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Natalya Vinogradova

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

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

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Nicholas H. Wasserman

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

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Yee-Min Cha and Scott A. Brown

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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Laura M. Crowley

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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Edited by Randy F. Hall

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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Ryan Brydges and Kevin Webster

Students analyze items from the media to answer mathematical questions related to the article. Exponential growth is the topic of both clips this month.

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Stephen F. Bismarck, Jeremy Zelkowski and Jim Gleason

“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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Eileen Fernández and Kristi A. Geist

Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy (see fig. 1). The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population, capacity is defined as “the maximum population that the environment is capable of sustaining in the long run” (Stewart 2008, p. 628).

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Maria L. Hernandez and Nils Ahbel

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.