Equivalent Expressions Assessment Item
Targeted Item Practice Order of Operations • Numerical Expressions
ITEM #24-M
Name:
Date:
Score:
1
Which value is equivalent to \( 7 - 2(3)^2 + 4 \)?
A \( -25 \)
B \( 5 \)
C \( -7 \)
D \( 49 \)
* Correct Answer: (C)
^ Highly Chosen Incorrect Answer: (D)
Step-by-Step Solution & Order of Operations
PEMDAS Protocol
1. Exponent First
Evaluate power before multiplication:
\( (3)^2 = 9 \)
\( 7 - 2(9) + 4 \)
2. Multiplication
Multiply the coefficient by base:
\( 2 \cdot 9 = 18 \)
\( 7 - 18 + 4 \)
3. Left-to-Right
Subtract, then add:
\( 7 - 18 = -11 \)
\( -11 + 4 = \mathbf{-7} \)
Diagnostic Distractor Rationale
Option A (\( -25 \)): Multiplied before applying the exponent:
\( 7 - (2 \cdot 3)^2 + 4 = 7 - 36 + 4 = -25 \)
Option B (\( 5 \)): Evaluated left to right through the exponent:
\( (7 - 2(3))^2 + 4 = (7 - 6)^2 + 4 = 1 + 4 = 5 \)
Option C (\( -7 \)) [Correct]: Followed order of operations precisely with accurate negative integers.
Option D (\( 49 \)) [^Key Trap]: Subtracted before multiplying/squaring:
\( (7 - 2)(3)^2 + 4 = 5(9) + 4 = 45 + 4 = 49 \)
Teaching Point: Emphasize that parentheses indicate multiplication by \(2\), not priority subtraction with \(7 - 2\). Highlight that exponents take precedence over multiplication.
