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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May 2020 For the Love of Mathematics Jokes

### Wayne Nirode

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

### Chris Harrow and Lillian Chin

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.

### Barbara M. Kinach

The meaningful use of symbols links context and generality.

### John H. Lamb

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

## Quick Reads: Engaging Geometry Students through Technology

### a good idea in a small package

### Janet B. Andreasen and Erhan S. Haciomeroglu

Dynamic software is used to teach geometry, tying into the Common Core's Standard 5, “Use appropriate tools strategically.”

### Wendy B. Sanchez

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

### Kevin Phillippi

This department showcases students' in-depth thinking and work on previously published problems. The August 2012 problem scenario leverages back-to-school shopping advertisements for this real-life scenario about making purchases using discount coupons. To access the full-size activity sheet, go to http://www.nctm.org/tcm, Back Issues.

### Abdulkadir Erdogan and H. Bahadir Yanik

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