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Well, it’s a bit hard to say without looking at the course; there may be some reasons of coherence that they wanted to put these standards in. G-GPE.6 connects with the work on ratios in Grades 6 and 7, and G-GPE.7 connects naturally with the Pythagorean theorem in Grade 8. So I can see why people might want to put them in. And, if these accelerated tracks are limited to the students who a really ready for them, then there is no harm done. But that’s a big if. The fact is, these topics can wait. Just because a topic fits naturally, doesn’t mean you have to put it in; that’s what got the U.S. curriculum into trouble in the first place.
Oops, I meant page 14, not page 13. But, also, we are talking about different versions. I am talking about the one here, which is a corrected version of the one you are looking at. It has the 3 ways for 549*8 at the top of page 14 in the margin. I didn’t give an opinion about those before, but I would say that only the one on the right is the standard algorithm. The one Scott was talking about is at the bottom in the margin on page 14 in this version. You can see the discussion here.
Yes, students should be able both to “recognize and generate equivalent fractions” (4.NF.1). The multiple choice question you propose is a nice idea.
As you say, Common Core in Grades 7–8 is already plenty rigorous. Mandating an accelerated curriculum for everybody is a bad idea, in my opinion.
The National PTA has some grade-level booklets for parents here.
There is a footnote on 7.NS.3 which says “Computations with rational numbers extend the rules for manipulating fractions to complex fractions.” (I agree it’s a little subtle!)
Andy, I just replied in the other forum, here. I’m not reluctant at all, but I work through replies to comments in the order in which I receive them. Since our semester started in late August I have found it more difficult to keep up, and unfortunately I cannot guarantee any specific turn-around time.
I agree it would be great if students learned rules for computing with scientific figures, but the standard doesn’t ask for that. One of the reason mathematics curricula get overstuffed is a sort of “eat-dessert-first” mentality which accepts all the topics that we (or science teachers) love.
Hi Gretchen, take a look at the second last page of the EE progression and let me know if it helps. Happy to answer more questions if not.
The standard doesn’t explicitly limit itself to proportional relationships, so that leaves the door open to using other types of relationship as examples. But I don’t agree with you that that opens the floodgates to “doing a lot with linear relationships.” The idea here is to get used to using equations in two variables to express relationships, and interpreting graphs and so on. You can do this with simple examples without going to either extreme.
Whether and when to teach the standard algorithm was a hotly contested topic during the writing of the standards, and now some of that debate has transferred to the meaning of the term. Some think it is the algorithm exactly as notated by our forebears, some think it includes the expanded algorithm, where you write down all the partial products of the base ten components and then add them up. Ultimately this is a question that has to be settled by discussion, not fiat. My opinion is that the standard algorithm has two key features; like the expanded algorithm it relies on the distributive law applied to the decomposition of the number into base ten components, but in addition it relies on the fact that the order of computing the partial products allows you to keep track of the addition of the partial products while you are computing them, by storing the higher value digit of each product until the next product is calculated. I don’t think different ways of notating this constitute different algorithms. So, in particular, the algorithm that Scott was talking about, bottom of page 13 in the margin, would qualify in my opinion, but the partial product algorithm in the middle of that page would not.
Scott, just to summarize your point to make sure I have it clear, you are worried about the conflict between the method of recording multiplication on p. 14 of the progression (bottom right) being out of sync with the traditional way of recording long division. I can certainly see this as a worry. But I guess the method on p. 14 is trying to get away from the other possible error students might make with the traditional way of recording the algorithm, namely that they add the carried 3 to the 2 above which it sits before multiplying by the 5. I don’t really have a definitive answer here; you are deep in the problems of curriculum design, for which the progressions are intended to provide ideas and support, but not all the answers. However, I do agree that it is worth noting this point in the progression, and will make sure it is included in the final draft. Thanks very much for this detailed reading.
Well, they are right that there isn’t much about 3-dimensional shapes in Grade 2. The focus in Grade 2 is on achieving mastery of addition and subtraction, so students can move on to multiplication and division in Grade 3. To achieve this you have to make room in the curriculum, which means giving up something else.
