Students apply geometric nets, trigonometry, coordinate geometry, transformations, symmetry, and precise constructions to design a structurally sound, visually balanced lantern from cardstock or balsa wood. Through light investigations, physical net models, peer critique, and revision, they test how measurements, angles, shapes, and openings affect form and shadow. Students collaborate and direct their design process while documenting mathematical decisions and responding to feedback. The experience culminates in a gallery-style exhibition and build review featuring each lantern, net, construction sketch, and explanatory exhibit card.

Students will create and analyze physical nets, cross-sections, and attributes of prisms, pyramids, cylinders, and other 3D forms to model a stable lantern. They will apply trigonometric ratios, the Pythagorean Theorem, angle and line theorems, and coordinate geometry to calculate dimensions and verify distance, parallelism, and perpendicularity. Students will use transformations, symmetry, and geometric constructions to produce precise, visually balanced patterns with rulers, compasses, and protractors. They will use testing, peer critique, and self-reflection to revise their designs and clearly justify their geometric decisions through a finished lantern, net, sketch, exhibit card, and presentation.

Students will create and test physical nets for forms such as cubes, pyramids, prisms, and cylinders, documenting cross-sections, dimensions, angles, and symmetry. They will develop flashlight-tested prototypes, coordinate-plane construction sketches, and revised full-scale patterns based on peer feedback and precision checks. The final product will be a freestanding cardstock or balsa-wood lantern displayed with its net, construction sketch, and labeled exhibit card explaining the measurements, transformations, symmetry, and geometric constructions used. These artifacts will be presented in a Lantern Gallery Walk and Shape and Light Museum.

Students begin with a Flashlight Form Lab, shining battery-powered LED lights through paper and cardstock prototypes to investigate how openings, angles, and surface shapes affect shadows and light patterns. In teams, they rotate through sample forms such as cubes, pyramids, and cylinders, record observations, and sketch an initial lantern concept. The class then uses its findings to consider: What measurements, angles, and symmetry choices make a lantern structurally sound and visually balanced, and how can coordinate geometry and construction tools turn flat materials into a precise 3D form?

Students curate a “Shape and Light Museum,” displaying each finished lantern with its physical net, construction sketch, and labeled exhibit card explaining key measurements, symmetry, transformations, and geometric constructions. During a Lantern Gallery Walk, classmates examine how each structure stands independently and leave sticky-note praise and geometry questions. Each student then gives a brief build review, using mathematical evidence—including angles, distances, parallel or perpendicular relationships, and trigonometric or Pythagorean calculations—to defend design choices and reflect on revisions.