Mathematics · Grade 6

Active learning ideas

Evaluating Algebraic Expressions

Active learning works because evaluating algebraic expressions demands procedural precision and conceptual fluency. Students must remember BEDMAS and substitution rules while seeing how small changes in variables produce tangible outcomes. Hands-on activities help them internalize these steps through movement, discussion, and error analysis, which builds confidence and accuracy.

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

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

Activity 01

• Collaborative Problem-Solving
• 25 min · Pairs

Pairs Challenge: BEDMAS Relay

Partners alternate substituting values into 10 expressions and evaluating with BEDMAS. They check each other's work before passing a card to the next pair in line. First team to finish all correctly wins a point.

Justify why we must follow a specific order of operations when evaluating expressions.

Facilitation Tip

During BEDMAS Relay, give each pair a timer and a stack of expression cards so they rotate quickly and stay engaged.

What to look for

Present students with the expression 3x + 5 and ask them to calculate its value when x = 4. Then, ask them to calculate it again when x = 10, prompting them to describe how the result changed.

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

Activity 02

• Collaborative Problem-Solving
• 35 min · Small Groups

Small Groups: Variable Change Tracker

Groups receive expressions and test three values per variable, recording results in shared tables. They graph changes and predict outcomes for new values. Discuss patterns as a group before sharing with class.

Evaluate algebraic expressions for given values of their variables.

Facilitation Tip

For Variable Change Tracker, ask groups to compare their tables side-by-side to spark noticing patterns.

What to look for

Provide students with the expression 2(y - 3) + 4. Ask them to substitute y = 7 and show their work, ensuring they follow BEDMAS. On the back, ask them to write one sentence explaining why BEDMAS is important.

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

Activity 03

• Collaborative Problem-Solving
• 40 min · Whole Class

Whole Class: Expression Error Hunt

Project expressions with deliberate BEDMAS mistakes. Students identify errors in pairs, then vote class-wide on corrections with justifications. Reveal correct evaluations and revisit key questions.

Analyze how changing the value of a variable impacts the result of an expression.

Facilitation Tip

In Expression Error Hunt, circulate and listen for students explaining errors to peers to reveal their understanding.

What to look for

Pose the question: 'If you have the expression 5a - b, and you double the value of 'a' but keep 'b' the same, what do you predict will happen to the total value of the expression? Why?' Facilitate a class discussion where students justify their predictions using substitution.

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

Activity 04

• Collaborative Problem-Solving
• 20 min · Individual

Individual: Custom Expression Builder

Students create three expressions, swap with a partner for evaluation, then verify and discuss discrepancies. Compile class examples for a shared anchor chart.

Justify why we must follow a specific order of operations when evaluating expressions.

Facilitation Tip

With Custom Expression Builder, provide blank expression templates so students focus on structure first.

What to look for

Present students with the expression 3x + 5 and ask them to calculate its value when x = 4. Then, ask them to calculate it again when x = 10, prompting them to describe how the result changed.

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

A few notes on teaching this unit

Start with concrete examples before moving to abstract symbols. Use calculators only after students can evaluate by hand to prevent reliance on order-of-operations features. Emphasize that variables represent real numbers, so substitution is not optional, it is fundamental. Teach error analysis early so students develop a habit of checking their work systematically.

Students will consistently apply substitution and BEDMAS to evaluate expressions correctly and explain their reasoning. They will predict how changing variables alters results, using clear language and justifications. Group work should show students teaching each other, while individual tasks demonstrate independent mastery of the steps.

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Watch Out for These Misconceptions

• During Pairs Challenge: BEDMAS Relay, watch for students performing operations strictly left to right, ignoring operation type.

  Require partners to pause after each card and verbally justify the next step using BEDMAS before writing anything, turning the relay into a verbal protocol.

• During Small Groups: Variable Change Tracker, watch for students skipping variable substitution when the expression looks simple.

  Provide number tiles or cards so students must physically place values in placeholders, making skipped steps impossible and visible to peers.

• During Whole Class: Expression Error Hunt, watch for students assuming that changing a variable’s value has no predictable effect.

  Ask groups to predict the new result before substituting, then compare predictions to actual results to highlight proportional changes clearly.

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Methods used in this brief

• Collaborative Problem-Solving