It's a little dangerous in my book to take each standard individually without looking at the full school year's worth of content. A full school year's at the very least. Ideally, it would be nice to have a grasp of all the different strands and progression of topics from K through 12. Technically, I can study all of that, I do have the time to so this summer. Unfortunately, I'm a lazy bum and can only take so much studying per diem when I'm on vacation mode.
In the number sense category for 5th grade, there are two main standards, each with their own sub-topics:
1.0 basically involves students being able to manipulate very large and very small integers, fractions, decimals, percents and understand the relationships between all of them. Students should also know how to visually represent these numbers, most commonly on a number line, but I like to use other things as well.
Example: know that 50% of 100 is 50/100, and it is also 1/2, as well as "50 items out of 100 possible items" etc.
2.0 involves actual computation of said numbers. This standard is more straightforward, and thus less open to misinterpretation than 1.0.
Example: add, subtract, multiply, divide, blah blah blah. Know the relationships between multiplication, division, and fractions.
I really had some issues with the way my previous CT taught 1.0. Maybe it's because I have serious issues with the standard itself. It really just assumes that you are working in base 10, which makes students get stuck in base 10 mode, which is not necessarily a bad thing, but it doesn't allow for much number sense flexibility either. And the whole point of number sense is to BE flexible with numbers! I had such problems adjusting to non-base 10 systems, and I blame it on the fact that we are taught in elementary school only using base 10.
And it doesn't really make sense. The American measurement system is not base 10. How we count time is not base 10. How we count memory on computers isn't in base 10. Dude, how we count eggs is not base 10. So the excuse of it "not being practical" is really no excuse at all.
Granted, this topic is probably taught later, and addressed in another grade. But why wait? Why not introduce it now? It fits right in with primes and factorization, so might as well, no? Well, teachers do wait, for a multitude of reasons. Some valid, some not so much. I do have many troubles with sticking to teaching one particular standard, not just in math. Doesn't any one else see all the different connections and relationships from one area to another and back to itself again? Like I said before, it's dangerous to take things outside of context sometimes. It's also dangerous to include too much context. There just isn't enough time in a school day to make it work. So I guess I have to pick and choose.
I also had issues with my CT's insistence that students must estimate always and forever. He had the students estimate, and then have them calculate the exact answer. And I could tell that some students go a little resentful of this - I certainly did. Why on earth do you need to estimate when you are also required to calculate the exact answer? More often than not, the students were repeating themselves in their reasoning and really not seeing the difference between estimation and actual calculation. You can say "it's just an educated guess" until the cows come home, but when the method of getting that educated guess and the actual answer are the same, it might bring on unwanted complications.
I also did not like that he only used 0, 1/2, and 1 as points of reference. This might contribute to the fact that many people have no clue what "3/7ths of a tank of gas" is.
Disclaimer: I'm not dissing on the standards themselves. They are a good and mighty thing, and unifies education like no other (I'm a HUGE proponent for nationwide standards - as well as nationwide requirements for teaching certification, but that's another story). It's just that different people take it in different ways, sometimes ignoring certain parts of the whole. That bugs me.
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