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## Cultural Responsiveness and Mathematical Practices

Off You Go is a PK–12 mathematical routine that leverages children’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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## Problems to Ponder

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–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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## 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

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## Developing Preservice Teachers’ Understanding of Area Through a Units Intervention

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

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## Bridging Modeling and Environmental Issues

The Great Pacific Garbage Patch activity involves an urgent environmental issue that students can discuss. It engages students in the interpretation of visual data, measurements, units, and the area of regular and irregular figures.

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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!

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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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## Cultural Connections: Exploring the Mathematics of Qatayef

Students grapple with the problem of finding the volume of two different folds of a traditional Levantine dessert using either geometry or calculus.