🛹 Full Throttle Learning: Introducing Quadratics with the Gravity Racer

Yesterday we mastered constant speed, but what happens when a vehicle has no engine? In this lesson, we introduce quadratic functions by analyzing a 'Gravity Racer' with constant acceleration. Welcome to Day 2 of the Velocity Design Lab!

📜 Mission Briefing

🎯 Mission Objective: Students will be able to identify key characteristics of quadratic functions and write an equation in the form y = ax² + c by analyzing a pattern's constant second difference.
⏳ Class Time: 1 x 75-minute period
📚 Subject & Level: Algebra 2 / Secondary Math 2
🗓️ Unit Schedule: Day 2 of our Comparing Functions Unit. You can see the full schedule for the entire quest here: Unit 1 Schedule
👻 The Adventure: Engineers will analyze a new prototype: the "Gravity Racer." They'll conduct a hands-on experiment to observe constant acceleration, learn to identify quadratic blueprints, and analyze performance data to master the characteristics of this new vehicle class.

🎒 The Armory

📋 Supply List:

Projector/Smartboard & Google Slideshow
A ramp and a toy car (like a Hot Wheels) for the "Gravity Racer"
The constant speed car from Day 1
Student Paper for (Starter ): Quadratic Activities
Worksheet 1 (Starter & Rotations): Quadratic Characteristics

👕 Costume & Prop Ideas:

The lab coat, safety goggles, and clipboard are back! Consistency in the theme helps students feel like they're returning to their important work as engineers.

🖼️ Digital Assets (The Magic!):

The Lab Entrance: Welcome to the Gravity Racer Trials!

The Velocity Design Lab with a Gravity Racer

(Prompt: "A high-tech, futuristic 'Velocity Design Lab,' in the style of a video game. In the center, a sleek 'Gravity Racer' sits at the top of a large, glowing test ramp. Holographic displays show a perfect parabolic curve and the equation y = ax² + c. The title 'Velocity Design Lab: Gravity Racer Trials' is displayed prominently.")

🗺️ The Walkthrough

✨ Introduction: The Prototype Showdown (Approx. 10 mins)

The Story: "Engineers, welcome back! Yesterday, you certified our 'Cruise Control Car.' Today, a new prototype has arrived: the 'Gravity Racer.' Before we analyze its blueprints, we need to run a simple, side-by-side performance observation."

The Activity: I start with a hands-on discovery. First, we run the constant speed car on a flat track to review "constant speed." Then, we release the toy car down a ramp. Students immediately see the difference: it starts slow and gets faster. This is the perfect moment to introduce our new key term: **constant acceleration**.

⚔️ Activity 1: Vehicle Identification (Approx. 10 mins)

The Story: "Now that you've seen acceleration in action, let's learn to spot its signature in the blueprints. A true engineer can identify a Gravity Racer's specs instantly."

The Activity: Students complete the "What Makes a Quadratic?" section of their activity sheet to practice identifying quadratic expressions.

⚔️ Activity 2: Performance Analysis (Approx. 25 mins)

The Story: "Now for the deep analysis. The key to the Gravity Racer is its constant acceleration, which we find in the **second difference** of its performance data. And here's the secret: the 'a' value in our blueprint is always **half of that acceleration**!"

The Activity: I use the "Quadratic Characteristics" document to guide them through a full example, from a pattern to the final equation `y = ax² + c`. Show they understand by doing the First section of this DESMOS Activity Desmos Activity to Check Characteristics

⚔️ Activity 3: Test Track Simulations (Approx. 20 mins)

The Story: "Your analysis is complete. Now it's time to run some simulations. Each guild will rotate through the simulation bays to test their skills on different Gravity Racer prototypes."

The Activity: Students work in their guilds on the Rotation Stations from their activity sheet, applying the new rules to find the 'a' and 'c' values for different scenarios.

👾 The Final Boss

📝 The Certification Exam (Exit Ticket)

The Story: "Engineers, your final certification test is here! Prove you can analyze a Gravity Racer's performance data and write its official blueprint."

[Exit Ticket Score Cards]

🏆 The Level Clear Screen: Engineer's Self-Assessment

The Story: "File your final performance review. A great engineer always reflects on their work."

The Activity: On the back of their Unit Check-off Schedule, students complete their Self-Reported Grade.

10 (Lead Gravitics Engineer!): I have mastered acceleration and can design my own gravity racers.
8 (Senior Engineer!): I am very close to mastery and confident with most blueprints.
6 (Junior Engineer!): I can follow a blueprint with some help but need more practice with acceleration.
4 (Intern...): I'm still getting the hang of this gravity thing and will need more guidance.