Operation Codebreaker Worksheet
LEVEL: OPERATIVE MATH DIVISION • DOSSIER #402
OPERATION CODEBREAKER
Agent:
Date:
Squad:
Score: / 100
Tactical Execution Order: PEMDAS Protocol
CRUCIAL: Left-to-Right Priority for Equal Tiers
1. P
Parentheses
\([ \dots ] \quad ( \dots )\)
2. E
Exponents
\(4^2 = 16, \; 2^3 = 8\)
3. M & D
Multiply & Divide
Left to Right →
4. A & S
Add & Subtract
Left to Right →
1
Guided Warm-Up: Funnel Down Each Step
Underline the operation you solve first.
Problem A: \( 28 - 4 \times (2 + 3) \)
Step 1 (Parentheses): \( 28 - 4 \times \) [ _____ ]
Step 2 (Multiply): \( 28 - \) [ _____ ]
Step 3 (Final Value):
Problem B: \( (7 + 1)^2 \div 8 - 5 \)
Step 1 (Parentheses): [ _____ ]\(^2 \div 8 - 5\)
Step 2 (Exponent): [ _____ ]\( \div 8 - 5\)
Step 3 (Divide & Sub):
2
Field Operations: Multi-Step Computations
Show step-by-step simplification in each box
- \( 16 + 4 \times 6 - 9 \) M → A → S
Final Output:
- \( 40 \div 5 \times 2 + 7 \) ⚠ Left → Right
Final Output:
- \( 50 - 2 \times (3 + 4)^2 \div 7 \) P → E → M/D
Final Output:
- \( 9 + (24 - 3 \times 6) + 2^4 \) Nested in ( )
Final Output:
- \( 35 - 12 + 8 - 4 \) ⚠ Left → Right
Final Output:
- \( 3 \times (15 - 2^3) + 24 \div 4 \) Double Group
Final Output:
SECURITY CLEARANCE: TOP SECRET DOSSIER PAGE 1 OF 2 CONTINUE TO MISSION PHASE 2 →
PHASE 2
Advanced Operations & Intelligence Verification
Agent Ref:
3
Forensic Audit: Identify the Calculation Error
Two rogue agents submitted flawed mission calculations. Pinpoint their mistake, explain what went wrong according to PEMDAS, and provide the correct calculation.
Intercept #1 Agent Rook's Work
Expression: \( 18 - 5 + 3 \)
Rook did: \( 18 - 8 = 10 \) ❌
Identify Flaw:
Correct Answer:
Intercept #2 Agent Nova's Work
Expression: \( 48 \div 6 \times 2 \)
Nova did: \( 48 \div 12 = 4 \) ❌
Identify Flaw:
Correct Answer:
4
Target Calibration: Insert Parentheses
Insert exactly one pair of parentheses \( ( \dots ) \) into each expression to make the statement mathematically true.
TARGET A
\( 6 + 4 \times 5 - 2 = 48 \)
Add \( ( \quad ) \) around 2 terms
TARGET B
\( 24 \div 8 - 2 + 1 = 5 \)
Add \( ( \quad ) \) around 2 terms
TARGET C
\( 5 \times 8 - 3 + 2 = 27 \)
Add \( ( \quad ) \) around 2 terms
5
Top Secret Cypher: Crack the Code
DECODER ACTIVE
Solve each letter value below. Match each numerical answer to the Cipher Key to reveal the classified agent rank.
Letter [M]
\( 2 \times (5 + 4) \)
Letter [A]
\( 16 \div 2^2 \)
Letter [S]
\( 10 - 6 + 3 \)
Letter [T]
\( 5 \times 2 + 20 \)
Letter [E]
\( 30 - 3 \times 6 \)
Letter [R]
\( 5^2 \times 1 \)
DECODED RANK (Ascending Values: 4, 7, 12, 18, 25, 30):
6
Tactical Mission Scenario: Fuel Calculation
An aerial reconnaissance drone has 4 auxiliary reserve cells providing 15 liters each. It performs 3 supersonic bursts that consume 6 liters each, and then receives an auxiliary battery boost equivalent to \( 2^3 \) liters.
Part A: Write the Complete Numerical Expression
Part B: Remaining Fuel
Liters
MISSION STATUS: READY FOR GRADING OPERATIVE CODE: PMDAS-2026 DOSSIER PAGE 2 OF 2
Operation Codebreaker Answer Key
MASTER KEY TEACHER DOSSIER • SOLUTIONS & SCORING
OPERATION CODEBREAKER [ANSWER KEY]
Total Value
100 PTS
Pg 1: 50 Pts (Warm-up + Calcs)
Pg 2: 50 Pts (Audit, Puzzle, Decode)
Grading Rule: Verify Left-to-Right evaluation for M/D and A/S tiers before awarding step credit.
FULL WORK REQUIRED
1
Guided Warm-Up Solutions
10 POINTS TOTAL (5 pts each)
Problem A: \( 28 - 4 \times (2 + 3) \)
Step 1 (Parentheses): \( 28 - 4 \times \) [ 5 ]
Step 2 (Multiply): \( 28 - \) [ 20 ]
Step 3 (Final Output): 8
Problem B: \( (7 + 1)^2 \div 8 - 5 \)
Step 1 (Parentheses): [ 8 ]\(^2 \div 8 - 5\)
Step 2 (Exponent): [ 64 ]\( \div 8 - 5\)
Step 3 (Final Output): 3
2
Field Operations: Step-by-Step Solutions
40 POINTS TOTAL (Step work: 4 pts, Final: 2.5 pts)
- \( 16 + 4 \times 6 - 9 \) ✓ M first
\( = 16 + 24 - 9 \)
\( = 40 - 9 = \mathbf{31} \)
Order: \( \times \) then \( + \) then \( - \)
Answer: 31
- \( 40 \div 5 \times 2 + 7 \) ⚠ L → R Trap
\( = 8 \times 2 + 7 \) (Divide first: \( 40 \div 5 = 8 \))
\( = 16 + 7 = \mathbf{23} \) [Trap: \( 40 \div 10 + 7 \neq 11 \)]
Division precedes mult here
Answer: 23
- \( 50 - 2 \times (3 + 4)^2 \div 7 \) ✓ P → E
\( = 50 - 2 \times 7^2 \div 7 = 50 - 2 \times 49 \div 7 \)
\( = 50 - 98 \div 7 = 50 - 14 = \mathbf{36} \)
P: (7), E: \(7^2=49\), M: 98, D: 14
Answer: 36
- \( 9 + (24 - 3 \times 6) + 2^4 \) ✓ Inner M
\( = 9 + (24 - 18) + 16 \)
\( = 9 + 6 + 16 = \mathbf{31} \)
Inside ( ): \(3 \times 6=18\) first
Answer: 31
- \( 35 - 12 + 8 - 4 \) ⚠ A/S Trap
\( = 23 + 8 - 4 \) (\( 35 - 12 = 23 \) first)
\( = 31 - 4 = \mathbf{27} \) [Trap: \( 35 - 20 - 4 \neq 11 \)]
Must subtract 12 before adding 8
Answer: 27
- \( 3 \times (15 - 2^3) + 24 \div 4 \) ✓ Dual Group
\( = 3 \times (15 - 8) + 6 \)
\( = 3 \times 7 + 6 = 21 + 6 = \mathbf{27} \)
\( 2^3=8 \), \( 15-8=7 \), \( 24\div4=6 \)
Answer: 27
