Unit Plan 14 (Grade 6 Math): Equivalent Expressions—Properties at Work
6th graders use the commutative, associative, and distributive properties to expand, factor, and combine like terms. They determine when expressions are equivalent through property reasoning or substitution, writing clear justifications that emphasize structure and precision.
Focus: Use properties to generate equivalent expressions; determine when two expressions are equivalent.
Grade Level: 6
Subject Area: Mathematics (Expressions & Equations – Structure and Equivalence)
Total Unit Duration: 5 sessions (one week), 45-60 minutes per session
I. Introduction
Students build fluency with the structure of expressions. They apply the commutative, associative, and distributive properties to rewrite, expand, and factor expressions; combine like terms; and decide if two expressions are equivalent using property reasoning and substitution. Emphasis: seeing subexpressions as single units, writing clear justifications, and checking reasonableness.
Essential Questions
- How do the properties of operations justify each step when I rewrite an expression?
- When are two expressions truly equivalent for all values, and how can I show it?
- How do like terms, factoring, and the distributive property change the form but not the value of an expression?
- When is substitution helpful, and what are its limits for proving equivalence?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Use commutative and associative properties to reorder/regroup terms and factors to create equivalent expressions.
- Use the distributive property to expand (for example, a(b + c) to ab + ac) and factor (for example, ab + ac to a(b + c)), including cases with negative coefficients and subtraction.
- Combine like terms accurately and explain why only like terms combine.
- Determine whether two expressions are equivalent by:
- a) applying properties and step-by-step reasoning, and
- b) using substitution to test values and, when needed, giving a counterexample.
- Communicate justifications with precise vocabulary and clear structure.
Standards Alignment — CCSS Grade 6
- 6.EE.3: Apply the properties of operations to generate equivalent expressions (for example, 3(x + 2) = 3x + 6; 24x + 18y = 6(4x + 3y)).
- 6.EE.4: Identify when two expressions are equivalent (that is, they name the same number regardless of the value substituted); use reasoning and substitution to decide equivalence.
- Mathematical Practices emphasized: MP.1 (make sense), MP.2 (quantitative reasoning), MP.3 (justify), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can expand and factor using the distributive property and combine like terms correctly.
- I can reorder/regroup using commutative/associative properties and explain why the value stays the same.
- I can decide if two expressions are equivalent for all values, and I can show a counterexample when they are not.
- I can write a clear, step-by-step justification naming the property used at each step.