Spooky Solvers Worksheet Name:
Date:
Period:
Spooky Solvers
One-Variable Equations • One-Step & Two-Step Haunted Practice
Standard: 7.EE.B.4a
1
The Crypt: One-Step Equations
Isolate the variable using inverse operations. Show all steps.
1. \( x + 17 = 42 \) Addition
\( x = \)
2. \( y - 29 = 15 \) Subtraction
\( y = \)
3. \( 7m = 63 \) Multiplication
\( m = \)
4. \( \frac{k}{6} = 9 \) Division
\( k = \)
5. \( w - 48 = 36 \) Subtraction
\( w = \)
6. \( 9p = 108 \) Multiplication
\( p = \)
2
Potion Lab: Two-Step Spells
Undo addition or subtraction first, then multiplication or division.
7. \( 3n + 8 = 29 \) 2 steps
\( n = \)
8. \( 5x - 14 = 31 \) 2 steps
\( x = \)
9. \( \frac{d}{4} + 9 = 15 \) 2 steps
\( d = \)
10. \( 8c - 25 = 39 \) 2 steps
\( c = \)
Spooky Solver Rule: Always keep the equation balanced! Whatever inverse operation you cast upon the left side of the equals sign, you must also cast upon the right side.
Spooky Solvers • Part II
Cauldron Word Problems & The Skeleton's Secret Code
Name:
3
Witches' Cauldron: Word Problems
Define variable, set up an algebraic equation, and solve.
11. Count Dracula's Candy Run: Count Dracula buys 4 identical bags of sour bat treats and a haunted carved pumpkin that costs $6. If his total bill comes to $38, write and solve an equation to find the cost \(b\) of one bag of sour bats.
Equation:
Cost \(b\) = $
12. Madame Morticia's Spiders: Madame Morticia harvested 75 spider legs. She set aside 15 legs for an invisibility potion and distributed the remaining legs equally into \(j\) potion jars, placing 12 legs in each jar. Write and solve an equation to find the number of jars \(j\).
Equation:
Jars \(j\) =
4
The Skeleton's Cipher Riddle
Solve each letter equation to decode the mystery punchline!
H #1
\( x + 9 = 16 \)
\( x = \)
E #2
\( 4x = 44 \)
\( x = \)
A #3
\( 2x - 3 = 17 \)
\( x = \)
D #4
\( \frac{x}{2} + 5 = 9 \)
\( x = \)
N #5
\( 3x + 2 = 14 \)
\( x = \)
O #6
\( x - 15 = 8 \)
\( x = \)
B #7
\( 5x - 7 = 23 \)
\( x = \)
Y #8
\( 2x + 9 = 15 \)
\( x = \)
Riddle: "Why didn't the skeleton go to the Halloween party?"
Match solution numbers to letters!
7
11
7
10
8
4
23
6
23
8
3
!
Spooky Bonus Challenge: Solve for \( z \): \( 3(z - 4) + 7 = 28 \)
\( z = \)
Spooky Solvers Answer Key Teacher Resource Grade 7 • Expressions & Equations
Answer Key & Scoring Guide
Spooky Solvers • Key
Master Solutions & Full Inverse Operations Guide (Page 1)
Max Score: 50 Points
1
The Crypt: One-Step Solutions
3 pts each (1 pt inverse step, 2 pts final value)
1. \( x + 17 = 42 \) Subtract 17
\( x = 42 - 17 \)
\( \mathbf{x = 25} \)
2. \( y - 29 = 15 \) Add 29
\( y = 15 + 29 \)
\( \mathbf{y = 44} \)
3. \( 7m = 63 \) Divide by 7
\( m = \frac{63}{7} \)
\( \mathbf{m = 9} \)
4. \( \frac{k}{6} = 9 \) Multiply by 6
\( k = 9 \times 6 \)
\( \mathbf{k = 54} \)
5. \( w - 48 = 36 \) Add 48
\( w = 36 + 48 \)
\( \mathbf{w = 84} \)
6. \( 9p = 108 \) Divide by 9
\( p = \frac{108}{9} \)
\( \mathbf{p = 12} \)
2
Potion Lab: Two-Step Solutions
4 pts each (1 pt sub/add, 1 pt div/mult, 2 pts final)
7. \( 3n + 8 = 29 \) Step 1: -8 • Step 2: ÷3
\( 3n = 29 - 8 \implies 3n = 21 \)
\( n = \frac{21}{3} \)
\( \mathbf{n = 7} \)
8. \( 5x - 14 = 31 \) Step 1: +14 • Step 2: ÷5
\( 5x = 31 + 14 \implies 5x = 45 \)
\( x = \frac{45}{5} \)
\( \mathbf{x = 9} \)
9. \( \frac{d}{4} + 9 = 15 \) Step 1: -9 • Step 2: ×4
\( \frac{d}{4} = 15 - 9 \implies \frac{d}{4} = 6 \)
\( d = 6 \times 4 \)
\( \mathbf{d = 24} \)
10. \( 8c - 25 = 39 \) Step 1: +25 • Step 2: ÷8
\( 8c = 39 + 25 \implies 8c = 64 \)
\( c = \frac{64}{8} \)
\( \mathbf{c = 8} \)
Common Misconception Alert: In two-step equations like #9 (\(\frac{d}{4} + 9 = 15\)), students often incorrectly multiply before subtracting the constant term. Remind them: Reverse PEMDAS (undo addition/subtraction before multiplication/division) when solving for an unknown!
Spooky Solvers • Key (Part II)
Word Problem Models & Skeleton Cipher Solutions
Solutions Page 2
3
Word Problem Models
5 pts each (2 pts equation setup, 3 pts solution & units)
11. Count Dracula's Candy Run: Total $38, 4 bags at cost \(b\), plus $6 pumpkin.
Steps:
Spooky Solvers Slides Grade 7 Algebra • Halloween Special
Standard: 7.EE.B.4a
Unraveling Haunted Unknowns
Spooky Solvers
Mastering one-step and two-step one-variable equations with inverse operations and algebraic spellcasting.
Inverse Spells
Undo operations
Reverse PEMDAS
Two-step strategy
Mystery Riddle
Decode the cipher
The Golden Balance Rule
Concept 01
Core Principle
Keep the Scale Balanced!
An equation is like a potion scale in equilibrium. Whatever operation you cast on one side, you must cast on the other side.
Left Side = Right Side
Addition \(\leftrightarrow\) Subtraction
To undo +17, subtract 17 from both sides.
\( x + 17 - 17 = x \)
Multiply \(\leftrightarrow\) Divide
To undo ×7, divide both sides by 7.
\( \frac{7m}{7} = m \)
Goal: Isolate the variable so it stands completely alone on one side of the equal sign!
Remember: Operations always come in inverse pairs! Step 1 of 2
The Crypt: One-Step Practice
Worked Examples
Example 1 Addition Trap
\( x + 17 = 42 \)
1 Identify operation: + 17
2 Apply inverse: Subtract 17 from both sides
\( x = 42 - 17 \implies \mathbf{x = 25} \)
Example 2 Multiplication Curse
\( 7m = 63 \)
1 Identify operation: Multiply by 7
2 Apply inverse: Divide both sides by 7
\( m = \frac{63}{7} \implies \mathbf{m = 9} \)
Quick Check: Substitute your answer back into the original equation to verify! \( 25 + 17 = 42 \quad \checkmark \)
Potion Lab: Two-Step Spells
Reverse PEMDAS
The Two-Step Order
When solving two-step equations, we work in reverse order of operations (undo addition & subtraction first, then undo multiplication & division).
Order to Undo:
1. Undo \( + \) or \( - \) (Constants)
2. Undo \( \times \) or \( \div \) (Coefficients)
Problem: \( 3n + 8 = 29 \)
Step 1: Undo Addition
Subtract 8 from both sides
\( 3n = 21 \)
Step 2: Undo Multiplication
Divide both sides by 3
