For example, my biology students always get choices of assignments for each topic. I usually include a poster option to help engage those with an artistic bent. Sometimes they will choose to paint a ceiling tile instead so that their work will make a permanent contribution to the classroom.
But these take a while, and if I'm not careful in planning, they're not always the most rigorous assignment. Making a poster or ceiling tile of mitosis is not particularly high in terms of Webb's Depth of Knowledge--it doesn't require the students to really understand deeply what they are describing.
It's funny, a student was looking up old Monte Carlos yesterday while he was supposed to be doing his assignment, and I said--"Hey, you could make a Monte Carlo mitosis poster--Monte Carlos getting duplicated and sorted out, like at a factory." Something like that would probably bring us up to DOK level 3. (Not sure how I could get to level 4 with mitosis--maybe studying cancer and that's what we're doing next.)
But I still just love to see them engaged. I see that as the biggest step. And the problem of not-high-enough-DOK is solvable. And asking them questions about their paintings is a great way way to assess, and teach. And not every activity needs to be high Depth of Knowledge. Maybe sometimes high Depth of Engagement can make up for it.
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