AOD is another site that I love. These usually take the entire period to get through so they may not be just a warm-up. I could certainly see starting the activity at the beginning of a unit and then asking students to draw a conclusion. When they indicate that they don't know how to justify their position, it creates a need for the unit that you are starting. Then you can come back to this activity again at the end of the unit and do the math to support or dispute their original claim.
Tim McCaffrey, the creator of this site has asked engaging questions that require 3-acts to reach their conclusion. The 3-acts typically involve posing a problem, giving more information, and finding a solution. Other tweeps have their own 3-act databases that are awesome too. I'll write about those in a later post. For now, enjoy these. This is a good place to get started with 3-act math because it is not too overwhelming.