Mathematics · 6th Grade

Active learning ideas

Evaluating Expressions

Active learning works well for evaluating expressions because students must repeatedly practice substitution and order of operations, two skills that require muscle memory and immediate feedback. By engaging in collaborative tasks and error analysis, students confront their own misunderstandings in real time and build confidence through shared problem-solving.

• Common Core State Standards
• CCSS.Math.Content.6.EE.A.1
• CCSS.Math.Content.6.EE.A.2c

• 20–35 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Evaluate and Justify

Give pairs an expression with at least one exponent and a value to substitute (e.g., evaluate 2x² + 3x − 1 for x = 4). Each student evaluates independently, then partners compare their step-by-step work to find where (if anywhere) they diverge. The focus is on identifying the step where errors occur, not just getting the final answer.

Justify why a standard order of operations is necessary for universal communication.

Facilitation Tip

During Think-Pair-Share, circulate and listen for students using the language 'x squared means x times itself' to clarify their reasoning.

What to look for

Provide students with the expression 3x² + 5 when x = 4. Ask them to: 1. Substitute the value of x. 2. Evaluate the expression, showing each step. 3. Write one sentence explaining why they performed the exponent calculation before the multiplication.

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

Activity 02

• Gallery Walk
• 30 min · Small Groups

Gallery Walk: Spot the Mistake

Post 6-8 worked examples of expression evaluation around the room, with one error deliberately introduced in each. Students circulate, identify the error, write the correct step on a sticky note, and explain what rule was violated. The class debrief ranks the most common error types.

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

Facilitation Tip

In the Error Analysis Gallery Walk, place a timer near each poster so students move efficiently and focus on identifying errors rather than debating them.

What to look for

Present students with a worked example of an expression evaluation that contains a common order of operations error (e.g., adding before multiplying). Ask students to identify the error, explain why it is incorrect, and then provide the correct solution.

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

Activity 03

• Stations Rotation
• 35 min · Small Groups

Collaborative Task: Expression Value Table

Groups receive an expression and a table with five different values of the variable. Each group member evaluates the expression for one or two values, then the group assembles the complete table and looks for patterns (e.g., does the expression increase or decrease as x increases?). Groups present their pattern observations to the class.

Critique common errors in applying the order of operations.

Facilitation Tip

For the Expression Value Table, assign each pair a different starting value so the class collects multiple examples to discuss together.

What to look for

Students work in pairs to evaluate two different expressions. After completing their evaluations, they swap papers and check each other's work. They must identify at least one step where their partner correctly applied the order of operations and one step where they could improve their explanation.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach this topic by anchoring substitution in concrete examples first, then connecting it to the symbolic form. Use worked examples that deliberately include common errors so students recognize patterns in missteps. Research shows that students benefit most when they explain their reasoning aloud before writing it down, so incorporate verbal rehearsal before formal work.

Successful learning shows when students consistently substitute values correctly, apply operations in the proper order, and justify their steps with clear reasoning. They should be able to explain why exponentiation comes before multiplication and why left-to-right isn’t enough.

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Watch Out for These Misconceptions

• During Think-Pair-Share, watch for students calculating 3² as 3 × 2 = 6 instead of 3 × 3 = 9.

  During Think-Pair-Share, ask students to expand the exponent first by writing out 3 × 3 before computing the value. Have partners check that the written expansion matches the symbolic form before calculating.

• During Error Analysis Gallery Walk, watch for students applying operations left to right without following PEMDAS.

  During Error Analysis Gallery Walk, direct students to highlight the first operation done correctly and the first error. Then, ask them to rewrite the solution in the correct order using PEMDAS as a guide.

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Methods used in this brief

• Think-Pair-Share
• Gallery Walk
• Stations Rotation