Review of Expressions and Equations

Active learning works for expressions and equations because the shift to algebra demands students move from computing with numbers to reasoning about relationships. Hands-on tasks let students physically manipulate symbols, test ideas, and see why procedures like inverse operations matter, turning abstract rules into concrete understanding.

• 6th Grade
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Differentiate between expressions, equations, and inequalities by identifying their defining characteristics.
2. Evaluate algebraic expressions for given variable values using order of operations.
3. Solve one-step linear equations and inequalities using inverse operations.
4. Construct a real-world scenario that can be accurately modeled by a given algebraic equation.
5. Compare and contrast equivalent expressions by applying properties of operations.

Inquiry Circle

⏱ 40 min·Small Groups

Inquiry Circle: Equation Writing Workshop

Present three real-world scenarios and ask students to independently write an equation for each before comparing with their group. Groups reconcile any differences and determine which equations are equivalent. The class discussion highlights cases where two different-looking equations are both mathematically correct.

Prepare & details

Differentiate between an expression, an equation, and an inequality.

Facilitation Tip: During the Equation Writing Workshop, circulate and press pairs to explain the meaning of the equal sign in each equation they write to reinforce that it signals equivalence, not just ‘the answer.’

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Problem-Based Learning

⏱ 25 min·Pairs

Card Sort: Expression, Equation, or Inequality?

Provide cards with algebraic statements and ask pairs to sort them into three categories: expressions (no equals sign), equations (equals sign), and inequalities (comparison symbol). Pairs must also identify the variable in each and explain what it represents in a real-world context.

Prepare & details

Explain the process of solving one-step equations using inverse operations.

Facilitation Tip: For the Card Sort, listen for students to justify their choices using precise language—ask, ‘How do you know this card is an equation and not an expression?’ to surface misconceptions early.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Gallery Walk

⏱ 35 min·Small Groups

Gallery Walk: Solve and Check

Post six one-step equations and inequalities around the room, each accompanied by a student's partial or incorrect solution. Groups rotate to identify where the error occurred, complete the correct solution, and verify by substituting back into the original equation or inequality.

Prepare & details

Construct a real-world problem that can be modeled by an algebraic equation.

Facilitation Tip: During the Gallery Walk, assign each pair a specific equation to solve and post, so you can quickly scan for systematic errors like forgetting to check their solution.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

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

Think-Pair-Share

⏱ 30 min·Pairs

Think-Pair-Share: Dependent Relationships

Present a table of x and y values and ask students to write an equation relating x and y individually. Pairs compare, discuss which variable is dependent, and graph two or three points to verify the relationship, connecting to the 6.EE.C.9 standard on dependent and independent variables.

Prepare & details

Differentiate between an expression, an equation, and an inequality.

Facilitation Tip: In the Think-Pair-Share, watch for students who confuse independent and dependent variables—prompt them to rephrase the relationship using ‘if…then’ language to clarify directionality.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Teach this topic by building discourse norms first: require students to restate what others say, ask for evidence, and use materials like algebra tiles or number lines to ground abstract ideas. Avoid rushing to procedures—instead, let students discover properties through repeated reasoning. Research shows that students who verbalize their steps while solving retain concepts longer and transfer skills more effectively.

What to Expect

Successful learning shows when students clearly distinguish between expressions, equations, and inequalities, apply properties of operations to generate equivalent forms, and solve equations and inequalities with purpose and verification. Missteps become visible early, so teachers can redirect thinking before habits form.

Watch Out for These Misconceptions

Common Misconception

During Card Sort: Expression, Equation, or Inequality?, watch for students who treat all symbolic statements as equations.

What to Teach Instead

Redirect them by asking, ‘Does this statement make a claim about equality or inequality?’ and have them place the card under the correct heading before explaining why it belongs there.

Common Misconception

During Gallery Walk: Solve and Check, watch for students who solve equations but skip verification.

What to Teach Instead

Require them to write their solution, substitute it back into the original equation, and annotate whether it makes the equation true—use a red pen to highlight the verification step.

Common Misconception

During Think-Pair-Share: Dependent Relationships, watch for students who see inequalities as having a single solution.

What to Teach Instead

Have them graph the solution on a number line and list three values that satisfy it, then explain why values like 3.0001 or 100 also work.

Assessment Ideas

Exit Ticket

After Card Sort: Expression, Equation, or Inequality?, collect student cards and review their labels and one-sentence justifications for accuracy and reasoning.

Quick Check

During Gallery Walk: Solve and Check, scan student work for correct inverse operations and accurate solutions; use whiteboards to collect answers from three students to assess immediate understanding.

Discussion Prompt

After Think-Pair-Share: Dependent Relationships, circulate and listen for students to identify the unknown quantity as the cost per notebook and articulate that the equal sign means ‘the same total cost’ when writing 4n = 12.

Extensions & Scaffolding

• Challenge early finishers to write a real-world scenario that fits an inequality like 2n + 5 < 20, then trade with a partner to solve and interpret the solution set.
• For students who struggle, provide equation strips with one operation per step and ask them to match inverse operations before solving.
• Deeper exploration: Have students research how inequalities model real constraints, such as budget limits, and present their findings to the class.

Key Vocabulary

Variable	A symbol, usually a letter, that represents an unknown quantity or a value that can change.
Expression	A mathematical phrase that contains numbers, variables, and operation symbols, but no equal sign or inequality sign.
Equation	A mathematical statement that two expressions are equal, indicated by an equal sign (=).
Inequality	A mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥, indicating that they are not equal.
Inverse Operation	An operation that undoes another operation, such as addition and subtraction, or multiplication and division.