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## Technology Tips: High-Leverage iPad Apps for the Mathematics Classroom

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).

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## Media Clips: Boulder Lottery; The Probability of Slot Machines

Students analyze items from the media to answer mathematical questions related to the article. The clips this month, from the Colorado State lottery and a Marilyn vos Savant column on probability, involve probability and counting problems.

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## What Does It Mean to Do Something Randomly?

Similar assumptions seem to give rise to conflicting answers when students approach probability questions differently.

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## The Back Page: My Favorite Lesson: The Bulldog Lottery

Several years ago I became the lead teacher for a newly created statistics course. I wanted the course to emphasize projects that would allow students to apply statistical knowledge to real-world situations. My Bulldog Lottery lesson allows students to apply the concepts of probability and expected value to a real-world phenomenon.

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## Farkle Fundamentals and Fun

The dice game Farkle provides an excellent basis for four activities that reinforce probability and expected value concepts for students in an introductory statistics class. These concepts appear in the increasingly popular AP statistics course (Peck 2011) and are used in analyzing ethical issues from insurance and gambling (COMAP 2009; Woodward and Woodward 1994). In addition to investigating these four fun activities, we also investigate a strategy to optimize a player's score on a turn in Farkle and indicate possible additional explorations.

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## Reader Reflections – April 2012

Readers react to published articles or submit their own mathematical explorations.

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## Reader Reflections – April 2012

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## Using Data to Motivate the Use of Empirical Sampling Distributions

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.

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## Reader Reflections – September 2013

Readers comment on published articles or offer their own ideas.

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## Calendar and Solutions – January 2013 and February 2013

A set of problems of many types.