Mathematics · Grade 7

Active learning ideas

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.

• Ontario Curriculum Expectations
• 7.EE.A.1

• 25–35 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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.

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

Activity 02

• 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.

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.

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

Activity 03

• 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.

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.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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Methods used in this brief

• Stations Rotation