Vault Breakers Activity
M.I.A. Classified Dossier Level 6 Entry Protocol
Operation Vault Breaker
4 Security Locks
Team Problem-Solving Lab
Team Code Name:
Agents:
Period/Date:
① Facilitator Reads clues aloud & keeps team pacing
② Scribe Documents verified work & lock keys
③ Quality Checker Double checks math & tests logic
④ Spokesperson Explains group reasoning to class
1
Security Lock #1: The Prime Code Logic
Deduce the 2-digit numeric combination using the security clues.
Target: 2-Digit Number
CLUE A The code is a two-digit odd number strictly less than 50.
CLUE B The sum of its two digits is a multiple of 4 (e.g., 4, 8, 12...).
CLUE C The code is a prime number (has exactly two factors: 1 and itself).
CLUE D The tens digit is greater than the ones digit.
Team Scratchpad / Elimination:
Lock #1 Pin:
2
Security Lock #2: The Balance Chamber
Analyze the balanced beam scales to determine each geometric shape's hidden value.
Target: Final Code Value
Scale 1 (Balanced)
● ●
=
■
2 Circles balance 1 Square
Scale 2 (Balanced)
■
= 18
1 Square + 1 Circle = 18
Scale 3 (Balanced)
■
-
▲
= 7
1 Square - 1 Triangle = 7
Circle (●)
Square (■)
Triangle (▲)
Lock #2 Formula: (■ − ●) × ▲
Verify Lock #1 and Lock #2 with your checker before advancing to Sector 2.
Page 1 of 2
Operation Vault Breaker: Sector 2
Coordinate Infiltration & Operational Relay
Locks 3 & 4 + Master Vault
3
Security Lock #3: The Coordinate Gridlock
Plot the security sensors on the grid, connect them in order, and calculate the boundary area.
Target: Sensor Area (sq units)
5 4 3 2 1 0 1 2 3 4 5 6
A(1,4)
B(5,4)
C(5,1)
D(1,1)
X-Axis: Horizontal Y-Axis: Vertical
Step 1: Sensor Dimensions
Length (from x = 1 to 5):
Width (from y = 1 to 4):
Step 2: Geometric Analysis
Name of polygon created:
Lock #3 Code: Area of Boundary (sq units)
4
Security Lock #4: The Team Relay Chain
Each team agent calculates one step and passes their result to the next agent.
Target: Final Relay Output
Agent 1
\( (36 \div 4) + 7 \)
Output A =
Agent 2
\( \text{Output A} \times 2 - 8 \)
Output B =
Agent 3
\( (\text{Output B} + 9) \div 3 \)
Output C =
Agent 4
\( \text{Output C} \times 5 - 4 \)
Lock #4 =
Final Protocol: Master Vault Override Key
Combine all 4 Lock Values
Insert your four verified lock codes into the Master Security Equation:
[ Lock #1 ] + [ Lock #2 ] − [ Lock #3 ] + [ Lock #4 ] =
Teacher Clearance:
[ Verified & Approved ]
Mission Debrief: Team Problem-Solving Reflection
1. Which lock required the most team communication, and why?
2. One specific way our team helped each other succeed today:
6th Grade Mathematics • Collaborative Problem Solving Protocol Page 2 of 2
Vault Breakers Answer Key
Teacher Dossier & Key First-Week Math Lab
Vault Breakers Answer Key
Master Key Verified
Quick-Check & Facilitation Guide
Rapid-Scan Walk-Around Solution Strip Glance check as you circulate the classroom
Lock #1 31
Lock #2 30
Lock #3 12
Lock #4 51
Master Vault 100
1
Lock #1: The Prime Code Logic • Solution: 31
Target Concept: Number Properties & Deductive Logic
Step-by-Step Deductive Trail:
- • Clue A (Odd < 50): Candidates are 11, 13, 15, ..., 49.
- • Clue C (Prime): 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
- • Clue B (Digit sum multiple of 4): Test digit sums: \( 1+3=4 \) (13), \( 1+7=8 \) (17), \( 3+1=4 \) (31).
- • Clue D (Tens > Ones): In 13, \( 1 < 3 \) (no); in 17, \( 1 < 7 \) (no); in 31, \( 3 > 1 \) (yes!).
Common Misconceptions
Students often mistake odd composites (like 15, 21, or 27) for primes, or reverse Clue D to pick 13.
Teacher Coaching Prompt:
“Check your candidate list: does every number have exactly two factors? Look closely at your tens and ones digits.”
2
Lock #2: The Balance Chamber • Code: 30
Target Concept: Pre-Algebra & Substitution
Step-by-Step Algebraic Logic:
- Scale 1: \( \text{■} = 2 \times \text{●} \) (1 Square equals 2 Circles).
- Scale 2: \( \text{■} + \text{●} = 18 \). Substitute: \( (2\text{●}) + \text{●} = 18 \Rightarrow 3\text{●} = 18 \Rightarrow \mathbf{\text{●} = 6} \).
- Find Square: \( \text{■} = 2 \times 6 = \mathbf{12} \). Check: \( 12 + 6 = 18 \).
- Scale 3: \( \text{■} - \text{▲} = 7 \Rightarrow 12 - \text{▲} = 7 \Rightarrow \mathbf{\text{▲} = 5} \).
- Lock Formula: \( (\text{■} - \text{●}) \times \text{▲} = (12 - 6) \times 5 = 6 \times 5 = \mathbf{30} \).
Key Value Check
● = 6
■ = 12
▲ = 5
Teacher Coaching Prompt:
“If 1 Square is worth 2 Circles, how many Circles total are resting on Scale 2? How can that help you find one Circle?”
Teacher Guide • Operation Vault Breaker Solutions Page 1 of 2
Answer Key: Sector 2 & Master Override
Geometry, Relay Fluency, and Team Debrief Protocols
Locks 3 & 4 Solutions
