Grade 3-4Division5 min read
Division Facts: Strategies Beyond Memorization
Division Is Related to Multiplication
The most important thing to understand: division is the inverse of multiplication.
If 6 × 4 = 24, then:
- 24 ÷ 4 = 6
- 24 ÷ 6 = 4
This means kids who know multiplication facts already know division facts!
Two Ways to Think About Division
Sharing (Partitive): "I have 12 cookies for 3 friends. How many does each get?"
- Dividing into equal groups
- Answer tells you the size of each group
Grouping (Quotative): "I have 12 cookies. If each bag holds 3, how many bags?"
- Making groups of a certain size
- Answer tells you how many groups
Strategies for Division Facts
Use multiplication: "What times 4 equals 28?" → 7
Skip counting: For 35 ÷ 5, count by 5s: 5, 10, 15, 20, 25, 30, 35. That's 7 jumps.
Halving: For dividing by 2, just find half.
Patterns:
- Dividing by 1: The number stays the same
- Dividing by itself: The answer is always 1
- Dividing by 10: Remove the zero (for multiples of 10)
The Relationship to Fractions
Division is the same as fractions:
- 12 ÷ 4 = 12/4 = 3
- 1 ÷ 2 = 1/2 = 0.5
Understanding this connection helps later with fraction operations.
Common Struggles
Remainders: When numbers don't divide evenly
- 14 ÷ 3 = 4 remainder 2
- Practice with concrete objects first
Dividing by larger numbers: 6 ÷ 12 confuses kids
- "Can 12 people share 6 cookies? Yes, but each gets less than 1."
- This connects to fractions: 6 ÷ 12 = 6/12 = 1/2
Zero confusion:
- 0 ÷ 5 = 0 (zero divided by anything is zero)
- 5 ÷ 0 = undefined (you can't divide by zero)
Practice Order
- Division by 2 (halving)
- Division by 5 and 10
- Division by 1
- Division by 3 and 4
- Division by 6, 7, 8, 9
Practice Resources
Build division fluency: