Keying off Disney's 1959 Donald Duck in math land movie, I'm thinking of stories we might be using to contextualize some traditional content.
Yes, I have some non-traditional content up my sleeve as well, but the same technique applies: provide lore, ala Disney, and you'll have a better experience learning (and teaching) the skills.
Lore: with polynomials up and going, thanks to the new Algebra coming from Baghdad through Pisa, a high culture on the Italian peninsula actually turned their factoring and solution (in terms of roots) into a sport. Patrons would sponsor tournaments, and those contestants with secret algorithms for finding solutions could actually win bets for their compatriots.
Lore: when Newton and Leibniz introduced the ideas of Calculus, there was some intense backlash from Bishop Berkeley, the same one for whom UC Berkeley is named. He decried use of infinitesimals as elements in proofs and excoriated Newton and Leibniz for doing so. The next 100 years or so of Calculus development might be characterized as a formalization aimed at plugging the holes Bishop Berkeley (and other skeptics) had been poking.
Lore: the European Renaissance had a lot to do with the rediscovery of Greek contributions to civilization, much of that knowledge kept in Arabic translations during the so-called "dark ages" interim. The introduction of abacus-based positional notation and the algorithms for bookkeeping into European cultures, made intelligent management of money more doable and a merchant class was able to thrive and patronize the arts and sciences. Much of our current mathematics got started in this period, which led to the development of perspective, the illusion of depth in a flat canvas. XY and XYZ coordinates come down to us from these days of radical pioneering.
I admit right off the bat that none of these three stories seems to directly answer the question "but why does that mean *I* should be learning this material?" Rather, each story embeds aspects of math's importance and the kinds of role it plays: in competitive fields where one seeks advantage; in formalizing new techniques in need of logical defense against skeptics; in empowering human beings to take more control of their own affairs and enjoy higher living standards as a consequence.
Moving closer to the present and maybe upping the controversy level as a result, here's another story for sharing:
Lore: the rectilinear XYZ-based practices developed as a result of the discovery of perspective techniques in the Renaissance Era, provided a strong bias in favor of 90-degree angles as "normal" and "orthodox". Perpendicularity became king. As microscopes and other instruments brought in more data about naturally occurring shapes and designs, a more 60-degree aesthetic began to emerge, as symbolized by the hexane ring of organic chemistry. XYZ math may these days be taught side-by-side with some contrasting alternative in some curriculum segments. We will be doing a chapter entitled Tetrahedral Kites for the next few meetings. You will find a syllabus at our web site.
This last bit is from a teacher training, not a direct to high school students class, although those are also available in some zip code areas.** There's a Tetrahedral Kites lesson plan, using non-traditional volumes (tetrahedron as unit, octahedron as 4x, same edge length) at the NCTM site, plus a lot of Alexander Graham Bell sites to consult. The story continues through the octet truss, with links to NASA, and ends in basic chemistry, where the CCP and FCC lattice amount to the same thing.
If you're an elementary school teacher and a member of a faculty motivated to include some of the above pre middle school, then you will be the one responsible for making the lore accessible to your students, in ways you know they'll appreciate. Collaborate with your peers. Find out what is already out there why not? "Being responsible" doesn't mean always having to work solo.
Ditto for middle school or high school versions: the teacher translates to her or his local community in a way she or he thinks will work best. This is not about dictating outcomes so much as planting seeds. Shape how the plants grow. Tend to your own garden. This is sometimes called a "place based" curriculum and is highly respectable in international circles (UNICEF etc) because it encourages keeping the material localized and therefore relevant.
Now you might ask what, pray tell, the above stories could possibly mean for some child in the hills of Borneo. Why learn about Italians, Greeks, Arab scholars? Well, you may not be up to date on how it's going in Borneo, but some of those hill kids have Internet already, thanks to micro-hydro power. Learning about the big world out there, ala National Geographic, is what's on everyone's plate these days. Developing a healthy respect for many cultures is a feature many teachers look for, when considering what curriculum to teach.
Remember: all mathematics is ethno-mathematics (comes from somewhere, has subcultural roots).
Disney's 1959 movie was G rated and suitable for showing in elementary schools, although some zip code areas might have been scandalized by the inclusion of jazz music, considered "of the devil" by some (I'm not the big ethno- musicologist in the room, so feel free to chime in, anyone more familiar with that lore -- math and music are conjoined at many levels, as Disney well knew).
Getting back to XYZ, one might expect some raised eyebrows regarding my tracing it as far back as the Italian Renaissance, as we call these Cartesian or perhaps Fermatian coordinates and these gentlemen lived quite a bit later in time. Please consider all of the above lore as highly abbreviated, fine to add all these details.
In my defense: you will find that painters were using a grid system much earlier, to map the visual field to a canvas. The roots of XYZ thinking trace to polyhedral geometry and to individual "solids" such as the cube. Crediting the Greeks is not that far-fetched (we also like to tell that story about how the discovery of irrational numbers was somewhat crazy-making to the original Pythogoreans -- Carl Sagan tells it well -- but that's for another day).
** in business, we speak of B2C vs. B2B. That's business to consumer and business to business. I think of teacher trainings as B2B. Imagine Intel a sponsor, and teachers getting paid to be there (on the clock, serving the public).
 Founders' Rock: On this outcropping located on the north side of the campus near the corner of Hearst Avenue and Gayley Road, 12 trustees of the College of California stood on April 16, 1860, to dedicate just-purchased property as a future campus for their college. In 1866, a group of College of California men stood at Founders' Rock, watching two ships out at sea through the Golden Gate. One of the men, Frederick Billings, was reminded of the lines of Bishop Berkeley, "Westward the course of empire takes its way." He suggested that the town and college site be named for the 18th-century Irish philosopher. On Charter Day, 1896, the senior class commemorated the dedication of the campus by placing a memorial tablet on Founders' Rock.