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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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## 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 studentsâ€™ reasoning when comparing fractions.

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## Cultural Responsiveness and Mathematical Practices

Off You Go is a PKâ€“12 mathematical routine that leverages childrenâ€™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 studentsâ€™ reasoning and proof skills.

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## Exploring Sequences Related to Medial Triangles

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## Math, Will You Be My Valentine?

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## Problems to Ponder

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PKâ€“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 studentsâ€™ geometric reasoning, we present guidelines and suggestions for implementing a Guess My Shape minilesson that focuses studentsâ€™ attention on properties and attributes of geometric shapes.

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## Non-Euclidean Geometry Lesson Promotes Mathematical Reasoning

A two-day lesson on taxicab geometry introduces high school students to a unit on proof.

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## GPS: Perceiving Variability in Graphs

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