We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

### Amber G. Candela, Melissa D. Boston, and Juli K. Dixon

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

### Samuel Otten and Andrew Otten

Students make strategic choices–and justify them–to solve a system of two linear equations.

A set of problems of many types.

### Darla R. Berks and Amber N. Vlasnik

Two teachers discuss the planning and observed results of an introductory problem to help students nail a conceptual approach to solving systems of equations.

### Connie Colton and Wendy M. Smith

A multiphase lesson on selling T-shirts guides students from single-variable equations to linear relationships.

### Rachel Levy

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.

### 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.

### 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.

### Sheldon P. Gordon

The idea of a function of several variables–important in other disciplines–can be introduced in secondary school mathematics courses.