Mathematics · Grade 6

Active learning ideas

Writing Expressions from Real-World Problems

Active learning works for writing expressions because students need to physically manipulate quantities and operations to see how variables function. Hands-on tasks create mental models that bridge concrete scenarios to abstract symbols, reducing confusion about what each part of an expression means.

• Ontario Curriculum Expectations
• 6.EE.A.2.A
• 6.EE.A.2.B

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 30 min · Pairs

Pairs: Expression Match-Up

Provide cards with real-world problems on one set and expressions on another. Pairs match them, then explain their choices to each other. Extend by having pairs create new matches for the class to solve.

Construct an algebraic expression to represent a real-world problem.

Facilitation Tip

During Expression Match-Up, circulate and listen for students explaining how they matched expressions to scenarios, not just verifying answers.

What to look for

Present students with a scenario, such as 'Sarah bought 4 notebooks at $3 each and a pen for $2. Write an expression to represent the total cost.' Ask students to write their expression on a whiteboard and hold it up. Observe for correct use of variables and operations.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 45 min · Small Groups

Small Groups: Budget Builders

Groups receive a budget scenario with unknowns, like total cost with variable quantities of items. They write expressions, test with numbers, and compare results. Share one group expression with the class for feedback.

Analyze how different variables can represent different unknown quantities in a problem.

Facilitation Tip

In Budget Builders, provide calculators for checking totals but require students to explain each line of their budget before calculating.

What to look for

Provide each student with a card describing a simple real-world situation (e.g., 'You have 10 apples and receive 'a' more apples each day for 5 days. Write an expression for the total apples after 5 days.'). Ask them to write the expression and then explain what each part of their expression represents.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 40 min · Pairs

Whole Class: Scenario Gallery Walk

Post 6-8 word problems around the room. Students walk in pairs, write expressions on sticky notes, and post them. Class discusses and votes on accurate ones.

Explain the meaning of each term within an algebraic expression in context.

Facilitation Tip

For the Scenario Gallery Walk, assign each group a specific poster to critique, ensuring all voices are heard during feedback rounds.

What to look for

Pose a problem like: 'A store sells shirts for $12 each. Write an expression for the cost of buying 's' shirts. What if there was a $5 discount? How would the expression change?' Facilitate a class discussion where students share their expressions and justify their reasoning.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 25 min · Individual

Individual: Personal Problem Creator

Students write a real-world problem from their life, like gaming scores or snack sharing. They create the expression and swap with a partner for verification.

Construct an algebraic expression to represent a real-world problem.

What to look for

Present students with a scenario, such as 'Sarah bought 4 notebooks at $3 each and a pen for $2. Write an expression to represent the total cost.' Ask students to write their expression on a whiteboard and hold it up. Observe for correct use of variables and operations.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach this topic by starting with physical manipulatives, like counters or coins, to represent quantities before moving to symbols. Avoid rushing students to abstract notation; allow them to draw pictures or act out scenarios first. Research shows students need multiple exposures to the same problem in different forms to internalize the connection between words and expressions.

Students will confidently translate real-world situations into algebraic expressions, explaining each term and operation. They will also justify their expressions by substituting values and connecting back to the context. Group discussions will reveal their ability to critique and revise collective thinking.

---

Watch Out for These Misconceptions

• During Expression Match-Up, watch for students treating variables as single-digit placeholders instead of unknowns.

  Ask students to substitute values like 10 or 100 into their matched expressions to test if the variable truly represents any number, not just a single digit.

• During Budget Builders, watch for students assuming the order of terms in their budget expression doesn’t affect the total.

  Have students rearrange their budget lines and recalculate to see if the total changes, prompting discussion about why order matters in some contexts but not others.

• During Scenario Gallery Walk, watch for students inserting variables for every noun in a problem rather than identifying key unknowns.

  Provide sticky notes for students to label which parts of the scenario they turned into variables and which stayed as constants, then discuss as a class.

---

Methods used in this brief

• Problem-Based Learning