The construction requested is unclear: does "equal to" mean both the "same length and parallel to" ? If it doesn't, most of the construction is unnecessary--drawing a line from A in any direction and measuring it with a compass to be the same length as BC suffices. 2-3 steps, max.
If it needs to be parallel to BC, we know how to construct a line parallel to another using the opposite internal angles theorem. And then measure with BC.
I must be missing something here.
As far as naming things goes, I got lost with rings and fields, etc. in linear algebra. Never quite understood why anyone bothered to name things like that.
Agree about trapezoids. When I use the notion, it's always in the context of "midline of a trapezoid", but this could just as well be restated as "midline between two parallel segments", and I'm not sure if this even belongs into regular K-12. And strategic questions about definitions can be illustrated on many other questions (non-primeness of 1, empty sums and products, gcd(0, 0), integral from a larger to a smaller number, maps to/from the empty set, binomial coefficients with negative parts, ...).
I use "subtrahend" every once in a while: e.g., saying that two differences have the same subtrahend, and such things. When the subtrahends are themselves complicated expressions, this beats just writing them out. Not exactly a vital concept, though. But I guess it is good to say the same thing in several different ways when teaching maths, and one instance of this is to rewrite formulas in words whenever reasonable (no, I'm not asking for (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 to be rewritten in words).
Multiplicands are just known as factors, or is there some subtle distinction?
I like this idea quite a lot. It would be good to move away from teaching about formulas no one cares about to teaching things that are useful, and even better, why they are useful. You are correct; I have never needed to find the area of a trapezoid. But even if I did need to calculate the area of such a shape(even though no one in regular life ever has) the right method is to derive the formula or look it up, not memorize it. Part of education is learning the difference between things you should memorize, things you can figure out yourself, and things you can(and should) look up when necessary.
The construction requested is unclear: does "equal to" mean both the "same length and parallel to" ? If it doesn't, most of the construction is unnecessary--drawing a line from A in any direction and measuring it with a compass to be the same length as BC suffices. 2-3 steps, max.
If it needs to be parallel to BC, we know how to construct a line parallel to another using the opposite internal angles theorem. And then measure with BC.
I must be missing something here.
As far as naming things goes, I got lost with rings and fields, etc. in linear algebra. Never quite understood why anyone bothered to name things like that.
Agree about trapezoids. When I use the notion, it's always in the context of "midline of a trapezoid", but this could just as well be restated as "midline between two parallel segments", and I'm not sure if this even belongs into regular K-12. And strategic questions about definitions can be illustrated on many other questions (non-primeness of 1, empty sums and products, gcd(0, 0), integral from a larger to a smaller number, maps to/from the empty set, binomial coefficients with negative parts, ...).
I use "subtrahend" every once in a while: e.g., saying that two differences have the same subtrahend, and such things. When the subtrahends are themselves complicated expressions, this beats just writing them out. Not exactly a vital concept, though. But I guess it is good to say the same thing in several different ways when teaching maths, and one instance of this is to rewrite formulas in words whenever reasonable (no, I'm not asking for (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 to be rewritten in words).
Multiplicands are just known as factors, or is there some subtle distinction?
I like this idea quite a lot. It would be good to move away from teaching about formulas no one cares about to teaching things that are useful, and even better, why they are useful. You are correct; I have never needed to find the area of a trapezoid. But even if I did need to calculate the area of such a shape(even though no one in regular life ever has) the right method is to derive the formula or look it up, not memorize it. Part of education is learning the difference between things you should memorize, things you can figure out yourself, and things you can(and should) look up when necessary.