Order of Operations Practice

Unit: Expressions and Equations Exploration

Lesson 2 of 13

Grade: 6th Grade

Duration: 71 minutes

Class Size: 50 students

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Common Core State Standards (CCSS) Alignment

• CCSS.MATH.CONTENT.6.EE.A.2
  Write, read, and evaluate expressions in which letters stand for numbers.
• CCSS.MATH.CONTENT.6.EE.A.2.C
  Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems.
• CCSS.MATH.PRACTICE.MP1
  Make sense of problems and persevere in solving them.
• CCSS.MATH.PRACTICE.MP3
  Construct viable arguments and critique the reasoning of others.

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Learning Objectives

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

1. Correctly apply the order of operations (PEMDAS/BODMAS) to evaluate expressions involving multiple operations and parentheses.
2. Collaborate with peers to solve challenging problems, justify their reasoning, and adjust strategies based on group feedback.
3. Build confidence and fluency with complex expressions that involve parentheses, exponents, multiplication, division, addition, and subtraction.
4. Use mathematical vocabulary (e.g., parentheses, exponent, simplify, expression) accurately in verbal and written explanations.

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Materials Needed

• Whiteboard and markers
• Printed problem sets (2 per student) with complex expressions
• Individual student whiteboards and dry erase markers (1 per student)
• Large poster-size PEMDAS reminder chart
• Timer or stopwatch
• "Expression Exploration" collaborative activity cards
• Exit tickets with 3 order of operations problems
• Clipboards or hard surfaces for writing during group work

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Lesson Breakdown

1. Warm-Up: Mental Math (10 minutes)

• Activity: Quick-write on individual whiteboards.
• Teacher displays 3 short expressions on the board that require applying order of operations (e.g., 8 + 3 × 2, (6 + 4) ÷ 2, 2³ – 5).
• Students solve individually and hold up their answers.
• Teacher corrects any misconceptions immediately with brief explanations.
• Purpose: Activate prior knowledge and assess baseline fluency.

2. Explicit Instruction & Guided Practice (15 minutes)

• Teacher-led mini-lesson:
  • Review the order of operations using the PEMDAS acronym. Emphasize that multiplication/division and addition/subtraction are performed left to right if at the same level.
  • Use the large poster chart, write and solve a complex expression step-by-step on the board (e.g., 3 × (4 + 2)² ÷ 3 – 5).
  • Highlight thinking processes aloud; encourage students to verbalize what comes next and why.
• Guided Practice:
  • Call on volunteer students to come up to the board and solve a similar expression collaboratively.
  • Discuss any tricky spots or common errors.

3. Collaborative Activity - Expression Exploration (25 minutes)

• Setup:
  • Divide the class into 10 groups of 5 students.
  • Each group receives a set of 5 "Expression Exploration" cards, each with one complex expression problem to solve. Examples involve nested parentheses, exponents, mixed operations.
• Task:
  • Groups solve the problems together on clipboards or paper, recording step-by-step evaluations.
  • One student acts as a "recorder", others contribute ideas and strategies.
  • Groups must reach consensus on the answer and explain their reasoning clearly.
• Teacher Role:
  • Circulate, listen to conversations, ask probing questions, and highlight exemplary justifications from groups.
  • Encourage students to identify mistakes and correct them collaboratively.

4. Class Discussion & Debrief (12 minutes)

• Ask groups to share one challenging problem and walk the class through their reasoning.
• Facilitate a discussion on common pitfalls (e.g., forgetting to do operations inside parentheses first, confusing exponents with multiplication).
• Reinforce mathematical vocabulary and best practices for handling complex expressions.

5. Independent Practice / Exit Ticket (7 minutes)

• Hand out exit tickets containing 3 varied order of operations problems (increasing difficulty).
• Students work silently and independently to solve the problems on their own.
• Collect exit tickets to assess individual understanding.

6. Closing & Reflection (2 minutes)

• Quick round-robin: Each student says one word or phrase reflecting their feeling about the lesson (e.g., “confident,” “challenging,” “fun”).
• Preview next lesson: Applying order of operations to solving equations with variables.

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Differentiation Strategies

• For struggling students:

  • Provide a simplified PEMDAS/PEMDAS chart with color-coded steps.
  • Pair with stronger students during group work for peer support.
  • Offer more guided practice before independent attempts.

• For advanced learners:

  • Challenge them with problems involving rational numbers or multiple nested parentheses.
  • Encourage creating their own complex expressions for classmates to solve.

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Assessment & Feedback

• Formative:

  • Observations during warm-up, guided practice, and group work.
  • Exit ticket results analyzed for mastery and misconceptions.

• Summative:

  • Use results from the unit quiz after several lessons covering expressions and equations.

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Extensions and Enrichment

• Technology Integration:

  • Use a classroom set of tablets/computers with interactive algebra apps that allow manipulating expressions and visualizing operation hierarchy.

• Real-world Connection:

  • Pose “code-breaking” puzzles where correct evaluation of expressions unlocks a clue or “treasure” in the classroom. This gamifies order of operations practice.

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Teacher Notes

• Emphasize growth mindset and assure students it’s okay to make mistakes while learning complicated rules.
• Keep a positive, energetic tone to maintain engagement given the abstract nature of the content.

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This detailed and interactive lesson plan will help 6th graders deeply understand and apply the order of operations standard, providing robust practice aligned with Common Core expectations and preparing them for more complex algebraic reasoning ahead.