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Ana is finally getting it, math-wise
In our extra math, we're back to doing mental math. I don't think they cover this much at school (or at all), and every time mental math has come up over the past few years Ana has been reluctant to do it. It's been hard for her, and she struggled with it, and then she'd get upset.
This time she just breezed through it. It was so easy for her, in fact, that I just let on every page do the last (that is, the hardest) 10 problems or so on the grounds that if she got them all right I could trust she didn't need to practice any more than that. Addition with 99s and 98s? Easy as pie. Three digit and two digit subtraction in her head? Piece of cake. PIe, cake - it's all so similar!
Then we came to mental multiplication, which is new. One digit by a multiple of ten - 5 x 30, 6 x 90, that sort of thing. For somebody who understands her times tables, this should be pretty simple - it's one digit multiplication, times ten.
It's a bit new to her, though, doing this in her head. She looked at the first few problems, and after doing a few asked me "Connie? Does it work in reverse too?"
Me: Does what work in reverse?
Ana: The math.
Me: ...huh?
Ana: Well, let's say somebody isn't good with her 4 times tables yet. This is 50 x 4. Could I do it the other way around? So I wouldn't have to do the 4s?
Me: You mean... could you do 40 x 5 instead of 50 x 4?
Ana: (thrilled that I got it) YES! That's what I mean!
Me: Yes, absolutely. 50 x 4 is the same as 40 x 5. Because, you know, they're both
Ana: Four times five times ten.
Me: You know, that's very good mathematical thinking there. In fact, it's so impressive and important that I'm not even that concerned that you don't have your fours down yet.
Ana: Oh, I have my four times tables. It's just seven I'm worried about.
So I promised to show her how to do basic prime factorization later. I showed her last year, but I don't think it stuck because she wasn't there yet. Using factoring for multiplication and division is the best trick ever, and in my experience other people don't quite grasp how you did it, so they think you're just brilliant.
Not that factorization at this stage is going to help her much with the sevens. She's still doing two by one digit. I showed her a little yesterday, at the doctor's office, how to do double digit multiplication, but only briefly. I promised her we'd go over it again and again and she doesn't have to have it by heart just yet, and that understanding the basic concept is way more important than understanding the usual algorithm.
This time she just breezed through it. It was so easy for her, in fact, that I just let on every page do the last (that is, the hardest) 10 problems or so on the grounds that if she got them all right I could trust she didn't need to practice any more than that. Addition with 99s and 98s? Easy as pie. Three digit and two digit subtraction in her head? Piece of cake. PIe, cake - it's all so similar!
Then we came to mental multiplication, which is new. One digit by a multiple of ten - 5 x 30, 6 x 90, that sort of thing. For somebody who understands her times tables, this should be pretty simple - it's one digit multiplication, times ten.
It's a bit new to her, though, doing this in her head. She looked at the first few problems, and after doing a few asked me "Connie? Does it work in reverse too?"
Me: Does what work in reverse?
Ana: The math.
Me: ...huh?
Ana: Well, let's say somebody isn't good with her 4 times tables yet. This is 50 x 4. Could I do it the other way around? So I wouldn't have to do the 4s?
Me: You mean... could you do 40 x 5 instead of 50 x 4?
Ana: (thrilled that I got it) YES! That's what I mean!
Me: Yes, absolutely. 50 x 4 is the same as 40 x 5. Because, you know, they're both
Ana: Four times five times ten.
Me: You know, that's very good mathematical thinking there. In fact, it's so impressive and important that I'm not even that concerned that you don't have your fours down yet.
Ana: Oh, I have my four times tables. It's just seven I'm worried about.
So I promised to show her how to do basic prime factorization later. I showed her last year, but I don't think it stuck because she wasn't there yet. Using factoring for multiplication and division is the best trick ever, and in my experience other people don't quite grasp how you did it, so they think you're just brilliant.
Not that factorization at this stage is going to help her much with the sevens. She's still doing two by one digit. I showed her a little yesterday, at the doctor's office, how to do double digit multiplication, but only briefly. I promised her we'd go over it again and again and she doesn't have to have it by heart just yet, and that understanding the basic concept is way more important than understanding the usual algorithm.
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*standing applause* Way to go, , woohoo, that is some rockin' math analysis!!!!
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