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## Mathematical Connections: Many Faces of the Truncated Icosahedron

Examine this geometric figure in light of a set of connections among fields such as architecture, geometry, science, sports, technology, and associated uses, models, and discoveries.

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## Centering Families’ Mathematical Practices in a Multilingual Space

Rethink family mathematics nights by drawing on an asset-based perspective in a virtual environment, centering multilingualism and community mathematics knowledge.

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## The Mathematical Wonders of 3D Printing

We share how engaging in the mathematical process of 3D printing captured and elevated our interest in discovering the wonder, joy, and beauty of mathematics in the world around us.

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## GPS: The Dog Leash Problem

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

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## Challenging but Achievable Math for Young Children

Learning trajectories help teachers challenge children at just the right level for their best learning.

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## Math Chat Opportunities Abound!

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

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## Exploring Sequences Related to Medial Triangles

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## The Discovery of Wonderful Ideas

This article presents an example of discovering an idea through creative play. After some trial and error, I drew a wonderful image, which I later learned was a two-dimensional view of a four-dimensional shape called tesseract.

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## Problems to Ponder

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

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## Developing Property-Based Geometric Reasoning

Recognizing the complex nature of students’ geometric reasoning, we present guidelines and suggestions for implementing a Guess My Shape minilesson that focuses students’ attention on properties and attributes of geometric shapes.