Students work in teams to design a realistic student hangout for a 20-by-30-foot campus space that balances usefulness, welcome, fun, safety, and cost. Across the project, they use measurement, scale drawings, area, perimeter, decimals, budgeting, and 3D modeling to answer a real design question with real constraints and feedback from community partners. The work builds mathematical modeling, strategic tool use, argumentation, and revision as students defend trade-offs, respond to critique, and improve their plans. By the end, students create and present a proposal that shows how math can shape spaces that serve a school community well.

Students will use measurement, scale drawings, area, perimeter, decimals, estimation, and budgeting to design a 20-by-30-foot hangout space that fits real constraints and serves multiple users well. They will model with mathematics by creating and revising floor plans, budgets, and labeled 3D nets or mockups, while using tools such as graph paper, rulers, price lists, and digital design tools strategically. Students will construct viable arguments and critique the reasoning of others as they defend trade-offs, respond to feedback from peers and community partners, and revise their designs for safety, usefulness, and cost. They will strengthen collaboration and communication by sharing decisions, resolving disagreement, and presenting a final proposal, model, and math portfolio to an authentic audience.

Students will create rough sketches, price comparison sheets, and a math portfolio with calculations, revisions, and notes from weekly reflection circles as they develop their ideas. Each team will produce a labeled scale floor plan for the 20-by-30-foot space and a complete budget that uses real-world prices, decimals, estimation, and measurement vocabulary to justify trade-offs. By the end, groups will present a labeled 3D scale model or digital mockup showing zones, circulation paths, area, perimeter, proportion, and any 3D features represented with nets and surface area thinking. They will also create a final floor-plan poster and short pitch that defends how their design serves the most students well within the budget and safety constraints.

Start with a Scale Space Sprint in the actual or taped-out 20-by-30-foot area, where teams use measuring tapes, floor grids, and movable paper “furniture” pieces with real prices to create a first-draft hangout in 20 minutes. Add role cards such as gamer, reader, skater, artist, and student who wants a quiet place so groups must design for different users while staying inside a surprise budget cap. Midway through, introduce a quick “facilities update” from the school facilities manager that adds a real constraint like walkway clearance, safety limits, or weather protection. End with a fast share-out where teams defend one design choice, one trade-off, and one question they still have about building the most useful and welcoming space.

Turn the room into a “Build the Hangout Showcase” design studio where each team presents its labeled 3D model or digital mockup, scale floor plan, and budget poster to classmates, families, staff, the facilities manager, and a teen center or recreation partner. During a gallery walk, visitors use sticky notes to vote on the most useful, welcoming, and realistic design while students explain their area, perimeter, scale, surface area, and budget trade-offs using math vocabulary. End with a short pitch-and-question session in which each group defends how its 20-by-30-foot plan fits the budget, meets safety needs, and serves different kinds of student users. Display math portfolios alongside the final products so guests can see revisions, price comparisons, and how teams changed decisions after critique and feedback.