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## GPS: Triangle Explorations and Constructions Using Robots

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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## 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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## Teaching Angle as Turn Using a Code.org Lesson

Elementary school students use physical manipulatives (e.g., pattern blocks) to make sense of the geometry and measurement ideas in a Code.org block-based programming lesson.

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## Point-Line Ellipses and Hyperbolas

The author alters the definitions of ellipses and hyperbolas by using a line and a point not on the line as the foci, instead of two points. He develops the resulting prototypical diagrams from both synthetic and analytic perspectives, as well as making use of technology.

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## NCTM’s Activity Gems for the Classroom

Ear to the Ground features voices from several corners of the mathematics education world.

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## Delving Deeper: What Else Comes after 1 + 2 = 3?

The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.

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## Teaching Is a Journey: From Apathy to Passion

This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

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## Using Number Talks to Compare Fractions

Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.

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## Cultural Responsiveness and Mathematical Practices

Off You Go is a PK–12 mathematical routine that leverages children’s home resources and assets to support them in developing conceptual precision. We provide a guide for how to adapt this routine to engage students at any grade in argumentation and attending to precision.

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## Developing Skills with Visual Representations

This article describes how visual representations can help develop students’ reasoning and proof skills.