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Which means she can start the next one before the second term of school, and if we work over the summer she'll even be a little ahead next year!
To make things better, the last two sections are two she enjoys, time (she actually squealed) and geometry. The LAST section was comparing fractions with different denominators, and she was not so impressed. I'm finding, though, that often she struggles to get through a section, takes a break, and when it comes up in review she whizzes through it. For example, long division was super hard (as it should be), but when we came back to it after the summer break she had it all memorized, even though that didn't seem the case when we finished that section before.
She hasn't even touched on long division in her school curriculum (a teacher who saw her working on it last year commented that it's end of fourth/early fifth grade work, which doesn't sound right to me, but what do I know?), but they're doing stuff I know I didn't learn until middle school, like order of operations or the term variable. I don't mind them using variables - I mean, if they decide to write problems as x + 3 = 6 instead of 3 + 3 = ? or 6 - 3 = ? it probably doesn't do any harm and may do some good - but I wish they wouldn't use the term. They don't seem to have actually explained it, and Ana now tries throwing it around in all sorts of occasions where it doesn't make sense. It's the same as the whole "label the axes" debacle last year. They told her one was x and one was y, and it was the better part of two weeks to convince her that they never, ever, ever want you to label them literally "x" and "y" because that would be stupid.
And sometimes, in her homework at least, the textbook authors seem to have deliberately chosen the most verbose phrasing possible. "Show which numbers, out of the set 8, 9, 10, 11, make the following inequalities true." I'm certain there must have been a simpler way to phrase that. At least it didn't ask her to explain her answer, which is the new vogue. Ana has lost points on tests, math tests, for failing to adequately explain her answer. I'm looking at 2010's state math test now. Five lines provided to say explain how you figured out that Jose's math pattern was "add 2, subtract 5, add 2, subtract 5...." It really is so much silliness, and that's what they expect kids to do. I read an article about how this great school had low scores on the 8th grade tests despite actually working above grade level, and they specifically blamed this fetish for "explaining" as the reason. Some commenters refused to believe it, but I do. It's hard to explain these, especially when you understand them enough to just do the math without counting or drawing pictures! It really penalizes kids who work at a level where they don't have to think it all through, and it's tedious as well.
As for Evangeline, she's doing multi digit subtraction with borrowing, or regrouping as we say today. In school they're doing two digit plus one digit addition with carrying, and they've only just started, but she's pretty much mastered subtraction at home. Funny thing, her mistakes are completely different from Ana's! When Ana started with that level of subtraction, sometimes she'd forget and, if the top digit was smaller than the bottom, subtract the smaller digit from the larger instead of adding a ten. So if she had 78 - 69 she would get 11 as her answer. Eva has yet to do that. However, when SHE gets careless she starts borrowing to digits that don't need it! So if she has 531 - 140 she might absent mindedly take away from the 30, and then get stuck when her answer makes no sense. In math, she's better at catching silly answers than Ana is, though. (Ana is better at catching silly mistakes in reading.)
To make things better, the last two sections are two she enjoys, time (she actually squealed) and geometry. The LAST section was comparing fractions with different denominators, and she was not so impressed. I'm finding, though, that often she struggles to get through a section, takes a break, and when it comes up in review she whizzes through it. For example, long division was super hard (as it should be), but when we came back to it after the summer break she had it all memorized, even though that didn't seem the case when we finished that section before.
She hasn't even touched on long division in her school curriculum (a teacher who saw her working on it last year commented that it's end of fourth/early fifth grade work, which doesn't sound right to me, but what do I know?), but they're doing stuff I know I didn't learn until middle school, like order of operations or the term variable. I don't mind them using variables - I mean, if they decide to write problems as x + 3 = 6 instead of 3 + 3 = ? or 6 - 3 = ? it probably doesn't do any harm and may do some good - but I wish they wouldn't use the term. They don't seem to have actually explained it, and Ana now tries throwing it around in all sorts of occasions where it doesn't make sense. It's the same as the whole "label the axes" debacle last year. They told her one was x and one was y, and it was the better part of two weeks to convince her that they never, ever, ever want you to label them literally "x" and "y" because that would be stupid.
And sometimes, in her homework at least, the textbook authors seem to have deliberately chosen the most verbose phrasing possible. "Show which numbers, out of the set 8, 9, 10, 11, make the following inequalities true." I'm certain there must have been a simpler way to phrase that. At least it didn't ask her to explain her answer, which is the new vogue. Ana has lost points on tests, math tests, for failing to adequately explain her answer. I'm looking at 2010's state math test now. Five lines provided to say explain how you figured out that Jose's math pattern was "add 2, subtract 5, add 2, subtract 5...." It really is so much silliness, and that's what they expect kids to do. I read an article about how this great school had low scores on the 8th grade tests despite actually working above grade level, and they specifically blamed this fetish for "explaining" as the reason. Some commenters refused to believe it, but I do. It's hard to explain these, especially when you understand them enough to just do the math without counting or drawing pictures! It really penalizes kids who work at a level where they don't have to think it all through, and it's tedious as well.
As for Evangeline, she's doing multi digit subtraction with borrowing, or regrouping as we say today. In school they're doing two digit plus one digit addition with carrying, and they've only just started, but she's pretty much mastered subtraction at home. Funny thing, her mistakes are completely different from Ana's! When Ana started with that level of subtraction, sometimes she'd forget and, if the top digit was smaller than the bottom, subtract the smaller digit from the larger instead of adding a ten. So if she had 78 - 69 she would get 11 as her answer. Eva has yet to do that. However, when SHE gets careless she starts borrowing to digits that don't need it! So if she has 531 - 140 she might absent mindedly take away from the 30, and then get stuck when her answer makes no sense. In math, she's better at catching silly answers than Ana is, though. (Ana is better at catching silly mistakes in reading.)
