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## The Right Place at the Right Time

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.

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## Battleship Trig

This lesson provides an opportunity for students to use mathematical modeling and explore right-triangle trigonometry in the context of protecting battleships.

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## Geometry and Trigonometry Interplay

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.

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## Closed Circular Chains

Tangent circles, sequenced to form annular Steiner rings, are photographed in the windows of ancient buildings.

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## Wartime Trigonometry

An excerpt from a 2015 Pulitzer Prize–winning novel prompts questions about trigonometry.

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## Encouraging Students with Learning Disabilities

Emotional and contextual support can help students step toward confidence and success with challenging mathematics.

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The Geoboard Triangle Quest yields many results. The challenge for students is to verify which—if any—are correct.

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## Making STEM Connections

Acting as quality control engineers and service providers, students collaborate to engage, explore, and explain their results.

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## Improving Student Reasoning in Geometry

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.