Because number lines are an integral part of mathematics after they are introduced in second grade, connecting number sense to a linear view of numbers establishes a foundation for number line use in all levels of mathematics.

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### Lucy A. Watson, Christopher T. Bonnesen, and Jeremy F. Strayer

Teachers can offer opportunities for K–12 students to reflect on the nature of mathematics (NOM) as they learn.

### Paul A. Frisoli and Richard A. Andrusiak

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

### LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

### Tim Erickson

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.

### Patrick Sullivan

Is the “Last Banana” game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by examining theoretical probabilities