Ok, so I wasn't really the president of a chocolate factory. But pretending sure made for some fun in 3rd grade!
One lesson involves an investigation of multiplication arrays. The students have been working with arrays for about a week already, so they have a basic understanding of what an array is, and how arrays relate to multiplication.
I would define this lesson (really a series of lessons) as "problem-based" learning.
The problem was set up like this: I had a (pretend) meeting with the marketing team of my chocolate company. My (pretend) marketing team wanted to know how many different ways we could arrange boxes of 6, 12, and 24 chocolates. Mrs. Root, the co-teacher I work with, told the design team (aka: students) that I needed some help. So, my design team (errr... students) worked with grid paper to figure out different arrays for boxes of 6, 12, and 24 chocolates. Working in pairs, the students drew and cut out various arrays on grid paper. Then, they wrote me a memo describing the different options they found, and what their recommendations were.
They got back into their small groups, and chose a number (1-36) from a bowl. Then they used manipulatives to design different arrays with that number. Here is one student's work for the number 12: