Division — Deep Dive Learning

Share equally, find groups, and divide step by step

What is Division?

  • Division means sharing or splitting into equal parts.
  • We use the ÷ sign for division.
  • Example: 12 ÷ 3 means "share 12 equally into 3 groups".
  • Division is the opposite of multiplication.
  • We use division every day — sharing food, splitting costs, working out how many bags we need.

What Division Means — Sharing Equally

  • Division means sharing things out equally.
  • Everyone gets the same amount.
  • Example: 12 sweets shared between 3 children.
  • 12 ÷ 3 = 4
  • Each child gets 4 sweets.
  • Ask yourself: how many does each person get if we share equally?

Division as Groups

  • Division also means splitting things into groups of a certain size.
  • Example: 20 biscuits put into groups of 4.
  • 20 ÷ 4 = 5
  • That makes 5 groups.
  • Ask yourself: how many groups can I make?
  • The answer tells you the number of groups.

Fact Families

  • Multiplication and division are connected.
  • If you know a times table fact, you know a division fact too.
  • 3 × 4 = 12
  • So: 12 ÷ 4 = 3
  • And: 12 ÷ 3 = 4
  • These three facts are called a "fact family".
  • Learning your times tables helps with division!

Bus Stop Method

  • The bus stop method is a way to divide bigger numbers.
  • Write the number inside a "bus stop" shape.
  • Example: 84 ÷ 4
  • Step 1: How many 4s go into 8? → 2. Write 2 above.
  • Step 2: How many 4s go into 4? → 1. Write 1 above.
  • Answer: 84 ÷ 4 = 21

Remainders

  • Sometimes numbers do not divide exactly.
  • What is left over is called the remainder.
  • Example: 14 ÷ 4
  • 4 × 3 = 12 (closest to 14 without going over)
  • 14 − 12 = 2 left over
  • So: 14 ÷ 4 = 3 remainder 2
  • We write "r 2" to show remainder 2.

Worked Examples

Example 1: Bus Stop Method — 84 ÷ 4

  1. Write 84 inside the bus stop shape. We are dividing by 4.
  2. Look at the first digit: 8. How many 4s go into 8? → 2.
  3. Write 2 above the 8.
  4. Look at the next digit: 4. How many 4s go into 4? → 1.
  5. Write 1 above the 4.
  6. Answer: 84 ÷ 4 = 21

Example 2: Division with a Remainder — 17 ÷ 5

  1. We want to divide 17 by 5.
  2. Count in 5s: 5, 10, 15, 20. 20 is too big.
  3. So 5 goes into 17 three times: 5 × 3 = 15.
  4. 17 − 15 = 2 left over.
  5. Answer: 17 ÷ 5 = 3 remainder 2

Practice Problems

  • 15 children sit in 3 equal rows. How many children are in each row?
    Hint: Think: 15 ÷ 3 = ? Count in 3s to help: 3, 6, 9, 12, 15.
    Answer: 5
  • 36 pencils are shared equally between 6 children. How many does each child get?
    Hint: Think: 36 ÷ 6 = ? Use the 6 times table.
    Answer: 6
  • 19 apples are put into bags of 4. How many full bags, and how many apples are left over?
    Hint: 4 × 4 = 16. That is the closest without going over 19. 19 − 16 = 3 left over.
    Answer: 4 bags remainder 3

Challenge Question

A school orders 144 exercise books. They are shared equally between 6 classes. How many books does each class get?

Hint: Use the bus stop method. Divide 144 by 6 one step at a time.

Answer: 24

6 into 14 goes 2 times (2 × 6 = 12), remainder 2. Bring down 4 to make 24. 6 into 24 goes 4 times. Answer: 144 ÷ 6 = 24.

Common Mistakes to Avoid

  • Mistake: Mixing up the order: thinking 12 ÷ 4 = 4
    Correction: 12 ÷ 4 = 3. Count in 4s to check: 4, 8, 12 — that is 3 steps.
    Why: The bigger number goes first in division. Always check by multiplying back: 3 × 4 = 12.
  • Mistake: Forgetting the remainder: saying 14 ÷ 4 = 3
    Correction: 14 ÷ 4 = 3 remainder 2. Check: 4 × 3 = 12. 14 − 12 = 2.
    Why: Always check by multiplying back and finding what is left over.
  • Mistake: Thinking division makes numbers bigger
    Correction: Division always makes numbers smaller (or the same).
    Why: 20 ÷ 4 = 5. The answer is always less than or equal to the number you started with.
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