Order of Operations

Overview

This 60-minute lesson focuses on reviewing the Order of Operations (PEMDAS) for Grade 6 students, aligned with the British Columbia Mathematics Curriculum (2023). The goal is to deepen students' understanding and application of order of operations when solving numerical expressions, preparing them for future algebraic reasoning.

Curriculum Connection

Curricular Competencies:

Develop and apply multiple strategies to approach problem solving.
Reason and analyse mathematical ideas using patterns and relationships.
Communicate mathematical thinking in many ways.

Content:

Apply the order of operations to evaluate numerical expressions involving whole numbers, including powers and roots (BC Ministry of Education, Grade 6 Mathematics Curriculum).

Learning Objectives

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

I can explain the purpose of the order of operations.
I can correctly apply the order of operations (PEMDAS) to evaluate expressions with brackets, exponents, multiplication, division, addition, and subtraction.
I can communicate my step-by-step solution to an order of operations problem clearly.

Success Criteria

I will know I am successful when:

I consistently use the correct order when solving expressions.
I can explain why the order of operations is important to get the right answer.
I can identify errors in incorrect solutions and explain how to fix them.
I can solve problems accurately and justify the steps I took.

Materials Needed

Whiteboard and markers
Printed worksheets with progressive order of operations problems
Mini whiteboards or individual slates for students
Card sets with mixed expressions (for group activities)
Timed Kahoot-style quiz or interactive game (optional)

Lesson Breakdown

1. Introduction (10 minutes)

Hook: Begin with a puzzling expression written on the board without any brackets: 8 + 6 × 3
Ask: "What answer do you get? Does everyone get the same answer?"
Discuss briefly why some might add first, some might multiply first.
Introduce the concept of PEMDAS (Brackets, Exponents, Multiply/Divide, Add/Subtract) as the agreed rule for everyone to get the same answer.
Write a clear PEMDAS acronym on the board and explain each step.
I can statement introduced for today's lesson.

2. Guided Practice (15 minutes)

Solve 3 progressively challenging examples together on the board:
1. Simple: (3 + 7) × 2
2. Intermediate: 4² + (6 - 2) × 3
3. Challenging: (5 + 2) × 3² - 8 ÷ 4
For each, verbalise each step: brackets first, then exponents, etc.
Students write the step-by-step solution on mini whiteboards; teacher monitors and gives immediate feedback.
Reinforce the importance of performing operations left to right within the same hierarchy (e.g., multiplication and division).

3. Collaborative Group Activity (15 minutes)

Split class into 5 groups of 5 students.
Provide each group with a deck of cards, each card having one numerical expression requiring order of operations.
Groups shuffle cards, then take turns selecting a card and collaboratively solving the expression, explaining their steps out loud.
After solving, the group ranks their card from “easy” to “hard.”
Circulate to provide support, encourage reasoning, and ask probing questions:
- Why did you perform that step first?
- What would happen if you changed the order?

4. Independent Practice and Formative Assessment (15 minutes)

Distribute a differentiated worksheet:
- Standard: 5 questions with brackets, exponents, multiply/divide, and add/subtract.
- Extension: Extra problems with nested brackets and larger numbers.
- Support: Scaffolded questions with prompts for each step.
Students work independently; teacher circulates to offer help.
Collect completed worksheets for assessment purposes.

5. Wrap-Up and Reflection (5 minutes)

Recap with a quick oral quiz: Teacher gives expressions verbally and students shout out or use thumbs up/down if order is correctly understood.
Ask reflective questions:
- Why do we follow a specific order for operations?
- What strategies helped you remember the order today?
Share success criteria and have students self-assess: “I can explain the order,” “I can solve expressions correctly,” etc.

Differentiation Strategies

Learner Type	Strategy	Example
Visual learners	Use colour-coded PEMDAS chart; highlight parts of expressions where each operation applies	Different colour for brackets, exponents, etc.
ELLs (English Lang. Learners)	Provide word banks & visual aids for vocabulary like 'brackets,' 'exponents'	Label expressions with pictures or icons
Students needing support	Use manipulatives (number tiles, operation cards)	Physically reorder steps to concretely see order
Advanced learners	Challenge with problems including nested brackets, powers & roots	Ask for explanations or create own expressions
Kinesthetic learners	Use movement or “operation stations” around the room where students ‘perform’ each operation	Acting out operations or moving between stations

Assessment Ideas

Formative:
- Observation of student participation during group activity.
- Review of student whiteboard solutions during guided practice for immediate feedback.
- Collect worksheets to assess accuracy and understanding.
Summative:
- Short quiz in following lessons on order of operations to solidify understanding.
- Peer-assessment: students swap work and identify errors related to order of operations, explaining corrections.

Additional Notes

Throughout the lesson, embed opportunities to foster curricular competencies: encourage students to explain their thinking, reason orally and in writing, and apply problem-solving strategies.
Emphasise the relevance of order of operations in real-world contexts (e.g., coding, mathematics in everyday life).
Use questions that challenge students to justify their reasoning, such as "How do you know that your answer is correct?"

This lesson plan provides a balanced, engaging, and inclusive approach to mastering order of operations for Grade 6 students in British Columbia.

Teaching Instructions