Operation Undo Worksheet
Classified Mission Brief
OPERATION: UNDO
Subject: Isolating Variables via Inverse Tactics
Clearance Level
Level 1 Math Agent
Agent Name:
Agent Code Name:
Date of Assignment:
The Agent's Toolkit: Inverse Operations
RECON ONLY
In algebra, your primary goal is to isolate the variable (get the mystery letter by itself). To unmask a variable, you must undo whatever operation is happening to it by using its inverse operation.
Operation + Addition
Inverse Tool - Subtraction
Operation - Subtraction
Inverse Tool + Addition
Operation × Multiplication
Inverse Tool ÷ Division
Operation ÷ Division
Inverse Tool × Multiplication
The Golden Rule: An equation is a balanced scale. Whatever you do to one side of the equals sign, you must do exactly the same to the other side to keep it balanced!
Case File A: Undo Addition
Equation to Solve:
\( x + 7 = 15 \)
-
Identify: The variable \( x \) has 7 added to it.
-
Apply Inverse: Subtract 7 from both sides to keep balance.
\( x + 7 - 7 = 15 - 7 \)
-
Solve & Check: Calculate the final answer.
\( x = 8 \)
Case File B: Undo Division
Equation to Solve:
\( \frac{y}{4} = 6 \)
-
Identify: The variable \( y \) is divided by 4.
-
Apply Inverse: Multiply both sides by 4 to keep balance.
\( \frac{y}{4} \cdot 4 = 6 \cdot 4 \)
-
Solve & Check: Calculate the final answer.
\( y = 24 \)
TOP SECRET // OPERATION UNDO BRIEFING PAGE 1 OF 4
Training Ground
Mission phase: Guided Simulation Practice
Training Orders
Fill in the missing undo steps
Before you hit the field, practice your inverse tactics on these 4 targets. Show exactly how you balance each scale by applying the inverse tool to both sides of the dashed line!
Training Target 1 (Addition)
\( a + 5 = 12 \)
How to undo \( +5 \)? Subtract \( 5 \) from both sides:
\( a + 5 - 5 = \)
(Compute both sides!)
Isolate Variable: a =
Training Target 2 (Subtraction)
\( b - 8 = 11 \)
How to undo \( -8 \)? Add \( 8 \) to both sides:
\( b - 8 + 8 = \)
(Compute both sides!)
Isolate Variable: b =
Training Target 3 (Multiplication)
\( 3c = 18 \)
How to undo times \( 3 \)? Divide both sides by \( 3 \):
\( \frac{3c}{3} = \)
(Compute both sides!)
Isolate Variable: c =
Training Target 4 (Division)
\( \frac{d}{5} = 4 \)
How to undo divide by \( 5 \)? Multiply both sides by \( 5 \):
\( \frac{d}{5} \cdot 5 = \)
(Compute both sides!)
Isolate Variable: d =
TOP SECRET // OPERATION UNDO TRAINING GROUND PAGE 2 OF 4
FIELD OPERATIONS
Mission phase: Independent Tactical Solutions
Required Mission Actions
Show work & solve for codes
Field Orders: Solve each case below independently. You MUST write down the inverse step in the workspace box to get credit. Then match your numerical answers to crack the secret password!
Mission Code: T Target 1
\( x + 11 = 15 \)
Workspace
x =
Mission Code: A Target 2
\( y - 9 = 12 \)
Workspace
y =
Mission Code: R Target 3
\( 6z = 48 \)
Workspace
z =
Mission Code: G Target 4
\( \frac{w}{5} = 3 \)
Workspace
w =
Mission Code: E Target 5
\( p - 7 = 11 \)
Workspace
p =
Mission Code: T Target 6
\( 4q = 16 \)
Workspace
q =
Declassify the Code: Secret Location
DECRYPTOR
Your targets are solved! Match your final numeric answers to the mission codes above to uncover the location of the enemy coordinates. Fill in the letters corresponding to the answers below:
Value: 4
Value: 21
Value: 8
Value: 15
Value: 18
Value: 4
Location Code Decoded: _ _ _ _ _ _
TOP SECRET // OPERATION UNDO FIELD MISSIONS PAGE 3 OF 4
Level 2 Math Agent
ADVANCED MISSIONS
Mission phase: Two-Step Variable Conflicts
Tactical Upgrade
Undo two Operations
The Advanced Toolkit: SADMEP Method
LEVEL 2 Clearance
When an equation has two operations, you must undo them in the **reverse** order of operations. Think of it as peeling back layers! We use SADMEP (PEMDAS backwards):
Step 1: SA
Undo Subtraction & Addition
Always get rid of the loose numbers added or subtracted first!
Step 2: DMEP
Undo Division & Multiplication
Then undo any multiplication/division attached directly to the variable!
Example: Solve \( 2x + 5 = 13 \)
1. Undo +5 (Subtract 5):
\( 2x + 5 - 5 = 13 - 5 \)
\( 2x = 8 \)
2. Undo ×2 (Divide by 2):
\( \frac{2x}{2} = \frac{8}{2} \)
\( x = 4 \)
Advanced Target 1 Classified File
\( 3g + 4 = 19 \)
1. Undo +4
2. Undo ×3
Two-Step Workspace
g =
Advanced Target 2 Classified File
\( 2h - 7 = 11 \)
1. Undo -7
2. Undo ×2
Two-Step Workspace
h =
Advanced Target 3 Classified File
\( \frac{j}{3} + 2 = 6 \)
1. Undo +2
2. Undo ÷3
Two-Step Workspace
j =
Advanced Target 4 Classified File
\( \frac{k}{5} - 4 = 2 \)
1. Undo -4
2. Undo ÷5
Two-Step Workspace
k =
TOP SECRET // OPERATION UNDO ADVANCED MISSIONS PAGE 4 OF 4
Operation Undo Answer Key
Teacher Answer Key
OPERATION: UNDO
Subject: Isolating Variables via Inverse Tactics // Solutions Manual
Clearance Level
Master Instructor
Note for Instructors: All solutions, intermediate algebraic steps, and code decryptor answers are highlighted below in red / magenta. Use this guide to verify student workspace calculations and final results.
The Agent's Toolkit: Inverse Operations
RECON ONLY
In algebra, your primary goal is to isolate the variable (get the mystery letter by itself). To unmask a variable, you must undo whatever operation is happening to it by using its inverse operation.
Operation + Addition
Inverse Tool - Subtraction
Operation - Subtraction
Inverse Tool + Addition
Operation × Multiplication
Inverse Tool ÷ Division
Operation ÷ Division
Inverse Tool × Multiplication
The Golden Rule: An equation is a balanced scale. Whatever you do to one side of the equals sign, you must do exactly the same to the other side to keep it balanced!
Case File A: Undo Addition
Equation to Solve:
\( x + 7 = 15 \)
-
Identify: The variable \( x \) has 7 added to it.
-
Apply Inverse: Subtract 7 from both sides to keep balance.
\( x + 7 - 7 = 15 - 7 \)
-
Solve & Check: Calculate the final answer.
\( x = 8 \)
Case File B: Undo Division
Equation to Solve:
\( \frac{y}{4} = 6 \)
-
Identify: The variable \( y \) is divided by 4.
-
Apply Inverse: Multiply both sides by 4 to keep balance.
\( \frac{y}{4} \cdot 4 = 6 \cdot 4 \)
-
Solve & Check: Calculate the final answer.
\( y = 24 \)
TOP SECRET // ANSWER KEY BRIEFING PAGE 1 OF 4
Training Ground Solutions
Mission phase: Guided Simulation Answers
Training Orders
Verify algebraic steps below
Training Target 1 (Addition)
\( a + 5 = 12 \)
How to undo \( +5 \)? Subtract \( 5 \) from both sides:
