Mathematics · Grade 6 · Algebraic Thinking and Expressions · Term 2

Evaluating Algebraic Expressions

Substituting values for variables and evaluating expressions using the order of operations.

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

About This Topic

Evaluating algebraic expressions requires substituting given values for variables and applying the order of operations, or BEDMAS: Brackets, Exponents, Division and Multiplication from left to right, Addition and Subtraction from left to right. In Grade 6, students evaluate expressions such as 2x + 3y - 4 when x=5 and y=2, resulting in 17. They justify BEDMAS to ensure consistent results across calculators and people, and analyze how increasing a variable changes the expression's value, building predictive reasoning.

This topic fits Ontario's Grade 6 mathematics curriculum in algebraic thinking, linking to patterns and number operations from earlier grades. It prepares students for equations and proportional reasoning by treating variables as flexible placeholders. Real-world contexts, like calculating costs with tax rates or sports scores with bonuses, make the skill relevant.

Active learning benefits this topic greatly. Collaborative substitution races expose BEDMAS errors instantly, while group tables tracking variable changes reveal linear patterns through data. These approaches turn abstract rules into observable cause-and-effect relationships, boosting confidence and retention through peer explanation.

Key Questions

1. Justify why we must follow a specific order of operations when evaluating expressions.
2. Evaluate algebraic expressions for given values of their variables.
3. Analyze how changing the value of a variable impacts the result of an expression.

Learning Objectives

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

Before You Start

Order of Operations (BEDMAS)

Why: Students must be proficient with BEDMAS to correctly evaluate expressions after substituting values for variables.

Introduction to Algebraic Expressions

Why: Students need a foundational understanding of what variables and expressions are before they can substitute values into them.

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.

Watch Out for These Misconceptions

Common Misconception

Operations are always performed left to right, ignoring type.

What to Teach Instead

BEDMAS dictates priority: multiplication before addition. Partner verification tasks help students catch left-to-right errors quickly and explain the rule to peers, reinforcing consistency.

Common Misconception

Substituting variables is optional if the expression looks simple.

What to Teach Instead

Every variable must be replaced for evaluation. Hands-on substitution with number tiles or cards makes this step visible, and group challenges show how skipped steps lead to wrong results.

Common Misconception

Changing a variable's value has no predictable effect on the outcome.

What to Teach Instead

Larger inputs yield proportionally larger results in linear terms. Tracking tables in small groups helps students spot and articulate these patterns through repeated trials.

Active Learning Ideas

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.

25 min·Pairs

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.

35 min·Small Groups

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.

40 min·Whole Class

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.

20 min·Individual

Real-World Connections

• A sports analyst might use algebraic expressions to calculate a player's total points, substituting their number of goals, assists, and bonus points into a formula like 2G + A + B.
• Retailers use algebraic expressions to calculate the final price of an item after discounts and taxes. For example, Price = (OriginalCost * (1 - DiscountRate)) * (1 + TaxRate).
• In coding, variables in expressions are used to represent user inputs or game states, allowing programs to calculate scores or outcomes dynamically.

Assessment Ideas

Quick Check

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.

Exit Ticket

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.

Discussion Prompt

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.

Frequently Asked Questions

How do I teach BEDMAS effectively in Grade 6 math?

Start with mnemonics like BEDMAS and visual anchors showing operation layers. Use number lines or flowcharts for practice. Progress to expressions with mixed operations, incorporating peer teaching where students lead mini-lessons on one operation. This builds automaticity and addresses Ontario expectations for justification.

What are common errors when evaluating algebraic expressions?

Students often ignore BEDMAS, doing addition before multiplication, or mishandle brackets. They may forget to substitute all variables or misapply negatives. Regular error analysis in pairs, followed by class correction votes, clarifies these issues and ties back to key questions on order and impact.

How can algebraic expressions connect to real life for Grade 6?

Use scenarios like recipe scaling (double ingredients: 2x flour), budgeting (total cost: price x quantity + tax), or sports (score: points x games + bonus). Students substitute real numbers to evaluate, then adjust variables to predict changes, making abstract skills practical and engaging.

How does active learning help with evaluating algebraic expressions?

Active methods like relay races and variable trackers make BEDMAS rules experiential rather than memorized. Pairs catch errors through immediate feedback, small groups uncover patterns via data collection, and whole-class hunts build justification skills. These reduce anxiety around variables and solidify understanding through movement and talk, aligning with student-centered Ontario practices.