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## GPS: How Long? Estimating Length and Time

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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## Revisiting Reinhart for Uncertain Teaching Times

Process-oriented, question-asking techniques provide a framework for approaching modern challenges, including modality pivots and student agency.

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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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## Building Powerful Mathematical Thinkers with dINBs

The Teaching for Robust Understanding framework facilitates online collaborative problem solving with digital interactive notebooks that position all students as doers of mathematics.

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## Puddle Play!

For the Love of Mathematics

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## Student Engagement with the “Into Math Graph" Tool

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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## Pack a Truck: Decontextualizing and Contextualizing a Task

We describe how a group of eighth-grade students reasoned abstractly and quantitatively after the teacher fostered their engagement by using moves such as inviting students to draw and revoicing talk in a real-world context task.

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## The Nature of Mathematics: Let’s Talk about It

Teachers can offer opportunities for K–12 students to reflect on the nature of mathematics (NOM) as they learn.

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## Launching a Mathematical Modeling Lesson

Five teacher discussion strategies and outcomes of students’ responses to each are illustrated with examples.

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## Structuring Boardspace to Facilitate Repeated Reasoning

The planful use of boardspace can help move the structure and regularity to the visual realm and make it more readily perceivable by students.