Mathematics · 6th Grade

Active learning ideas

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.

• Common Core State Standards
• CCSS.Math.Content.6.EE.A.2a

• 20–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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.

What to look for

Provide students with three verbal phrases: 'a number increased by 10', 'twice a number', and 'a number divided by 3'. Ask them to write the corresponding algebraic expression for each and identify the variable and constant in each expression.

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

Activity 02

• 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.

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.

What to look for

Write the expression '3n + 5' on the board. Ask students to write two different verbal phrases that could be represented by this expression. Discuss the variety of correct answers and why they are equivalent.

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

Activity 03

• 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.

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.

What to look for

Present the scenario: 'Sarah is saving money. She already has $20 and saves $5 each week.' Ask students to write an algebraic expression to represent the total amount of money Sarah will have after 'w' weeks. Facilitate a discussion on why '5w + 20' is the correct expression and why '20w + 5' would be incorrect.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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Methods used in this brief

• Think-Pair-Share
• Chalk Talk
• Gallery Walk