Over a year ago, I blogged about The 1–10 Card Investigation. I didn't provide a solution to the problem and no one who commented asked for one. But a newly posted comment requested the solution. That pushed me into a conversation with myself about how I should respond, and about giving answers in general.
The children's book 17 Kings and 42 Elephants by Margaret Mahy is one of my long-time favorites. In this post I describe a division lesson that I’ve taught to third graders but recently revisited with fourth- and fifth-grade classes. With the older students, we tried extensions that differentiated the experience and put students in charge of deciding on problems for themselves. It was exciting to me to expand a lesson I've taught many times into a multi-day investigation. 
Will Multiplication Bingo guarantee that students learn the multiplication facts? No. But it will help familiarize them with factors and multiples, engage them in a game that involves both luck and strategy, encourage them to make conjectures, and have them use data to guide decisions. Plus, the game provides a way to send home information to families about how their children are being asked to think and reason in math class.