The math department at my school is working to implement instructional routines in our classes for several reasons. The first reason is to increasingly apply the standards for mathematical practice on a daily basis. The second reason is to improve our communication as a department by creating common language centered around shared routines and activities.
One of the instructional routines we plan to implement is Contemplate then Calculate (#CthenC on twitter). Created by Amy Lucenta and Grace Kelemanik at the Boston Teacher Residency, #CthenC is a highly structured routine that simultaneously allows for open mathematical thinking and problem solving. Contemplate then Calculate highlights looking for and making use of mathematical structure in problem solving.
In an effort to assist the implementation of Contemplate then Calculate at our school, I created this activity to do with my class as a model for implementation and discussion.
Here is the task:
How many dots?
It can be based on these content standards:
Expected student strategies are:
- Making tens
- Adding doubles
- Possibly skip counting
David Wees, who has done amazing work with Contemplate the Calculate, noted that teacher annotation of student strategies is very important during the routine. Amy Lucenta also advised to anticipate the ideal meta-reflection students would have at the end. This way you can refine the reflection prompts to better target those ideal takeaways.
So here are my questions:
- How would you annotate these strategies so the structure was clear to all the students in the classroom?
- Here is a google drive folder with copies of the task you can annotate.
- What meta-reflection would you see as ideal after completing this task?
andrewgael.com 