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James Metz
In the 1928 movie Steamboat Bill, Jr., as Buster Keaton stands in front of a house, the front wall of the house falls toward him. Keaton is unharmed as the open attic window passes over him. See photographs 1 and 2 for two views of the scene.
Thérèse Cozzo and Joseph Cozzo
This lesson provides an opportunity for students to use mathematical modeling and explore right-triangle trigonometry in the context of protecting battleships.
Arsalan Wares
Determining exact values of trigonometric ratios remains an integral part of the high school mathematics curriculum. Students learn to use 45-45-90° triangles and 30-60-90° triangles to determine exact function values of angles of 30°, 45°, and 60°. Such exact-value ratios can help to determine trigonometric ratios for nonstandard angle measures when trigonometric identities and algebra are used. In this lesson, students apply a geometric approach to determine exact-value trig ratios for angle measures of 22.5°, 67.5°, 15°, and 75°. Some students can extend that approach to other nonstandard angle measures.
Günhan Caglayan
Tangent circles, sequenced to form annular Steiner rings, are photographed in the windows of ancient buildings.
Albert Goetz
An excerpt from a 2015 Pulitzer Prize–winning novel prompts questions about trigonometry.
Casey Hord, Samantha Marita, Jennifer B. Walsh, Taylor-Marie Tomaro, and Kiyana Gordon
Emotional and contextual support can help students step toward confidence and success with challenging mathematics.
Michael S. Meagher, Michael Todd Edwards, and S. Asli Özgün-Koca
The Geoboard Triangle Quest yields many results. The challenge for students is to verify which—if any—are correct.
Sheryl L. Stump, Joel A. Bryan, and Tom J. McConnell
Acting as quality control engineers and service providers, students collaborate to engage, explore, and explain their results.
Bobson Wong and Larisa Bukalov
Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.
