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.

2nd grade math - addition & subtraction word problems with unknowns*Mia Buljan, Glassbrook Elementary School, Hayward Unified School District, Hayward, California*

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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:

- builds in tens in ones…
- combines by putting tens with tens and ones with ones (big idea: we add and subtract only things that are alike) …
- recognizes that sometimes we have so many ones that we can make another ten, and/or we have so many tens we can make a hundred.

Then, at each place on the trajectory, there’s the additional layer of how we are communicating our thinking:

- “What can a recording look like for my idea?
- “What can I do to revise my recording to make my thinking more usable by somebody else?
- “What models will make my thinking more visible to others?”

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.