Numberless Math Word Problems
It sounds like a contradiction in words, but in fact it's a great way to get student to think about math in new ways. The basic idea is that you give students a math scenario in which none of the quantitative aspects have been defined. Then the students have the liberty to either add numbers to define those aspects, or to work entirely conceptually to create solutions.
Things this process does:
1. Allows students to think about math conceptually. This is very important for the long term development of skills in algebra and calculus. While there is no arguing that formulas and proofs are a big part of these types of math, the need for conceptualization skills in problem manipulation is pervasive.
2. Reduced math anxiety by removing the aspect that most people fear, the numbers. Math anxiety so often comes from the fear of not being able to get the right answer. When there is simply no one right answer, just a right approach, then students can focus more on the process.
3. Allows for natural differentiation. Students will naturally work at their own skill level. By removing the numbers, you can remove the innate academic level associated with them. Doing so will allow students to work through the problem at their actual skill level. If students want to create large complex problems to show their exceptional math skills, they can. If students are new to some math concepts, you'll be able to see that in how they approach their solutions.
In addition to the practical aspects, these types of problems can be fun. In this case it was about pirates and treasure, which in itself can be more interesting than traditional numeric math problems.