*5 Practices for Orchestrating Productive Mathematics Duscussions*. The title isn't all that creative, but it does speak for itself. In 13 years of teaching and a masters in math education, I don't think I've read anything nearly this helpful. Anyway, they parse apart a tiling task in one of the chapters that I thought worked brilliantly. It starts out concrete and moves towards abstraction with baby steps.

In Algebra 1, we've spent our last week looking at how to create rules and equations from patterns we see in numbers. Being a thoughtful caring teacher, I decided to let someone else do the pre-planning work for me--I used one of the lessons from the book. I decided to spend two days on the concept--modeling is a big deal later on in my class; it's worth losing a day to deepen the foundation. But that meant I needed another task dealing with the same ideas without being the same thing over again. Enter Dan Meyer's work on makeover Mondays this past summer. He remade a checker boarder tiling problem with many of the same problem-solving skills in the 5 Practices task. I spliced the two together in the following handout for students.

Students came up with several expected solutions to the patio problem: