Each day, I start class with a math routine. Whether it is a Number Talk string, If I Know Then I Know, Closest Estimate or Quick Image, those first 10-15 minutes are always my favorite math conversations of the day! Today I added Fawn’s (@fawnnguyen) Visual Patterns into the mix. I spend a lot of class time having students look for patterns and regularity in their math work, but this visual brought a wonderfully different “feel” to their work. As Fawn had previously blogged, the Visual Patterns have an entry level for everyone and every student in my classroom engaged immediately with the images.
I chose this one to kick off our work today:
I asked the students to work as a group to find the number of unit for Steps 1 – 6, 13, 43, and then n. Being their first time, we had to deal with what the “n” meant and after the initial “Is this algebra?” followed by numerous stories of siblings who are doing this math with letters, they were on their way. It was interesting to see some students go straight to drawing each image, others started looking for what was changing as the steps progressed, and then there were the students who love going straight for an expression for finding 13 and 43. After they all had the table completed, we came together to fill it in. I was so impressed with their work and their ability to find the expression for the nth shape, however the BEST part of the conversation was taking that expression and connecting it back to the images. Why was n doubling? Why is that 1 being subtracted?
I love how this student used a specific example to connect his expression (or almost an expression, we’ll get there:)
These two students then put a different spin our our work. Every group in the room came to the expression n x 2 -1, and as one student was explaining how the 1 needed to be subtracted because it was being double counted, another student exclaimed that his group figured out that if you just split that block in half and made each said a mixed number you just had to multiply that by 2. For example on step 4, if you made each side 3 1/2 x 2, you would arrive at the same answer. How awesome!