Students will investigate the essential question: How can we use mathematics to create affordable, comfortable sleeping and studying spaces for children in crowded or multigenerational households? In design teams, they will use area, volume, surface area, scale drawings, and physical or digital models to develop a practical, budget-conscious space solution. Students will identify patterns and structures, select appropriate tools, test and revise ideas, and use mathematical evidence to critique competing designs. They will present and reflect on a final proposal that responds empathetically to household needs and demonstrates shared decision-making.

Students will investigate: How can we use mathematics to create affordable, comfortable sleeping and studying spaces for children in crowded or multigenerational households? They will calculate area, surface area, and volume for composite two- and three-dimensional designs and use appropriate measurement and modeling tools strategically. Students will identify geometric structures and repeated reasoning to compare layouts, material use, and costs. In design teams, they will make shared decisions, critique mathematical arguments respectfully, revise solutions, and present an evidence-based design that responds empathetically to community needs.

Teams will create a needs-and-constraints profile, annotated floor-plan sketches, and a materials budget for a realistic household scenario. They will maintain a design log showing area, volume, and surface-area calculations, including repeated reasoning and geometric structures used to improve efficiency. Each team will produce a labeled scale model or digital 3D design of an affordable sleeping-and-study space that addresses the essential question. Teams will present a concise design proposal, respond to peer critiques with mathematical evidence, and submit a final revision and individual reflection.

Begin with a “small-space design challenge” using a taped floor outline or scaled grid representing a crowded bedroom, plus movable paper models of beds, desks, and storage with dimensions and prices. In teams, students arrange the models to preserve sleeping and studying areas, calculate occupied and open area, and stay within a set budget. Teams share one design choice, explain their mathematical reasoning, and offer respectful feedback on another team’s solution. Close by asking, “How can we use mathematics to create affordable, comfortable sleeping and studying spaces for children in crowded or multigenerational households?”

Host a “Small-Space Design Expo” where teams present scale models, floor plans, and affordable material budgets to families, classmates, and local housing or design professionals. Students explain how area, volume, surface area, and repeated calculations guided their response to the essential question. Each team member takes a presentation role and uses diagrams, physical models, or digital tools to communicate design choices. Visitors leave warm and cool feedback, and teams defend or revise one decision based on audience questions.