We started the year using Math Arguments 180, then I discovered Would You Rather, and finally recently the Which One Doesn't Belong? site came into being. This year they've been sequential, but now that I know about all three I'll mix them up better too add more variety next year.
When we do a Would You Rather type question I have the class vote first before we start discussing (after the three minute timer when they fill in the sentence frame - not just for ELL's!). When the number of tallies doesn't add up to the number of students in class, I scan the class and ask the kids who didn't vote what they choose (yea, there really were 6 kids present in class that day - this is harder to do with 30 but still possible). There's no opting out and sometimes kids don't vote for good reason - they're equal, they want to know more information (how long is the trip?) or they want to choose an alternative (I'd take the bus or get a ride from a friend). Frequently the reasons they choose have nothing to do with computations - If I take a taxi I won't have to worry about my car in that parking lot. And I value all those reasons. Then we do some calculations (either kids bring them up or I do). I still let the kids direct that conversation. Different classes calculate different things, but we always consider a few cases to figure out if the best choice depends on any factors.
When we do a Which One Doesn't Belong I ask kids to come up with as many reasons as they can in three minutes. Then I have kids share one at a time. They sometimes struggle with the belonging aspect of this prompt. They might say "9 is smaller than all the others" but that doesn't tell me what the other three have in common. We practice "attending to precision" and figure out exactly what makes 9 different - it is a single digit number. You may notice that we had a conversation on even and odd that was substantial enough to include notes. You recall this is a fundamentals of algebra class, right? Yea. But! What an awesome opportunity to uncover the misconceptions and gaps they have. Because if I want to teach place value, even, perfect squares, primes or any of those other concepts that they've "done" already I get eye rolls and complaints. But when kids ask the questions and the opportunity to reteach arises naturally, I get engagement. I think many high school teachers would feel that my class openers are a waste of time for 14 year olds, but I have to meet the kids where they are. And this is a much more fun way of doing that than skill practice sheets.