Mathematics · 5th Grade

Active learning ideas

Writing Simple Expressions

Active learning turns the abstract task of writing expressions into a concrete, social process. When students translate words to symbols and justify their choices aloud, they build fluency in mathematical language and see that expressions are tools for communication, not just computation steps.

• Common Core State Standards
• CCSS.Math.Content.5.OA.A.2

• 15–25 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Translation Station: Words to Symbols

Pairs receive a set of verbal descriptions such as 'subtract 14 from twice the number 30' and a set of expression cards. They match them, then write at least two new pairs of their own. Pairs compare with another team and resolve any disagreements, building shared vocabulary for mathematical language.

Construct a numerical expression to represent a given calculation.

Facilitation Tip

During Translation Station, have students read their expressions aloud to a partner before writing, forcing them to connect words and symbols before committing to paper.

What to look for

Present students with a word problem, for example, 'Sarah bought 3 packs of pencils with 10 pencils in each pack. She gave 2 pencils to her friend.' Ask students to write an expression that represents this situation, such as '3 * 10 - 2'.

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

Activity 02

• Gallery Walk
• 20 min · Individual

Gallery Walk: What Does This Say?

Post 8 to 10 numerical expressions around the room. Students move through the gallery and write in their own words what each expression describes, without evaluating it. Responses are posted below the expression and compared during debrief, highlighting different but equally valid phrasings.

Interpret the meaning of a numerical expression without performing the calculation.

Facilitation Tip

In the Gallery Walk, post student interpretations next to each expression, then ask the class to vote on which matches the expression’s intended meaning most closely.

What to look for

Give students an expression, for example, '5 + (4 * 2)'. Ask them to write two sentences describing what this expression means without calculating the answer. For instance, 'This expression means adding 5 to the product of 4 and 2.'

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

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Same Calculation, Different Expression

Give pairs two expressions that produce the same result but look different, such as 5 times (8 + 4) versus 5 times 8 plus 5 times 4. Ask: do they represent the same calculation? Is one description more efficient? Partners reason aloud before sharing with the class to explore the distributive property through language.

Compare different ways to write an expression that represents the same calculation.

Facilitation Tip

For Think-Pair-Share, assign each pair a different expression so that when they present, the class hears a variety of ways to express the same calculation.

What to look for

Pose the question: 'Is the expression '2 + 3 * 4' the same as '4 * 3 + 2'? Discuss why or why not, focusing on how the order of operations affects the meaning of the expression.'

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

Activity 04

• Think-Pair-Share
• 20 min · Whole Class

Expression Auction

Read aloud 5 verbal descriptions, and students bid by holding up number cards to show which expression from a posted set best matches. After each round, the class justifies the correct match and examines common errors, building precise vocabulary for describing calculations in symbols.

Construct a numerical expression to represent a given calculation.

Facilitation Tip

Run the Expression Auction in rounds: first silent bidding, then verbal justifications, to push students to explain their reasoning before confirming correctness.

What to look for

Present students with a word problem, for example, 'Sarah bought 3 packs of pencils with 10 pencils in each pack. She gave 2 pencils to her friend.' Ask students to write an expression that represents this situation, such as '3 * 10 - 2'.

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

A few notes on teaching this unit

Teach this topic by prioritizing verbal articulation over calculation. Use consistent language such as ‘the product of’ and ‘the sum of’ to reinforce structure. Avoid premature evaluation by modeling expressions with questions like ‘What is being grouped here?’ and ‘What operation connects these parts?’ Research shows that students who practice interpreting expressions without computing build stronger conceptual foundations than those who rush to solve.

Students will write accurate expressions from verbal descriptions, interpret existing expressions without calculating values, and recognize that parentheses change meaning even when the result stays the same. They will also articulate how different expressions can describe the same situation using precise mathematical language.

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Watch Out for These Misconceptions

• During Translation Station, watch for students who add an equals sign or a value to an expression.

  During Translation Station, use a two-column chart: one side for the expression, one for the equation. Ask students to circle the difference between ‘5 × 3’ and ‘5 × 3 = 15’ and explain why the first is a process and the second is a statement of equality.

• During Translation Station or Gallery Walk, students claim parentheses are only needed when the answer changes.

  During Translation Station, present pairs like ‘7 × (5 + 2)’ and ‘7 × 5 + 2’. Ask students to write the verbal description for each and compare how the words dictate grouping even when the final result differs only if parentheses are used.

• During Gallery Walk or Think-Pair-Share, students assume they must calculate the expression to understand it.

  During Gallery Walk, place a ‘No Calculating’ sign on each card. After students write their interpretations, ask them to underline the operations and circle the groups to demonstrate comprehension without numbers.

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Methods used in this brief

• Think-Pair-Share
• Gallery Walk