I love finding rich problems to share with students and to get them working collaboratively with each other. Jo Boaler has inspirational math activities on her website that I like to use as they fit in with our curriculum. Last week, we learned the difference between linear and non-linear sequences. A linear sequences is a set of numbers that differ from the same amount each time; 2, 4, 6, 8, ... A non-linear sequence is a set of numbers that do not increase or decrease from term-to-term by a constant amount. The lesson from the book has students finding an expression that fits with a linear sequence of numbers. The Jo Boaler activity shows three patterns with different amounts of blocks in each pattern. To begin, students work on their own for 5ish minutes with the question, "How do you see the shapes growing?" Students used colored pencils, markers, etc. to color in blocks as they visualize how they see the pattern grow.
After several minutes of individual work (I also worked on it!), I asked for volunteers to share their ideas on the board. 6 out of 8 of my students (small class) shared their ideas on the board. One student commented on the fact that all the methods or ideas were different! One of my instructors in a math conference defined differentiation as (in my case) 8 different brains coming up or looking at a problem in 8 different ways. Love that! I have pictures of their methods below. They also named their strategies! The trickling method, the plant method, the rainbow method, the other trickling method, the birds wing method, the big brain method to name several.
After sharing their strategies for how the shapes are growing, I asked how they can find the number of blocks in the 10th case? I have a couple of short videos of some conversations as students began figuring out how to find the 10th case. I was so excited to see students jump in right away! I had large poster paper so students could stand, draw with markers and split them up into two groups of four. One student in particular was really enjoying and stated a love for these types of problems!
By the end of the class, both groups had used different methods to figure out the 10th case! A further goal was to find the 100th case and for students to build an expression. One group, while working to find the 10th case, realized the bottom row of blocks was a linear sequence while the entire case was non-linear! They found an expression to model the bottom row of the tenth case.
The next day, I had students begin class by finishing some problems in the textbook so they would be prepared for the homework that night. Two of my students were done very quickly so they moved over to keep working on the pattern problem of finding an expression to model the 100th case. As students finished, they gravitated over and I could see the excitement building. The shape question pulled their interest far more than working on problems out of the coursebook! I helped guide their thinking by pointing out what they had already found and asking them questions. I love growing in this area of creating more of an inquiry based classroom. I am not there yet but striving to head in that direction. They did figure out an expression for the 100th case by the end of class and were so proud of themselves! It was the process that was so much more meaningful than the solution! I was helping a student who was working through the coursebook problems then moved over to help the students working on the shape problem. Another student (so proud of this student!) stepped in to help the student I was helping a few minutes before!
My prayer for these students is that we will bond and be a collaborative math community! They will realize their potential; that they can persevere to solve rich problems. Please pray for me as well as I continue to find rich problems to fit in with our curriculum as we move forward.
In case anyone is interested, here is the link to the activity we did in class.
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