As far as the foil method, when solving algebraically you can use it anytime you have a multi-part phrase (polynomial). Technically, you can use it anytime, since if you have 2 x 5 = 10, you can also do (2)(5) = (2+0) (5+0) = 10+0+0+0 = 10. Or (2)(5) = (1+1)(3+2) = 3+2+3+2 = 10. But, that is a really roundabout way of doing things, and you usually would only use it if variables are involved, otherwise there are simpler ways to solve. But, yeah, technically you could use that method for any multiplication problem, at least as far as I can think of right now. Also, on an amusing note, I was just typing this up and realized I, at multiple points, accidentally typed "2x5=15." Whoops.
I think we need to get foreign languages in our kindergartens, if not our preschools, because that is really the most applicable time-oriented brain development area. Learning to speak is very time-oriented as well, so is learning to recognize faces (ever wonder why if you lived near white people your whole life, black people tend to look the same, or why someone who lived on a farm can tell which cow is which without effort, while you struggle to tell them apart?). But, I've never seen anything to say learning science, math, rules and regulations of grammar, or reading is time-oriented. That doesn't mean it's not, I just haven't seen anything to show so. So, yeah, especially in the early years we need a more well-rounded curriculum based, probably until somewhere between third and fifth grade, around language (especially non-native language) and art--in my opinion. But in high schools, a more science-based curriculum makes sense, I feel, despite how much I would love to see more arts in schools.
Also, the brain has a tendency to double-up in some cases. It is just like the stroke victims who could sing words but not speak them, because that capacity was in a different area of the brain, in a lot of cases an activity which uses a certain thought-process a lot (such as poetry with rigid numerical structure) will be able to continue without the area of the brain which normally does that function. I don't know if this is the case with the examples you gave, but from what I do know, I would say it's very likely to be the case. Another interesting example of this is motor-memory against other types of memory, where somebody who can't remember his wife's face could get out of bed in his home, go to the kitchen in the dark, make a cup of coffee, clean up, and go out to get the paper without actually being able to to tell you where he is, or how to get where he needs to be. Because the brain needs to call upon memory to perform motor tasks, it has a separate area for that specific kind of memory. I'd suspect that if the brain needed a specific kind of math for poetry, it would have a more effective way of doing this math than by firing up all cylinders and wasting a ton of relative time with computations in two very different parts of the brain, including a back-and-forth of information. For good reason, it doesn't like to do that much, especially when involving the outer layers of the brain.
The reason I've been, up to this point, so adamant about students doing their artistic learning on their own time if resources aren't available in schools is because the question was originally asked about high schools (or, rather, in interpreted it that way because of the talk about "English class"--not something which existed in my elementary experience because all my classes were one). More art in young children, less history and memorization of facts, way more foreign language--and I'd like to see our math and science at this stage to become more "understanding and puzzle" based than "memorization of rules" based. I'd like students to, instead of learning multiplication tables, learn the process of multiplying very well. Tables should come after a really solid understanding, rather than as a quick-cut to speed. Subjects which require a lot of memorization and little else should still be taught, but as the minority rather than the majority in young students. If you make them smart, they'll be able to memorize later. It's not like their memories aren't already getting enough work from life that they wont develop... But that's just me.