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## For ELLs: Vocabulary beyond the Definitions

A classroom teacher discusses ambiguities in mathematics vocabulary and strategies for ELL students in building understanding.

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## Exploring Klein Bottles through Pottery: A Steam Investigation

Mathematics and art share perspective and prominence in this collaborative learning experience.

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## Blended Math

Photographs are a springboard for mathematical inquiry.

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## Activities for Students: Classifying Triangles and Quadrilaterals

The classification of shapes in middle and high school geometry often seems very mysterious to students, featuring strange terms such as isosceles, trapezoids, and kites, which are defined by a mixture of parallelism and metric ideas. The activities introduce a more natural way to classify triangles and quadrilaterals.

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## Conversations to Transform Geometry Class

Share practice and culture through three explicit discussions about the nature of mathematics.

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## Mathematical Lens: How Many Chips off the Old Block?

The sculpture entitled Four-Sided Pyramid by Sol LeWitt (1928-2007) is located in the National Gallery of Art Sculpture Garden on the National Mall in Washington, D.C. Installed in 1999, the sculpture takes on a different appearance depending on light conditions and the location of the sun. The square pyramid consists of rectangular blocks stacked twenty-four levels high. It comprises twenty-three vertical slices of blocks from the front to the back of the pyramid and forty-seven rows of blocks from one corner of the base to the opposite corner. The blocks are rectangular prisms of dimensions 1 × 1 × 2 units; thus, each block can be thought of as consisting of two cubes.

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## Addressing Misconceptions in Secondary Geometry Proof

Use these ideas to diagnose and address common conceptual obstacles that inhibit students' success.

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## Closed Circular Chains

Tangent circles, sequenced to form annular Steiner rings, are photographed in the windows of ancient buildings.

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## The Joy of Paper Folding

A paper-folding problem is easy to understand and model, yet its solution involves rich mathematical thinking in the areas of geometry and algebra.

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## From Blueprints to Labyrinths

Labyrinths inspire questions about measuring path lengths and representing patterns.