Antoinette Villarin asks her student pairs to share their discussions with the whole group. She models academic language — constraints, rate of change, initial value, starting situation — that she expects her students to use.

Once a student pair has shared, Antoinette asks the larger group to add on additional details that helped them identify a matched pair of graphs that show the flow of liquid between a given pair of containers.

Antoinette refers back to her anchor chart of the lesson vocabulary and sentence frames that she expects the students to use, and she names and reinforces students’ use of academic language.

8th Grade Math - Representing Constant Rate of Change*Antoinette Villarin, Westborough Middle School, South San Francisco Unified School District, South San Francisco, California*

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- Lesson: Comparing Lines and Linear Equations by the Mathematics Assessment Project Web Link
- Handout: Recording Sheet and Gallery Walk Guide Word Document
- Student Work: The Race PDF
- Student Work: Graphs PDF
- Student Work: Matching Poster PDF
- Student Work: Recording Sheet and Gallery Walk Guide PDF
- Student Work: Exit Ticket PDF

Transcript coming soon

My students learn a lot through stories. When you connect it to the concrete, they retain more and understand it from an applied level: For example, in 8th grade, when you're looking at a graph, asking students what story could it be describing gives it context. I like to teach in context whenever I can. It can be hard to do. It's a lot of research and finding resources. I was a pure math teacher and I always joke with other teachers that I know the pure math, but sometimes I have to research where it gets applied.

With graphs, it's such a perfect place to be connecting it to a story: what could be happening when you're looking at the rate of change increasing, when it's constant, or when it's decreasing?

It's just a very symbolic way to look at a situation in the real world that middle school kids are learning about. I think the more you do that, I think the more connections are made in student learning. I think they can easily connect it to something that they've seen before, whether it's a soda bottle or water flowing out. They can hopefully transfer those connections to other things when they see other graphs in the future, which is also good.