Mastering the Order!

Grade Level: 5th Grade
Subject: Math
Curriculum Focus: Common Core Standards: 5.OA.A.1 (Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.)
Duration: 40 Minutes
Class Size: 20 Students

---

Lesson Objectives

By the end of this lesson, students will:

1. Understand and correctly apply the Order of Operations using parentheses, brackets, and braces.
2. Evaluate and create numerical expressions with multiple grouping symbols.
3. Develop confidence solving real-world problems involving the Order of Operations.

---

Materials Needed

• Whiteboard and markers
• Dry-erase paddles and markers for each student
• A soft foam die with grouping symbols written on each side (e.g., {}, (), [], numbers or "+" and "×").
• Printable “Expression Builder” cards (pre-prepared cards with numbers and operators, e.g., 4, 2, ×, +)
• Student math journals/notebooks
• “Solve-It Stars” worksheet for independent/group practice

---

Lesson Outline

1. Warm-Up: Math Magic (5 Minutes)

• Objective: Engage students in a fun Order of Operations thought activity.
• Write the following on the board:
  • 6 + 2 × (5 – 3)
• Ask: Which operation would you do first?
  • Have students discuss briefly (1 minute) with their shoulder partner and then share their reasoning.
  • Solve the problem on the board together, emphasizing that operations inside the parentheses come first.

---

2. Teaching Moment: The Math “PEMDAS” Machine (10 Minutes)

• Objective: Explicitly teach the hierarchy of the Order of Operations, including parentheses, brackets, and braces.

Step-by-Step Explanation:

1. Ask students: “Have you ever given directions and told someone to do things in a certain order? Why does the order matter?”
   Use this relatable example to introduce the concept of operations having an agreed rule like the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Highlight that grouping symbols (parentheses, brackets, braces) must always come first.

2. On the board, draw a tiered "PEMDAS Machine" where parentheses, brackets, and braces are at the top, showing their priority.
   Example:

      {   }  
     [      ]  
    (        )  
      ↓  
    Exponents  
      ↓  
    × ÷  
      ↓  
    + −  
   

3. Demonstrate using the following examples:

   • [4 × (2 + 5)] ÷ 3
     Walk through step-by-step, bolding and labeling each part for clarity.

---

3. Interactive Game: Build an Expression (15 Minutes)

• Objective: Let students explore and internalize the concept of the Order of Operations by physically building expressions and solving them in teams.

Activity Instructions:

1. Split students into teams of four.
2. Provide each team with their Expression Builder cards (numbers, operators, and grouping symbols). Each team will collaboratively create a math problem for the other team to solve.
3. Once their problem is ready, have one student from each team roll the foam die.
   • Whatever grouping symbol comes up on the die (e.g., parentheses, brackets, braces), they must incorporate it into their new problem.
   • Example: Team 1 creates [{6 ÷ 2} + (3 × 2)] for Team 2.
4. Teams will rotate to “solve” another team’s original problem together on their whiteboard paddles.
5. Award points for the correct solution and bonus points if the creating team used a variety of grouping symbols effectively (e.g., all three—parentheses, brackets, and braces).

---

4. Independent Practice: Solve-It Stars (10 Minutes)

• Objective: Students independently solve expressions using grouping symbols to solidify understanding.
• Hand out the “Solve-It Stars” worksheet! It includes problems of varying difficulty, such as:
  • Easy: (3 + 5) × 2
  • Medium: [8 – (6 ÷ 2)] + 4
  • Challenging: {[(9 × 2) ÷ 3] + (6 – 4)} × 5
    Encourage students to show all steps in their math journals.
• Early finishers will write their own Order of Operations problem using braces, brackets, and parentheses.

---

5. Cool-Down: Reflect & Wrap-Up (5 Minutes)

• Ask students to complete one sentence in their math journals:

  • “Today I learned that when solving a math expression, I must always start with ________.”
  • Share a few responses.

• End with a quick mini-challenge on the board:

  • Solve: 12 ÷ [6 ÷ (3 × 1)] + 2
  • Promise extra “classroom dollars” or stars for the first 3 correct responses!

---

Differentiation Options

For Struggling Learners: Provide step-by-step color-coded notes that map out “PEMDAS” for each example. Offer extra one-on-one support during the interactive activity.

For Advanced Learners: Challenge them to solve creative real-world problems that incorporate more grouping symbols or higher-order thinking. Example: “Write and solve an expression showing how 3 friends share a total bill of $48 after applying a $6 discount and then tipping 15%.”

---

Assessment of Learning

Formative Assessment: Actively monitor group participation during the “Build an Expression” activity. Check for appropriate use of grouping symbols and correct solutions.

Summative Assessment: Review the “Solve-It Stars” worksheet to assess mastery of grouping symbols and the Order of Operations.

---

Homework Assignment

Complete 4 additional problems requiring parentheses, brackets, and braces. Example:

1. [5 × (7 – 3)] + {2 × 4}
   Encourage students to create their own problem to bring in and challenge a parent or sibling to solve!

---

Reflection Note for Teachers:
This lesson blends explanation, collaboration, and creativity to engage students while meeting US education standards. Tailor it to suit your class's pace and needs! 😊