Understanding Equality Expressions

Learner Outcome

Students will develop a conceptual understanding of mathematical equality and expressions, and will demonstrate the ability to write equations representing equality between numbers and expressions according to Alberta Grade 3 Mathematics Curriculum.

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Lesson Objective: KUSP’s

• Know: The meaning of equality, mathematical expressions, and equations.
• Understand: How to recognise when two expressions represent the same number and can be written as an equation.
• Show: How to write equations that represent equality between a number and an expression or between two expressions representing the same number.
• Practice: Writing and evaluating equations both independently and collaboratively.

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Student Objectives

Students will be able to:

1. Explain what equality means in mathematics using concrete and visual examples.
2. Identify expressions and distinguish between numbers, expressions, and equations.
3. Write equations representing equality between a number and an expression, and between two expressions.
4. Verify equations by evaluating both sides to show they represent the same number.

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Materials/Resources

• Whiteboard and markers
• Small dry-erase boards and markers (one per student)
• Math balance scales (physical or illustrated manipulatives)
• Counters or cubes (approximately 20 per student)
• Pre-prepared equation cards (with numbers and expressions)
• “Equation Matching” worksheet (simple equations to match expressions and numbers)
• Visual Posters: Definitions of Equality, Expressions, Equations
• Interactive smartboard or projector (optional for virtual balance scales or diagrams)

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Review (5 minutes)

• Begin with a brief recap of what an expression is (e.g., 3 + 4, 10 - 2) and what equality means ("same as", "=").
• Ask students to share examples of expressions they can think of.
• Pose a quick question: “Is 5 + 2 equal to 7? How do we know?” Encourage quick responses, reinforcing the concept of equality.

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Introduction and Hook (5 minutes)

• Show a physical balance scale with cubes on each side.
• Demonstrate equality by placing the same number of cubes on both sides to balance the scale.
• Pose the question: “If 5 cubes on one side balance with a box of cubes on the other side, how many cubes are in that box?”
• Connect this to an equation: 5 = __
• Introduce the idea that sometimes one side is a number, and the other side is an expression.
• Build curiosity by promising students they will become “equation builders” today.

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Procedure / Learning Activity Sequence (25 minutes)

1. Direct Instruction (10 minutes)

• Define key terms using posters:
  • Equality: Both sides represent the same amount or value.
  • Mathematical Expression: A combination of numbers and operations (e.g., 4 + 3).
  • Equation: A statement that two expressions are equal (e.g., 4 + 3 = 7).
• Demonstrate writing equations that represent equality between a number and an expression. Example:
  • Show 6 cubes = 3 + 3 cubes, then write 6 = 3 + 3.
• Model how to verify equations by substituting numbers or counting cubes on each side.
• Highlight the equal sign “=” meaning “is the same as” rather than “and now do something.”

2. Student-Centred Activity – Equation Builders (15 minutes)

• Part A: Paired Manipulative Exploration (8 minutes)

  • Students work in pairs with cubes and balance scales.
  • Each pair receives equation cards with expressions/numbers to physically balance or show equality. For example, pairs explore:
    • 7 = 4 + 3
    • 5 + 2 = 6 + 1
    • 9 = 10 - 1
  • Pairs write the equation on their whiteboards and physically verify equality using cubes or scales.
  • Teacher circulates, asking guiding questions like: “Why do you think these two sides are equal?” and “Can you write this equality as an equation?”

• Part B: Independent Equation Matching (7 minutes)

  • Hand out the “Equation Matching” worksheet.
  • Students match numbers to equivalent expressions and write equations.
  • Support students to verify each match by evaluating or counting values on each side.

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Closure (Quick) (5 minutes)

• Invite 3 or 4 students to share one equation they wrote and explain why it shows equality.
• Recap key messages:
  • The equal sign means both sides are the same.
  • An equation is a special sentence that shows equality between expressions or between a number and an expression.
• Reinforce how they are now “Equation Builders.”

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Assessment / Evaluation

Formative Assessment

• Teacher observation during manipulatives activity and paired discussions.
• Monitor student whiteboards for accuracy in equation writing.
• Review completed “Equation Matching” worksheet.

Summative Assessment (Informal)

• End-of-lesson exit slip: Write an equation that shows equality between a number and an expression. Example: “Write an equation for ‘8 equals 5 plus a number’.”
• Collect and quickly assess for conceptual understanding.

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Differentiated Instruction

Accommodations

• Provide additional manipulatives/counters for tactile learners or students needing concrete reinforcement.
• Use equation templates with blanks to scaffold equation writing.
• Pair students strategically to support peer tutoring.
• Provide verbal and visual instructions for students with language processing needs.

Extensions

• Challenge advanced students to create and solve their own equality equations using larger numbers or more complex expressions.
• Introduce simple variable notation (e.g., 5 + x = 8) as an extension for higher thinkers, emphasizing the concept of “unknown number.”
• Incorporate storytelling problems that require writing equality equations involving real-life situations like sharing or grouping.

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Alberta Curriculum Alignment

Mathematics – Grade 3
Number Strand – Patterns and Relations

• Specific Outcome: Develop an understanding of equality and write equations that represent equality between a number and an expression or between two expressions representing the same number.
• Outcome Code: 3-4
• Competency Focus: Reasoning and communication – Students represent, apply, and justify expressions and equations involving equality.
• Supporting Competencies: Use concrete materials and drawings to explore equality and express solutions precisely.

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This lesson plan balances conceptual understanding with hands-on explorations and written work, tailored to Alberta’s Curriculum, fostering a deep and intuitive grasp of equality and mathematical expressions for Grade 3 learners.