In the day’s math workshop, Mia Buljan and her 2nd-grade students return to a “put-together” mentor problem they had worked with in the beginning of the school year, called “Diva’s Stickers”: “Diva has _______ stickers. She then goes to the store and gets _________ more. How many stickers does Diva have now?”
In this problem, Mia introduces two 2-digit numbers to the problem structure: 67 and 83. Mia’s students use their “math bags” (bags of tools and manipulatives) to work with the numbers.
Some students immediately identify the tens within the problem; others struggle with making this connection, and I invite students to share their thinking with each other. During their investigations, I circulate around the classroom, working with students and their tools. I’m looking at a trajectory of learning using this 2-digit addition problem. First, I identify where students are in this trajectory, and then I try to use questioning, partnerships, and examples/non-examples to push them to the next place in their thinking.
The trajectory, in its simplest form in my mind, looks something like this:
Then, at each place on the trajectory, there’s the additional layer of how we are communicating our thinking:
I think it’s clear in the video pieces that I’m dealing with each student or set of students by identifying where they are on this trajectory or spectrum.