Evaluating with Substitution

Lesson Overview

Grade: 6
Unit: Expressions and Equations Exploration (Lesson 2 of 4)
Duration: 30 minutes
Class Size: 15 students

This lesson builds on students’ prior understanding of algebraic expressions by teaching them how to evaluate expressions through substitution. The approach includes explicit, step-by-step instruction and collaborative peer teaching using a Kagan cooperative learning structure.

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Common Core State Standards (CCSS) Alignment

Standard:
CCSS.MATH.CONTENT.6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.

Learning Objectives:

• I can substitute given values for variables in an expression.
• I can correctly evaluate algebraic expressions using order of operations.
• I can explain my thinking clearly to a peer.

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I Can Statements

• I can evaluate an expression by substituting values for variables.
• I can follow steps accurately to simplify expressions after substitution.
• I can teach a classmate how I solved an expression.

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Success Criteria

• I substitute values correctly for each variable.
• I simplify expressions step-by-step following order of operations.
• I communicate the evaluation process clearly when peer teaching.

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Materials Needed

• Whiteboard and markers
• Individual mini whiteboards and markers for each student
• Worksheet with 5–6 algebraic expressions for substitution practice
• Visual step-by-step example poster or slides on evaluating an expression
• Timer
• Colored overlays or dyslexia-friendly fonts for printed materials

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Lesson Breakdown

1. Introduction & Review (5 minutes)

• Activate Prior Knowledge by briefly revisiting what an algebraic expression is and variables as placeholders (from Lesson 1).
• Present a simple expression (e.g., 3x + 4) and ask: “What does this expression mean?”
• Explain today's goal: “We will learn to find the value of an expression by putting in numbers for the variables.”

Strategy: Use a large, clear example on screen/board. Check for understanding with a quick hand signal.

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2. Explicit Instruction with Modeling (8 minutes)

• Walk through a detailed example:
  Expression: 2y + 5, where y = 3
  Step 1: Substitute 3 for y → 2(3) + 5
  Step 2: Calculate multiplication → 6 + 5
  Step 3: Add to find the answer → 11

• Write each step visibly and explain the reasoning aloud using "I can" language:
  “I substitute 3 for y. I multiply 2 times 3. Then I add 5. The answer is 11.”

• Provide a second example, slightly more complex (e.g., evaluate 4x – 2 for x = 5).

• Use a think-aloud to emphasize order of operations and substitution precision.

Dyslexia-Friendly Tip: Use dyslexia-friendly font handouts and provide each student with colored overlays to reduce visual stress. Speak clearly and write neatly with spacing between numbers and symbols.

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3. Guided Practice in Small Groups with Kagan Structure (12 minutes)

• Organize students into groups of three. Assign roles:

  • Explainer: Describes their substitution and simplification process out loud.
  • Listener: Asks clarifying questions and paraphrases the explanation.
  • Checker: Confirms the answer and helps correct mistakes.

• Provide each group with 3 expressions and corresponding variable values to evaluate.

• Rotate roles after each problem. Encourage students to use sentence starters such as:
  “First, I substituted ___ for ___. Then I... I got ___.”

• Teacher circulates to provide support, ask probing questions, and encourage peer teaching.

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4. Independent Quick Check (4 minutes)

• Distribute a short worksheet with 2 expressions for individual evaluation (e.g., 5a + 3, a=4; 3m - 7, m=6).
• Students solve independently and write their answer with steps on mini whiteboards.
• Collect mini whiteboards or have quick oral sharing, providing immediate feedback.

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5. Closure & Reflection (1 minute)

• Ask students to share one step they found easy or challenging.

• Summarize: “Today, you learned how to substitute values into expressions and explain your thinking to others.”

• Preview next lesson: solving simple one-step equations.

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Differentiation Strategies

• For struggling learners:

  • Use simpler expressions with one variable and smaller numbers.
  • Provide sentence frames and visual models.
  • Offer one-on-one guidance during group work.

• For students with dyslexia:

  • Provide dyslexia-friendly print materials with increased spacing, consistent font (e.g., OpenDyslexic), and use of colored overlays.
  • Present instructions both verbally and visually.

• For advanced learners:

  • Challenge with expressions containing multiple terms and more than one variable (e.g., 2x + 3y where x and y have given values).
  • Introduce the concept of evaluating expressions with fractions or decimals for substitution.

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Extension Activities

• Create your own expression and select values to substitute. Explain your steps to a partner.
• Explore real-world problems where substitution in expressions is used, such as calculating costs or measurements.

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Assessment

• Observe student participation and accuracy during group peer-teaching activities.
• Evaluate answers and reasoning on independent mini whiteboard work.
• Listen for clarity and mathematical language during peer explanations.

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This highly interactive and scaffolded approach ensures students gain confidence in evaluating expressions by substitution, supporting multiple learning styles and fostering mathematical communication skills critical for algebra readiness.