Properties of Addition

Overview

This 71-minute lesson introduces 6th grade students to the properties of addition and subtraction — focusing on the commutative, associative, and identity properties. Through interactive examples, collaborative group work, and guided practice, students will develop a foundational understanding consistent with Common Core State Standards. This lesson is part 7 of 13 in the "Expressions and Equations Exploration" unit.

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Standards Alignment

• CCSS.MATH.CONTENT.6.EE.A.3
  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to factor a linear expression; write the expression 3(x + 4) as 3x + 12.

• CCSS.MATH.PRACTICE.MP7
  Look for and make use of structure.

• CCSS.MATH.PRACTICE.MP3
  Construct viable arguments and critique the reasoning of others.

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Learning Objectives

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

1. Define and identify the commutative, associative, and identity properties of addition and subtraction.
2. Apply these properties to rewrite and simplify expressions.
3. Explain why subtraction does not fully share the commutative and associative properties.
4. Collaborate effectively to solve group problems focused on these properties.

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Materials Needed

• Whiteboard and markers
• Projector or interactive display
• Printed task cards with expressions showing properties of addition and subtraction
• Individual dry erase boards and markers for students
• Chart paper for group work
• Exit ticket worksheets

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Lesson Breakdown

1. Warm-up and Activation (10 minutes)

Objective: Activate prior knowledge of addition and subtraction.

• Begin with a quick mental math activity: Call out addition and subtraction problems (e.g., 7 + 3, 12 - 4) and have students solve them on mini whiteboards, showing answers simultaneously.
• Ask: “Did you notice anything special about changing the order of the numbers for addition? What about for subtraction?”
• Brief class discussion introducing the idea that addition and subtraction follow different rules.

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2. Introduction to Properties (15 minutes)

Objective: Introduce commutative, associative, and identity properties through direct instruction and examples.

• Define each property clearly with examples written on the board:
  • Commutative Property of Addition: a + b = b + a
  • Associative Property of Addition: (a + b) + c = a + (b + c)
  • Identity Property of Addition: a + 0 = a
• Highlight that these properties apply fully to addition but not subtraction (briefly show a subtraction example where properties fail).
• Use visual aids such as number blocks or icons to illustrate why properties work for addition.

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3. Guided Group Exploration (20 minutes)

Objective: Solidify understanding through group problem solving and discussion.

• Divide class into 10 groups of 5 students each.
• Give each group a set of task cards with mixed addition and subtraction expressions. Some demonstrate properties, others break them (e.g., 5 - 3 ≠ 3 - 5).
• Groups work together to:
  • Sort cards into “Use property” or “Does not follow property.”
  • Rewrite or rearrange expressions using properties of addition.
• Circulate and ask guiding questions emphasizing reasoning and use of vocabulary: “Why does this expression show the associative property?” or “What happens when we swap numbers in subtraction?”
• Groups note their reasoning on chart paper to share later.

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4. Class Discussion and Debrief (15 minutes)

Objective: Share group findings, reinforce correct use of terminology and reasoning.

• Each group presents 1-2 examples they identified, justifying their sorting and expression rewrites. Encourage use of math vocabulary.
• Teacher corrects misunderstandings, emphasizes key points:
  • Subtraction is NOT commutative or associative.
  • Identity property clearly defines that adding zero leaves the number unchanged.

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5. Independent Practice (8 minutes)

Objective: Apply knowledge individually to deepen mastery.

• Distribute an exit ticket worksheet with problems asking students to:
  • Identify which property (commutative, associative, or identity) applies to given addition expressions.
  • Explain why certain subtraction expressions do not illustrate these properties.

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6. Closure and Reflection (3 minutes)

Objective: Summarize and connect to next lesson.

• Briefly recap the three properties and highlight their importance in simplifying expressions.
• Preview: Next lesson will focus on the distributive property and its connections to these properties.
• Ask a reflective question aloud: “Why is it helpful to know these properties when working with numbers?”
• Collect exit tickets.

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Assessment

• Observation during group activities and class discussion (formative)
• Individual exit tickets evaluating understanding of the properties and exceptions with subtraction (summative for this lesson)
• Participation and articulation of reasoning during presentations.

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Differentiation and Support

• For struggling learners: Provide explicit vocabulary cards and visual aids; pair with stronger students during group work.
• For advanced learners: Challenge to create their own expressions that demonstrate or defy each property; introduce basic algebraic expressions (variables).
• For ELL students: Use sentence frames and graphic organizers focusing on keywords like “commutative,” “associative,” “identity,” “equal.”

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Teacher’s Notes:

• Encourage use of math terms to build precision in communication.
• Use questioning strategies that prompt students to explain why properties work or don’t work for subtraction.
• Consider recording student group presentations for self-review and peer feedback in future lessons.

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By engaging students through direct explanation, cooperative learning, and guided practice aligned with CCSS standards, this lesson ensures a clear and lasting understanding of the fundamental properties of addition and subtraction essential for algebraic thinking.