🏎️ The Great Velocity Race: A Grand Finale for Comparing Functions

Comparing Linear, Quadratic, and Exponential Functions

The training is complete, the prototypes are certified, and the track is hot. It's time for the ultimate showdown! In this lesson, we conclude our Velocity Design Lab adventure with a head-to-head race between our three vehicle classes. Welcome to the final, epic quest of the unit!

📜 Mission Briefing

• 🎯 Mission Objective: Students will be able to compare the key features and long-term behavior of linear, quadratic, and exponential functions from graphs, tables, and equations.

• ⏳ Class Time: 1 x 75-minute period

• 📚 Subject & Level: Algebra 2 / Secondary Math 2

• 🗓️ Unit Schedule: The final lesson of our Comparing Functions Unit. You can see the full schedule for the entire quest here: Unit 1 Schedule

• 👻 The Adventure: Engineers will analyze data from two classic races to prepare for the main event. Their mission is to use graphs, tables, and equations to determine which of the three prototypes—the Cruise Control Car, the Gravity Racer, or the Rocket Sled—is truly the most powerful vehicle in the lab.

🎒 The Armory

• 📋 Supply List:

  • Projector/Smartboard & Google Slideshow

  • Student devices for the Desmos activity Link to Desmos Activity

  • The "Great Velocity Race" Analysis Packet (Copy to Worksheet after Desmos)

• 👕 Costume & Prop Ideas:

  • The Lead Engineer's lab coat and clipboard are a must for this final, high-stakes event!

• 🖼️ Digital Assets (The Magic!):

  • The Race Track: (An image to set the scene for the day) (Prompt: A cinematic, wide-screen image of a futuristic, multi-lane race track at night, with glowing lines. The starting line has three empty spots labeled "Linear," "Quadratic," and "Exponential." The title "The Great Velocity Race" is displayed on a giant screen above the track.)

🗺️ The Walkthrough

• (This is where you would do your final motivational message and power statement!)

• ⚔️ Warm-Up: Analyzing a Classic Race (Approx. 20 mins)

  • The Story: "Engineers, before our main event, we're going to analyze data from a classic, historical race. The subject was a snail, but the data is surprisingly relevant. Log in to the simulation and analyze the performance of 'Gary the Snail' to sharpen your skills for the big race."

  • The Activity: Students work through the amazing SpongeBob Desmos Activity. This is a perfect, high-engagement warm-up.

• ⚔️ The Main Event: The Race Analysis (Approx. 40 mins)

  • The Story: "The simulation is complete. Now for the main event! Using the official race data from your analysis packet, your guild must create a full performance report. You will map the progress of all three prototypes on the same timeline and determine, once and for all, which design is superior."

  • The Activity: Students work in their guilds to complete your fantastic Race Analysis Worksheet. This is where they will have their big "Aha!" moment and prove that the Rocket Sled (exponential) always wins in the long run.

👾 The Final Boss

• 📝 The Final Performance Review (At Home Quiz)

  • The Story: "The race is over, and the results are clear! Now it's time to file your final performance review. This will certify your status as a Master Engineer."

  • The Activity: Students complete the final check for understanding on idocourses.com.

  • Link to the idocourses.com At Home Quiz (Note for teachers: To get access to this amazing resource, please contact darcistone@alpinedistrict.org!)

• 🏆 The Grand Finale: Victory Screen!

  • To celebrate the end of the unit, we show the epic final race from a first-person perspective! Here is the prompt used to create the final video:

  A cinematic, first-person point-of-view video from inside the cockpit of a futuristic Rocket Sled on a multi-lane test track. The style is like a high-speed racing game. The video starts slow, showing the Cruise Control Car ahead. A Gravity Racer accelerates and passes us. We then watch the Gravity Racer overtake the Cruise Control Car. Suddenly, our engines ignite, and we blast past both vehicles, leaving them far behind. The video freezes on the open track ahead. Epic text appears on the screen: "EXPONENTIAL POWER! FINAL LEVEL CONQUERED!"

• 🏆 The Level Clear Screen: Engineer's Self-Assessment SA 1-5 Exit Ticket

 

• The Story: "The race is over, the data is clear, and your final report is filed. Now for the final debrief. A great engineer always reflects on their performance."

• • The Activity: On the back of their Unit Schedule, students complete their Self-Reported Grade on the following scale:

    • 10 (Lead Engineer!): I have mastered all three vehicle classes and can predict the winner of any race.

    • 8 (Senior Engineer!): I am very close to mastery. I'm confident analyzing all three prototypes.

    • 6 (Junior Engineer!): I can follow the data with some help but need more practice comparing the vehicles.

    • 4 (Intern...): I'm still getting the hang of these different prototypes and will need more guidance.

💡 The Debrief

• My Thoughts:

• Student Reactions: