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

### Dorothy Y. White

Use this activity to support students in working together, recognizing one another’s contributions, and leveraging their mathematical strengths to solve challenging problems.

### Allyson Hallman-Thrasher, Susanne Strachota, and Jennifer Thompson

Teachers can use a pattern task to promote and foster generalizing in the mathematics classroom, presenting opportunities to build on students’ thinking and extending ideas to new contexts.

### Michael S. Meagher, Michael Todd Edwards, and S. Asli Özgün-Koca

Using technology to explore a rich task, students must reconcile discrepancies between graphical and analytic solutions. Technological reasons for the discrepancies are discussed.

### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

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.

### William DeLeeuw, Samuel Otten, and Ruveyda Karaman Dundar

The planful use of boardspace can help move the structure and regularity to the visual realm and make it more readily perceivable by students.

### Christine Taylor and Jean S. Lee

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

### Sarah Ferguson, Thomas Johnston, Christopher Karhan, and Eric Lefevbre

Students explore the relationship between thrill-seeking rides and their algebra 1 curriculum in an informative, engaging, student-centered lesson that was designed using a project-based-instruction (PBI) framework.

### Kelly Curtis, Katrina Lindo, and Amanda Jansen

When a ninth-grade teacher used discourse moves aligned with responding to students’ thinking and explicitly promoting productive dispositions, her students reported having positive experiences.