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## How Much Will My Car Be Worth?

Show your students how useful mathematics can be in real-world applications.

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## Making Connections Between Representations

Three approaches to the Doughnut task highlight how representing functions in multiple ways can support student understanding in interpreting key features of functions within a context.

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## Exploring Sequences Related to Medial Triangles

Sequences are an important topic—not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns that can be discovered with the use of dynamic geometry software (DGS) such as GeoGebra or Web Sketchpad. In addition, exploring sequences with DGS allows learners to formulate and test conjectures, an important mathematical process. In this article, I describe how my students used GeoGebra and geometric reasoning to visualize, discover, formulate,

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## Sea of Cycles

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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## Area of a Changing Triangle: Piecing It Together

Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.

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## Trigonometry and the World Water Crisis

This full unit in trigonometry introduces the world water crisis. Students engage in real-world problem-solving activities that access 21st-century skills while learning mathematics.

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## Promoting Exploration through Synthesis

The author discusses “synthesizing" teaching practice, which encourages students to explore patterns and its underlying mathematics structure through technology.

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## Routines for Learning Modeling Practices and Content

The authors share a teacher-designed mathematical modeling routine geared to support teachers and to leverage opportunities for their students in learning important modeling practices and mathematical content.

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## From Notes to Strings

Four teachers and a teacher educator move from guided notes to strings in a series of problems that support students in increased engagement, reasoning, sense making, and problem solving.

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## Leveraging Student Identities to Develop Pedagogical Fluency

Mathematics education can be positioned as fertile ground for societal change. This article deconstructs the complex work of supporting students’ positive mathematical identities by introducing pedagogical fluency to embody equitable beliefs and practices.