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📡 Codebreaker's Guild - Part 2: Operation: Shield-Break

Shauna November 14, 2025

 

📡 Codebreaker's Guild - Part 2: Operation: Shield-Break

Mission: Find the exact coordinates to disable the enemy's Quadratic Shield.

Find the Exact point where the laser (line) hits the shield.(Parabola)
Find the exact point where the laser (line) hits the shield (parabola)
"A rival guild has protected their HQ with a 'Quadratic Shield.' Our visual plots (graphing) are just *estimates*. We need *exact coordinates* (algebra) to fire our disabling pulse. Your mission is to master the three intercept techniques. The "Master Key" (Formula) is for practice. This... this is the real thing." - The Guild Master
   

📜 Mission Briefing

   
           
  • 🎯Mission Objective: Learn three methods (graphing, substitution, elimination) to find the *exact* coordinates to disable an enemy's "Quadratic Shield."
    •        
  • ⏳Class Time: 3 Class Periods (20-min "Mission Briefings," 30+ min "Formula Marathon").
    •        
  • 📚Subject & Level: Secondary Math 2 (Quadratics Unit)
    •        
  • 👻The Adventure: A 3-day "Shield-Break Bootcamp." Day 5 is the "Simulator." Day 6 is finding "Exact Hit Coordinates." Day 7 is disabling "Dual Shields."
    •    
   

🎒 The Armory

        

🔧 Decoder's Toolkit (Days 5-7)

      

🧑‍🏫 Guild Support (Video)

   
   

🗺️ The Walkthrough: A Teacher's Field Guide

       

🔥 Day 5: The "Shield Simulator" (20 min)

The "Hattie Hat" Check: Clarity (d=0.75), Spaced Practice (d=0.60), Feedback (d=0.70).

Teacher Instructions:

  1. (5 mins) The Entry Event: As students enter, have the "Spy Thriller" music playing.
    • Start class. "Codebreakers. We have an urgent mission. Stand by for the Guild Master's briefing."
    • Play your 30-second "Operation: Shield-Break" video on the main screen.
  2. (15 mins) The "Simulator" & "Certification":
    • "Your first task is to get familiar with the enemy's tech. Open the 'Shield Simulator' (IDO 3734). This is your training. Learn the difference between a 'Hit' and a 'Ghost Signal.'"
    • "Once you've run the simulator, you must pass the 'Certification' (IDO 3322). This proves you can visually identify a target."
    • While they work, you are monitoring... and hyping the *next* part.
  3. (30+ mins) The Marathon:
    • "Certification complete? Good. Now, practice your Master Key. Open the 'Quadratic Formula Marathon' and begin your drills. We can't have rusty skills on a live mission."

Part 1: Self-Reported Grade (d=1.33)

Check the box that best describes your mastery of today's "Hit vs. Miss" simulator.
 3-5 Exit Tickets 

🔟 Master Decoder (A "10" Report)

I can look at any graph of a system and immediately tell if it has 0, 1, or 2 real solutions ("Hits"). I know why a "Miss" happens and what a "Ghost Signal" (a complex answer) means for our mission.

🎱 Skilled Decoder (An "8" Report)

I can easily find the "Hit" coordinates if I see them on the graph. I'm still a little fuzzy on the "Ghost Signal" part, but I definitely know what a "Hit" vs. a "Miss" looks like.

⭐ Decoder-in-Training (A "6" Report)

I was present and I understand the idea of a "Hit" (they cross) and a "Miss" (they don't), but I'm not sure how to tell them apart without the computer doing it for me.

Part 2: Cognitive Task Analysis (CTA) (d=0.69)

Answer the question that matches your grade level above.

  • For "10" Decoders: Draw a quick sketch of a "Miss" (0 real solutions). In your own words, what does this mean our "laser" is doing relative to the "shield"?

    (Your Answer):

    • For "8" Decoders: When you find a "Hit" at (2, 5), what do those two numbers mean? What is at that exact location?

      (Your Answer):

    • For "6" Decoders: In your own words, what is the difference between a "Hit" and a "Miss"?

      (Your Answer):

🔥 Day 6: The "Substitution Cipher" (20 min)



The "Hattie Hat" Check: Worked Example (d=0.57), Cooperative Learning (d=0.54), Multiple Representations (d=0.79).

Intro Idea: The "Live" Guild Master Briefing (3 Mins)

You don't need a video today. You are live. This is a different energy. Stand in front of them in your "Guild Master" costume (the iPad prop is perfect here).

  • (The "Hook"): "Recruits. Yesterday was a success. You passed the simulator. You can visually identify a 'Hit' vs. a 'Miss.' But visuals are just estimates. A good spy never estimates."

  • (The "Why"): "To guarantee a 'Shield-Break,' we must fire our pulse at the exact algebraic coordinates. Today, we learn the 'Substitution Cipher'—the algebra behind the hit."

  • (The "Mission"): "We've intercepted 'Targeting Packages' from the rival guild. But they're scrambled. [Hold up one of the manila envelopes]. Your mission is to work in your cells to re-assemble these packages. You must match the [System] to its [Cipher] and its [Exact Coordinates]. The 'Codebook' (answer key) is at my desk. Get your packages verified. Go!"

How to "Make it Pop" (The "Special Sauce")

  • The Prop (The "Feel"): Don't just give them a baggie of cards. Put each set of 15-18 scrambled cards into a manila envelope. On the front, write (or put a sticker) "CONFIDENTIAL: TARGETING PACKAGE" or a "Codebreaker Guild" logo. Handing them a mission file instead of a "math worksheet" changes everything.

  • Labels for Envelopes






  • The "Win State" (The "Feedback"): This is your Immediate Feedback (d=0.70). When a team has their cards matched, they can't just "be done." They must bring their entire envelope of matched sets to you (the "Guild Master") for verification against the "Codebook" (your answer key).

  • The "Reward" (The "Gamification"): When a team is 100% correct, give them a "Protocol Conquered" sticker (a biohazard sticker, a checkmark, a gold star) to put on their manila envelope. This small physical reward is huge for engagement and "Mastery Learning" (d=0.65).

Teacher Instructions:

  1. (10 mins) The "Guild Master's Briefing" (A Worked Example):
    • "Recruits. Yesterday's visual plots were just *estimates*. A good spy *never* estimates. We need *exact coordinates*. Today, you learn the 'Substitution Cipher.'"
    • On the whiteboard, do ONE worked example (like Set 1 from your card doc). Physically *draw* the cards.

    • 1. Teacher-Worked Example (Your 10-min Briefing)

      "Codebreakers, yesterday's visual plots were just estimates. A good spy never estimates. We need the exact coordinates for the 'hit.' Today, you learn the 'Substitution Cipher.'

      Mission Target:

      • Shield (Card A): y = x² - 4x + 6

      • Laser (Card A): y = x + 2

      Step 1: Set the paths equal. If y equals the shield and y equals the laser, then the shield must equal the laser. x² - 4x + 6 = x + 2

      Step 2: Get the "Cipher" (Set to 0). We must get all terms on one side. I'll subtract x and subtract 2 from both sides. x² - 4x - x + 6 - 2 = 0 x² - 5x + 4 = 0 This is your "Cipher" (Card B). It's the single quadratic that holds the solution.

      Step 3: Solve the "Cipher". We can factor this. We need two numbers that multiply to 4 and add to -5. That's -1 and -4. (x - 1)(x - 4) = 0 Our exact x-coordinates for the "hits" are x = 1 and x = 4.

      Step 4: Find the "Exact Coordinates" (Card C). Now we plug our x-values into the easiest equation (the laser path!) to find their partners.

      • If x = 1: y = (1) + 2 = 3. First Hit: (1, 3)

      • If x = 4: y = (4) + 2 = 6. Second Hit: (4, 6)

      These are your "Exact Coordinates" (Card C). This is the three-card set you are matching in your 'Targeting Packages.' Go!"

    • "This is **Card A: The System**. This is **Card B: The Cipher**. And this... [box the answer]... is **Card C: The Exact Coordinates**. Your mission is to see how they're all connected."
  2. (10 mins) The "Targeting Packages" Activity:
    • Put students in groups. Give each group a baggie of the "scrambled" cards (from your Google Doc).
    • "I've given you five scrambled 'Targeting Packages.' Your mission is to re-assemble them. Match the [System] to its [Cipher] and its [Coordinates]. You will need to check off your work with me. Make sure you have work for each example.  Go!"
  3. (30+ mins) The Marathon:
    • "Packages secured? Good. Back to the Marathon. Keep those skills sharp."
   

End-of-Shift Report: Mission 006 (The Substitution Cipher)

Your Name: _________________________

Part 1: Self-Reported Grade (d=1.33) Exit Ticket

Check the box that best describes your mastery of today's "Targeting Package" card sort.

🔟 Master Decoder (A "10" Report)

I can match all 3 cards (System, Cipher, Coordinates). I understand exactly how to get from "Card A" (The System) to "Card B" (The Cipher) using substitution and setting it to zero.

🎱 Skilled Decoder (An "8" Report)

I can match the "System" (Card A) to the "Coordinates" (Card C) and I understand the idea of the "Cipher" (Card B). I might make a small algebra mistake setting it up, but I know what the goal is.

⭐ Decoder-in-Training (A "6" Report)

I can match "Card A" (System) to "Card C" (Coordinates) using a calculator, but I was confused about what "Card B" (The Cipher) was, how to get it, or why it was important.

Part 2: Cognitive Task Analysis (CTA) (d=0.69)

Answer the question that matches your grade level above.

  • For "10" Decoders: When you go from "Card A" to "Card B," what is the most common mistake a rookie codebreaker might make with their algebra?

    (Your Answer):

  • For "8" Decoders: In your own words, what is the "Cipher" (Card B) and how do you get it from the "System" (Card A)?

    (Your Answer):

  • For "6" Decoders: What is the first step of substitution? (What do you set equal to what?)

    (Your Answer):

🔥 Day 7: The "Elimination Protocol" (20 min)

Day 7 Lead-In: "The Urgent Update"

(The 5-Minute "Entry Event")

As students enter, have the same "Spy Thriller" music playing, but maybe a little faster-paced or more tense. You're standing at the front of the room (in costume) with your iPad prop.

Your Script (as Guild Master):

"Codebreakers, get seated. We have a new development.

Yesterday, your teams successfully decoded the 'Targeting Packages.' We confirmed the 'Substitution Cipher' works, and we have the exact coordinates for a single laser hit.

(You tap on your iPad prop, look concerned)

"But we have a problem. Intel just came in. The rival guild... they know we're on to them. They've upgraded.

(On the whiteboard, quickly sketch two intersecting parabolas. No numbers, just the visual)

"They're not using a single shield anymore. They've deployed 'Dual-Shield Technology.'

"This is a mess. Our 'Substitution' tactic is too slow and complicated. By the time we run the algebra, they'll have triangulated our position.

"But... our analysts found a 'Weak Point.' (Circle the intersection points on your sketch). Where the two shields overlap... they create a harmonic frequency... and a vulnerability.

"Today's mission is the 'Elimination Protocol.' It's a power move. We are going to stack their shield equations and eliminate the noise. This is the fastest, most direct way to find the exact coordinates of that Weak Point.

"I will show you the protocol one time... then you are live. The 'Weak Point' coordinates are posted around this room. Find three. Get them verified. Go."

Then, you transition directly into the Teacher-Worked Example for Day 7 from the day_6_and_7_briefing_assets.md file.

This script:

  1. Validates yesterday's work (Substitution).

  2. Raises the stakes (Dual Shields!).

  3. Creates a "why" for the new method (Substitution is too "messy").

  4. Connects the math term ("Elimination") to the theme ("Elimination Protocol").

This live briefing is all you need to make Day 7 just as exciting as the previous two.



The "Hattie Hat" Check: Worked Example (d=0.57), Cooperative Learning (d=0.54), Immediate Feedback (d=0.70).

Teacher Instructions:

  1. (10 mins) The "Guild Master's Briefing" (A Worked Example):
    • "Urgent update! The rival has *two* parabolic shields. [Show a quick sketch of two intersecting parabolas]. Substitution is too messy. We must use the 'Elimination Protocol'—stacking the signals—to find where the *two shields intersect*. This is their 'Weak Point.'"
    • On the whiteboard, do ONE worked example (like Poster 1). Show how you stack them and *why* subtraction is the key move.
  2. (10 mins) The "Weak Point" Gallery Walk:
    • (Have your posters already up). "The 'Weak Point' protocols are posted around the room. In your pairs, go to any poster. Copy the system. Solve it on your mission file. Check your answer with the key on the poster. Your goal: Successfully find *three* weak points. Go!"
  3. (30+ mins) The Marathon:
    • "Weak points found? Excellent. Final day on the Marathon. Make it count."
   

👾 The Final Boss

   

📝 The Final Targeting Solution

   

The Story: You've mastered all three techniques. Now, file your final targeting solutions for three different shields.

   

The Activity: A 3-problem "at-home" quiz.
Problem 1: Solve by Graphing (A visual plot).
Problem 2: Solve by Substitution (A line & shield).
Problem 3: Solve by Elimination (A dual shield).

   

🏆 The Level Clear Screen: Performance Review

   

The Activity: A daily "End-of-Shift" report (Exit Ticket).

        
       

🔟 Master Decoder (A "10" Report)

         

I can confidently use all 3 methods. I know *why* we need algebra for an "Exact Hit" and *when* to use Elimination (Dual Shields) vs. Substitution (Laser & Shield).

         

My Reflection (CTA for Day 7): (Look at this Dual-Shield system: `y = 3x² + 5x` and `y = x² + 5x - 4`. Why is 'Elimination' the superior tactic here?)

       

🎱 Skilled Decoder (An "8" Report)

         

I can find the "Exact Hit," but I strongly prefer one method. The "Dual Shield" (Elimination) problems were tricky, but I get the idea.

         

My Reflection (CTA for Day 6): (For this mission, why is getting the *algebraic answer* (Card C) better than just *looking at the graph* (Day 5)?)

       

⭐ Decoder-in-Training (A "6" Report)

         

I passed the "Simulator" (Day 5), but the algebra on Day 6 & 7 was confusing. I'm not sure when to pick which method.

  T-size: x-small;">← Previous Mission: Part 1 - Unveiling the Master Key          

My Reflection (CTA for Day 5): (Draw a quick sketch of a "Miss" (0 real solutions). What does this mean for our mission?)

   
   

🧐 Hattie Expert Debrief (For Teachers)

   

This 3-day design is a deliberate balance, prioritizing fluency-building while introducing new concepts. The "Shield-Break" mission provides the *why*.

   
           
  • Spaced Practice (d=0.60): The "Quadratic Formula Marathon" is a prime example of this. Instead of one "drill and kill" day, students practice the skill over multiple days, moving it from short-term to long-term memory.
  • Worked Examples (d=0.57): The 10-min "Guild Master's Briefing" each day is a classic, high-impact 'I Do' that sets the success criteria for the cooperative activity.
    • T-size: x-small;">← Previous Mission: Part 1 - Unveiling the Master Key        
  • Clarity (d=0.75) & Scaffolding (d=0.53): The unit progresses logically: Day 5 (The Visual), Day 6 (The "Easy" Algebra - Subst.), Day 7 (The "Hard" Algebra - Elim.). The mission provides a clear narrative for *why* we are learning each new step.
  • Cooperative Learning (d=0.54): The "Targeting Packages" (Day 6) and "Weak Point" Gallery Walk (Day 7) get students out of their seats, talking math, and providing feedback to each other.
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  • Metacognitive Strategies (d=0.69): The CTA prompts are now tied directly to the mission. "Why is algebra better than graphing *for this mission*?" This links the skill to the purpose.
   ← Previous Mission: Part 1 - Unveiling the Master Key   Next Mission: Part 3 - Reverse-Engineering the Blueprint →
Shauna

Posted by Shauna

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