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Expression Explorer

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Lesson Plan

Expression Explorer Lesson Plan

Students will expand, factor, and simplify three linear expressions with rational coefficients to build fluency with algebraic manipulations.

Mastering expansion, factoring, and simplification lays the groundwork for solving equations and more advanced algebra topics, boosting student confidence and readiness.

Audience

7th Grade Students

Time

30 minutes

Approach

Guided, hands-on practice with immediate feedback

Materials

Expression Explorer Worksheet, Expression Explorer Answer Key, and Mini Whiteboards and Dry-Erase Markers

Prep

Review and Prepare Materials

5 minutes

Step 1

Hook & Objective Introduction

5 minutes

  • Pose a warm-up challenge: "Expand ½(4x – 6), factor ¾x + 9/8, and simplify 2/3x + 4/6x + 5"
  • Introduce the lesson goal: fluency in expanding, factoring, simplifying expressions
  • Display the three target problems on the board or slide
  • Distribute mini whiteboards and markers for real-time student work

Step 2

Guided Practice with Three Targeted Problems

20 minutes

  • Problem 1: Expand ½(4x – 6)
    • Students work on whiteboards, show answers simultaneously
    • Discuss the distribution of fractions and signs
  • Problem 2: Factor ¾x + 9/8
    • Guide students to identify the greatest common factor
  • Problem 3: Simplify 2/3x + 4/6x + 5
    • Combine like terms with rational coefficients
  • Circulate to offer targeted support and prompt deep thinking

Step 3

Review & Reflection

5 minutes

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Slide Deck

Expression Explorer

A 30-minute 7th-grade lesson to practice expanding, factoring, and simplifying linear expressions with rational coefficients (Standard 7.EE.4a).

Welcome everyone! Introduce the lesson title and goals. Explain you’ll use mini whiteboards for real-time practice. Set a positive tone and remind students this is a 30-minute Tier 1 fluency builder.

Learning Objectives

• Expand a linear expression with a fractional coefficient
• Factor an expression with rational coefficients
• Simplify expressions by combining like terms with rational coefficients

Read each objective aloud. Emphasize fluency and the connection to future equation solving. Ask students to note these goals on their worksheets.

Problem 1: Expansion

Expand: ½(4x – 6)

Prompt students to work on their whiteboards. After 1–2 minutes, have everyone raise boards and share. Then reveal and discuss the solution.

Problem 2: Factoring

Factor: ¾x + 9/8

Guide students to identify the greatest common factor. Encourage them to show their factor-out work on boards. Confirm the factored form and discuss why the chosen factor works.

Problem 3: Simplification

Simplify: 2/3x + 4/6x + 5

Have students combine like terms step by step. Remind them to convert 4/6x into an equivalent fraction before adding. Share the simplified result.

Review & Reflection

• Record answers on the Expression Explorer Worksheet
• Check solutions with the Expression Explorer Answer Key
• Reflection Questions:
– Which skill was easiest?
– Which would you like more practice with?

Ask students to record their final answers on the worksheet. Use the answer key to verify as a class. Lead the reflection discussion with the prompts below.

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Worksheet

Expression Explorer Worksheet

Name: ____________________________ Date: _______________

Instructions: Solve each problem below. Show your work and write your final answer in the space provided. After finishing, you may check your answers with the Expression Explorer Answer Key.

1. Expand: ½(4x – 6)












2. Factor: ¾x + 9/8












3. Simplify: 2/3x + 4/6x + 5












Reflection

a) Which skill was easiest for you?







b) Which skill would you like more practice with?







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Answer Key

Expression Explorer Answer Key

This answer key provides detailed, step-by-step explanations for each problem to guide grading and support student understanding.

1. Expand: ½(4x – 6)

Goal: Use the distributive property to multiply each term inside the parentheses by ½.

  1. Distribute ½ to the first term: ½ × 4x = 2x
  2. Distribute ½ to the second term: ½ × (–6) = –3

Answer:

½(4x – 6) = 2x – 3

2. Factor: ¾x + 9/8

Goal: Find the greatest common factor (GCF) of the coefficients and factor it out.

  1. Rewrite both terms with a common denominator to compare:
    • ¾x = 6/8 x
    • 9/8 = 9/8
  2. Identify the GCF of 6/8 and 9/8. Both are divisible by 3/8, since:
    • (6/8) ÷ (3/8) = 2
    • (9/8) ÷ (3/8) = 3
  3. Factor out 3/8:
    • 6/8 x + 9/8 = (3/8) · (2x) + (3/8) · (3)
    • Combine: (3/8)(2x + 3)

Answer:

¾x + 9/8 = (3/8)(2x + 3)

Note: Factoring out 3/8 leaves integer coefficients inside the parentheses, which is often the preferred simplest form.

3. Simplify: 2/3x + 4/6x + 5

Goal: Combine like terms (terms containing x) and leave the constant term unchanged.

  1. Rewrite 4/6x with an equivalent fraction that has denominator 3:
    • 4/6 x = 2/3 x (since 4/6 = 2/3)
  2. Combine the x-terms:
    • 2/3 x + 2/3 x = (2/3 + 2/3)x = 4/3 x
  3. Bring down the constant +5.

Answer:

2/3x + 4/6x + 5 = 4/3x + 5

Use this key to verify student work and discuss any common errors:

  • Missing negative sign when distributing
  • Choosing a smaller-than-maximum GCF
  • Forgetting to convert fractions to like denominators when combining terms

For further practice, refer students to the Expression Explorer Worksheet and revisit any steps needing reinforcement.

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Expression Explorer • Lenny Learning