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## 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.

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## You Must Be Joking!

May 2020 For the Love of Mathematics Jokes

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## GPS: Working Backward with Data

This month's Growing Problem Solvers focuses on Data Analysis across all grades beginning with visual representations of categorical data and moving to measures of central tendency using a “working backwards” approach.

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## 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.

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## 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).

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## Using Scaffolding to Scale-up Justifications

Encouraging students to justify earlier as they attempt to solve an open-ended task can lead to greater understanding and engagement.

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## Patterns on a Calendar

### big solutions to little problems

Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored.

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## The Locker Problem: An Open and Shut Case

The Mathematics Teaching Practices open the door to helping students engage with meaningful mathematics.

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## Mediants Make (Number) Sense of Fraction Foibles

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

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## The Spot Problem Revisited

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