In this 3-part activity, students use paper-folding and an interactive computer sketch to develop the equation of a parabola given the focus and directrix.

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### Devon Gunter

A hands-on approach to studying quadratic functions emphasizes the engineering design process.

### Larry Lesser

Short items from the media focus mathematics appropriate for classroom study.

### Eric Weber, Amy Ellis, Torrey Kulow, and Zekiye Ozgur

Modeling the motion of a speeding car or the growth of a Jactus plant, teachers can use six practical tips to help students develop quantitative reasoning.

### 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.

### Dung Tran and Barbara J. Dougherty

The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

### J. Vince Kirwan and Jennifer M. Tobias

A task using multiple representations helps students write explicit algebraic equations.

### Marla A. Sole

My favorite lesson introduces algebra students to a key concept from calculus: instantaneous rate of change. In this lesson, I help students develop an intuitive understanding of this abstract concept by framing questions within a real-world context.

### Kevin C. Moore and Kevin R. LaForest

A connected introduction of angle measure and the sine function entails quantitative reasoning.

### Daniel R. Ilaria, Matthew Wells, and Daniel R. Ilaria

Students analyze items from the media to answer mathematical questions related to the article. This month's problems involve reading slopes from graphs, finding average rates of change, and interpreting linear graphs.