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## Using Judicious Telling to Strengthen Literacy in Mathematics

Language is a conduit for communicating and understanding mathematical ideas. This article explores how we can use judicious telling to attend to students’ written and spoken literacy in mathematics.

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## Ready, Set, Launch!—The Engineering Cycle for Productive Struggle

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

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## Pythagoras, PVC Pipes, and Pianos

This practitioner article describes a lesson carried out in a high school classroom at the conclusion of a unit on exponential growth. Two teachers use a series of music-related activities to engage students in using and connecting multiple representations of exponential growth while exploring musical frequencies on a piano.

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## Focusing on Visual Representations in Mathematics

The authors outline the importance of using variety when teaching mathematics.

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## Triangle Center Technology

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

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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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## Technology Tips: Teaching Inverses with Technology Is “Sweeeet”

A wonderful experience occurred in a class that I was teaching recently. It was a precalculus class, the last period of the day. The local university had brought over its cadre of preservice secondary school mathematics teachers to observe my class, so there were twenty-four additional eyes on me that day.

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## Using Covariation Reasoning to Support Mathematical Modeling

Table representations of functions allow students to compare rows as well as values in the same row.

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## The Back Page: My Favorite Lesson: Modeling Exponential Decay

Our favorite lesson, an interactive experiment that models exponential decay, launches with a loud dice roll. This exploration engages students in lively data collection that motivates interest in key components of the Common Core State Standards for Mathematics: functions, modeling, and statistics and probability (CCSSI 2010).

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## Connecting Algebra to Economics

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