1. Algebraic Steps (Distributive / Combining):
Properties: Distributive Commutative Associative Identity
2. Solve with PEMDAS Test: \(x = \text{___}\)
( ) Grouping:
× Multiply:
+ Final Sum:
Matches simplified expression value
STOP #7 Station Letter: Codeword Letter:
Next Station Answer:
1. Algebraic Steps (Distributive / Combining):
Properties: Distributive Commutative Associative Identity
2. Solve with PEMDAS Test: \(x = \text{___}\)
( ) Grouping:
× Multiply:
+ Final Sum:
Matches simplified expression value
STOP #8 Station Letter: Codeword Letter:
Next Station Answer:
1. Algebraic Steps (Distributive / Combining):
Properties: Distributive Commutative Associative Identity
2. Solve with PEMDAS Test: \(x = \text{___}\)
( ) Grouping:
× Multiply:
+ Final Sum:
Matches simplified expression value
STOP #9 Station Letter: Codeword Letter:
Next Station Answer:
1. Algebraic Steps (Distributive / Combining):
Properties: Distributive Commutative Associative Identity
2. Solve with PEMDAS Test: \(x = \text{___}\)
( ) Grouping:
× Multiply:
+ Final Sum:
Matches simplified expression value
STOP #10 Station Letter: Codeword Letter:
Next Station Answer:
1. Algebraic Steps (Distributive / Combining):
Properties: Distributive Commutative Associative Identity
2. Solve with PEMDAS Test: \(x = \text{___}\)
( ) Grouping:
× Multiply:
+ Final Sum:
Matches simplified expression value
Secret Codeword Decoder:
Record all 10 letters collected in your journey:
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
Order of Operations Reflection: Why must you multiply \(3 \times (2x + 4)\) in Station A before adding the 5?
Page 2 of 2 • Property Patrol Scavenger Hunt Equivalence Verified: Both expressions name the same value for any variable input!
| • Repeated like terms
• GCF Factoring: \(6(x+2)\) | \(x = 4\)
PEMDAS: \(12+8+6+4+6\)
\(= \mathbf{36}\) | Station F
\(6x + 12\) |
Post cards across the room perimeter. Assign student pairs to different starting stations (A, G, C, J, B, etc.) so students circulate evenly without crowding.
Ensure students calculate the Order of Operations column step-by-step: evaluate inside parentheses first, perform multiplications, then complete additions.
Page 1 of 2 • Property Patrol Facilitator Guide See Page 2 for Stations F, I, D, H, E & Misconception Protocols
Master Solutions (Continued) • Stations F, I, D, H, E & Instructional Notes
Standards: Indiana 6.NS.7 • Expressions & Data Analysis
| Station | Banner (Prev) | Expression & Algebraic Property Steps | ILEARN 6.NS.7 Model | PEMDAS Solve | Next (Letter) |
|---|---|---|---|---|---|
| F |
Letter: A
| \(6x + 12\) |
\(\frac{1}{2}(4x + 16) + 3x + 1\)
\(= 2x + 8 + 3x + 1 = (2x + 3x) + (8 + 1) = \mathbf{5x + 9}\)
| • Fraction coefficient (half)
• Combining like terms | \(x = 3\)
PEMDAS: \(\frac{1}{2}(28) + 9 + 1\)
\(= 14 + 10 = \mathbf{24}\) | Station I
\(5x + 9\) |
|
I
Letter: L
| \(5x + 9\) |
\(4(x + 2x + 1) + 7\)
\(= 4(3x + 1) + 7 = 12x + 4 + 7 = \mathbf{12x + 11}\)
| • Order of Operations in ( )
• \(3(2m+m+3m)\) spec model | \(x = 2\)
PEMDAS: \(4(7) + 7\)
\(= 28 + 7 = \mathbf{35}\) | Station D
\(12x + 11\) |
|
D
Letter: E
| \(12x + 11\) |
\(2(5x + 6) + x + 4\)
\(= 10x + 12 + 1x + 4 = (10x + 1x) + (12 + 4) = \mathbf{11x + 16}\)
| • Distributive without GCF
• \(6y + 18 = 2(3y + 9)\) spec | \(x = 2\)
PEMDAS: \(2(16) + 2 + 4\)
\(= 32 + 6 = \mathbf{38}\) | Station H
\(11x + 16\) |
|
H
Letter: N
| \(11x + 16\) |
\(3(2x + 1) + 2(2x + 5)\)
\(= 6x + 3 + 4x + 10 = (6x + 4x) + (3 + 10) = \mathbf{10x + 13}\)
| • Double distribution
• Multi-term regrouping | \(x = 2\)
PEMDAS: \(3(5) + 2(9)\)
\(= 15 + 18 = \mathbf{33}\) | Station E
\(10x + 13\) |
|
E
Letter: T
| \(10x + 13\) |
\(1(2x + 6) + 2(x + 4)\)
\(= 2x + 6 + 2x + 8 = (2x + 2x) + (6 + 8) = \mathbf{4x + 14}\)
| • Mult. Identity (\(1 \cdot a = a\))
• Distributive Property | \(x = 3\)
PEMDAS: \(1(12) + 2(7)\)
\(= 12 + 14 = \mathbf{26}\) | Station A
\(4x + 14\) |
Misconception 1: Adding Before Multiplying
In Station A (\(5 + 3(2x + 4)\)), students add \(5 + 3 = 8\) first.
Prompt: "What does PEMDAS say about multiplication vs addition? The 3 is multiplying the parentheses!"
Misconception 2: Skipping Grouping Combining
In Station G (\(2(3x + x + 4)\)), students distribute without simplifying inside grouping first.
Prompt: "Can you combine \(3x + x\) inside the parentheses before multiplying? Both methods yield \(8x + 8\)."
Misconception 3: Factoring vs Expanding
In Station B, students fail to see that \(6x + 12\) can be factored as \(6(x + 2)\).
Prompt: "What greatest common factor divides both 6 and 12? Factoring is the distributive property in reverse!"
1. The Power of PEMDAS in Algebra: "Why did evaluating the original expression and the simplified expression at \(x = 3\) produce the exact same number? How does this justify equivalence?"
2. Factoring & Expanding Connection: "Look at Station B: why are \(6x + 12\) and \(6(x + 2)\) equivalent? How do both expressions model the distributive property?"
Page 2 of 2 • Property Patrol Facilitator Guide Fully Aligned to Indiana 6.NS.7 Specifications • Classroom-Ready
