Introduction to Multiplication by Factors

Hello, Year 6! Today, we’re going to learn about multiplication by factors. This is an important part of maths that helps us understand how numbers work together. Let’s break it down step-by-step!

What Are Factors?

Factors are numbers that you can multiply together to get another number. For example, if we take the number 12, its factors are:

  • 1 and 12 (because 1 \times 12 = 12)
  • 2 and 6 (because 2 \times 6 = 12)
  • 3 and 4 (because 3 \times 4 = 12)

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Understanding Multiplication by Factors

When we multiply by factors, we are using two numbers that can combine to give us a bigger number. For example:

  • If we want to multiply 3 by its factor 4, we can write it as:

3 \times 4 = 12

  • Here, 3 and 4 are factors of the result, which is 12.

Key Rules

  1. Commutative Property: This means that the order of multiplication doesn’t matter. For example:4 \times 3 = 3 \times 4 = 12
  2. Multiplying by 1: Any number multiplied by 1 stays the same. For example:5 \times 1 = 5
  3. Multiplying by 0: Any number multiplied by 0 equals 0. For example:7 \times 0 = 0

Tips and Tricks

  • Break it down: If a multiplication problem seems hard, try breaking it into smaller parts. For example, if you need to calculate 6 \times 8, you can think of it as 6 \times (4 + 4) = (6 \times 4) + (6 \times 4) = 24 + 24 = 48.
  • Use Times Tables: Familiarity with your times tables makes it easier to find factors and calculate products.
  • Visual Aids: Drawing arrays (like dots in rows and columns) can help you visualise multiplication and understand factors better.

Practice Questions

Now it’s time to test what you’ve learned! Here are some questions for you to try:

Easy Level Questions

  1. What are the factors of 10?
  2. Calculate 2 \times 5.
  3. What is 1 \times 8?
  4. Find the product of 3 \times 3.
  5. What are the factors of 6?
  6. Calculate 4 \times 2.
  7. What is 0 \times 7?
  8. What are the factors of 9?
  9. Find the product of 5 \times 2.
  10. Calculate 1 \times 5.
  11. What are the factors of 4?
  12. Calculate 3 \times 2.
  13. What is 2 \times 1?
  14. Find the product of 6 \times 1.
  15. What are the factors of 8?
  16. Calculate 2 \times 4.
  17. What is 5 \times 0?
  18. What are the factors of 12?
  19. Find the product of 3 \times 1.
  20. Calculate 4 \times 3.

Medium Level Questions

  1. What are the factors of 15?
  2. Calculate 5 \times 4.
  3. What is 6 \times 7?
  4. Find the product of 4 \times 5.
  5. What are the factors of 14?
  6. Calculate 3 \times 6.
  7. What is 2 \times 9?
  8. Find the product of 8 \times 3.
  9. What are the factors of 18?
  10. Calculate 7 \times 2.
  11. What is 10 \times 5?
  12. Find the product of 12 \times 1.
  13. What are the factors of 20?
  14. Calculate 6 \times 3.
  15. What is 4 \times 6?
  16. Find the product of 9 \times 2.
  17. What are the factors of 16?
  18. Calculate 8 \times 1.
  19. What is 5 \times 5?
  20. Find the product of 7 \times 3.

Hard Level Questions

  1. What are the factors of 24?
  2. Calculate 12 \times 3.
  3. What is 9 \times 8?
  4. Find the product of 15 \times 2.
  5. What are the factors of 30?
  6. Calculate 18 \times 6.
  7. What is 11 \times 5?
  8. Find the product of 12 \times 4.
  9. What are the factors of 36?
  10. Calculate 14 \times 2.
  11. What is 7 \times 9?
  12. Find the product of 16 \times 3.
  13. What are the factors of 28?
  14. Calculate 20 \times 5.
  15. What is 8 \times 7?
  16. Find the product of 5 \times 6.
  17. What are the factors of 40?
  18. Calculate 21 \times 2.
  19. What is 12 \times 12?
  20. Find the product of 9 \times 4.

Answers

Easy Level Answers

  1. 1, 2, 5, 10
  2. 10
  3. 8
  4. 9
  5. 1, 2, 3, 6
  6. 8
  7. 0
  8. 1, 3, 9
  9. 10
  10. 5
  11. 1, 2, 4
  12. 6
  13. 2
  14. 6
  15. 1, 2, 4, 8
  16. 8
  17. 0
  18. 1, 2, 3, 4, 6, 12
  19. 3
  20. 12

Medium Level Answers

  1. 1, 3, 5, 15
  2. 20
  3. 42
  4. 20
  5. 1, 2, 7, 14
  6. 18
  7. 18
  8. 24
  9. 1, 2, 3, 6, 9, 18
  10. 14
  11. 50
  12. 12
  13. 1, 2, 4, 5, 10, 20
  14. 18
  15. 24
  16. 18
  17. 1, 2, 4, 7, 14, 28
  18. 8
  19. 25
  20. 21

Hard Level Answers

  1. 1, 2, 3, 4, 6, 8, 12, 24
  2. 36
  3. 72
  4. 30
  5. 1, 2, 3, 5, 6, 10, 15, 30
  6. 108
  7. 55
  8. 48
  9. 1, 2, 3, 4, 6, 9, 12, 18, 36
  10. 28
  11. 63
  12. 48
  13. 1, 2, 4, 7, 14, 28
  14. 100
  15. 56
  16. 30
  17. 1, 2, 4, 5, 8, 10, 20, 40
  18. 42
  19. 144
  20. 36

Happy learning, Year 6! Keep practising your multiplication by factors, and you’ll become a maths whizz in no time!