The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.

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### Patricia Wallace-Gomez

Three graphing activities lead students to discover the shapes and properties of the graphs for linear, quadratic, and absolute value functions and inequalities.

A set of problems of many types.

### Signe E. Kastberg, Beatriz S. D'Ambrosio, Kathleen Lynch-Davis, Alexia Mintos, and Kathryn Krawczyk

A Cherry Syrup problem can build links between ratio and graphing.

### Joel Amidon and Matt Roscoe

A monthly set of problems is aimed at a variety of ability levels.

### Victor Mateas

Economics can be an avenue for teaching such algebra concepts as graphing curves, writing linear equations, solving systems of equations, and shifting graphs.

### Courtney R. Nagle and Deborah Moore-Russo

Students must be able to relate many representations of slope to form an integrated understanding of the concept.

### Teo J. Paoletti

This historically significant real-life application of a cryptographic coding technique, which incorporates first-year algebra and geometry, makes mathematics come alive in the classroom.

Beginning Algebra: Teaching Key Concepts

### Kasi C. Allen

Students today come to first-year algebra with considerable prior experience and a wide range of skills. Teachers need to modify their instructional strategies accordingly.