When I wrote my DIS, in the year 2014, "Royals" was still a massive radio hit and every single one of my middle school kids knew it. I played them the FSU AcaBelles' arrangement of the song. They ate it up.
Of course, middle school is probably not the place to be discussing Mixolydian mode (unless you have that kind of program), but I bet if you played the song for your AP Theory class, upon hearing it your kids will say, "Oh, throwback!" And then you can say, "Oh, it's in Mixolydian mode!" And they'll stop talking based on the deep realization that something you've taught them is actually pertinent to the popular culture they regularly consume. Gasp!
UPDATE: Having now completed my Orff Level 1 training, I can confidently say that modes are discussed in elementary school music. There's no reason to not bring up this song in secondary ensemble class. (Insert painted nails emoticon here.)
"Royals" - Lorde
Intro: The youngest artist to appear on the Billboard charts since Tiffany in 1987, New Zealander singer-songwriter Lorde made a smash in 2013 with her debut album Pure Heroine. The album topped charts in New Zealand and Austrailia, and topped the Alternative Albums chart in the US. Essentially an alternative artist who crossed over to become a pop phenomenon, Lorde was the first female to hit #1 on the Billboard Alternative chart since 1996. She did so with the single “Royals”, which soon crossed over to the Hot 100 Chart, where it remained #1 for 9 weeks. “Royals” went on to win two Grammys for Best Pop Solo Performance and Song of the Year in 2014.
Analysis: Despite being published with a key signature of G major, "Royals" wastes no time establishing D as the tonic of the song (as it is the first chord). The song continues in the D mixolydian mode throughout, also avoiding traditional cadences while sounding close enough to Ionian as to be logical to a listener's ear. The chords that make up the song are D-C(add9)-G. If the song were in Ionian mode, a C chord would be non-diatonic, but in mixolydian mode, otherwise known as a G scale starting on the pitch of D, a C chord, with or without the added 9th would be diatonic to that particular mode.
Considerations for Teaching: While this song has seen extreme popularity within the past three years and most students know it well, the song's lyrics do make passing reference to drugs and alcohol ("Grey Goose / trippin' in the bathroom"), thus causing teachers to proceed using this as a listening example with caution.
More information on early church music and modes can be found here.
Very lightly edited for content on July 19th, 2018.