Properties of Operations

Students solidify their understanding of the Properties of Operations when they actively manipulate expressions. Using methods like Stations Rotation allows them to practice different properties in focused bursts, reinforcing how these properties serve as powerful tools for simplification.

• Grade 7
• Mathematics
• 3 activities
• 25 min–35 min

Stations Rotation

⏱ 30 min·Pairs

Property Sort: Expression Matching

Provide students with cards containing algebraic expressions. Students work in pairs to match equivalent expressions, justifying their matches using the commutative, associative, or distributive properties. For example, matching 3x + 5x with 8x using the distributive property.

Prepare & details

Explain how the properties of operations allow for flexibility in simplifying expressions.

Facilitation Tip: During the Stations Rotation, ensure students are physically moving the expression cards in the Property Sort activity to physically demonstrate the commutative and associative properties.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 25 min·Small Groups

Distributive Property Puzzles

Create puzzles where students must correctly distribute a term across a binomial or trinomial to reveal a hidden word or image. This gamified approach reinforces the application of the distributive property in a fun and engaging way.

Prepare & details

Compare and contrast the commutative and associative properties.

Facilitation Tip: In the Distributive Property Puzzles, observe if students are correctly matching the expanded form to the factored form, looking for consistent application of the distributive property.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 35 min·Individual

Simplification Showdown

Present a series of complex algebraic expressions. Students, individually or in teams, race to simplify them using the properties of operations, explaining their steps aloud. The first to correctly simplify wins.

Prepare & details

Justify the use of the distributive property in combining like terms.

Facilitation Tip: During Simplification Showdown, circulate to check students' work as they race to simplify; notice if they are strategically using properties or just applying steps mechanically.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Teaching This Topic

Teachers can approach the Properties of Operations by emphasizing their utility as shortcuts and tools for making math easier. Instead of rote memorization, focus on conceptual understanding through hands-on activities that allow students to discover the properties themselves. Avoid presenting these properties as abstract rules; instead, connect them to concrete examples and encourage students to articulate how a property helps them solve a problem more efficiently.

What to Expect

Successful learners will be able to identify and apply the commutative, associative, and distributive properties to simplify algebraic expressions. They will demonstrate flexibility in rearranging and regrouping terms, showing confidence in transforming complex expressions into simpler, equivalent forms.

Watch Out for These Misconceptions

Common Misconception

During the Property Sort activity, watch for students who struggle with the idea that order doesn't always matter.

What to Teach Instead

Redirect students to physically rearrange the expression cards in the Property Sort to verify that the commutative and associative properties yield the same result, even when terms or factors are reordered or regrouped.

Common Misconception

During the Distributive Property Puzzles, watch for students who believe the distributive property only applies to multiplication over addition.

What to Teach Instead

Prompt students to use the puzzle pieces for the Distributive Property Puzzles to show how the property can be applied in reverse (factoring) and also with subtraction, reinforcing its flexibility.

Assessment Ideas

Quick Check

After the Property Sort, quickly scan the matched pairs of expression cards to gauge students' ability to identify equivalent expressions based on properties.

Peer Assessment

During Simplification Showdown, have students briefly explain their simplification strategy to a partner, referencing which properties they used.

Exit Ticket

As an exit ticket after the Distributive Property Puzzles, ask students to write one expression that demonstrates the distributive property and one that demonstrates its reverse (factoring).

Extensions & Scaffolding

• Challenge: Ask students to create their own complex algebraic expressions that require multiple properties for simplification.
• Scaffolding: Provide partially completed expression cards for the Property Sort or templates for the Distributive Property Puzzles.
• Deeper Exploration: Introduce the concept of factoring as the reverse of the distributive property and have students practice both directions.