Students act as design companies to create and defend a compact carnival booth that is fair, efficient, and mathematically sound using ratios and unit rates. The work centers on a project notebook where teams document sketches, equivalent ratio tables, unit rate calculations, testing data, critiques, and revisions before building a simple one-desk prototype. Through the Design Company Launch Rally, Booth Boss Challenge, classroom team playtesting, and community partner swap, students use math to make decisions, explain their reasoning, and improve their designs for an authentic audience.

Students use ratio and rate reasoning to design a compact carnival booth that is fair, efficient, and workable within a fixed budget, limited materials, and desk-sized constraints. They model chances of winning, ticket systems, materials, and capacity with equivalent ratios, unit rates, tables, diagrams, and precise calculations, then use test data to revise their design. Students construct and communicate mathematical arguments during the Booth Boss Challenge, critique peer reasoning from scorecards and feedback, and refine their project notebook to show how their booth improved over time. Through team roles, partner debriefs, and the classroom/community partner swap, students strengthen collaboration, reflection, and strategic tool use while making sense of a real design problem.

Students create a project notebook with annotated sketches, ratio tables, unit-rate calculations, testing data, peer feedback, and revision notes that document how their booth becomes more fair and efficient. Each design company also produces a one-desk carnival booth prototype with a clear game, ticket system, capacity plan, and posted math explanation for visitors. During the Booth Boss Challenge, teams present their prototype and notebook evidence, collect scorecards from the classroom partner team, and revise before the final community partner swap. The culminating products are the revised compact booth, a polished presentation of the team’s mathematical reasoning, and a reflection comparing fairness, efficiency, and changes made after testing.

Kick off with a Design Company Launch Rally: read the client letter aloud, reveal the challenge to build a one-desk carnival booth, and show a few simple sample games or photos so students can quickly notice fairness, ticket ratios, and capacity. Then run a fast team challenge in which students sort possible game ideas into categories such as chance, skill, and accuracy and identify the ratios or unit rates each game would require. Have teams choose a company name, start a project notebook, and record initial claims about what makes a booth fair and efficient. Close with a brief share-out that introduces the upcoming Booth Boss Challenge and the classroom team visit as the authentic audience for their work.

End with a Math Carnival exchange in which each design company runs its one-desk booth for a partner classroom and then visits the partner class to play and analyze their games. During a Booth Boss Challenge, small groups present their prototype, defend their fairness, ticket, and capacity calculations from the project notebook, and invite guests to test the game using a short scorecard for fairness and efficiency. Display annotated sketches, ratio tables, unit-rate calculations, test data, and revision notes beside each booth so visitors can see how the design improved over time. Close with brief awards tied to the math, such as Best Mathematical Design, Most Efficient Booth, and Strongest Revision Based on Evidence.