🐉 Tracking the Quartic Leviathan

Mastering Quartics and the Two-Tiered Scryer's Rune

Quartic Leviathan Polynomials

The hunt gets deadlier! How do you track a beast of legend? You upgrade your magic. In this epic boss battle of a lesson, students will learn to hunt the Quartic Leviathan, mastering double-decker synthetic division to uncover its deepest secrets.

📜 Mission Briefing

🎯 Mission Objective: Students will find all roots of quartic polynomials by using a graphing calculator, applying synthetic division twice, and solving the resulting quadratic. They will also analyze graphs to determine the number of real vs. complex roots.
⏳ Class Time: 1 x 85-minute period
📚 Subject & Level: Secondary Math 3 / Algebra 2
👻 The Adventure: Students become "Cryptozoologists" on a hunt for the Quartic Leviathan. They'll use an "Aetherial Scanner" (graphing calculator) and a powerful "Two-Tiered Scryer's Rune" (double-decker synthetic division) to track the beast and its rare inverted counterpart, the "Shadow Leviathan."
Tracking the Quartic Leviathan Math Quest

🎒 The Armory

Projector/Smartboard & Intro Slides: Google Slide Show Intro
The Tracking Stations Worksheet: Get the Worksheet
The "Lair Map" Floor Puzzle: Get the Polynomial Cards
Video Field Guide (for support): Watch the Video

Quartic Polynomials

Costume & Prop Ideas: Continue the "Lead Cryptozoologist" theme. This is the big boss battle, so maybe add an "epic" prop, like a staff or a large, ancient-looking tome

🗺️ The Walkthrough

✨ Introduction: The Legend of the Leviathan (Approx. 10-15 mins)

The Story: "Cryptozoologists, today we hunt a legend: the Quartic Leviathan. Its path is a complex W-shape with up to four breach points. Our simple Scryer's Rune is not enough; we need the Two-Tiered Scryer's Rune (double-decker synthetic) to track it. Be warned: there are also reports of its dark reflection, the M-shaped Shadow Leviathan."

⚔️ Main Activity: The Tracking Stations (Approx. 45-50 mins)

The Story: "Your expedition teams will now travel to four known Leviathan territories to master the skills needed for the final hunt. Each station will test a different aspect of your tracking abilities."

The Activity: Teams rotate through the four stations, practicing the distinct skills: double-decker synthetic, full analysis from an equation, analyzing graphs, and reconstructing paths.

👾 Mini-Boss Challenge: The Lair Map Puzzle (Approx. 15 mins)

The Story: "Excellent work. Your skills have earned you access to the Guild's archives. Your final trial as a team is to reassemble the fragmented Lair Map of a legendary Leviathan."

The Activity: As teams finish the stations, they move on to the hands-on floor puzzle challenge, matching the giant graph pieces to the correct polynomial and its roots.

👾 The Final Boss

📝 The Final Report (At Home Quiz)

The Story: "The expedition is complete. Now you must file your final, individual report to the Cryptozoologist Guild to certify your mastery in tracking Quartic Leviathans."

The Activity: Students work individually on the At-Home Quiz to Show Mastery. (Note for teachers: To get access to this amazing resource, please contact darcistone@alpinedistrict.org! Also, please hit "submit" to start the quiz fresh, as it generates a new version on each attempt.)