PEMDAS Protocol Worksheet
Algebra 1 Core Topic 1.2 • Order of Operations
PEMDAS Protocol Worksheet
Scaffolded evaluation of algebraic expressions and operational priority
Name:
Date:
Period:
Score: / 25
Order of Operations Hierarchy Critical Rule: Work Left-to-Right for \(\times / \div\) and \(+ / -\)
1. Grouping (G/P)
\((\;)\), \([\;\]\), \(|\;|\), fraction bars
2. Exponents (E)
Powers & roots: \(x^2\), \(\sqrt{a}\)
3. Multiply / Divide
Strictly left \(\rightarrow\) right
4. Add / Subtract
Strictly left \(\rightarrow\) right
1 Part 1: Numerical Sequence & Scaffolding
Simplify one operation per line. Underline the next operation you will perform.
1. Evaluate: \(18 - 3 \times 4 + 2^3\)
Step 1 (Exponent): 18 - 3 × 4 + _____
Step 2 (Multiply): 18 - _____ + _____
Step 3 (Left-to-Right): _____
Final:
2. Evaluate: \(4 \times (7 - 2)^2 \div 5\)
Step 1 (Parentheses): 4 × (_____)\(^2\) ÷ 5
Step 2 (Exponent): 4 × _____ ÷ 5
Step 3 (L-to-R): _____ ÷ 5 = _____
Final:
2 Part 2: Algebraic Substitution & Evaluation
Given: \(a = 3\), \(b = -2\), \(c = 4\)
Substitute the given variable values into parentheses first, then apply PEMDAS to simplify completely.
3. Evaluate \(2a^2 - 5c\)
Show substitution with parentheses, exponent, multiplication, and final subtraction:
Answer:
4. Evaluate \(b^2 + 3(a + c)\)
Watch the sign when squaring \(b\): \((-2)^2\).
Answer:
5. Evaluate \(\dfrac{c^2 - 4b}{a + 1}\)
Treat numerator and denominator as grouped quantities.
Answer:
6. Evaluate \(5 - b(c - a)^2\)
Resolve inner parentheses \((c - a)\), exponentiate, then multiply by \(b\).
Answer:
Self-Check: Did you evaluate exponents before multiplying by coefficients?
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PEMDAS Protocol Worksheet • Part II
Advanced Grouping, Like Terms & Precision
Student:
3 Part 3: Nested Grouping Symbols
Work from the innermost symbols outward: \(( \; ) \rightarrow [ \; ]\)
7. Evaluate: \(3\big[24 - (3 + 2)^2\big] + 10\)
Show step 1 (innermost paren) and step 2 (brackets):
Answer:
8. If \(x = 5\), evaluate: \(2\big|x - 9\big| + (x - 2)^2\)
Note: Absolute value bars \(|\dots|\) act as grouping symbols!
Answer:
4 Part 4: Distribute & Combine Like Terms Following PEMDAS
Multiply (distribute) before combining addition/subtraction terms.
9. Simplify: \(4(2x - 3) + 7x - 2\)
Distribute 4 first, then combine like \(x\)-terms and constant terms:
Result:
10. Simplify: \(9y - 3(y - 4) + 2^3\)
Evaluate exponent \(2^3\), distribute \(-3\), then combine terms:
Result:
11. Simplify: \(5m^2 + 2m(m + 4) - 6m\)
Distribute \(2m\), notice \(m \times m = m^2\), then combine like terms:
Result:
12. Simplify: \(14k - \big(5k - 2(3k - 1)\big)\)
Distribute \(-2\) inside the brackets first, simplify, then distribute the outer negative:
Result:
5 Part 5: Error Analysis & Diagnostic Fix
Identify the exact PEMDAS violation
13. Marcus's Solution: Incorrect
Expression: \(20 - 4 + 6 \div 2 \times 3\)
Line 1: \(20 - 4 + 6 \div 6 = 20 - 4 + 1 = 17\)
Identify the mistake: Marcus multiplied before dividing. Correct evaluation:
14. Chloe's Solution: Incorrect
Expression: \(3x^2\) when \(x = -4\)
Line 1: \((3 \times -4)^2 = (-12)^2 = 144\)
Identify the mistake: Chloe multiplied before squaring. Correct evaluation:
6 Part 6: STEM Formula Challenge
Physics Application: Kinetic Energy & Motion
15. Projectile Kinetic Energy: The kinetic energy of an object is given by \(K = \frac{1}{2}m v^2\), where \(m\) is mass in \(\text{kg}\) and \(v\) is velocity in \(\text{m/s}\).
Calculate \(K\) when a drone has mass \(m = 6\text{ kg}\) and velocity \(v = 8\text{ m/s}\). Follow PEMDAS explicitly (exponent on velocity before multiplying by mass and \(\frac{1}{2}\)).
Show substitutions & steps:
\(K =\) Joules
Reflection: PEMDAS ensures unique, universally reproducible solutions in algebra!
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