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

### 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.

### Kristy B. McGowan and Nathan J. Lowe Spicer

Students analyze items from the media to answer mathematical questions related to the article. The clips this month, from the Colorado State lottery and a Marilyn vos Savant column on probability, involve probability and counting problems.

### Becky Hall and Rich Giacin

Tying your teaching approach to the Common Core Standard for Geometry and Congruence will help students understand why functions behave as they do.

### Mika Munakata and Leslie A. Cheteyan

The walls along the walkway leading to Shanghai's Guilin Garden are lined with geometric panels. The following questions refer to the wall panels shown in **photographs 1–8**. When answering these questions, assume that the patterns continue in all directions.

### Michael A. Jones and Brittany Shelton

This year [2011], July has 5 Fridays, 5 Saturdays and 5 Sundays. This happens once every 823 years.

### Lingguo Bu

The relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching.

### G. Patrick Vennebush and Diana Mata

Students analyze items from the media to answer mathematical questions related to the article. This month's clips discuss misrepresented formulas.

### Jeffrey J. Wanko, Michael Todd Edwards, and Steve Phelps

The Measure-Trace-Algebratize (MTA) approach allows students to uncover algebraic relationships within familiar geometric objects.

### Adam Poetzel, Joseph Muskin, Anne Munroe, and Craig Russell

Using simple materials, a Mathematica software application, and their knowledge of function transformations, students design and create real mathematical sculptures.