Mathematics · 6th Grade

Active learning ideas

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.

• Common Core State Standards
• CCSS.Math.Content.6.EE.A.1
• CCSS.Math.Content.6.EE.A.2
• CCSS.Math.Content.6.EE.A.3
• CCSS.Math.Content.6.EE.A.4
• +4 more

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.’

What to look for

Provide students with three statements: '5x + 2', '3y - 7 = 11', and '4a > 20'. Ask them to label each as an expression, equation, or inequality and briefly explain their reasoning for one of them.

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

Activity 02

• 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.

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.

What to look for

Write the equation 'n + 9 = 25' on the board. Ask students to write the inverse operation needed to solve for 'n' and then calculate the value of 'n' on a mini-whiteboard.

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

Activity 03

• 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.

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.

What to look for

Present the scenario: 'Maria bought 4 notebooks for a total of $12.' Ask students: 'What is the unknown quantity here?' 'How can we write an equation to represent this situation?' 'What does the equal sign mean in this context?'

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

Activity 04

• 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.

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.

What to look for

Provide students with three statements: '5x + 2', '3y - 7 = 11', and '4a > 20'. Ask them to label each as an expression, equation, or inequality and briefly explain their reasoning for one of them.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Inquiry Circle
• Problem-Based Learning
• Gallery Walk
• Think-Pair-Share