Topic: Primes, Highest Common Factor & Lowest Common Multiple
Introduction
Building on our knowledge of factors, this week we explore prime numbers—the special numbers that are only divisible by 1 and themselves. We'll use them to find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of numbers, powerful tools for solving problems.
Key Concepts Covered
- Prime Numbers: Identifying primes using methods like the Sieve of Eratosthenes.
- Prime Factorisation: Breaking down any number into a product of its prime factors using factor trees.
- HCF & LCM: Using prime factors (and Venn diagrams) to efficiently find the HCF and LCM of two or more numbers.
- Problem-Solving: Applying HCF and LCM to solve real-world problems, like finding when two events will happen at the same time.
In-Class Activities
Let's put these new tools into practice:
- Prime Number Bingo: A fun game to quickly identify prime numbers.
- Timetable Problems: Solve problems like: "A train leaves every 12 minutes and a bus every 20 minutes. If they both leave at 10:00, when will they next leave together?"
📝 Mini-Assessment (10 marks)
- List all factors of 36. (2 marks)
- Write 84 as a product of its prime factors. (2 marks)
- What is the HCF of 48 and 60? (2 marks)
- What is the LCM of 12 and 15? (2 marks)
- Two lighthouses flash their lights every 12 and 18 seconds respectively. If they flash together at midnight, when will they next flash together? (2 marks)
📖 Homework
This week's homework is a worksheet on collecting like terms and expanding brackets. This will give you a head start on next week's topic: Algebra!