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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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## Teaching Is a Journey: Fostering Student Thinking

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

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## Exploring Relative Size with Relative Risk

The Relative Risk Tool web app allows students to compare risks relating to COVID-19 with other more familiar risks, to make multiplicative comparisons, and to interpret them.

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## Math Chat Opportunities Abound!

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

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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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## 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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## Practicing Culturally Responsive Mathematics Teaching

As I walk down the hallway in East G Elementary School (pseudonyms have been used throughout), a largely African American school with a high population of students living in poverty, I hear chanting coming from Ms. Jacobs’s fifth-grade classroom. Student voices penetrate the usual silence in the school’s passageways as I get closer to the doorway. When I enter the classroom, I see students sitting at large tables in groups of four or five working with whiteboards and reading from “math journals.” A mixed number is up on the board—5 3/4—and students are working to change this mixed number

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## Conditional Reasoning Online with Mastermind

As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.