Higher Common Factors

Curriculum Area:

Mathematics – Number
Level: Key Stage 3, Year 7 (Cambridge Curriculum)

Lesson Objectives

• To understand the concept of factors.
• To identify factors of numbers.
• To find the highest common factor (HCF).

Keywords

• Factor: A number that divides another number exactly.
• Common Factor: A factor that is shared between two or more numbers.
• Highest Common Factor (HCF): The largest number that divides two or more numbers exactly.

Materials Needed

• Whiteboard and markers
• Student notebooks
• Projector
• Worksheets (pre-prepared)

Time Breakdown

0-10 Minutes: Introduction

• Greeting and Register

  • Take attendance and greet the students.

• Starter Activity:

  • Quick recap of prime numbers (as they will help in finding factors).
  • Ask students to list the first 10 prime numbers.

10-25 Minutes: Direct Instruction

• Explain Factors:

  • Define the concept of a factor.
  • Example: Factors of 12 are 1, 2, 3, 4, 6, and 12.

• Finding Common Factors:

  • Explain that common factors are factors shared between two or more numbers.
  • Example: Factors of 8 (1, 2, 4, 8) and 12 (1, 2, 3, 4, 6, 12). Common factors are 1, 2, 4.

• Introduction to HCF:

  • Explain that the highest common factor is simply the largest of the common factors.
  • Example: Highest common factor of 8 and 12 is 4.

25-45 Minutes: Guided Practice

• Example Exercise (Interactive):

  • Find and underline the HCF of the following pairs of numbers:
    • 18 and 24
    • 30 and 45
  • Walk through one example with the class, showing the step-by-step process:
    1. List the factors of each number.
    2. Identify the common factors.
    3. Determine the highest common factor.
  • Allow students to work through the other example in pairs. Circulate to assist as necessary.

• Worksheet Activity:

  • Distribute worksheets with a variety of problems focusing on finding the HCF.
  • Provide immediate feedback on completed worksheets.

45-55 Minutes: Individual Practice

• Independent Work:
  • Students will solve HCF problems individually from their textbooks or the worksheet provided.
  • Examples for practice:
    • 15 and 25
    • 21 and 35
    • 28 and 42

55-60 Minutes: Plenary

• Review and Recap:

  • Go over one or two problems from the independent practice as a class.
  • Reinforce the steps for finding the HCF.

• Exit Ticket:

  • Each student fills out a small slip of paper with the HCF of 32 and 48.

Homework Assignment

• Worksheet on finding common factors and HCF.
• Recommended websites for further practice:
  • BBC Bitesize: KS3 Maths
  • Maths is Fun

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(Note: Teachers should replace the placeholders with specific website links as appropriate.)

Assessment

• Observe students during guided and independent practice to assess their understanding.
• Review the exit tickets and the homework assignment for comprehension and mastery of the lesson objectives.

Differentiation

• Support:

  • Provide multiplication charts or factor tables to students needing extra help.
  • Pair students strategically with stronger peers.

• Challenge:

  • Ask advanced students to find the HCF of three numbers.
  • Introduce the concept of least common multiple (LCM) as an extension activity.

Reflection

• After the lesson, note which students grasped the concept and which need additional support.
• Adjust future lessons based on student performance and understanding of the concepts covered.