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## GPS: The Dog Leash Problem

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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## Five Core Routines for Teaching Mathematics Outside

Integrating mathematics and nature offers students benefits for physical and mental health and enriches their learning.

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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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## The Discovery of Wonderful Ideas

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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## Five Rs to Promote Equitable Norms and Culture

As mathematics teachers, we establish several norms, expectations, rules, and daily routines that result in culture building. Hence, in my classes, I decided to center the norms and culture building around five Rs: (1) rigor, (2) relevance, (3) responsiveness, (4) relationship, and (5) responsibility. Using these five Rs provided a norm to engage in our mathematical activities and reflections and established the expectation that everyone would contribute to mathematics teaching and learning (Boyce et al. 2021). Thus, this reflection describes how articles published this year (2021) in Mathematics Teacher: Learning and Teaching PK–12 (MTLT

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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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## 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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## Facilitating Student-Created Math Walks

An example of an after-school club activity gives educators some tools and suggestions to implement such an approach in their schools.

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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.