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## Advancing Agency Through Conjecturing

Support students in conjecturing in ways that can promote their agency in the learning process.

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## Making Sense of Algebraic Expressions in Context

Explore three challenges that students faced and how they made progress.

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## Balloons and Weights: Integer Subtraction in Context

Support students in developing contextual reasoning about integer subtraction.

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## Math, Will You Be My Valentine?

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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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## Puddle Play!

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## Examining Errors and Framing Feedback

Engaging mathematics students with peers in analyzing errors and formulating feedback improves disposition, increases understanding, and helps students uncover and correct misconceptions while informing opportunities for targeted instruction.

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## Promoting Discourse: Fractions on Number Lines

Examine fourth graders’ thinking about the unit, partitioning, order, and equivalence on the number line and consider ways to orchestrate mathematical discussions through the Five Practices.

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## The Opportunities of No-Solution Problems

When students encounter unusual situations or exceptions to rules, they can become frustrated and can question their understanding of particular topics. In this article, I share some practical tips.

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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.