Three approaches to the Doughnut task highlight how representing functions in multiple ways can support student understanding in interpreting key features of functions within a context.

# Browse

### Justin Gregory Johns, Chris Harrow, and Peter Nikolai

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.

### Catherine A. Little, Sherryl Hauser, Jeffrey Corbishley, and Introduction by: Denise M. Walston

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

### Jerilynn Lepak and Taren Going

Teaching transparently about the process and goals can support students as they make and support mathematical claims.

### Sandra Vorensky

Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.

### Blake Peterson

Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.

### Justin Gregory Johns, Chris Harrow, and Kaitlyn Alexander

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.

### Xiaobo She and Timothy Harrington

Get familiar with this visual instructional tool to help students make sense of mathematical relationships and select suitable operations for word problems at varied grade levels.

### Kate Degner

Using question 28 from the May Problems to Ponder in volume 114, the author and her seventh- and eighth-grade students launched into a discussion of creativity, linearity, piecewise, and recursive definitions of functions. This pattern to ponder provided rich mathematical opportunities for all students in my middle school classroom.

### Caleb Goff

This article describes how using music and the TikTok platform can help students recall mathematical definitions in a whimsical and relatable way.