Your Mission

Congratulations! You’ve been hired as the lead urban planner for a new city. You have a $125,000 construction budget and must design a city that houses at least 10,000 people while providing all essential services.

This isn’t just about calculating volume – you’ll optimize for efficiency, make strategic trade-offs, and justify every decision with mathematical evidence.

Phase 1: Research & Analysis (2-3 sessions)

You’ll investigate:

• Population capacity – How many people fit in different buildings?
• Service requirements – How close should fire stations be?
• Scaling relationships – What happens when you double dimensions?
• Optimization – Which building shapes are most efficient?
• Budget strategy – How do you cut costs without sacrificing quality?

Phase 2: Strategic Design (2-3 sessions)

You’ll create THREE different city designs:

• Design A: “Skyline City” – Tall buildings, vertical growth
• Design B: “Sprawl City” – Wide, short buildings, horizontal spread
• Design C: “Balanced City” – Your mathematically optimized design

Each design must meet population and budget requirements!

Phase 3: Comparative Analysis (1-2 sessions)

You’ll compare your three designs using:

• Total cost – Which came in under budget?
• Population capacity – Which houses the most people?
• Efficiency ratio – Which gives the best value?
• Service access – Which has best emergency response?
• Quality of life – Park space, livability factors

Then you’ll write a justification for which design is best, backed by mathematical evidence.

What Makes This Different?

This isn’t your typical math worksheet. You’ll be:

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  Making real decisions with no single “right answer”

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  Thinking strategically about trade-offs and optimization

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  Discovering patterns (like why doubling dimensions multiplies volume by 8!)

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  Using evidence to justify your choices

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  Connecting to real-world urban planning

This is how engineers, architects, and city planners actually think!