Graphing Quilt Blocks in Middle School Math

Following the Compound Inequality Survey Project, in which Algebra B students collected data from peers and translated it into mathematical comparisons, students moved into two-variable inequalities on a coordinate plane with the Quilt Block Project, combining algebraic reasoning with visual design.

The Quilt Block Project challenges students to graph systems of inequalities and use those graphs to create original visual “quilt” designs. The project marks a transition in the course: from describing data with numbers and symbols to using algebra as a creative tool for construction and composition. 

The shift is both mathematical and developmental. As math teacher Kristen Amouri explains, “Instead of a single comparison, students are now looking at the entire region of the plane where their inequality is true.” Those shaded regions become the building blocks of art. 

For example, a line like y = 3x + 2 becomes a boundary; y < 3x + 2 defines the space below it; shared regions of overlapping inequalities form a solution set, creating new shapes and colors.

Students used the Desmos graphing calculator to build their quilt blocks, layering inequalities, adjusting equations, and refining shaded regions. Throughout the process, students began to ask more precise questions: how to limit a graph to a specific section, how to “cut off” part of a shape, or how to isolate a particular overlap. These questions naturally lead to new mathematical concepts and tools that students can use to implement their ideas, including domain and range, systems of inequalities, and solution sets.

The project emphasizes iteration and persistence. Students test multiple equations, make incremental adjustments, and revise their work repeatedly to achieve the desired effect. The structure allows for a wide range of outcomes. Some students create simple geometric designs, while others experiment with complex layering or animation. “Students can be successful at many different levels, and they tend to push themselves once they see what’s possible,” says Kristen.

The Quilt Block Project reflects Field’s broader approach to teaching and learning: students are given choice within clear structures, asked to apply skills in new contexts, and encouraged to take intellectual risks. By moving from surveying peers to constructing original designs, students experience algebra as a flexible language they can use to explore, build, and communicate ideas.