Use fact families and check your work.
Advanced Division: Division involving larger numbers that require knowledge of multiplication tables and fact families.
Fact Family: A set of related multiplication and division facts using the same numbers.
- Fact Family Approach: Think of related multiplication facts
- Repeated Subtraction: Keep subtracting the divisor
- Division Tables: Use memorized division facts
Think: "What number times 6 equals 48?"
6 × ? = 48
We know: 6 × 8 = 48
If 6 × 8 = 48, then 48 ÷ 6 = 8
48 ÷ 6 = 8 because 6 × 8 = 48.
• Multiplication-Division Connection: If a × b = c, then c ÷ a = b
• Fact Families: 6, 8, and 48 form a fact family
• Verification: 8 × 6 = 48 ✓
Show your thinking using place value and fact families.
Place Value in Division: Breaking down larger numbers into tens and ones to make division easier.
Division Strategy: Using known facts to solve more complex problems.
We need to find how many groups of 9 are in 72.
Think of the 9 times table: 9 × 8 = 72
If 9 × 8 = 72, then 72 ÷ 9 = 8
72 ÷ 9 = 8 because 9 × 8 = 72.
• Pattern Recognition: 72 is in the 9 times table
• Division Verification: 8 × 9 = 72 ✓
• Mental Math: Use known facts for quick solutions
Multi-Step Problems: Problems requiring more than one mathematical operation to solve.
Problem-Solving Strategy: Break complex problems into simpler steps.
Emma keeps 3 stickers for herself: 63 - 3 = 60 stickers to share
Share 60 stickers equally among 7 friends: 60 ÷ 7
7 × 8 = 56, so 60 ÷ 7 = 8 remainder 4
Each friend gets 8 stickers, with 4 stickers left over.
Each friend gets 8 stickers, with 4 stickers remaining.
• Order of Operations: Solve in the logical sequence
• Multi-Step Problem Solving: Break into smaller problems
• Remainder Understanding: Interpret remainders in context
Dividend: The number being divided
Divisor: The number we divide by
Quotient: The result of division
Remainder: What's left over
- Fact Families: Use related multiplication facts
- Place Value: Break numbers into tens and ones
- Repeated Subtraction: Subtract the divisor repeatedly
- Mental Math: Use known facts for quick solutions
| Division | Answer | Check |
|---|---|---|
| 6 ÷ 6 | 1 | 1 × 6 = 6 |
| 12 ÷ 6 | 2 | 2 × 6 = 12 |
| 18 ÷ 6 | 3 | 3 × 6 = 18 |
| 24 ÷ 6 | 4 | 4 × 6 = 24 |
| 30 ÷ 6 | 5 | 5 × 6 = 30 |
| 36 ÷ 6 | 6 | 6 × 6 = 36 |
| 42 ÷ 6 | 7 | 7 × 6 = 42 |
| 48 ÷ 6 | 8 | 8 × 6 = 48 |
| 54 ÷ 6 | 9 | 9 × 6 = 54 |
| 60 ÷ 6 | 10 | 10 × 6 = 60 |
• Dividing by 6 gives one-sixth of the original number
• These facts help solve larger division problems quickly
• Practice until these become automatic
| Division | Answer | Check |
|---|---|---|
| 9 ÷ 9 | 1 | 1 × 9 = 9 |
| 18 ÷ 9 | 2 | 2 × 9 = 18 |
| 27 ÷ 9 | 3 | 3 × 9 = 27 |
| 36 ÷ 9 | 4 | 4 × 9 = 36 |
| 45 ÷ 9 | 5 | 5 × 9 = 45 |
| 54 ÷ 9 | 6 | 6 × 9 = 54 |
| 63 ÷ 9 | 7 | 7 × 9 = 63 |
| 72 ÷ 9 | 8 | 8 × 9 = 72 |
| 81 ÷ 9 | 9 | 9 × 9 = 81 |
| 90 ÷ 9 | 10 | 10 × 9 = 90 |
• Dividing by 9 gives one-ninth of the original number
• These facts are essential for grade 3 division mastery
• Notice the pattern: the answers increase by 1
Division: Splitting into equal parts or groups
Sharing: Giving equal amounts to each person/group
Grouping: Making equal-sized groups from a total
Fact Families: Related multiplication and division facts
- Understand the Problem: Identify what needs to be divided
- Choose the Method: Fact family, repeated subtraction, or mental math
- Apply the Method: Follow the steps of the chosen technique
- Check Your Work: Multiply quotient by divisor
• Any number divided by 1 equals itself
• Any number divided by itself equals 1
• Zero divided by any number (except 0) equals 0
• Division by zero is undefined
• Dividend = Divisor × Quotient + Remainder
Questions & Answers
Question: How can I help my students understand the connection between multiplication and division? They seem to struggle with seeing them as inverse operations.
Answer: Great question! Use fact families to show the relationship:
- Start with a multiplication fact: 6 × 8 = 48
- Show how it creates two division facts: 48 ÷ 6 = 8 and 48 ÷ 8 = 6
- Use visual models: 6 rows of 8 dots = 48 dots total
- Then ask: "If I have 48 dots and want 6 rows, how many in each row?" (48 ÷ 6 = 8)
- Or: "If I have 48 dots and want 8 in each row, how many rows?" (48 ÷ 8 = 6)
Concrete examples work best: "I have 48 cookies and 6 friends. How many does each friend get?" versus "I have 48 cookies and want to give 8 to each friend. How many friends can I feed?"
Question: Why do we sometimes have remainders in division? What do they mean?
Answer: Remainders occur when numbers don't divide evenly! Think of it like sharing:
- If you have 63 stickers and share them equally among 7 friends, each friend gets 9 stickers (7 × 9 = 63), and there are no stickers left over
- But if you had 64 stickers, each friend would get 9 stickers (7 × 9 = 63), and you'd have 1 sticker left over
- The remainder (1) represents what can't be shared equally
- So 64 ÷ 7 = 9 R1 means 9 groups of 7 with 1 left over
Remainders are completely normal in division - they just mean the division isn't perfectly even!
Question: My child gets confused about whether to divide or multiply in word problems. How can I help them identify the operation?
Answer: Teach your child to look for key words and visualize the problem:
- Division words: "shared equally," "each," "per," "in each group," "split into," "divided among," "how many in each"
- Multiplication words: "total," "altogether," "product," "times," "groups of," "multiplied by"
- Ask: "Am I finding the total, or am I splitting something up?"
- Have them draw pictures - if they're distributing items, it's division
- If they're combining equal groups, it's multiplication
Practice with real objects: "I have 48 cookies and want to put 6 in each bag - how many bags?" (48 ÷ 6 = 8 bags)
Division Facts Grade 3 - Complete Summary
Division: The process of splitting a number into equal groups or parts.
Dividend: The number being divided.
Divisor: The number we divide by.
Quotient: The result of division.
Remainder: The amount left over after division.
Fact Family: A set of related multiplication and division facts using the same numbers.
Division-Multiplication Connection: If a × b = c, then c ÷ a = b and c ÷ b = a
Division by 1: Any number ÷ 1 = itself
Division by Self: Any number ÷ itself = 1
Zero Division: 0 ÷ any number = 0
Division Formula: Dividend = Divisor × Quotient + Remainder
Remainder Rule: Remainder is always less than the divisor
1. Fact Family Method: Think of related multiplication facts
2. Repeated Subtraction: Keep subtracting the divisor
3. Mental Math: Use known facts for quick solutions
4. Place Value: Break numbers into tens and ones
5. Verification: Always multiply back to check
Simple: 12 ÷ 3 = 4 (because 3 × 4 = 12)
Medium: 36 ÷ 6 = 6 (because 6 × 6 = 36)
Advanced: 72 ÷ 9 = 8 (because 9 × 8 = 72)
With Remainder: 49 ÷ 6 = 8 R1 (because 6 × 8 = 48, 49-48=1)
Word Problem: 63 ÷ 7 = 9 (sharing 63 items among 7 people)
Memory Aid: "What times the divisor gives me the dividend?"
Check Your Work: Always multiply quotient × divisor to verify
Practice Tables: Master multiplication tables to improve division
Visualize: Draw pictures to represent division situations
Look for Patterns: Notice relationships in division facts
Confusing Dividend/Divisor: Pay attention to which number is being divided
Ignoring Remainders: Don't forget to include remainders when they exist
Not Checking: Always verify your answer by multiplying back
Mixing Operations: Be careful to identify whether to multiply or divide
Remainder Size: Remainders must always be smaller than divisors