Writing Algebraic Expressions

Active learning helps students move from passive reading to active sense-making with algebraic expressions. Students need to repeatedly practice translating between words and symbols to internalize the conventions of algebraic notation. These activities provide structured, collaborative opportunities to rehearse this translation in real time.

• 6th Grade
• Mathematics
• 3 activities
• 20 min–30 min

Learning Objectives

1. Identify the variable and constant in a given algebraic expression.
2. Translate verbal phrases representing addition, subtraction, multiplication, and division into algebraic expressions.
3. Construct an algebraic expression to represent a real-world scenario involving a single unknown quantity.
4. Compare two different verbal phrases to determine if they result in the same algebraic expression.
5. Explain the meaning of a variable in the context of a real-world problem.

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Verbal to Symbolic Translation

Give pairs a list of 8 verbal phrases and ask each student to independently write the corresponding algebraic expression. Partners then compare and discuss any differences, focusing on order-sensitive operations like subtraction and division. The class debrief covers the most common disagreements.

Prepare & details

Differentiate between a variable and a constant in a mathematical sentence.

Facilitation Tip: During Think-Pair-Share, circulate and listen for students who correctly order subtraction phrases like 'five minus a number' as 5 − n rather than n − 5.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Chalk Talk

⏱ 30 min·Small Groups

Collaborative Task: Expression from a Story

Provide each small group with a short scenario (e.g., 'A store sells items at price p. A customer buys 4 items and uses a $3 coupon'). Groups must identify all variables and constants, write an expression for the total cost, and explain each term in words. Groups share their expressions and compare for equivalence.

Prepare & details

Explain how to translate verbal phrases into accurate mathematical symbols.

Facilitation Tip: During Collaborative Task, ask groups to justify their expressions aloud so peers can hear the reasoning behind choices like 3n versus n + n + n.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Gallery Walk

⏱ 25 min·Pairs

Gallery Walk: Decode the Expression

Post algebraic expressions around the room (e.g., 2x + 7, n/3, 5 − k). Students write a verbal phrase that matches each expression, then a real-world scenario it could represent. Pairs compare their scenarios and discuss whether multiple verbal interpretations of the same expression are all valid.

Prepare & details

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

Facilitation Tip: During Gallery Walk, provide sticky notes for observers to leave feedback on posters, specifically asking them to identify the variable and operation in each expression.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Teaching This Topic

Teach this topic by emphasizing the precision of language in mathematics. Students often rush to symbols without anchoring phrases in actions, so model translating phrases verbally before writing. Use everyday language to connect to prior knowledge, and avoid rushing to abstract notation until students can explain what the expression means in context.

What to Expect

Successful learning looks like students confidently identifying variables and constants, correctly translating verbal phrases into algebraic expressions, and articulating their reasoning to peers. They should use proper notation without prompts and explain why different expressions can represent the same situation.

Watch Out for These Misconceptions

Common Misconception

During Think-Pair-Share, watch for students who write 'five minus a number' as n − 5 instead of 5 − n.

What to Teach Instead

Have the student act out the phrase aloud: 'Start with five, then take away a number.' Use a number line or counters to model 5 − n, emphasizing that the first number named is the starting point for subtraction.

Common Misconception

During Collaborative Task, watch for students who use multiplication signs (×) next to variables, such as writing 3 × n instead of 3n.

What to Teach Instead

Provide a mini-lesson on algebraic conventions, showing that 3n, 3·n, and (3)(n) all mean the same thing. Ask students to rewrite their expressions using juxtaposition and read them aloud to reinforce the convention.

Assessment Ideas

Exit Ticket

After Think-Pair-Share, collect students’ translations of three verbal phrases. Review their expressions for correct variable placement, operation order, and notation conventions to assess readiness for the next task.

Quick Check

During Collaborative Task, listen for groups that can articulate why '3n + 5' might represent 'three times a number plus five' and 'five more than three times a number.' Ask one group to share their reasoning with the class.

Discussion Prompt

After Gallery Walk, facilitate a whole-class discussion on common translations and misconceptions observed in the posters. Ask students to explain why expressions like '5w + 20' and '20w + 5' are not equivalent in the saving money scenario.

Extensions & Scaffolding

• Challenge: Provide phrases that include multiple operations, such as 'three more than twice the sum of a number and four,' and ask students to write the expression.
• Scaffolding: Give students a word bank with phrases like 'add,' 'subtract,' 'multiply by,' and 'divide by' to support translation.
• Deeper: Ask students to create their own story context that matches a complex expression like 4(n + 2) and exchange stories with peers to translate.

Key Vocabulary

Variable	A symbol, usually a letter, that represents a number that can change or is unknown.
Constant	A fixed value that does not change, represented by a number in an expression.
Algebraic Expression	A mathematical phrase that contains variables, constants, and operation symbols.
Translate	To convert a verbal phrase into a mathematical expression using symbols and variables.