I love when I read a blog post in which I can relate to how the teacher felt, learn from both the teacher and student thinking, want to hear what happens next, and leave with questions circling around in my head. This happened when I read Marilyn’s recent post. I really appreciated how her recount of the lesson demonstrated the importance of number choice and the honest way we all have felt when we made a decision during a lesson that we wished we hadn’t. It was really interesting to think about how changing the divisor from 4 to 5 changed what students experienced. I cannot wait to hear what they do when they try the original problem and see the remainder as 1 in the balloon context, 25¢ in the money context, 1/4 in the cookie context and .25 on the calculator. Awesome discussions could happen there!
I left this post still thinking about the math talk at the launch of the lesson. I was going to tweet about it, but because it seemed long and I have many questions of my own I want to play around with and revisit, I decided to put it here. I loved the connectedness of the number talk to the division task, and wondered how the recording of those strings could impact division patterns and structure students may see in future lessons. I started playing around with it in my journal in terms of how we think about recording a choral count.
I thought about:
- How many problems in each row?
- Does horizontal vs vertical recording impact what we see?
- What might students notice about the remainders in each row? column?
- What might students notice about the change in dividends in each row? column?
Not that I would launch the 4 Problems task with this following string, but I wondered what it would look like to change the divisor and what students might see here:
I think the number of problems with remainders at the bottom of the list versus the top is really interesting.
THEN, I started wondering about ways we could record the remainder and how that may impact how students interpret it? Not sure how this would work in terms of launch and facilitation, but I like thinking about the pink writing here.
Recording is one of those things I get so intrigued by and cannot wait to revisit this post, play around with patterns that could be elicited in different ways and think about tasks in which these talks could be connected.
Thank you, as always, Marilyn for sharing your work – you continue to be such an inspiration! My only hope is one day I can be in the room for one of your lessons!