What makes a rich task? It needs to be accessible to many students (have a low floor) yet offer enough extension to challenge advanced learners (have a high ceiling). Often, the task will have some sort of context or application. The task should be open enough that students could solve the problem in several ways and may even be able to come up with follow-up questions. The task may be solvable in an eloquent stream lined way and may be solved in unusual and creative ways. The task should encourage collaboration. It might result in a discovery of a new concept and it should certainly be a positive experience for students.
One of my favorite resources for rich tasks is the Mathematics Assessment Project. I wrote about it here about a year ago.
Another source that I like, but have not used quite as extensively as MAP is Illustrative Mathematics. They offer course blueprints aligned with the national Common Core standards. Here is the blueprint for algebra 2. My state does not use CC, but our standards are pretty close, so I still find the site useful. I love that each unit includes tons of rich tasks to choose from.
Yummy Math is a great site. I had a membership last year and need to renew. At less than $20, it is well worth it, especially if you are teaching a class with some flexibility in content. I used it a lot last year in a remedial class where I wanted students to see that math could be fun. Even with out a membership, you can access the lessons. The membership allows you to download editable documents, teaching resources in Excel, and answer keys.
Mathalicious is another favorite resource. They have a few free lessons. I wrote a grant application to obtain a subscription to the site. They lessons are interesting for students and also organized by course scope and sequence.
Other than MAP and Illustrative Mathematics, I'd love to hear about more free resources. If you have something you love, please share!