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Let's Hit the Target!

In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.

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You Must Be Joking!

May 2020 For the Love of Mathematics Jokes

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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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Technology-Enhanced Discovery

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

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Angry Birds Mathematics: Parabolas and Vectors

Vector properties and the birds' frictionless environment help students understand the mathematics behind the game.

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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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Fostering optimization ideas in early grades

iSTEM: Integrating Science, Technology, and Engineering in Mathematics authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K-grade 6 classrooms. This article describes how optimization ideas can be fostered in early grades through a game-based activity called Avoiding Invasion from Aliens

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Abby and the number line

Students say some amazing things. Back Talk highlights the learning of one or two students and their approach to solving a math problem or prompt. Each article includes the prompt used to initiate the discussion, a portion of dialogue, student work samples (when applicable) and teacher insights into the mathematical thinking of the students. In this month's episode, a six-year-old rising first grader uses a computer simulation to understand addition and subtraction on the number line.

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