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## Puddle Play!

For the Love of Mathematics

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## Student Engagement with the “Into Math Graph" Tool

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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## Constructing and Adapting Technology-Infused Lessons

Design principles are used to construct and refine a technology-infused lesson for beginning algebra students learning about systems of linear inequalities.

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## Quick Reads: Using Technology to Build a Pen for Browser

### a good idea in a small package

Making mathematics meaningful is a challenge that all math teachers endeavor to meet. As math teachers, we spend countless hours crafting problems that will energize students and help them connect mathematical topics to their everyday lives. Being successful in our efforts requires that we allow students to explore ideas before we provide explanations and demands that we ask questions to promote a depth of thinking and reasoning that would not occur without such probing (Marshall and Horton 2009).

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## Triangles from Three Points

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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## Teaching Straight-Line Graphs Using Autograph

Students often have difficulty with the topic of straight-line graphs. Perhaps they cannot relate to the abstractness of the concepts involved. Perhaps the sheer number and complexity of the skills required—reading algebra, substituting values, rearranging formulas, dealing with negative numbers, understanding coordinates and fractions—magnifies any misconceptions or weaknesses that students may have in other areas of mathematics, rendering them unable to come to grips with the topic as a whole.

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## Activities for Students: Soap and Slope: Mathematical Adventures in Fluid Dynamics

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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## Open-ended Questions and the Process Standards

Educating students—for life, not for tests—implies incorporating open-ended questions in your teaching to develop higher-order thinking.

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## Applications in Digital Image Processing

Use digital signal processing to capitalize on an exciting intersection of mathematics and popular culture.

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## Teaching and Learning with Real-World Tools

To better prepare students for their future careers, a fifth-grade teacher designs and implements a lesson that uses spreadsheet software to graph functions.