Nets to Nightlights: Geometry Lantern Lab

Learning Goals & Products

Learning Goals

Students will be able to define measurable criteria and constraints for a freestanding, visually balanced lantern to frame an authentic geometric engineering problem.

Students will be able to generate and evaluate at least three geometric lantern concepts using physical nets, cross-sections, three-dimensional attributes, and a weighted decision matrix to make evidence-based design trade-offs.

Students will be able to apply trigonometric ratios, the Pythagorean Theorem, and line and angle relationships to calculate and justify lantern dimensions, slopes, angles, and structural fit.

Students will be able to construct precise scale nets and coordinate-plane plans using distance, parallel and perpendicular relationships, transformations, symmetry, and geometric construction tools to translate a flat pattern into an accurate three-dimensional form.

Students will be able to test and optimize a lantern prototype using quantitative evidence about dimensional accuracy, stability, and light performance to improve specific design failure points.

Students will be able to communicate and justify collaborative lantern design decisions using mathematical evidence, empathetic peer feedback, and reflection to explain performance, trade-offs, revisions, and limitations.

Products

individual

Individual Lantern Engineering Design Portfolio and Build Defense

Each student submits a notebook-style portfolio containing measurable specifications, three distinct lantern concepts, annotated nets and coordinate sketches, calculations, a weighted decision matrix, test evidence, and revision reflections. The student also gives an individual build defense explaining how their analysis informed the team lantern and responding to geometry questions.

team

Tested Geometric Lantern Prototype and Shape-and-Light Museum Exhibit

Each team builds a freestanding cardstock or balsa-wood lantern illuminated only by a battery-powered LED, tests it against agreed specifications, and completes at least one data-driven revision. The final museum exhibit includes the lantern, full-scale net, coordinate construction plan, test comparison, exhibit card, and collaborative presentation of mathematical evidence, trade-offs, and limitations.

Rubric

Competency Progression Rubric Competency-first rubric

Category	Learning Goal	Stage 1	Stage 2	Stage 3	Stage 4
Deeper Learning Competencies	Effective Communication	I can share a simple description of my lantern idea, listen to partner feedback, and point to a few measurements, shapes, or construction choices in my sketch or prototype I can communicate my thinking with support by answering questions about what I noticed in the flashlight lab and what I plan to build next.	I can explain my lantern design using clear math vocabulary, including some measurements, angles, symmetry, or coordinate sketches, and I can describe how feedback helped me revise part of my net or prototype I can ask and answer geometry questions with a partner and use my exhibit card or notes to show my thinking.	I can present my finished lantern, net, and construction sketch with clear, organized explanations of the measurements, transformations, symmetry, and constructions I used I can use mathematical evidence such as distance, parallel or perpendicular relationships, angle measures, or trigonometric or Pythagorean reasoning to justify why my design is accurate and stands on its own.	I can communicate my design process and final product with precision, confidence, and purpose, using strong mathematical reasoning to explain how my choices created a structurally sound and visually balanced lantern I can respond to questions, connect feedback to revisions, and clearly defend my decisions with geometry evidence in a gallery walk, museum exhibit, or build review.
Deeper Learning Competencies	Collaboration	I can participate in a small group to share ideas, listen to peers, and help compare simple lantern net options, such as shape, size, and basic symmetry I can accept feedback and make at least one agreed-upon change to my draft with teacher or peer support.	I can work with my group to plan, measure, and adjust a lantern net using rulers, protractors, or coordinate sketches so the design begins to show accurate side lengths, angles, and symmetry I can explain my choices to teammates and use feedback to revise parts of the pattern before building.	I can collaborate with peers to test, compare, and refine a lantern design by using geometric evidence such as parallel or perpendicular relationships, distances, angle measures, symmetry, and constructions I can share responsibilities, contribute to problem solving, and justify our design decisions during critique and revision.	I can lead and sustain collaborative design work by helping the group integrate precise geometric reasoning, trigonometric or Pythagorean calculations, and construction tools into a polished lantern plan I can communicate clearly, respond thoughtfully to feedback, and help the team reach and explain a shared solution that produces a stable, visually balanced final lantern and exhibit materials.
Deeper Learning Competencies	Critical Thinking & Problem Solving	I can identify a possible geometric problem in my lantern design, use given shapes or examples to test simple net ideas, and make a basic plan with support I can use measurements or labels from a model to try one-step calculations or constructions, even if my work is incomplete or needs significant revision.	I can choose an appropriate lantern form and use nets, measurements, and geometric tools to solve design problems with some accuracy I can apply coordinate sketches, symmetry, or basic Pythagorean or trigonometric relationships to check parts of my design and explain my choices with some evidence.	I can independently analyze my lantern design using geometric reasoning, coordinate relationships, and precise constructions to solve problems in the project I can calculate and justify measurements, angles, symmetry, parallel or perpendicular relationships, and distance, then revise my net or prototype based on testing and feedback.	I can thoroughly and flexibly solve complex lantern-design problems by combining geometric constructions, transformations, symmetry, coordinate geometry, and trigonometric or Pythagorean reasoning I can justify why my design is structurally sound and visually balanced, evaluate alternatives, and refine my work with clear mathematical evidence and efficient problem-solving strategies.
Deeper Learning Competencies	Content Expertise	I can identify key geometric features of a lantern design and use familiar shapes, measurements, and basic tools to create a simple net or sketch with some guidance I can show partial understanding of symmetry, angle relationships, and 3D form, but my work may still need support to be accurate or complete.	I can use measurements, symmetry, and geometric constructions to build a lantern net that mostly matches my plan, and I can explain some of the math choices I made I can use coordinate sketches, rulers, protractors, or other tools to check distances, angles, and parallel or perpendicular lines with occasional prompting.	I can independently apply geometric relationships, transformations, coordinate geometry, and trigonometric or Pythagorean reasoning to design a precise lantern net and revise it based on feedback I can justify how my measurements, constructions, and symmetry choices help my lantern be structurally sound, visually balanced, and connected to the flashlight prototype tests.	I can confidently and accurately combine geometric modeling, constructions, transformations, symmetry, and trigonometric or coordinate reasoning to create a polished lantern that fits my design goals and stands on its own I can clearly explain and defend my choices with mathematical evidence, including distances, angle measures, line relationships, and revisions made from critique and testing, and I can transfer these ideas to new design challenges.
Deeper Learning Competencies	Self Directed Learning	I can use teacher or peer feedback and a checklist to make simple revisions to my lantern net, sketch, and prototype, showing that I notice when measurements, symmetry, or construction steps need improvement I can explain at least one change I made based on testing or feedback.	I can use feedback, reflections, and measurement checks to revise my lantern design with some independence, correcting angle measures, side lengths, and basic coordinate relationships so my pattern is more accurate and balanced I can document how my choices connect to the shape’s stability and appearance.	I can independently monitor my progress by comparing my net, prototype, and construction sketch to my design goals, then revising with evidence from peer critique, geometry tools, and calculations I can explain how my adjustments improve precision, symmetry, and structural soundness.	I can consistently direct my own learning by seeking and using feedback, testing multiple design options, and justifying revisions with clear geometric evidence from measurements, transformations, coordinate relationships, and trigonometric or Pythagorean reasoning I can reflect on my process to show how my decisions strengthened both the lantern’s function and visual balance.