Mathematics · Grade 5

Active learning ideas

Writing and Interpreting Numerical Expressions

Active learning lets students physically and visually connect verbal phrases to expressions, which builds the habit of precise mathematical language. Moving beyond symbols to concrete actions helps students internalize the role of grouping symbols and operation order before formal evaluation begins.

• Ontario Curriculum Expectations
• 5.OA.A.2

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Carousel Brainstorm
• 25 min · Pairs

Card Match: Phrases to Expressions

Create cards with 12 verbal phrases and matching numerical expressions. Pairs sort and match them, then write sentences explaining one match. Regroup to compare answers and resolve mismatches.

Translate a verbal phrase into a numerical expression.

Facilitation Tip

During Card Match, circulate to listen for students’ exact wording when pairing phrases and expressions; their oral explanations reveal gaps in precision.

What to look for

Provide students with the verbal phrase 'six more than the product of five and three.' Ask them to write the numerical expression and then explain what the '5' and the '×' represent in their expression.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 02

• Carousel Brainstorm
• 35 min · Small Groups

Manipulative Model: Build Expressions

Provide counters or base-10 blocks. Small groups select a verbal phrase, build the expression physically, photograph it, and label parts. Share models with the class to interpret peers' work.

Explain the meaning of each part of a given numerical expression.

Facilitation Tip

In Manipulative Model, require students to build each expression twice—once with and once without grouping—to make the effect of parentheses visible.

What to look for

Present students with two expressions, such as 2 × (3 + 4) and (2 × 3) + 4. Ask them to circle the expression that represents 'two times the sum of three and four' and explain why the other expression is different.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 40 min · Small Groups

Expression Comparison Gallery Walk

Groups write two expressions for the same situation, post on charts. Class walks the gallery, noting similarities and voting on clearest versions. Discuss criteria for effective writing.

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

Facilitation Tip

Set a 2-minute timer for each station in Expression Comparison Gallery Walk so students must justify their choices under time pressure.

What to look for

Pose the scenario: 'Sarah bought 3 packs of pencils with 10 pencils in each pack. She gave 5 pencils to her friend.' Ask students to write a numerical expression for this situation. Then, facilitate a discussion where students share their expressions and explain how each part represents the story.

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

Activity 04

• Carousel Brainstorm
• 20 min · Whole Class

Verbal Relay: Expression Chain

Divide class into teams. One student hears a phrase, writes expression on board, tags next teammate for interpretation. First team to complete five rounds wins; review all as class.

Translate a verbal phrase into a numerical expression.

Facilitation Tip

Use a clipboard with a simple rubric to note which students revert to left-to-right thinking during Verbal Relay so you can target reteaching.

What to look for

Provide students with the verbal phrase 'six more than the product of five and three.' Ask them to write the numerical expression and then explain what the '5' and the '×' represent in their expression.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with manipulatives to make grouping symbols tangible, then move to written phrases only after students can physically demonstrate why parentheses matter. Avoid rushing to symbolic notation; let students act out situations first so expressions emerge naturally from their actions. Research supports this progression because concrete experience anchors abstract symbols.

By the end of these activities, students will confidently translate phrases into expressions and justify why grouping symbols change meaning. They will also recognize multiple valid expressions for the same situation and explain how order matters even without calculating.

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Watch Out for These Misconceptions

• During Manipulative Model, watch for students who ignore grouping blocks and build expressions left-to-right.

  Have them rebuild the expression with and without the grouping blocks while explaining how the blocks force a different order. Ask them to point to which step happens first and why.

• During Expression Comparison Gallery Walk, watch for students who claim equivalent expressions are identical.

  Ask them to act out each expression with props (e.g., pencils for multiplication, erasers for addition) to show that different processes can share the same total value.

• During Verbal Relay, watch for students who default to left-to-right reading of phrases.

  Pause the relay and have the student underline the operation that should happen first in the phrase, then match it to the correct expression card from the deck.

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Methods used in this brief

• Carousel Brainstorm
• Gallery Walk