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.

• Grade 6
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Evaluate algebraic expressions by substituting given values for variables and applying the order of operations (BEDMAS).
2. Explain the necessity of a consistent order of operations (BEDMAS) for achieving accurate and reproducible results in mathematical expressions.
3. Analyze the impact of changing variable values on the overall result of an algebraic expression.
4. Calculate the value of algebraic expressions involving multiple variables and operations.

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Assessment Ideas

Quick Check

After Pairs Challenge: BEDMAS Relay, present the expression 3x + 5 and ask students to calculate its value when x = 4, then x = 10. Circulate to listen for students describing how doubling x doubled the constant term’s impact.

Exit Ticket

After Whole Class: Expression Error Hunt, provide the expression 2(y - 3) + 4 and ask students to substitute y = 7 and show their work. Collect tickets to check for correct use of brackets and BEDMAS, and read their sentence on BEDMAS importance to assess understanding.

Discussion Prompt

During Small Groups: Variable Change Tracker, 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?' Circulate to listen for predictions grounded in substitution and proportional reasoning.

Extensions & Scaffolding

• Challenge students to create an expression that always results in an even number, then evaluate it for different inputs in Custom Expression Builder.
• For Variable Change Tracker, provide a partially filled table to scaffold pattern recognition for students who struggle.
• Deeper exploration: Ask students to write a two-step expression that includes brackets and explain how removing the brackets affects the result using Expression Error Hunt.

Key Vocabulary

Variable	A symbol, usually a letter, that represents an unknown or changing value in an algebraic expression.
Expression	A mathematical phrase that contains variables, numbers, and operation signs, but no equal sign.
BEDMAS	An acronym representing the order of operations: Brackets, Exponents, Division and Multiplication (left to right), Addition and Subtraction (left to right).
Substitution	The process of replacing a variable in an algebraic expression with a specific numerical value.