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.

# Browse

### Joshua David Jones

To be literate in a society where the information shared online is often exploited, learners should be exposed to multiple aspects of contemporary predictive modeling. Explore a lesson in which students learned an algorithm used in practice to automate the process of making recommendations.

### F. Paul Wonsavage

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.

### 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.

### 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.

### Rebekah Elliott, Megan Brunner, Elyssa Stoddard, and Jenny White

The authors share a teacher-designed mathematical modeling routine geared to support teachers and to leverage opportunities for their students in learning important modeling practices and mathematical content.

### Johnnie Wilson

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.