Expression Duel Answer Key Classified File // Duel-Alpha-Key
Expression Duel
Teacher Intel: Official Answer Key
Security Clearance: Level 5 Only
Mission Summary
Total Cards
12
Max Value
50
Min Value
7.5
Complexity
High
Card 01 ID: X-DELTA
If \( x = 6.5 \), find \( 2(x + 3.5) - 4 \)
\( 2(6.5 + 3.5) - 4 \rightarrow 2(10) - 4 \)
FINAL VALUE: 16
Card 02 ID: Y-OMEGA
If \( y = 20 \), find \( \frac{3}{4}y + 12 \)
\( \frac{3}{4}(20) + 12 \rightarrow 15 + 12 \)
FINAL VALUE: 27
Card 03 ID: Z-THETA
If \( z = 4 \), find \( z^2 + 2.5z \)
\( 4^2 + 2.5(4) \rightarrow 16 + 10 \)
FINAL VALUE: 26
Card 04 [ELITE] ID: A-SIGMA
If \( a = 1.2 \), find \( 5(a - 0.2) + 10.5 \)
\( 5(1.2 - 0.2) + 10.5 \rightarrow 5(1) + 10.5 \)
FINAL VALUE: 15.5
Card 05 ID: B-GAMMA
If \( b = 15 \), find \( \frac{1}{2}b + 3^2 \)
\( \frac{1}{2}(15) + 9 \rightarrow 7.5 + 9 \)
FINAL VALUE: 16.5
Card 06 ID: M-BETA
If \( m = 5 \), find \( 3(m^2 - 10) \)
\( 3(25 - 10) \rightarrow 3(15) \)
FINAL VALUE: 45
Card 07 ID: N-KAPPA
If \( n = 12.4 \), find \( 100 - 5n \)
\( 100 - 5(12.4) \rightarrow 100 - 62 \)
FINAL VALUE: 38
Card 08 ID: X-PHI
If \( x = 3 \), find \( \frac{x}{0.2} + 5 \)
\( \frac{3}{0.2} + 5 \rightarrow 15 + 5 \)
FINAL VALUE: 20
Card 09 ID: Y-RHO
If \( y = 2.5 \), find \( 4(y + 0.5) + 7 \)
\( 4(3) + 7 \rightarrow 12 + 7 \)
FINAL VALUE: 19
Card 10 ID: P-ZETA
If \( p = 3 \), find \( p^3 - 2p \)
\( 27 - 6 = 21 \)
FINAL VALUE: 21
Card 11 ID: Q-LAMBDA
If \( q = 9 \), find \( \frac{2}{3}q + 1.5 \)
\( 6 + 1.5 = 7.5 \)
FINAL VALUE: 7.5
Card 12 ID: R-EPSILON
If \( r = 15 \), find \( (r - 10)^2 + 25 \)
\( 5^2 + 25 \rightarrow 25 + 25 \)
FINAL VALUE: 50
Teacher Engagement Protocol
Scoring Guidelines: In the 'Expression Duel' format, students should receive full credit for correct substitution even if the final calculation is incorrect. The 'Elite' card (Card 04) features decimal subtraction before multiplication; monitor students for decimal point placement accuracy.
Vault Escape Mission Log Vault Escape
Mission Log: Scavenger Hunt
Agent Name:
Date:
Mission Briefing
Locate a Keypad: Start at any keypad card hidden around HQ. Write the Keypad # in the first box.Record the Code: Write down the "Previous Code" from that card in the "Input" column.Evaluate the Expression: Solve the algebraic expression on the card. Show your work! The Next Key: Your answer is the Output . This number is the "Previous Code" for your next keypad.Escaping the Vault: Continue until you have cracked all 10 keypads and returned to your starting point.
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
Output →
Keypad #____ Input Code →
Show Work Here
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Keypad #____ Input Code →
Show Work Here
Output →
Vault Status
Mission complete when you return to your starting point.
Security Clearance
Verified
Agent Intel Teacher Guide Agent Intel
Top Secret / Teacher Facilitation Guide
Lesson: Variable Victory
Subject: 6th Grade Math
Mission Objective
Students will demonstrate mastery in evaluating algebraic expressions involving whole numbers, decimals, and fractions. This mission utilizes movement and mystery to keep agents engaged while practicing critical substitution and Order of Operations skills.
Mission Timeline (90 Minutes)
00-15m
Briefing & Warm-Up
Use Mission Briefing Slides to review substitution. Ensure students understand that coefficients (e.g., \( 3x \)) require multiplication.
15-30m
Field Training (Guided Practice)
Model complex examples on the slides, focusing on fractional and decimal substitution. Use "The Plug and Chug" method.
30-55m
Codebreaker Challenge
Individual/Pair work using the Codebreaker Worksheet . Advanced agents can proceed to the Elite Codebreaker version.
55-80m
Vault Escape (Scavenger Hunt)
Active movement phase! Hide the Vault Escape Cards around the room. Students use the Mission Log to track their progress through the circular keypad loop.
80-90m
Mission Debrief
Collect the Mission Debrief Exit Tickets . For early finishers during the lesson, have Expression Duel Cards ready at a station.
Vault Escape Setup
Print and cut the 10 Keypad cards. Place them non-sequentially around the room. The activity is self-correcting: if students solve correctly, they find the answer as the "Previous Code" on a different card. Loop: 13 → 15 → 14 → 8.5 → 10 → 35 → 7.5 → 12 → 21 → 9 → 13.
Supply List
Mission Briefing Slides
Codebreaker (Standard & Elite)
Vault Escape Cards (Cut & Hidden)
Vault Escape Mission Logs
Expression Duel Cards (Early finishers)
Exit Tickets
Critical Hazards
Coefficient Confusion
Agents often add when they see \( 3x \). Remind them that side-by-side placement means multiplication.
Fraction Phobia
Encourage agents to treat fractions as division: \( \frac{1}{2}x \) is the same as \( x \div 2 \) or half of \( x \).
Decimal Alignment
Ensure agents line up decimal points when adding results like \( 5 + 1.25 \). Remind them: \( 5 = 5.00 \).
Mission Briefing Slides Mission Control
Variable
Victory
Level 6 Agent Certification
The Variable Cipher
Substitution Protocol
A variable is a placeholder (usually a letter) for a secret number.
The "Plug & Chug"
REPLACE the variable with the value.
USE parentheses to keep it clean.
EVALUATE the expression.
If \( x = 5 \)
\( 3x + 4 \)
\( 3(5) + 4 = 19 \)
Operation Protocol
P
Parentheses
E
Exponents
M / D
Mult / Div
(Left to Right)
A / S
Add / Sub
(Left to Right)
"Failure to follow PEMDAS results in immediate mission termination!"
Field Test: Decimals
Intel Brief:
Evaluate the following expression if:
\( y = 0.5 \)
ACTIVE CODE
\( 10y + 1.25 \)
Step 1: \( 10(0.5) + 1.25 \)
Step 2: \( 5 + 1.25 \)
Solution: 6.25
Field Test: Fractions
Intel Brief:
Evaluate the following expression if:
\( z = \frac{1}{4} \)
ACTIVE CODE
\( 8z - 1 \)
Step 1: \( 8(\frac{1}{4}) - 1 \)
(Hint: 8 divided by 4?)
Step 2: \( 2 - 1 \)
Solution: 1
Expression Duel
01
Draw
Each pair gets a deck of expression cards. Draw one card each.
02
Evaluate
Substitute the variable on the "Intel Sheet" and solve as fast as you can.
03
Compare
The agent with the HIGHER value wins the round and takes both cards!
Vault Escape Answer Key Mission Intel
Vault Escape / Master Answer Key
Confidential: Teacher Use Only
Self-Correcting Loop
The scavenger hunt is designed as a circular loop. Students can start at any station. Their Output (answer) will be the "Previous Code" (Input) at the next station in the sequence. If they cannot find their answer on another card, they have made a substitution or calculation error.
Master Code Sequence
13 → 15 → 14 → 8.5 → 10 → 35 → 7.5 → 12 → 21 → 9 → 13
Keypad 01 INPUT: 13
\( 4x - 1 \) where \( x = 4 \)
\( 4(4) - 1 = 16 - 1 = 15 \)
OUTPUT: 15
Keypad 02 INPUT: 15
\( \frac{y}{3} + 10 \) where \( y = 12 \)
\( \frac{12}{3} + 10 = 4 + 10 = 14 \)
OUTPUT: 14
Keypad 03 INPUT: 14
\( 2.5z - 1.5 \) where \( z = 4 \)
\( 2.5(4) - 1.5 = 10 - 1.5 = 8.5 \)
OUTPUT: 8.5
Keypad 04 INPUT: 8.5
\( 2(a + 1.5) \) where \( a = 3.5 \)
\( 2(3.5 + 1.5) = 2(5) = 10 \)
OUTPUT: 10
Keypad 05 INPUT: 10
\( \frac{1}{2}b + 20 \) where \( b = 30 \)
\( \frac{1}{2}(30) + 20 = 15 + 20 = 35 \)
OUTPUT: 35
Keypad 06 INPUT: 35
\( c - 22.5 \) where \( c = 30 \)
\( 30 - 22.5 = 7.5 \)
OUTPUT: 7.5
Keypad 07 INPUT: 7.5
\( 4w + 2 \) where \( w = 2.5 \)
\( 4(2.5) + 2 = 10 + 2 = 12 \)
OUTPUT: 12
Keypad 08 INPUT: 12
\( m^2 - 4 \) where \( m = 5 \)
\( 5^2 - 4 = 25 - 4 = 21 \)
OUTPUT: 21
Keypad 09 INPUT: 21
\( \frac{3n}{2} \) where \( n = 6 \)
\( \frac{3(6)}{2} = \frac{18}{2} = 9 \)
OUTPUT: 9
Keypad 10 INPUT: 9
\( 1.5k + 8.5 \) where \( k = 3 \)
\( 1.5(3) + 8.5 = 4.5 + 8.5 = 13 \)
OUTPUT: 13
Mission Loop Closed
Output 10 (13) leads back to the Input for Keypad 01.
System Integrity
100% SECURE
Codebreaker Challenge Worksheet Classified
Codebreaker Challenge
Target: Level 6 Variable Mastery
Agent Name:
Mission Date:
Instructions
Evaluate each algebraic expression using the provided variable value. Once you find the solution, match it to the Cipher Key on the final page to decode the secret message. Show all substitution work!
CODE #1 \( x = 4 \)
\( 5x - 7 \)
Value:
CODE #2 \( y = 12 \)
\( \frac{1}{2}y + 10 \)
Value:
CODE #3 \( z = 4 \)
\( 2.5z + 1 \)
Value:
CODE #4 \( b = 2 \)
\( 15 - 3b \)
Value:
Codebreaker Continued
Part 2: Complex Evaluations
CODE #5 \( c = 2 \)
\( 1.25c + 0.75 \)
Value:
CODE #6 \( x = 20 \)
\( \frac{x}{4} + 15 \)
Value:
CODE #7 \( w = 3.5 \)
\( 2(w + 5) \)
Value:
CODE #8 \( m = 6 \)
\( m^2 - 10 \)
Value:
CODE #9 \( w = 2 \)
\( 10w + 2 \)
Value:
CODE #10 \( x = 10.5 \)
\( x - 5.5 \)
Value:
CODE #11 \( x = 4 \)
\( \frac{12}{x} \)
Value:
The Final Cipher
Secret Transmission
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
Cipher Key Protocol
13 = M
16 = A
11 = T
9 = H
3.25 = I
20 = S
17 = P
26 = O
22 = W
5 = E
3 = R
---
Codebreaker Answer Key Agent Intel: Answer Key
Codebreaker Challenge Solutions
Code # Expression & Substitution Solution Letter 1 \( 5(4) - 7 = 20 - 7 \) 13 M 2 \( \frac{1}{2}(12) + 10 = 6 + 10 \) 16 A 3 \( 2.5(4) + 1 = 10 + 1 \) 11 T 4 \( 15 - 3(2) = 15 - 6 \) 9 H 5 \( 1.25(2) + 0.75 = 2.5 + 0.75 \) 3.25 I 6 \( \frac{20}{4} + 15 = 5 + 15 \) 20 S 7 \( 2(3.5 + 5) = 2(8.5) \) 17 P 8 \( (6)^2 - 10 = 36 - 10 \) 26 O 9 \( 10(2) + 2 = 20 + 2 \) 22 W 10 \( 10.5 - 5.5 \) 5 E 11 \( \frac{12}{4} \) 3 R
Decoded Transmission
MATH IS POWER
Mission Complete // Level 6 Clearance Verified
Expression Duel Cards Expression Duel
Elite Tactical Engagement Cards / Deck Omega (HARD)
6 Cards Per Page
Card 01
If \( x = 6.5 \)
\( 2(x + 3.5) - 4 \)
Card 02
If \( y = 20 \)
\( \frac{3}{4}y + 12 \)
Card 03
If \( z = 4 \)
\( z^2 + 2.5z \)
Card 04
Elite Challenge
If \( a = 1.2 \)
\( 5(a - 0.2) + 10.5 \)
Card 05
If \( b = 15 \)
\( \frac{1}{2}b + 3^2 \)
Card 06
If \( m = 5 \)
\( 3(m^2 - 10) \)
Expression Duel Cont.
Deck Omega / Page 2
Card 07
If \( n = 12.4 \)
\( 100 - 5n \)
Card 08
If \( x = 3 \)
\( \frac{x}{0.2} + 5 \)
Card 09
If \( y = 2.5 \)
\( 4(y + 0.5) + 7 \)
Card 10
If \( p = 3 \)
\( p^3 - 2p \)
Card 11
If \( q = 9 \)
\( \frac{2}{3}q + 1.5 \)
Card 12
If \( r = 15 \)
\( (r - 10)^2 + 25 \)
Mission Debrief Exit Ticket Mission Debrief
Final Agent Certification Check
Agent:
Code:
"Final clearance is required to exit HQ. Evaluate the three priority codes below. Failure is not an option, Agent."
Task 01: Whole Numbers
\( x = 8 \)
\( 4x - (10 + 2) \)
Substitution & Work
Final Value:
Task 02: Decimals
\( y = 0.4 \)
\( 10y + 1.6 \)
Substitution & Work
Final Value:
Mission Debrief Cont.
Agent:
Task 03: Fractions
\( z = \frac{1}{3} \)
\( 9z + 2 \)
Substitution & Detailed Work
Final Value:
Certified Level 6 Agent
Elite Codebreaker Worksheet ELITE LEVEL
Elite Codebreaker
MISSION: OMEGA CLEARANCE
Agent ID:
Date:
Operational Directives
Agents must substitute the variable values into the complex expressions provided. Use PEMDAS protocols to ensure precision. Failure to show work will result in immediate disqualification from the Elite Division. Decode the final transmission on Page 3.
CODE ALPHA-01 \( x = 1.5 \)
\( 3(x + 2.5) \)
Value Matrix:
CODE ALPHA-02 \( y = 15 \)
\( \frac{1}{3}y + 2 \)
Value Matrix:
CODE ALPHA-03 \( z = 3 \)
\( z^2 - 0.75 \)
Value Matrix:
CODE ALPHA-04 \( b = 0.5 \)
\( 4(2.5 + b) \)
Value Matrix:
Operational Phase 2
CODE ALPHA-05 \( c = 20 \)
\( \frac{1}{4}c + 3^2 \)
Value Matrix:
CODE ALPHA-06 \( w = 4 \)
\( 2w^2 - 10 \)
Value Matrix:
CODE ALPHA-07 \( m = 10 \)
\( 3(m - 4) \)
Value Matrix:
CODE ALPHA-08 \( n = 22.5 \)
\( \frac{n}{5} + 0.5 \)
Value Matrix:
CODE ALPHA-09 \( k = 5 \)
\( 1.2k + 6 \)
Value Matrix:
CODE ALPHA-10 \( p = 3 \)
\( p^2 + 10 \)
Value Matrix:
CODE ALPHA-11 \( d = 10 \)
\( 5(d - 4) \)
Value Matrix:
CODE ALPHA-12 \( h = 5 \)
\( 10(h - 4.5) \)
Value Matrix:
Elite Transmission
Intercepted Cipher
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
Omega Cipher Protocols
12 = C
7 = R
8.25 = A
14 = K
22 = T
18 = H
5 = E
19 = O
30 = D
UNAUTHORIZED ACCESS FORBIDDEN
Elite Codebreaker Answer Key Elite Answer Key
Mission: Omega Clearance / Classified Solutions
Code ID Evaluation Protocol Value Cipher ALPHA-01 \( 3(1.5 + 2.5) = 3(4) \) 12 C ALPHA-02 \( \frac{1}{3}(15) + 2 = 5 + 2 \) 7 R ALPHA-03 \( (3)^2 - 0.75 = 9 - 0.75 \) 8.25 A ALPHA-04 \( 4(2.5 + 0.5) = 4(3) \) 12 C ALPHA-05 \( \frac{1}{4}(20) + 3^2 = 5 + 9 \) 14 K ALPHA-06 \( 2(4)^2 - 10 = 2(16) - 10 \) 22 T ALPHA-07 \( 3(10 - 4) = 3(6) \) 18 H ALPHA-08 \( \frac{22.5}{5} + 0.5 = 4.5 + 0.5 \) 5 E ALPHA-09 \( 1.2(5) + 6 = 6 + 6 \) 12 C ALPHA-10 \( (3)^2 + 10 = 9 + 10 \) 19 O ALPHA-11 \( 5(10 - 4) = 5(6) \) 30 D ALPHA-12 \( 10(5 - 4.5) = 10(0.5) \) 5 E
Decoded Transmission
CRACK THE CODE
Verification Status: Mission Accomplished
Vault Escape Cards Vault Escape
SCAVENGER HUNT / KEYPADS 01-04
Security Clearance: Lvl 6
Keypad 01
Previous Code
13
Evaluate for \( x = 4 \)
\( 4x - 1 \)
Input result into next keypad
Keypad 02
Previous Code
15
Evaluate for \( y = 12 \)
\( \frac{y}{3} + 10 \)
Input result into next keypad
Keypad 03
Previous Code
14
Evaluate for \( z = 4 \)
\( 2.5z - 1.5 \)
Input result into next keypad
Keypad 04
Previous Code
8.5
Evaluate for \( a = 3.5 \)
\( 2(a + 1.5) \)
Input result into next keypad
Vault Escape
SCAVENGER HUNT / KEYPADS 05-08
Keypad 05
Previous Code
10
Evaluate for \( b = 30 \)
\( \frac{1}{2}b + 20 \)
Input result into next keypad
Keypad 06
Previous Code
35
Evaluate for \( c = 30 \)
\( c - 22.5 \)
Input result into next keypad
Keypad 07
Previous Code
7.5
Evaluate for \( w = 2.5 \)
\( 4w + 2 \)
Input result into next keypad
Keypad 08
Previous Code
12
Evaluate for \( m = 5 \)
\( m^2 - 4 \)
Input result into next keypad
Vault Escape
SCAVENGER HUNT / KEYPADS 09-10
Keypad 09
Previous Code
21
Evaluate for \( n = 6 \)
\( \frac{3n}{2} \)
Input result into next keypad
Keypad 10
Previous Code
9
Evaluate for \( k = 3 \)
\( 1.5k + 8.5 \)
Input result into next keypad
(Vault Space Empty)
(Vault Space Empty)
Teacher Intel: Correct Code Loop
13 → 15 → 14 → 8.5 → 10 → 35 → 7.5 → 12 → 21 → 9 → 13 (Loop)
