Mathematics · Grade 7

Active learning ideas

Writing and Evaluating Expressions

Active learning works because translating between words and symbols requires repeated, low-stakes practice with immediate feedback. Students need to manipulate language and numbers quickly to build automaticity in identifying operations and order. These activities provide that hands-on repetition while keeping engagement high through movement and collaboration.

• Ontario Curriculum Expectations
• 7.EE.A.2

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• RAFT Writing
• 30 min · Pairs

Card Sort: Verbal to Algebraic Match

Prepare cards with verbal phrases on one set and algebraic expressions on another. In pairs, students match them, such as 'five less than x' to 'x - 5', then justify matches aloud. Extend by evaluating matched pairs with given values.

Differentiate between an expression and an equation.

Facilitation Tip

During Card Sort, circulate and ask pairs to explain their matching choices before revealing the answer key to encourage immediate justification.

What to look for

Present students with a list of verbal phrases and a list of algebraic expressions. Ask them to draw lines to match each phrase to its correct expression. Include a few distractors. For example, 'five more than a number' (n + 5) and 'five times a number' (5n).

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 02

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Real-World Translations

Set up stations with scenarios like sports scores or shopping budgets. Small groups write expressions, evaluate for sample values, and rotate to check peers' work. Conclude with a gallery walk to share solutions.

Construct an algebraic expression to represent a real-world scenario.

Facilitation Tip

For Station Rotation, prepare real-world examples that require different operations to reinforce the connection between context and symbolic representation.

What to look for

Give students the expression 3x - 7. Ask them to: 1. Write a verbal phrase that represents this expression. 2. Evaluate the expression when x = 4.

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

Activity 03

• RAFT Writing
• 20 min · Whole Class

Relay Race: Evaluate Expressions

Divide class into teams. Each student evaluates one expression with a given variable value on a board, tags next teammate. First team done correctly wins. Review order of operations errors as a group.

Evaluate the importance of precise language when translating between verbal and algebraic forms.

Facilitation Tip

In Relay Race, provide scratch paper for visible calculations so errors become teachable moments for the whole group.

What to look for

Pose the following scenario: 'Sarah wrote the expression for 'a number decreased by 10' as 10 - n. Mark wrote it as n - 10. Who is correct and why? What does this tell us about the importance of language in math?'

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 04

• RAFT Writing
• 25 min · Individual

Build-Your-Own Scenario: Individual Challenge

Students write a real-life scenario, create its expression, and evaluate for three variable values. Swap with a partner for verification and discussion of precision in wording.

Differentiate between an expression and an equation.

What to look for

Present students with a list of verbal phrases and a list of algebraic expressions. Ask them to draw lines to match each phrase to its correct expression. Include a few distractors. For example, 'five more than a number' (n + 5) and 'five times a number' (5n).

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

A few notes on teaching this unit

Start with concrete examples before abstract symbols, using familiar contexts like money or measurements to ground the work. Model think-alouds during the first activity to demonstrate how to parse phrases word by word. Avoid rushing to rules; instead, let students discover patterns through repeated exposure and discussion. Research shows that students solidify understanding when they teach concepts to peers, so structure partner work intentionally.

Successful learning looks like students confidently converting verbal phrases to correct algebraic expressions and evaluating them accurately with substitutions. They should explain their reasoning using precise mathematical language and recognize when expressions represent relationships rather than solutions. Peer discussions should highlight these distinctions naturally.

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Watch Out for These Misconceptions

• During Card Sort: Verbal to Algebraic Match, watch for students who insist expressions must include an equals sign to be complete.

  Ask them to defend their matches by explaining what the expression represents. Use the matched pairs to highlight that expressions show relationships, while equations show equality. Have peers rephrase why '2x + 3' stands alone as a relationship.

• During Relay Race: Evaluate Expressions, watch for students who perform operations out of order.

  Provide a visible PEMDAS checklist at each station. When errors occur, pause the group to re-evaluate the expression step-by-step on the board, asking students to identify which operation should come first and why.

• During Build-Your-Own Scenario, watch for students who treat variables only as unknowns to solve for.

  Have them test multiple substitutions for their variable directly in their scenarios. Ask them to explain how the same expression can represent different values, normalizing the idea that variables are flexible placeholders.

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Methods used in this brief

• RAFT Writing
• Stations Rotation