriculum that led people to consider all sorts of acceleration and tracking. So I would urge people planning to replicate previous schemes to give some thought to the possibility that they are no longer necessary.
Without knowing the syllabus in detail it’s hard to say much. But one question: is there a regular curriculum based on the CCSS Grades 6–8? Apart from that question, I would just say that whatever the acceleration scheme, it should be based on thorough knowledge of what’s in the standards, since that provides the foundation for more advanced courses.
Without knowing the syllabus in detail it’s hard to say much. But one question: is there a regular curriculum based on the CCSS Grades 6–8? Apart from that question, I would just say that whatever the acceleration scheme, it should be based on thorough knowledge of what’s in the standards, since that provides the foundation for more advanced courses.
So, just to make sure I understand the question, is the issue that the example’s requirement to explain goes beyond the standard’s requirement to identify? I guess it depends on what you count as an identification; I might detect what seems to be a pattern, but without at least an informal explanation for it I can’t be sure the pattern goes on forever. The gist of the example is that the process of identifying a pattern goes beyond the simple discovery phase.
Unfortunately the $\pi$ conspiracy extends beyond the shores of this country. One of the specifications for the writing of CCSS is that they be internationally benchmarked, and so we were unable to adopt this admittedly enlightened suggestion from Bob Palais. Alas, this change will have to come from the grass roots, perhaps with the formation of a $\tau$-Party who paint themselves in patriotic colors on $\pi$-day and stage protests across the country against the tyrants who make them write so many 2s.
Thanks Jim, I like the way you answered your own question … soon you’ll be able to answer everybody else’s as well and I can take a break!
Your answer is basically right, although I can imagine raising the question of where to round 2.5 in a Grade 5 class room and discussing the possible answers and the need for a convention. But making it a focus of assessment does seem inappropriate to me.
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.
I’m not sure how final this document is or how consequential; maybe it was just a useful exercise for teacher leaders, so I’m hesitant to single it out. But I agree it’s a useful basis for discussion and I agree that there is a worry here. Work like this has to pay attention to the structure of the standards, the language of the cluster headings, and the way domains fit together. It cannot be done one standard at a time. To give just one example, consider the following cluster:
Understand and apply properties of operations and the relationship between addition and subtraction.
1.OA.3. Apply properties of operations as strategies to add and subtract.
1.OA.4. Understand subtraction as an unknown-addend problem.
The document highlights the first standard as a priority standard but not the second one. But understanding that subtraction is an auxiliary operation derived from addition is crucial to the progression here. You can’t pull on that thread without unraveling the whole thing. This is a bit like deciding which leg has priority, the right or the left.
Looking through the document I see many cases where clusters are subdivided into some standards that are priority standards and some that are not. This is probably not a good approach, and is subject to the problems in the example above. I would recommend as a general rule that it should be done at the cluster level if it happens at all.
Note also that the PARCC assessment consortium’s classification of clusters into major, supporting, and additional clusters does indeed operate at the cluster level.
Sometimes this sort of work is driven by a desire to reduce the standard count. But in the example above, removing one of the standards makes for more work, not less. To return to my analogy, it’s like trying to walk on one leg instead of two.
Note that there is some overlap between the Grade 8 and High School Algebra standards, with material on linear equations being revisited at greater depth in high school. Students who can handle an acceleration can probably also afford to eliminate this overlap. Otherwise squeezing two grades into one would be an awful stretch (or do a mean an awful squeeze?).
