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## Connecting Parabolas and Quadratic Functions

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

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## The Stature of Salary: Raised Expectations or a Tall Tale?

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

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## Six Principles for Quantitative Reasoning and Modeling

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.

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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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## Authenticity of Mathematical Modeling

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

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## Multiple Representations and Connections with the Sierpinski Triangle

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

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## Back Page: My Favorite Lesson: Bridging Algebra and Calculus

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.

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## The Circle Approach to Trigonometry

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

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## Lawn and Garden//Pulp Paper

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.