Teacher Guide: Order of Operations

FL B.E.S.T. Standard MA.5.AR.2.2 | Grade 5 Mathematics

Lesson Time: 8-12 minutes

Standard MA.5.AR.2.2

Evaluate multi-step numerical expressions using order of operations involving parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

🎯 Learning Objectives

By the end of this lesson, students will be able to:

Common Misconceptions

Misconception 1: Left to Right for Everything

Students solve expressions strictly left to right, ignoring operation hierarchy.

Example Error: 3 + 4 x 2 = 7 x 2 = 14 (instead of 3 + 8 = 11)

Fix: Use PEMDAS anchor chart. Have students circle multiplication/division first, then perform those operations before adding/subtracting.

Misconception 2: Multiplication Before Division Always

Students think M always comes before D, and A always before S.

Example Error: 12 ÷ 4 x 3 = 12 ÷ 12 = 1 (instead of 3 x 3 = 9)

Fix: Emphasize that M/D are on the SAME level (left to right), and A/S are on the SAME level (left to right). Use "MD partners" and "AS partners" language.

Misconception 3: Forgetting Exponents

Students skip over exponents or don't know what they mean.

Example Error: 2 + 3² = 5² = 25 (instead of 2 + 9 = 11)

Fix: Review that exponents mean repeated multiplication (3² = 3 x 3 = 9). Evaluate exponents BEFORE multiplication.

Misconception 4: Ignoring Parentheses

Students don't realize parentheses change the order of operations.

Fix: Show the same numbers with different parentheses placement: (2 + 3) x 4 = 20 vs 2 + (3 x 4) = 14. Parentheses are like a "solve first" signal.

📖 Lesson Flow

Hook: The Calculator Puzzle (2 min)

Write on board: "5 + 3 x 2 = ?" Ask students to solve. Some will say 16, some 11. Reveal that calculators give 11! Why? Because there's a special ORDER we follow.

Introduce PEMDAS (3 min)

Display the PEMDAS poster. Explain each letter with the mnemonic "Please Excuse My Dear Aunt Sally." Emphasize that M/D are partners (same level, left to right) and A/S are partners.

Model with Think-Aloud (3 min)

Solve 2 + 3² x (4 - 1) step by step: "First I look for Parentheses: 4 - 1 = 3. Next Exponents: 3² = 9. Then Multiply: 9 x 3 = 27. Finally Add: 2 + 27 = 29."

Guided Practice (2-3 min)

Solve together: 18 ÷ 6 + 2 x 5. Have students tell you what to do first (18 ÷ 6 = 3 and 2 x 5 = 10, then 3 + 10 = 13). Circle operations as you identify them.

Release to Independent Practice (1 min)

Distribute practice worksheet. Remind students: "P-E-MD-AS. Check parentheses, then exponents, then multiply/divide left to right, then add/subtract left to right."

💬 Teaching Scripts

Introducing PEMDAS:

"When we have a problem with lots of different operations, we need to know which one to do first. We use a special order called PEMDAS. P is for Parentheses - always first! E is for Exponents - like 3 squared. Then M and D work together - Multiplication and Division, from left to right. Finally, A and S are partners - Addition and Subtraction, from left to right."

Explaining Left-to-Right Rule:

"Here's a tricky part: Multiplication doesn't always come before division! They're on the same level. When you see both, go left to right, like reading a book. Same with addition and subtraction - they're partners. If you see 8 - 3 + 2, go left to right: 8 - 3 = 5, then 5 + 2 = 7."

Addressing Errors:

"I see you solved left to right. That's a good instinct for reading, but math has special rules. Let's use our PEMDAS checklist: Any parentheses? No. Any exponents? No. Any multiplication or division? Yes! Let's do those first, then come back for the addition."

🛠 Materials Needed

PEMDAS anchor chart or poster
Student concept worksheets
Colored pencils (for circling operations)
Practice worksheets
Whiteboard/markers for modeling
Calculator (for verification demo)

📈 PEMDAS Reference Chart

Step Operation What to Look For Example
P Parentheses ( ), [ ], { } (3 + 5) = 8
E Exponents Small raised numbers 4² = 16
MD Multiply/Divide x, ÷ (left to right) 12 ÷ 4 x 2 = 6
AS Add/Subtract +, - (left to right) 10 - 3 + 2 = 9

Recommended IXL Skills

5.T.1 Evaluate numerical expressions involving parentheses
5.T.2 Evaluate numerical expressions involving exponents
5.T.3 Evaluate numerical expressions: mixed review
5.T.4 Add and subtract parentheses: where do they go?

IXL Tip:

Assign skill 5.T.1 first to focus on parentheses, then 5.T.2 for exponents. Use 5.T.3 as a comprehensive review. SmartScore goal of 80+ indicates proficiency.