Based on the recommendations of multiple people, I read 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.
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.
I have more of the files for this lesson located here.
Students jumped right in. Drawing the 4th and 5th patios ended up being incredibly helpful for my more concrete learners. It seems so trivial to me at times, I'm tempted to skip over such steps. In Algebra 1, especially at the beginning of the year, I remind myself to slow down and move from concrete to abstract. Bring in all the students and then start climbing up the ladder of abstraction together.
Students came up with several expected solutions to the patio problem:
Students came up with several expected solutions to the patio problem:
And two separate groups came up with a way I had not thought of:
These groups said, "When I look at the patio, I see three rows of tiles that are each two longer than the patio number with the center cut out. So, on patio 4, there are 3 rows of 6 tiles each and then I can subtract the 4 out of the center". Brilliant.
I did add an extra step of complexity during our class discussion of the cafeteria tiling problem. After figuring out how many colored squares there are in the 100th iteration of the pattern, I ask what it would cost to purchase all of the tiles included in the floor design (white and colored)? I hopped on Home Depot's site and found tiles I liked: light colored tiles are $3.19 per square foot and the darker colored tiles were $3.45. It gives a little twist to the problem that isn't trivial after we've already found the number of colored squares.
RSS Feed
