A free tool encourages students to engage in the authentic practices of statistics and data analysis.

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### Alfinio Flores

The striking results of this coin-tossing simulation help students understand the law of large numbers.

### Ayanna D. Perry, Emily P. Thrasher, and Hollylynne S. Lee

The use of iPads® in the classroom is growing. In the 2013–14 school year, 57 percent of schools planned to invest in iPads (Netop 2013). This investment can benefit mathematics classrooms only if teachers know which apps they can use to help students develop deeper mathematical understanding. Although learning about and developing facility with various apps is valuable for mathematics teachers, the process can be difficult, overwhelming, and time-consuming. To get started, we recommend one app, Dropbox, that can be used to share materials within the classroom setting, and then we suggest three free, easy-to-use mathematics apps: Sketchpad Explorer, Data Analysis, and MathGraph (see the **table** on p. 711).

### Hollylynne S. Lee, Tina T. Starling, and Marggie D. Gonzalez

Research shows that students often struggle with understanding empirical sampling distributions. Using hands-on and technology models and simulations of problems generated by real data help students begin to make connections between repeated sampling, sample size, distribution, variation, and center. A task to assist teachers in implementing research-based strategies is included.

### Rachel Levy

The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.

### Alison L. Mall and Mike Risinger

Our favorite lesson, an interactive experiment that models exponential decay, launches with a loud dice roll. This exploration engages students in lively data collection that motivates interest in key components of the Common Core State Standards for Mathematics: functions, modeling, and statistics and probability (CCSSI 2010).

### Jeremy F. Strayer

Using the TI-Nspire, students can see that polling results from a small group will suffice for determining the opinion of the whole population.

Readers comment on published articles or offer their own ideas.

### Jonathan D. Baker

The outcome distribution for rolling a single die is horizontal; for rolling a pair of dice it is a triangle. What happens when more than two dice are rolled? What happens when the die has other than six sides? These and other questions are answered in an accessible and useful treatise.

### Michael Dempsey

When understood and applied appropriately, mathematics is both beautiful and powerful. As a result, students are sometimes tempted to extend that power beyond appropriate limits. In teaching statistics at both the high school and college level, I have found that one of students' biggest struggles is applying their understanding of probability to make appropriate inferences.