Operation Protocol Worksheet
Operation Protocol
Order of Operations Practice • Grade 8 Level
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The PEMDAS Execution Rules Standard Convention
P / G
Grouping
\(( ), [ ], | |, \frac{\text{top}}{\text{bot}}\)
E
Exponents
\(x^n, \sqrt{x}\)
M / D
Mult / Div
Left to Right \(\rightarrow\)
A / S
Add / Sub
Left to Right \(\rightarrow\)
Worked Example
\(4 - 2[3^2 - (-1)] + \frac{12}{-4}\)
\(= 4 - 2[9 + 1] + (-3)\)
\(= 4 - 20 - 3 = \mathbf{-19}\)
A Foundational Multi-Step Expressions (Questions 1–10)
Show all intermediate steps clearly
- \( 18 - 3 \cdot 2^3 + 7 \)
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- \( -4 \cdot (6 - 9)^2 + 15 \)
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- \( \frac{32 - 4 \cdot 5}{(-2)^2 + 2} \)
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- \( 5^2 - [14 - (8 - 11)] \)
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- \( -3 \cdot | -8 + 2 | + 5^2 \)
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- \( 48 \div (-4)^2 \cdot 3 - 11 \)
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- \( 9 + 3 \cdot (16 - 2^3) \div (-6) \)
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- \( \frac{-28 + (-2)^3}{18 - 4 \cdot 5} \)
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- \( 14 - 2 \cdot | 3 - 10 | + 6 \)
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- \( (5 - 8)^3 \div 9 + 6 \cdot (-3) \)
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Grade 8 Mathematics • Unit: Numerical Reasoning Page 1 of 2 • Continue on reverse
Operation Protocol | Part II & Challenge Applications
Questions 11 – 20
B Nested Grouping, Radicals & Fractions (Questions 11–16)
Work systematically from inside out
- \( 3 \cdot [ 4^2 - 2(5 - 8) ] \div 11 \)
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- \( \frac{4 \cdot (-3)^2 - 16}{| -15 - 5 |} \)
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- \( -3^2 + 5[ 24 \div (-4) + 2^3 ] \)
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- \( \sqrt{64} - 2 \cdot | 5 - 3^2 | + (-4)^2 \)
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- \( \frac{3^3 - (-1)^5 + 12}{2 \cdot (9 - 14) + 16} \)
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- \( 2 \cdot [ 45 - 3(2^4 - 7) ] - (-8) \)
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C Substitution & Critical Error Analysis (Questions 17–20)
Apply accurate mathematical reasoning
- \(a=-4, b=2, c=7\)
\( a^2 - 3(b - c) \)
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- \(x=-3, y=5\)
\( \frac{|2x - y^2|}{x + y} \)
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- \(m=-2, n=44\)
\( -2m^3 + \sqrt{n + 5} \)
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20 Error Analysis Protocol
Diagnose & Correct
Student's Incorrect Work
Evaluate: \( 50 - 2(4 + 1)^2 \div 5 \)
Step 1: \( 50 - 2(5)^2 \div 5 \)
Step 2: \( 48(5)^2 \div 5 \) [Error!]
Step 3: \( 48(25) \div 5 = 240 \)
Describe the exact rule violated and provide the correct step-by-step evaluation:
Correct Final Answer:
Operation Protocol • Answer Key Available Separately Page 2 of 2 • End of Assignment
