Can you remember your typical elementary school field day? In this article, we provide details on hosting a mathematics field day, focused on embedding rich mathematics into authentic fun-filled field day experiences.

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### Elaine M. Purvinis and Joshua B. Fagan

In first- and second-year algebra classrooms, the all-too-familiar whine of “when are we ever going to use this in real life?” challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect to time, and typical lessons include uninspiring textbook practice problems that portray dropping or shooting objects from given distances or at particular time intervals. For a novel approach to exploring quadratics, we chose to step outside the classroom to look at some phenomena in the field of acoustics. Our activity incorporates mathematical modeling to provide a multirepresentational view of the math behind the physics and to provide a conceptual basis for analyzing and understanding a real-world quadratic situation.

### Edited by Anna F. DeJarnette and Stephen Phelps

A monthly set of problems is aimed at a variety of ability levels.

### Jennifer M. Mayer, Mary Ann Huntley, Nicole L. Fonger, and Maria S. Terrell

In a recent Mathematics Teacher article, Fonger and her colleagues explain why teachers should engage in research studies: Researchers working alone lack the information needed to effectively address problems of practice that matter most-problems that are highly contextual and based on teachers' day-to-day experience. (2017, p. 462)

### Michelle L. Meadows and Joanna C. Caniglia

Imagine that you and your language arts colleagues are teaching Edgar Allan Poe's short story, “The Pit and the Pendulum.” This thrilling story takes us to the Inquisition during which a prisoner is surrounded by hungry rats and bound to a table while a large pendulum slowly descends. The prisoner believes that the pendulum is 30-40 feet long and estimates that it should take about 10-12 swings before he is hit, leaving him with about a minute or a minute and a half to escape. Are his estimations correct? If so, will he make it out in time?

### Terri L. Kurz, Mi Yeon Lee, Sarah Leming, and Wendy Landis

Algebraic reasoning is often promoted through an analysis of and generalizations about patterns that appear in mathematics, in nature, or in everyday situations (Driscoll 1999; Kieran 2006; Lee 1996). In accordance with this tendency, the Common Core (CCSSI 2010) emphasizes finding patterns and expressing such regularity in repeated reasoning as an important mathematical practice. NCTM (2000) also recommends that students participate in patterning activities by asking them to describe numeric and geometric patterns; generalize patterns to predict what comes next while providing a rationale for their predictions; and represent patterns in multiple ways, including drawings, tables, symbols, and graphs.

### Christina M. Krause

This Brief Report addresses the fundamental role that sign language plays in the mathematics classroom of deaf and hard-of-hearing (DHH) students. Selected findings are gathered from an ongoing study of signs and gestures used by DHH students and their teachers when encountering and communicating mathematical ideas at a German special-needs school that focuses on hearing and communication. The focus rests primarily on iconic aspects of mathematical ideas as reflected in the gestural–somatic modality of sign language. A categorization of iconicity in mathematical signs as used by the students is presented and used to reconstruct a case of meaning making in a Grade 5 geometry classroom. Insights gained from these observations lead beyond the DHH mathematics classroom by providing new perspectives on the interplay between language and communication, individual experience, and shared conceptualization.

### Cassandra R. Seiboldt, Lorraine M. Males, and Joshua R. Males

A university mathematics teacher educator and a math department chair reflect on how various assignments and structures can support early-career teachers in anticipating student thinking and solutions to purposefully plan lessons.

### Craig Russell

Use trigonometry to improve your students' global literacy.

### Haiwen Chu and Leslie Hamburger

Five types of engaging peer-interaction structures can support English learners as they make sense of mathematics and explore important mathematical relationships.