Mathematics · 7th Grade

Active learning ideas

Equivalent Expressions

Equivalent expressions are the bedrock of algebraic manipulation, and active learning helps students build a strong foundation. When students actively engage with properties and representations, they move beyond rote memorization to a deeper conceptual understanding.

• Common Core State Standards
• CCSS.Math.Content.7.EE.A.1
• CCSS.Math.Content.7.EE.A.2

• 25–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 30 min · Small Groups

Format Name: Expression Puzzles

Provide students with sets of expression cards. Students work in small groups to match cards that represent equivalent expressions, using properties of operations to justify their matches. For example, matching '2(x + 3)' with '2x + 6'.

How does rewriting an expression in different forms clarify the relationship between quantities?

Facilitation Tip

During the Stations Rotation, ensure groups are consistently moving and that each station offers a distinct way to practice a specific skill, like combining terms or applying the distributive property.

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

Activity 02

• Stations Rotation
• 40 min · Pairs

Format Name: Algebra Tile Exploration

Using algebra tiles, students can visually represent linear expressions. They can combine like terms by physically grouping tiles and use the tiles to demonstrate factoring and expanding. This tactile approach helps solidify understanding of the distributive property.

Why is the distributive property essential for simplifying complex expressions?

Facilitation Tip

During Think-Pair-Share, give students ample quiet time to grapple with the initial problem individually before encouraging discussion with their partner.

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

Activity 03

• Stations Rotation
• 25 min · Individual

Format Name: Property Sort

Create cards with various algebraic manipulations. Students sort these cards into categories based on the property of operations used (commutative, associative, distributive) or whether the expression is being expanded or factored.

When are two algebraic expressions considered truly equivalent?

Facilitation Tip

During the Property Sort activity, circulate to observe how students categorize the algebraic manipulations and prompt them to articulate the reasoning behind their choices.

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

A few notes on teaching this unit

Focus on the 'why' behind equivalent expressions by connecting them to the properties of operations. Use visual aids and manipulatives to build intuition before moving to abstract symbols. Emphasize that equivalent expressions are simply different ways of writing the same quantity.

Students will successfully demonstrate understanding by rewriting expressions using properties of operations and justifying their steps. They will be able to recognize and create equivalent expressions, explaining why different forms represent the same value.

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Watch Out for These Misconceptions

• During Algebra Tile Exploration, watch for students attempting to combine unlike terms, such as stating that 3x + 2y equals 5xy.

  Redirect students by having them physically arrange the algebra tiles for '3x' and '2y' side-by-side to visually demonstrate that they are distinct and cannot be merged into a single term.

• During Expression Puzzles, watch for students misapplying the distributive property, like matching 3(x + 2) with 3x + 2.

  Prompt students to use algebra tiles or draw an area model for 3(x + 2) to show that it represents three groups of 'x' and three groups of '2', thus leading to 3x + 6.

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Methods used in this brief

• Stations Rotation