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I’m not sure which unpacked document you are talking about, do you mean the NBT Progressions document? Anyway, to answer your question, I think it is limited to what it says, just adding 10 or 100. Notice that it is about mental computation only. In 2.NBT.7 students are expected to add and subtract within 1000, so that certainly includes 243 + 30 and 472 + 400. But this standard is about mental work only. The point is not so much computation as encouraging a clear understanding of the base ten system. If a student can add 10 mentally to 243, then adding 30 is more cognitively demanding but doesn’t show a better grasp of the base ten system.
No, I don’t think this is quite accurate. The full sentence is “Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.” The “can” indicates that arguments using concrete referents are acceptable, not that they are required. And the “such as” indicates that objects, drawings, diagrams and actions are examples of possible concrete referents; not a list of requirements.
By the way, over the last few years there have been articles discrediting the whole theory of learning styles, e.g., this 2010 one in the New York Times.
Send me an email privately (you can find my email address by googling my name) and I will put you in touch with someone who probably knows.
I don’t think “three measures of angles or sides” means the same thing as “three measures of angles or three measures of sides.” That is, I interpret the standard as referring to six possible measures (angles or sides), any three of which may be chosen. Of course, in some cases this leads to ambiguity, such as SSA, but that is covered by the later “more than one triangle.” So, basically, I don’t think this standard is ambiguous, and I think that it allows examples such as the Arizona one. I find the publishers’ interpretations you refer to quite puzzling.
Some people like to run marathons, I guess, and some students might enjoy showing off their algebraic manipulation skills. Such problems could serve a purpose in some sort of math competition. But no, I can’t see a need for them at all in the regular curriculum.
Children should grow up knowing that there are 12 months in a year and 10 decades in a century, but it is not obvious to me that it is the math teacher’s responsibility to teach them. Some (most?) kids will learn this at home, some in reading, writing, social studies, or science (it sort of comes up everywhere, doesn’t it?). So, there’s no harm in having a math problem that puts this knowledge to use. “How many months in 5 years?” becomes a question about understanding multiplication once you know that there are 12 months in one year.
But it seems strange to me to treat this as some sort of conversion rule to be memorized, and I wouldn’t be in favor of having a special unit about it in the curriculum. That way lies curricular bloat.
My personal opinion is that a primary focus on metric units is a good bet, although obviously they still have to learn about customary units. Better still, students should leave school carrying some approximate conversion factors in their heads, and have the computational fluency to be able to use them mentally.
I think the standard is pretty clear in limiting conversion to within systems, and I think your understanding of that is correct. Can you give an example from one of the sample PARCC test questions? If they are requiring conversion between different systems in Grade 5, that goes beyond the standards.
Yes, I think it is a reasonable interpretation to limit assessment focused on this standard to those fractions. And decimals forms are fine as well; the point of view taken in the Common Core is that decimals are fractions (with denominator 10, 100, etc.), and that 0.25 and 1/4 are just two ways of naming the same fraction. In Grade 5 students are working with decimals to the thousandths (5.NBT.3).
Polynomials as a topic in their own right are not introduced until high school, and there the emphasis is on seeing them as a system (like the integers) of “numbers” that can be added, subtracted, and multiplied. Introducing monomials earlier and separately doesn’t fit well with this approach. In fact, I don’t see a good reason for introducing them at all, except possibly as a piece of terminology. And even there I’m not sure; you can talk about the monomials in a polynomial as terms in a sum. Certainly problems like the one Lane suggested are beyond the scope of Grade 8, and I would say that even the simpler multiplication of degree two monomials suggested by sbrockley is straying off track.
The focus of algebra in Grades 6–8 is linear expressions, equations and functions. The laws of exponents are limited to numerical expressions (8.EE.1).
Yes, this sounds about right to me. MP5 (Use appropriate tools strategically) puts the ball in the court of curriculum developers to make these decisions, but I think Statistics and Probability is an obvious area where technology will play a role, simply because the subject doesn’t really come to life until you start looking a data sets of a decent size.
In 5.MD.2 the first sentence lists “fractions of a unit (1/2, 1/4, 1/8).”
Are these the only fractions that should be assessed, as there’s no qualifier as is used elsewhere (such as “e.g.” or “including”)?
Also, is the decimal form of those fractions included, or is there something particular about the common fraction format on line plots that we need to get across to students?
