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.

• Grade 7
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Translate verbal phrases representing mathematical relationships into algebraic expressions.
2. Evaluate algebraic expressions by substituting given variable values and applying the order of operations.
3. Compare and contrast algebraic expressions and algebraic equations, identifying key distinguishing features.
4. Analyze the impact of precise language on the accuracy of translating verbal phrases into algebraic expressions.
5. Create algebraic expressions to model simple real-world scenarios involving unknown quantities.

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.

Prepare & details

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.

Setup: Standard classroom seating, individual or paired desks

Materials: RAFT assignment card, Historical background brief, Writing paper or notebook, Sharing protocol instructions

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

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.

Prepare & details

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.

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

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.

Prepare & details

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.

Setup: Standard classroom seating, individual or paired desks

Materials: RAFT assignment card, Historical background brief, Writing paper or notebook, Sharing protocol instructions

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

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.

Prepare & details

Differentiate between an expression and an equation.

Setup: Standard classroom seating, individual or paired desks

Materials: RAFT assignment card, Historical background brief, Writing paper or notebook, Sharing protocol instructions

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Card Sort: Verbal to Algebraic Match, present students with a list of verbal phrases and algebraic expressions to match. Include distractors like 'three less than n' (n - 3) and 'n less than three' (3 - n). Collect matches to check for correct interpretation of phrases.

Exit Ticket

After Station Rotation: Real-World Translations, give students the expression 3x - 7. Ask them to 1. Write a verbal phrase that matches this expression and 2. Evaluate it for x = 4. Collect tickets to assess both translation and evaluation skills.

Discussion Prompt

During Build-Your-Own Scenario, pose the scenario: 'Jamie wrote the expression for 'a number increased by 5' as 5 + n, while Taylor wrote it as n + 5. Who is correct and why?' Use responses to discuss the commutative property and the importance of clear language in math.

Extensions & Scaffolding

• Challenge early finishers to create their own verbal phrase and expression pair, then trade with a partner to match. They should also write a brief explanation of why their phrase matches their expression.
• For students struggling with order of operations, provide color-coded expression strips where each operation type is highlighted to visually separate steps.
• Deeper exploration: Have students research how expressions model real-world scenarios beyond the classroom, such as sports statistics or baking measurements, then present one example to the class.

Key Vocabulary

Variable	A symbol, usually a letter, that represents an unknown quantity or a number that can change.
Expression	A mathematical phrase that contains numbers, variables, and operation signs, but no equals sign.
Algebraic Expression	An expression that contains at least one variable, along with numbers and operations.
Evaluate	To find the numerical value of an expression by substituting values for the variables and performing the operations.
Constant	A fixed value in an expression that does not change, represented by a number.