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## Extreme Numbers and Estimation Skills

Using estimation helps increase numerical fluency and gives meaning to large numbers.

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## 42 Folds to the Moon; Lottery Players Seeing Double

Clips about paper folding and lottery numbers inspire questions about exponential growth and probability.

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## A Rationale for Irrationals: An Unintended Exploration of e

The practice of problem posing is as important to develop as problem solving. The resulting explorations can be mathematically rich.

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## Media Clips: Global Population Explosion; U.S. Population Growth

Students analyze items from the media to answer mathematical questions related to the article. Linear and exponential models for population growth are explored, and dimensional analysis is used.

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## The Back Page: Financing a College Education

A favorite lesson is presented by a teacher. This lesson involves student participation in planning post-secondary school financing. Compound interest and the present and future value formulas are the mathematical basis for the lesson.

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## Media Clips: NFL Players' Life Expectancy; Transit of Venus

Students analyze items from the media to answer related mathematical questions. The mathematics involved in this month's clips includes percent loss and gain, proportional reasoning, and the application of Kepler's laws, which involve exponential equations and regression.

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## Teaching Human Rights through Mathematics

Human Rights Education, or HRE, can be applied to allocation of scarce resources, such as food production.

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## Activities for Students: Predicting Future Gas Prices Using the Standards for Mathematical Practice

“How much do you think gas will cost when I graduate from high school?” Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninetyminute block or two forty-five-minute classes, students build functions and interpret them in context. This article presents the activity, describes its implementation, provides sample student work, and discusses its relationship to the Standards for Mathematical Practice from the Common Core State Standards. Data used in the activity are available at http://data.bls.gov/cgi-bin/surveymost?ap.

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## Using Radioactive Decay to Investigate Exponential Functions

During the thirteen years that I taught high school physics and mathematics, I found that my physics students typically came to class excited to learn. As in all science classes, they interacted with fellow classmates while performing laboratory investigations and other group activities requiring higher-order thinking skills. To create a similar experience for my mathematics students, I developed a laboratory investigation for my precalculus class. These students responded just as favorably as my physics students to hands-on data collection activities.

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## Technology Tips: Using FluidMath to Explore Recursive and Explicit Functions

luidMath™ (www.fluiditysoftware.com), a new mathematics software tool for Tablet devices, computers, and interactive whiteboards, can create a dynamic graph or table with a simple gesture and recognize written expressions as the mathematical relationship they intend. The software uses a stylus as its input device. By changing constant values in an equation to parameters, the user can create sliders instantly and see graphs and tables change dynamically. The CAS (Computer Algebra System) functionality allows simplification of algebraic expressions and solution of equations and can perform all the calculations from algebra through calculus. FluidMath uses standard mathematical notation to explore explicitly and implicitly defined functions, parametric functions, polar functions, and recursively defined functions.