🚀 The Celestial Engineer's Gauntlet- Solving Graphically and Maximum Volume

A Mission in Graphical Analysis, Optimization, and Remediation

Solving Graphically and Max Math Mission

How do you challenge your advanced students while providing a crucial safety net for those who need it? You create a Divergent Mission! In this epic lesson, the entire class faces the 'Simulation Gauntlet' before splitting into specialized teams: one to design a starship, the other to reinforce the foundations of the guild.

📜 Mission Briefing

• 🎯 Mission Objective: Students will solve complex systems of equations graphically and find the maximum of a function to solve an optimization problem. A separate group of students will engage in targeted remediation to master previous essential standards.
• ⏳ Class Time: 1 x 85-minute period
• 📚 Subject & Level: Secondary Math 3 / Algebra 2
• 👻 The Adventure: Students are members of the Celestial Engineers Guild. They first face the "Simulation Gauntlet" (graphical analysis). Then, based on their certification status, they are assigned to either the "Prototype Division" (building the Star-Sail Barge) or the "Certification Strike Team" (targeted remediation).
• 
  
  
  
  

🎒 The Armory

• Projector/Smartboard & Intro Slides: Get the Intro Slides
• Amplify Design Console: Access the Console
• Remediation Quest Guide: Get the Quest Guide
• Printable Mission Reports (Exit Tickets): Get the Exit Tickets
• Costume & Prop Ideas: A futuristic vest, a lab coat, or a holographic-looking data pad to become the "Guild Master."

✨ Introduction: The Guild Master's Address (Approx. 5 mins)

(As the "Guild Master" at the front of the Engineering Bay)

"Engineers, welcome. Today, you face the Gauntlet. You will be presented with complex simulations, alien technology, and design challenges that will push the limits of your analytical skills. When you look at these problems, it's natural for your mind to see chaos. It might tell you, 'This is too complex,' or 'There are too many moving parts.'

That feeling is the signal that you are at the edge of your current abilities. A fearless engineer doesn't run from that feeling; they lean into it. They see a complex system not as a barrier, but as a puzzle waiting to be solved. They know that every chaotic problem has an elegant, underlying pattern.

Today, your mission is to find that pattern. Whether you are in the advanced design division or reinforcing the foundations of our guild, your focus is the same: trust your training, trust your tools, and find the simple truth hidden inside the complex problem."

(Now, lead the class in your power statement)

"Are you ready to build the future? Let me hear it!"

• "I Got This! I Can Do This!"

• "I Got This! I Can Do This!"

• "I Got This! I Can Do Thi

  "Excellent. Power on your design consoles."

🗺️ The Walkthrough

Finding Intersections

✨ Phase 1: The Simulation Gauntlet (Approx. 40 mins)

The Story: "Welcome, Celestial Engineers. Today, you all face the Simulation Gauntlet. This is a series of advanced graphical challenges designed to test your analytical skills under pressure. Every engineer must pass through the Gauntlet." 

Paper assignment if needed

The Activity: The entire class works together on the fun, epic graphical solving problems (Kaiju vs. Drone, Chrono-Sprite's Escape, etc.) using Desmos or graphing calculators.

Finding Max Volume Mission

⚔️ Phase 2: Divergent Missions (Approx. 40 mins)

The Story: "Excellent work in the Gauntlet. The simulations are complete. Now, we have two critical, parallel missions that require specialized teams. Your next assignment is based on your current certification status."

The Activity: The class splits into two groups.

• Mission A: The "Prototype Division" (Extension): Students who have mastered previous standards are tasked with designing the "Star-Sail Barge." They use the Amplify activity to find the optimal dimensions and then build their physical boats to compete. When they are done with the build you can use this Worksheet if you desire. 
• Mission B: The "Certification Strike Team" (Remediation): Students with outstanding certifications embark on a "Data Recovery Mission." They use the Quest Guide to partner up and work on targeted practice to restore their foundational knowledge to 100%.
• 
  
  

  

  Finding Max Volume and Boat Mission

  
  

🏆 The Level Clear Screen: Performance Review

The Story: "The missions are complete. Report back to the Guild Master and file your performance reviews. A great engineer always documents their work."

The Activity: Students use their specific Printable Exit Ticket to report on their mission's success.