Factors and Multiples: The Building Blocks of Number
This lesson introduces Year 7 students to the fundamental concepts of factors and multiples. It covers identifying factor pairs, listing multiples, and finding common factors/multiples (HCF and LCM). The lesson uses systematic listing methods to ensure accuracy and builds towards solving worded problems.
Learning objectives
- Find all factor pairs of a given number systematically.
- Identify the first ten multiples of any number up to 12.
- Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two numbers.
- Recognise the relationship between factors and multiples within number patterns.
Lesson plan (60 minutes)
Starter · 5 min
Retrieval Practice: Grid multiplication and division facts warm-up.
Introduction · 15 min
Direct Instruction: Explaining factors and multiples using the 'Factor Bug' and 'Multiple Mountains' methods. Discussion of HCF and LCM.
Guided Practice · 10 min
Guided Practice: Completing a worked example on the board with student input. Identifying the 'Factor-Multiple' relationship.
Independent Practice · 20 min
Independent Practice: Students work through Support, Core, or Stretch worksheets based on confidence.
Plenary · 10 min
Plenary: 8-question multiple-choice quiz to check for understanding and address misconceptions.
Key vocabulary
- Factor
- A number that divides into another number exactly with no remainder.
- Multiple
- The result of multiplying a whole number by another whole number (its times table).
- Highest Common Factor (HCF)
- The largest factor that is shared by two or more numbers.
- Lowest Common Multiple (LCM)
- The smallest multiple that is shared by two or more numbers.
- Factor Pair
- Two numbers that multiply together to give a specific product.
Core worksheet (first questions)
- Find all the factors of 30.
- Find all the factors of 28.
- List the first ten multiples of 7.
- List the multiples of 15 that are less than 100.
Quiz (sample)
1. What is the definition of a factor?
- A. A number that is in another number's times table.
- B. A number that divides exactly into another number without a remainder.
- C. The result of multiplying two numbers together.
- D. A number that only has two factors.
2. Which list contains all the factors of 20?
- A. 1, 2, 4, 5, 10, 20
- B. 2, 4, 5, 10
- C. 20, 40, 60, 80
- D. 1, 2, 5, 10, 20, 40
3. What are the first five multiples of 7?
- A. 1, 7
- B. 7, 17, 27, 37
- C. 7, 14, 21, 28, 35
- D. 14, 21, 28, 35, 42
The full pack is waiting
Support and Stretch worksheets, every answer and model answer, the teaching explainer and common misconceptions, editable and ready to print as PDF or Word.
Start your 14-day trial