Neighborhood Boundary Project

I tried to use some Buck Institute Project-Based Learning materials and methods for a few days with Algebra Project Cohort students.  If you are not familiar with their free DIY guide, I recommend it.
http://www.bie.org/diy/

Fig. 1

This came after we spent a good deal of time with students on the idea that when "solving" a linear inequality in one variable, we were putting an equals sign in place of the inequality symbol in order to identify the boundary points (Fig 1). After finding the boundary points we were then able to find the solution set by testing left/right of the boundary point on the number line.

The Neighborhood Boundary Project was an attempt to extend the idea for two variables.

Hook

The original hook involved overlaying multiple definitions of our neighborhood (zip codes, city council districts, community member-made street line drawing) and asking who was right?

Who decides the neighborhood boundary lines?

Fig. 2 Neighborhood Boundary deck. See the .key for the actual animation

Fig. 3 Eagle Rock product

Purpose

The idea was to teach a geometric interpretation of linear inequalities as boundary lines with a shaded region above/below the boundary line in the y-direction or left/right of the boundary line in the x-direction.

Students had to define their own system of linear inequalities such that the overlapping solution areas would generate the community they were assigned to.

Fig. 4 Highland Park product

Learning Outcomes

Students did a good job of explaining why they chose particular inequality symbols to get the correct shading. However, not all students were able to produce the symbolic representations of the boundary lines, which is the major skill on standardized tests. Therefore, in future iterations it would be important to provide an opportunity for students to practice and repeat this skill in a way that does not detract from the engagement of the project.

Extensions

We did not put together a composite graph due to time constraints, even though the students were all using the same coordinate system.

I would have loved to have students argue about the boundary lines that were defining adjacent regions. We alluded to gerrymandering of district lines, and this could have made that idea more relevant.

There need to be other ways to get students reflecting on their abstract symbolic inequalities.

Grab the files and adapt as you please. Let me know how it goes.
https://app.box.com/s/km6sgf2h1oybrc4fp1hw