Finding the GCF

Lesson Overview

Grade: 6
Duration: 30 minutes
Class Size: 14 students
Unit: Mastering GCF, LCM & Distributive
Lesson: 1 of 4
Topic: Finding the Greatest Common Factor (GCF) using lists and models

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Common Core Standards

CCSS.MATH.CONTENT.6.NS.B.4
Find the greatest common factor (GCF) of two whole numbers less than or equal to 100 and find the least common multiple (LCM) of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a product of a factor and a sum.

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Learning Objectives

By the end of this lesson, students will be able to:

• I can find the factors of two given numbers by making lists.
• I can identify the greatest common factor (GCF) of two numbers using lists and number models.
• I can explain how I found the GCF using sentence frames and models.

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Success Criteria

Students will demonstrate success by:

• Correctly listing all factors of two given numbers.
• Accurately identifying all common factors and isolating the greatest one.
• Clearly articulating their process of finding the GCF using sentence frames.
• Engaging with hands-on models or visual aids to support understanding.

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Materials Needed

• Whiteboard and markers
• Individual student dry-erase boards
• Counters or linking cubes for hands-on modeling
• Factor list charts (printed, with dyslexia-friendly font and high-contrast colors)
• Sentence frames printed on strips (e.g., “The factors of ___ are ___”, “The common factors are ___”, “The greatest common factor is ___”)
• Challenge worksheets for extension activity

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Lesson Plan Breakdown

1. Introduction / Hook (5 minutes)

• Activate prior knowledge: Ask students if they know what factors are. Use a simple example like factors of 12. Write factors on the board (1, 2, 3, 4, 6, 12).
• Introduce GCF by saying, “The Greatest Common Factor is the biggest number that goes evenly into two (or more) numbers.”
• Show a real-life scenario: e.g., Two friends have 12 and 18 candies and want to divide them in equal groups without leftovers. What’s the biggest group size they can make?
• Display the I can objectives on the board for students to see.

2. Guided Practice (12 minutes)

• Model how to list factors of two numbers step-by-step on the whiteboard (e.g., 24 and 36):
  • List factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  • List factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  • Circle common factors, then highlight the greatest
• Use counters/linking cubes as manipulatives to build visual factor sets (divide the cubes into groups) for smaller numbers.
• Distribute dry-erase boards and assign pairs of numbers (e.g., 30 and 45; 16 and 24) for students to list factors and find the GCF. Circulate and support with hands-on tools or charts.
• Encourage students to use the sentence frames aloud or write short explanations on their boards (e.g., “The factors of 30 are ... The common factors are ... The greatest common factor is ...”).

3. Independent Practice / Quick Formative Assessment (8 minutes)

• Provide 2-3 new pairs of numbers on a worksheet, such as:
  • 18 and 27
  • 20 and 50
  • 14 and 35
• Students work individually to:
  1. Write the factors of each number.
  2. Circle common factors.
  3. Write the GCF.
• Use sentence frames to have them explain their answer in writing or orally.
• Collect worksheets for quick assessment.

4. Closure and Reflection (3 minutes)

• Have 3-4 students share how they found the GCF. Use sentence frames to support their speech.
• Revisit the I can statements and success criteria.
• Reinforce that understanding factors helps with many math problems ahead (like LCM & distributive property).
• Preview next lesson: Finding the Least Common Multiple.

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Differentiation Strategies

Learner Type	Strategy
Visual Learners	Use color-coded factor lists and manipulatives (counters, cubes) for hands-on learning.
Students with Dyslexia	Provide factor lists and sentence frames printed in dyslexia-friendly fonts and high contrast. Use clear spacing and bullet points.
English Language Learners	Pair visuals with simple vocabulary. Use sentence frames and model language before independent work.
Students Needing Extra Support	Work in small guided groups with teacher or aide. Use step-by-step factor cards or matching activities.

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Extension Activity for Advanced Learners

• Challenge students with finding the GCF of three or more numbers (e.g., 24, 36, and 48).
• Have them create factor trees to visualize prime factors and then use these to find the GCF.
• Encourage them to explain the process in full sentences and to create their own word problem involving GCF.

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Notes for Teachers

• Emphasize mathematical vocabulary such as factor, common factor, greatest, and divide evenly.
• Reinforce that GCF is related to division without remainder.
• Use positive, encouraging feedback to build student confidence.
• Continually check for understanding by asking students to explain concepts in their own words.

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This lesson is designed to build foundational understanding of GCF with meaningful visuals, hands-on interaction, clear language supports, and opportunities to communicate mathematical thinking effectively—setting a solid base for the next lessons in the unit.