Factoring Fun!

Overview

This lesson plan focuses on teaching 7th grade students the concepts of factoring and divisibility, aligned with the California Common Core State Standards for Mathematics. The aim is to enhance students' understanding of factors, greatest common factors (GCF), least common multiples (LCM), and divisibility rules to build a solid foundation for future algebraic concepts.

Standards

• CCSS.MATH.CONTENT.7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
• CCSS.MATH.CONTENT.6.NS.B.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple 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 multiple of a sum of two whole numbers with no common factor.

Objectives

• Understand and apply divisibility rules for numbers 2–10.
• Factor whole numbers and identify prime factors.
• Find the greatest common factor (GCF) and least common multiple (LCM) of given numbers.

Materials

• Whiteboard and markers
• Projector and presentation slides
• Factoring and divisibility worksheets
• Scissors for a paper folding activity
• Large sheets of coloured paper for group activities

Lesson Plan

Introduction (10 minutes)

1. Hook: Start with a brain teaser that involves factors and divisibility, like: "What 3-digit number can be evenly divided by both 3 and 5?"
2. Objective Discussion: Explain the objectives of the lesson related to factoring and divisibility.
3. Relevance: Discuss how these skills are used in real-world situations, such as in finance and engineering.

Direct Instruction (15 minutes)

1. Divisibility Rules Presentation: Use slides to outline divisibility rules for numbers 2 through 10. Provide several simple examples on the board.
2. Factoring Explanation: Discuss the concepts of factors and prime numbers. Demonstrate how to factor simple numbers, like 12 and 30.
3. GCF & LCM: Explain how to find the greatest common factor and least common multiple through examples on the board.

Guided Practice (15 minutes)

1. Group Activity: Divide students into groups of five. Assign each group a different set of numbers to find their GCF and LCM using coloured paper and scissors to create factor trees.
2. Class Discussion: Reconvene and let each group present their factor trees and explanations. Address misconceptions and emphasize correct methods.

Independent Practice (10 minutes)

1. Worksheet Completion: Distribute a worksheet with a mix of factoring and divisibility problems. Circulate the classroom, offering individual help.
2. Challenge Problem: Include a bonus question: "Find two numbers between 1 and 50 that have a GCF of 5 and an LCM of 100."

Conclusion (5 minutes)

1. Exit Ticket: Ask students to write down one new fact they learned about divisibility and one about factoring.
2. Preview of Next Lesson: Briefly introduce how these concepts will relate to solving algebraic equations and expressions in upcoming classes.

Assessment

• Formative: Monitor group activity participation and discussion contributions.
• Summative: Evaluate completed worksheets and the accuracy of exit tickets in relation to lesson objectives.

Additional Notes

• Encourage students to think creatively and critically about patterns they observe.
• Adaptations for students with diverse learning needs might include more visual aids or one-on-one support during independent tasks.
• Reinforce the use of mathematical language to enhance understanding and communication.

This approach aims not only to meet educational standards but also to captivate students' interest through engaging activities and practical applications.