Unpacking Distributive Property

Grade Level

7th Grade

Duration

30 minutes

Common Core State Standards Addressed

• CCSS.MATH.CONTENT.6.EE.A.3: Apply the properties of operations to generate equivalent expressions.
• CCSS.MATH.CONTENT.6.EE.A.3.A: Apply the distributive property to remove parentheses.
• CCSS.MATH.CONTENT.6.EE.A.3.B: Identify when two expressions are equivalent.

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Learning Objectives ("I can..." Statements)

• I can explain what the distributive property is and why it works.
• I can use the distributive property to simplify algebraic expressions.
• I can recognize when two expressions are equivalent by applying the distributive property.

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Success Criteria

• I can correctly distribute a number over addition or subtraction inside parentheses.
• I can explain in my own words why the distributive property produces equivalent expressions.
• I can solve practice problems by rewriting expressions using the distributive property.

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Materials Needed

• Whiteboard and markers
• Individual mini-whiteboards or notebooks for each student
• Colored markers or pencils
• Pre-prepared expression cards for group activity
• Exit tickets (small slips for quick formative assessment)

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Lesson Structure

1. Introduction & Hook (5 minutes)

• Teacher Activity:
  Write the expression: 3 × (4 + 5) on the board. Ask students: “How might we solve this step-by-step?”

• Student Activity:
  Allow 1-2 students to explain solving inside the parentheses first, then multiply.

• Mini-Discussion:
  Introduce the idea that sometimes distributing the 3 can make expressions easier to understand or solve when variables are involved (e.g., 3 × (x + 5)).

• I Can Statement:
  “I can describe the distributive property and understand how multiplying a sum works.”

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2. Explicit Teaching & Modelling (8 minutes)

• Step-by-Step Explanation:

  • Write: 3 × (4 + 5) = 3 × 4 + 3 × 5
  • Show the calculation for both sides (27 = 12 + 15)
  • Highlight: This is called the distributive property.
  • Introduce the algebraic expression: 3(x + 5) = 3x + 15
  • Explain how breaking it apart helps simplify expressions with variables.

• Student Engagement:
  Ask students to predict what 2(y + 7) would become when using distributive property. Write their predictions and confirm by distributing.

• I Can Statement:
  “I can apply the distributive property to both numbers and variables.”

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3. Guided Practice with Peer Collaboration (10 minutes)

• Materials:
  Expression cards with problems like:

  • 4(a + 6)
  • 5(3 + b)
  • 2(x + 9)
  • 3(m − 2) (introduce subtraction inside)

• Activity:

  • Students get into pairs. Each pair is given one or two expression cards.
  • They distribute and simplify expressions together, discussing reasoning aloud.
  • Teacher circulates for support and formative feedback.

• Differentiation Strategies:

  • For struggling learners: Provide numeric examples first (e.g., 2 × (3+4)) before variable expressions. Use color-coding to highlight multiplication terms.
  • For English Language Learners (ELLs): Use word banks and visual models showing grouping.
  • For students with IEPs: Provide extra guided prompts and allow use of calculators to verify multiplication.

• I Can Statement:
  "I can work with a partner to apply the distributive property in different expressions."

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4. Independent Practice & Formative Assessment (5 minutes)

• Task:
  Students individually complete 3 short problems on their mini-whiteboards/notebooks:

  1. 6(x + 2)
  2. 4(5 + y)
  3. 7(a − 3)

• Exit Ticket:
  Collect a quick exit ticket asking students to write one sentence explaining why the distributive property works or why it is useful.

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5. Extension Activity for Advanced Learners (If Time Allows or Homework)

• Challenge students to create their own expressions using the distributive property involving two different variables (e.g., 3(x + 2y)) and simplify them fully.
• Introduce the idea of factoring as reverse-distributive property, e.g., rewrite 6x + 12 as 6(x + 2).

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Reflection & Teacher Notes

• Observe pairs to identify misconceptions (e.g., forgetting to distribute the multiplier to both terms).
• Use exit tickets to personalize next-day instruction.
• Encourage peer explanations for deeper concept mastery.

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Summary

By the end of this 30-minute session, students will confidently explain and apply the distributive property using both numbers and variables. The lesson uses hands-on collaboration, guided practice, and formative assessments aligned with CCSS.MATH.CONTENT.6.EE.A.3 to ensure mastery and engagement. Differentiation and extension activities ensure every learner is challenged appropriately.