We have finished fractions!!!
Mar. 15th, 2013 06:20 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
conulyWe just plowed through it, on the grounds that the faster we moved the quicker we'd be able to move onto the next topic. The last few assignments were all word problems, and I am thrilled to say that Ana breezed through them! And they weren't easy things, either. "So-and-so spent 2/5 of his money on a book and had $18 left. How much did he start out with?" At Ana's level of skill, that's not that easy. But she a. refrained from wild guessing about which numbers to work with (and what to do to them), b. showed all her work in a neat and organized way, c. explained her thinking aloud to me and d. got the right answers! (I've been trying to get through to her the idea that, when it says "show work", getting the right answer is almost like a bonus. Sure, it's the ostensible goal, but I'm just happy if her reasoning makes sense.) And without fussing.
I have shown her how we multiply fractions by fractions, and even how I cancel out as I do it, but I don't expect her to do that. She seems to have the concept, though, and who can blame her? Canceling out fractions is FUN, always has been. You take some monstrosity like 18/55 x 25/36 and by the time you're done you don't even have to do the work. When I learned how to do this I rapidly applied the concept to all multiplication and division, to the consternation of those teachers who noticed. (This, by the way, is the real meaning of "the associative property of multiplication", not that anybody is likely to tell Ana that besides me. Bet you a dollar the people writing the tests don't really grasp it either, nor why anybody should care.)
Here's something. My mother has a coworker who swears there IS no way to get a square root besides using a calculator. LOL, talk about illogic! Scary, though. Just like that short story with the calculators.
http://downlode.org/Etext/power.html
I have shown her how we multiply fractions by fractions, and even how I cancel out as I do it, but I don't expect her to do that. She seems to have the concept, though, and who can blame her? Canceling out fractions is FUN, always has been. You take some monstrosity like 18/55 x 25/36 and by the time you're done you don't even have to do the work. When I learned how to do this I rapidly applied the concept to all multiplication and division, to the consternation of those teachers who noticed. (This, by the way, is the real meaning of "the associative property of multiplication", not that anybody is likely to tell Ana that besides me. Bet you a dollar the people writing the tests don't really grasp it either, nor why anybody should care.)
Here's something. My mother has a coworker who swears there IS no way to get a square root besides using a calculator. LOL, talk about illogic! Scary, though. Just like that short story with the calculators.
http://downlode.org/Etext/power.html
