The Common Core standards (different from the Common Core modules, which are ass) spend a lot more time developing number sense and making sure kids understand why things work, which make problems like this very doable for a 12-year-old.
It's strange because as someone who taught at the college level, this is the type of problem I'd absolutely expect a 12 year old to reason through, and a first year university student to struggle with. Probably because something about high school math beats any reasoning skills out of you. Although there's another reason, often when we ask these types of problems in calculus or linear algebra classes, instead of the little box going "what's this number", we'll use a letter to denote a parameter (say "a"). Which is a better way to communicate with colleagues, but it seems to short circuit a lot of students' brains.
Im having flashbacks to like an entire year of high school in which every two weeks, we were given arbitrary and confusing instructions to essentially reformat an equation, followed by a test which I would bomb because they wanted me to reformat the equations MORE, followed immediately by the next class lesson being like "okay here's why we needed that shit reformatted, here is a new equation to plug it all into that makes it very obvious if you did last weeks exercises correctly"
literally just getting C's and D's back every second Monday, and then 20 minutes later they actually explain what the fuck we were doing and now I know how to do last Friday's test
Even for high school that's really bad teaching. I know one issue I see is students will sometimes do a manipulation they know without thinking about what goal they need to reach. This seems like it would actively feed that impulse.
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The Common Core standards (different from the Common Core modules, which are ass) spend a lot more time developing number sense and making sure kids understand why things work, which make problems like this very doable for a 12-year-old.
It's strange because as someone who taught at the college level, this is the type of problem I'd absolutely expect a 12 year old to reason through, and a first year university student to struggle with. Probably because something about high school math beats any reasoning skills out of you. Although there's another reason, often when we ask these types of problems in calculus or linear algebra classes, instead of the little box going "what's this number", we'll use a letter to denote a parameter (say "a"). Which is a better way to communicate with colleagues, but it seems to short circuit a lot of students' brains.
Im having flashbacks to like an entire year of high school in which every two weeks, we were given arbitrary and confusing instructions to essentially reformat an equation, followed by a test which I would bomb because they wanted me to reformat the equations MORE, followed immediately by the next class lesson being like "okay here's why we needed that shit reformatted, here is a new equation to plug it all into that makes it very obvious if you did last weeks exercises correctly"
literally just getting C's and D's back every second Monday, and then 20 minutes later they actually explain what the fuck we were doing and now I know how to do last Friday's test
Even for high school that's really bad teaching. I know one issue I see is students will sometimes do a manipulation they know without thinking about what goal they need to reach. This seems like it would actively feed that impulse.
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Oh that's so dumb. I agree with the antimath guy on this question in particular