This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices found in "Principles to Actions: Ensuring Mathematical Success for All." These processes, explored during a classroom activity on proportional relationships, are discussed in this article, another…

This article describes a project in which students investigate the question: What dihedral angles between pairs of mirrors in a kaleidoscope result in perfectly symmetric images? The unit culminates with students building their own kaleidoscopes. This content aligns with parts of the Common Core's standards for fifth grade (classify…

Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

Open-ended mathematical tasks provide great opportunities for students to engage in authentic mathematical practices, such as conjecturing, generalizing, and justifying. Supporting students in open-ended tasks can be challenging. Appropriate scaffolding of a task has been linked to more opportunities for student learning and better student…

Geometric transformations have long been topics of middle school mathematics. Generations of middle school students have learned to reflect, rotate, and translate geometric objects. Historically, though, the mathematics of "movement" might have been considered a departure from other more central middle-grades geometric content areas,…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

Describes an activity in which students develop a conceptual understanding of the formulas of the circumference and area of a circle by exploring pi. (YDS)

Presents an activity in which students investigate geometric probability at a school fair. (YDS)

Uses the Paper Balloon origami form to help students discover the relationship between ratios of corresponding distance, area, and volume measures in similar solids. (YDS)

Presents an activity in which students explore properties of quadrilaterals using geoboards. (YDS)

Describes the processes used by middle school students to expand their thinking about the formula for the area of a parallelogram by observing patterns in the operation of a flexible parallelogram. (YDS)

Presents student solutions to a problem using different strategies that focus on kitchen geometry. (YDS)

Presents a measurement problem that can be explored by students of varying ability. Discusses aspects that make it accessible in a heterogeneous class. (YDS)

Explains the basics of spherical geometry and describes a series of activities developed for grade 6 middle school students. (YDS)

Shows how students explored geometric properties of the South Korean flag using proportional reasoning. (YDS)