# Browse

## You are looking at 1 - 10 of 63 items for :

• Reasoning/Sense Making/Proof
• Other Topic
• All content
Clear All
Restricted access

## Seeing Algebraic Structure: The Rubik's Cube

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

Restricted access

## You Must Be Joking!

May 2020 For the Love of Mathematics Jokes

Restricted access

## Triangle Center Technology

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

Restricted access

## How High Is the High?

When visitors enter the High Museum in Atlanta, one of the first pieces of art they encounter is Physic Garden, by Molly Hatch (details in photographs 1 and 2). Physic Garden consists of 456 handpainted dinner plates arranged to form a rectangle with 24 horizontal rows and 19 vertical columns and extends from the floor to the ceiling of the first floor. The design of the “plate painting” was inspired by two mid-18th-century English ceramic plates from the museum's collection (photograph 3).

Restricted access

## Mediants Make (Number) Sense of Fraction Foibles

Enhance students' number sense and illustrate some surprising properties of this alternative operation.

Restricted access

## The Spot Problem Revisited

Reinforce the difference between inductive and deductive reasoning using a small number of points around a circle.

Restricted access

## Mission Impossible: How Do We Know?

Proofs of impossibility—very important in the history of mathematics—can provide additional opportunities for the development of reasoning, as recommended by the Common Core State Standards.

Restricted access

## Six Principles for Quantitative Reasoning and Modeling

Modeling the motion of a speeding car or the growth of a Jactus plant, teachers can use six practical tips to help students develop quantitative reasoning.

Restricted access

## Triangles from Three Points

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

Restricted access

## Technology-Enhanced Discovery

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.