🎒 The Armory Quadratic x & y-Intercepts to Sketch Quadratic

 ⚒️ Classroom Quests: The Archaeologist's Cipher

x and y-Intercepts to Graph Cipher Unlock Treasure Hunt

Kicking off a new unit on quadratics can be a challenge, but what if we turned it into an exciting treasure hunt for a legendary lost treasure? For this adventure, I was inspired by my research into the Utah outlaw Butch Cassidy. The legends of his hidden loot right here in Utah got me thinking... what if his treasure map wasn't a map at all, but a puzzle? An ancient, mathematical cipher disk?

Using x and y intercepts on Quadratics for a Treasure Hunt

Today, we're becoming relic hunters. We've found the artifact—now we must learn to read its ancient quadratic code to unlock the path to the treasure. Welcome to the quest!

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🎒 The Armory

• 📋 Supply List:

  • Projector/Smartboard

  • The Cipher Disk Google Slides: Google Slide presentation

  • Archaeologist's Worksheet / Digital Practice: The Cipher Story & Practice Problems on IDO IDO Fun Archaeoligist's Graphing to Activate Ciphers

    (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.)

  • Ancient Tablet Fragments (Matching Cards): An optional hands-on activity. Get the cards here.

  • Video Field Guide: A video for extra help on the lesson. Watch the video here.

• 👕 Costume & Prop Ideas:

  • Go for the adventurous archaeologist look! A fedora or wide-brimmed hat, a vest with pockets, and maybe even a toy magnifying glass.

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🖼️ Digital Assets: The Cipher Disk Sequence

Google Slide Show for First part of Lesson

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🗺️ The Walkthrough (85-Minute Class)

• ✨ Introduction: 

• The Story: "Welcome, archaeologists! We've made an incredible discovery: an ancient cipher disk rumored to lead to Butch Cassidy's lost treasure. The disk has 10 rotating rings, locked by a quadratic code. Our mission is to solve these codes, align the rings, and unlock the map to the treasure!"

• Instructions: Introduce the factored form y = a(x - p)(x - q). Explain that solving for the x- and y-intercepts is the key to "deciphering the code" for each ring.

  The Legend of the Lost Cipher

  As many of you know, I love to hike and explore all over the Southwest. One place we've explored a lot is the San Rafael Swell, and this summer, I started to learn about a fascinating mystery that started right here in Utah.

  It began with a boy just your age who desperately needed a pair of overalls and some shoes. One night, he broke a window to a shop and stole them, but left a promise note that he would pay for them later. That boy was Butch Cassidy, and this event started the fascinating story of him becoming a robber of the rich before mysteriously disappearing.

  Some believe that he had to run too quick across the Mexico border to escape the law, but others believe he hid right here in Utah, and that his loot is still here. A more interesting theory connects to the awful treatment of the mine workers in the San Rafael region. They were living in crazy poverty and dying like flies from unsafe conditions. Some say Butch was a modern-day Utah Robin Hood, stealing from the rich mine owners to help provide for the hundreds of fatherless families left behind.

  Who knows the real story? But it got me thinking...

  Today, you are on your own archaeology dig. You're trying to use your knowledge of x- and y-intercepts to find a lost cipher he left behind—a secret mathematical map that might finally lead to his treasure.

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  Launch Starter for x and y-Intercepts for Quadratics
  
  

• THE ARCHAEOLOGIST'S CODE 5 Practice Problems for x & y Intercepts

• Archaeologist's Code"—a mantra they must know to read the maps.

  • To find the x-intercept (where it hits the ground):

    "To find the spot on the ground below, let the 'y' equal zero!"

  • To find the y-intercept (the launch point):

    "To find the height where the path did start, let 'x' be zero and do your part!

• Every ancient map follows a parabolic path. To read it, you must know the code for its two most important locations:
  The Landing Spots (x-intercepts):
  To find the spot on the ground below, Let the 'y' equal zero!
  The Launch Point (y-intercept):
  To find the height where the path did start, Let 'x' be zero and do your part! Let's practice deciphering these five transmissions from our field team...

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  Connect The Tiles to Find Location of the Cipher
  
  

• ⚔️ Activity 1:  Reassembling the Tablets (Approx. 20 mins)

  • Objective: For teams that finish the cipher early or for a different hands-on approach.

  • The Story: "Your team has decoded the main artifact! Now, let's analyze these smaller tablet fragments found at the dig site."

  • Instructions: Teams work together with the Ancient Tablet Fragments (matching cards).

• 👾 The Final Discovery (Approx. 15 mins)

  • The Story: "Incredible work! You found the cipher.  Now you just need to activate it to find the treasure. Now you must face one last challenge on your own to activate the cipher and prove you've truly mastered the ancient code and can claim the treasure."

  • The Activity: Students work individually on the Final Challenge on IDO and then the exit challenge and ticket.

    (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.)

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  Cipher Discovered - Not is time to Power it UP

  
  

  
  

• The Legend of the Cipher Disk

• ⚔️ Main Activity: Decoding the Cipher (Approx. 40 mins)

  • Objective: To solve 10 quadratic problems to progressively unlock the cipher disk.

  • The Story: "The artifact is dormant. Each quadratic you solve provides the key to align one more ring. Let's begin the decoding sequence!"

  • Instructions:

    1. Put students into expedition teams. Direct them to the IDO Cipher Story activity, where the 10 problems are located.

    2. Continue this process for all 10 problems, using the Google Slides to guide the story as students work through the problems on IDO.

• 👾 The Final Chamber (The Boss Challenge)

  (Approx. 10-15 mins)

  • The Story: "Incredible work, Archaeologists! The cipher has revealed the location of the treasure chamber. But there's one final obstacle: the chamber door is sealed by a complex quadratic lock. You must use everything you've learned to decipher this final inscription on your own to unlock the vault and claim the treasure!"

  • The Activity: Students will now work individually on the final boss challenge to show what they have learned.

    • Unlock the Final Chamber on IDO (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.)

  • The Reward: Successfully completing this challenge unlocks the final reward: the true story of Butch Cassidy's treasure!

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  • THE ARCHAEOLOGIST'S CODE

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  • Every ancient map follows a parabolic path. To read it, you must know the code for its two most important locations:

    The Landing Spots (x-intercepts):

    To find the spot on the ground below, Let the 'y' equal zero!

    The Launch Point (y-intercept):

    To find the height where the path did start, Let 'x' be zero and do your part!

    Let's practice deciphering these five transmissions from our field team...

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🏆 Level Clear Screen: Archaeological Skills Assessment

Printable for Exit Cards for 1D

• The Story: "Excellent work, archaeologists! Your ability to decode the ancient cipher and uncover the treasure's location has been evaluated."

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

• 10 (Master Archaeologist!): I can effortlessly decode any quadratic cipher. The treasure is mine!

• 8 (Skilled Decoder!): I'm confident with the code but might double-check my calculations on a tricky ring.

• 6 (Junior Explorer!): I can decode the cipher with my team but need more practice on my own.

• 4 (Needs a Guide...): I'm still learning the symbols. I'll need to study the ancient texts further.

My Butch Cassidy Video Link if you are interested in continuing the treasure Hunt.