2025 ASEE Annual Conference & Exposition

Understanding geometric angles is crucial for students, as angles are the basis for more advanced mathematical concepts and real-world applications. Existing work aims to teach angles via hands-on learning and by making real-world connections. However, there is relatively little software or engaging lessons in this area. This paper describes a classroom module that teaches angles and angle addition to freshman and sophomore mathematics learners using a combination of Geogebra software; an angle addition simulator tool built using HTML5 Canvas and JavaScript; and a protractor to make abstract concepts tangible. This approach aims to enhance students' geometric understanding, critical thinking, and problem-solving skills, while integrating traditional and digital tools to engage Gen Z learners, ultimately preparing them for academic and professional success in fields like architecture, engineering, and navigation. The module was evaluated in a class of 25 students using pre- and post-tests and an opinion survey. Students found the approach engaging and effective, noting that the combination of hands-on tools like protractors and interactive software such as GeoGebra helped demystify complex concepts. Survey results indicated increased confidence in understanding geometric angles and improved problem-solving skills, with many students appreciating the real-world connections made during the lessons.