Interchangeable Expressions

Overview

Grade: 3
Duration: 45 minutes
Class Size: 12 students
Unit: Exploring Equations and Equality (Lesson 3 of 18)
Curriculum Reference:

• Alberta Mathematics Program of Studies, Grade 3
• Number Strand - Patterns and Relations Specific Outcomes:
  • [3–3] Represent and describe problem situations involving equality and inequality using a variety of strategies (e.g., equations, drawings, manipulatives).
  • [3–4] Demonstrate an understanding of equations as statements of equality between expressions and explore the interchangeability of equivalent expressions.

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Learning Objectives (KUSPs)

Knowledge	Understanding	Skills
Know the meaning of “equivalence” in expressions and equations.	Understand that two equal expressions can be interchanged within an equation without changing its truth.	Skillfully rearrange and exchange parts of equations to create equivalent expressions and equations.

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Materials and Resources

• Equation cards (pre-prepared sets with simple expressions and equations, some equivalent, some not)
• Whiteboard and markers
• Individual mini whiteboards for each student (optional)
• Balance scale visual aids (physical or drawn)
• Magnetic equation pieces or sticky notes for interactive equation rearranging on the board

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Alberta Curriculum Alignment

• Mathematics K-6 Program – Patterns and Relations – Outcome 3-4: Use equations to represent equality and explore properties of equality (e.g., expressions can be rearranged or interchanged while maintaining equality).
• Mathematical Process Skills: Communication, Reasoning & Proving, Connections
• Cross-Curricular Competencies: Critical Thinking, Problem Solving

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Lesson Breakdown

1. Review (5 minutes)

• Begin with a quick recap of the previous lesson where students used a balance scale model to represent equality (e.g., 3 + 2 = 5).
• Ask: “What does it mean when two sides are balanced?”
• Reinforce that equality means both sides have the same value.
• Introduce the phrase: “If expressions are equal, we can swap them in an equation.”

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2. Introduction and Hook (7 minutes)

• Show two equivalent equations on the whiteboard side by side:
  • Example 1: 4 + 3 = 7
  • Example 2: 2 + 5 = 7
• Ask students: “Are these two expressions 4 + 3 and 2 + 5 interchangeable?”
• Use a visual balance scale (physical or diagram) to show how both expressions balance the same number.
• Highlight the key message: “We can replace one expression with another equivalent one anywhere in an equation.”

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3. Guided Practice: Rearranging Equations (15 minutes)

• Present equation cards or magnetic pieces on the board such as:
  • Equation A: 8 = 5 + 3
  • Equation B: 5 + 3 = 8
  • Equation C: 4 + 4 = 8
• Invite students, one at a time, to rearrange equation parts to show equivalence.
• Use think-alouds: “If 4 + 4 = 8, can I swap 5 + 3 with 4 + 4 in this equation?”
• Encourage students to explain their reasoning.
• Use individual mini whiteboards for students to try rewriting equations on their own, then share.
• For students who need support, provide simpler cards (e.g., single-digit additions like 3 + 2 and 5).

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4. Activity: Equation Swap Game (10 minutes)

• Divide the class into pairs (6 groups).
• Provide each pair a set of equation cards with expressions and equations.
• Objective: Work together to identify which expressions are equivalent and physically swap the cards on a board or table to create true equations.
• Examples of pairs:
  • 7 = 4 + 3
  • 7 = 5 + 2
  • 7 = 6 + 1
• Encourage discussion about which swaps keep the equation balanced and why.
• Teacher circulates to guide thinking and prompt with questions like: “How do you know these are equal?”

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5. Closure (5 minutes)

• Group discussion: “What did we learn about equality and expressions?”
• Highlight that equal expressions can be switched without changing the equation.
• Ask: “How can this help you solve math problems?”
• Emphasise the idea that equations are balanced statements and expressions on either side are interchangeable as long as equality is maintained.

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Assessment

• Formative: Observe and record participation during rearranging on the board and the card game activity.
• Listen for correct reasoning during explanations.
• Check students' written work on their mini whiteboards for evidence of interchangeability.
• Use an exit slip with a simple equation and ask students to rewrite it with an equivalent expression.

Example exit slip prompt:
Rewrite this equation using an equivalent expression for the right side:
6 = 2 + 4
Possible response: 6 = 3 + 3

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Differentiated Instruction

• For Students Needing Support:
  • Use simpler numbers (1–5)
  • Provide visual aids and concrete manipulatives (e.g., counters) to build expressions.
  • Pair with supportive peers during activities.
• For Advanced Students:
  • Challenge them with 3-term expressions (e.g., 2 + 3 + 2 = 7)
  • Introduce reasoning about the commutative property (swapping numbers within an expression).
  • Encourage creating their own equivalent equations.

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Teacher Reflection Questions

• Did students demonstrate understanding of interchangeability of expressions?
• Were all students actively engaged in the manipulative and rearrangement activities?
• How effectively did the balance model support understanding?
• What misconceptions emerged that need reinforcing in future lessons?

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This lesson combines concrete, visual, and kinesthetic learning styles perfectly suited for third graders, aligned tightly with the Alberta mathematics curriculum outcomes, and promotes deep conceptual understanding of equality and expression interchangeability.