On Tuesday night, I blogged about a math activity that we did in class. Kelly McCrory, our fantastic math facilitator, responded to my blog post with this question:
Her comment got me thinking, and so on Wednesday morning, I created this new math problem that we did in class today:
This math problem addressed Kelly’s question, and I was very interested to see what the children did and if they could figure it out.
Students worked in partners with a bag of shapes (more than what they needed) and the math question. Just like with our previous problem, they could show their thinking on a white board, on the Livescribe Pens, or on various screencasting iPad apps.
When I started walking around talking to the groups of children, I noticed what I would have expected to see. Most of the students looked at the hexagon and the trapezoids, and figured out how to put two trapezoids together to make a hexagon. The majority of groups had more difficulty with the rhombuses. Some groups put the rhombuses down beside the hexagon and tried to move them around to create a hexagon. Other groups tried sticking the rhombuses underneath the hexagon until they made a hexagon shape of their own. Still other groups figured out to put the rhombuses on top of the hexagon.
There was one group that finished quicker than the other ones. I went to talk to this partner group, and I asked them, can you mix the rhombuses and the trapezoids to make a hexagon? How do you know? I walked away, and let them play. A few minutes later it was time to tidy up and discuss our findings, and that’s when this partner group came running up to me so excited: “Look, Miss Dunsiger! Look what we did!”
I was amazed! I created this problem, and I was sure that I knew the solutions, but this group did something that I didn’t expect. This group did something that I’m not even sure I could recreate. Wow! This is when “incredible” happens …
All of a sudden, our “reflect and connect” conversation changed. Now we looked at what this group created, and we discussed if this hexagon could replace the one in our picture and why. Below is a pencast of our conversation:
Now I know that I led the students to come to this conclusion. What could I have done differently, but still ended with the same result? The thinking that the children share is great, and I’m glad that they explain why they changed their mind, but I wish that I didn’t sound so “leading.” I’d love to hear some suggestions about changes that I could make!
While I know that I wasn’t perfect here, seeing a student push my thinking gave me an even better appreciation for the math problem solving process. I was genuinely thrilled when I saw this photograph, and I hope that I’ll continue to have more amazing problem solving moments like I had today. When have students surprised you by their answers? I’d love to hear your stories too!