Show your work using pictures and number sentences.
Division: Division is the process of sharing equally or grouping objects into equal parts. It's the opposite of multiplication.
Division Symbol: ÷ means "divided by" or "shared equally among"
- Sharing Equally: Distribute items evenly among groups
- Repeated Subtraction: Keep subtracting the divisor until reaching zero
- Using Multiplication Facts: Think "What times 4 equals 24?"
We need to find how many groups of 4 can be made from 24, or how many items each person gets if 24 items are shared equally among 4 people.
Draw 24 circles and group them into sets of 4:
○○○○ | ○○○○ | ○○○○ | ○○○○ | ○○○○ | ○○○○
We can make 6 groups of 4.
If 24 ÷ 4 = 6, then 6 × 4 should equal 24.
6 × 4 = 24 ✓
24 ÷ 4 = 6 because 6 groups of 4 make 24.
• Division Relationship: Dividend ÷ Divisor = Quotient
• Multiplication Check: Quotient × Divisor = Dividend
• Equal Groups: Division creates equal-sized groups
How many are left over?
Division with Remainder: When division doesn't result in equal groups, some items are left over.
Remainder: The amount left over after dividing as much as possible.
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25 (too big!)
23 - 20 = 3 (the leftover amount)
23 ÷ 5 = 4 remainder 3, or 4 R3
23 ÷ 5 = 4 R3 because 4 groups of 5 make 20, leaving 3 remaining.
• Division Formula: Dividend = (Divisor × Quotient) + Remainder
• Remainder Rule: Remainder must be less than the divisor
• Verification: 5 × 4 + 3 = 20 + 3 = 23 ✓
Word Problem Strategy: Identify key words like "each," "per," "groups of," or "shared equally" to determine if division is needed.
We need to find how many groups of 6 can be made from 36.
Total ÷ Items per group = Number of groups
36 ÷ 6 = ?
We know that 6 × 6 = 36, so 36 ÷ 6 = 6
Mary needs 6 pages to hold all 36 stickers.
Mary needs 6 pages because 36 ÷ 6 = 6.
• Word Problem Steps: Read → Identify → Plan → Solve → Check
• Division Keywords: "per," "each," "in all groups," "shared equally"
• Context: Always answer in the context of the problem
Dividend: The number being divided
Divisor: The number we divide by
Quotient: The result of division
Remainder: What's left over
- Equal Sharing: Distribute items equally
- Grouping: Make equal-sized groups
- Repeated Subtraction: Subtract the divisor repeatedly
- Multiplication Facts: Use known multiplication facts
| Division | Answer | Check |
|---|---|---|
| 4 ÷ 4 | 1 | 1 × 4 = 4 |
| 8 ÷ 4 | 2 | 2 × 4 = 8 |
| 12 ÷ 4 | 3 | 3 × 4 = 12 |
| 16 ÷ 4 | 4 | 4 × 4 = 16 |
| 20 ÷ 4 | 5 | 5 × 4 = 20 |
| 24 ÷ 4 | 6 | 6 × 4 = 24 |
| 28 ÷ 4 | 7 | 7 × 4 = 28 |
| 32 ÷ 4 | 8 | 8 × 4 = 32 |
| 36 ÷ 4 | 9 | 9 × 4 = 36 |
| 40 ÷ 4 | 10 | 10 × 4 = 40 |
• Dividing by 4 gives one-fourth of the original number
• These facts are essential for grade 3 division mastery
• Practice daily for fluency
| 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
• Notice that answers increase by 1 each time
• These facts help solve larger division problems quickly
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: Sharing, grouping, or using multiplication facts
- 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: 4 × 6 = 24
- Show how it creates two division facts: 24 ÷ 4 = 6 and 24 ÷ 6 = 4
- Use visual models: 4 rows of 6 dots = 24 dots total
- Then ask: "If I have 24 dots and want 4 rows, how many in each row?" (24 ÷ 4 = 6)
- Or: "If I have 24 dots and want 6 in each row, how many rows?" (24 ÷ 6 = 4)
Concrete examples work best: "I have 24 cookies and 4 friends. How many does each friend get?" versus "I have 24 cookies and want to give 6 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 23 candies and share them equally among 5 friends, each friend gets 4 candies (5 × 4 = 20), and you have 3 candies left over
- The remainder (3) represents what can't be shared equally
- Remainders are always smaller than the divisor - otherwise, you could divide further!
- So 23 ÷ 5 = 4 R3 means 4 groups of 5 with 3 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"
- Multiplication words: "total," "altogether," "product," "times," "groups of"
- 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 36 cookies and want to put 6 on each plate - how many plates?" (36 ÷ 6 = 6 plates)
Division Facts.com Resources
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. Equal Sharing: Distribute items equally among groups
4. Grouping Method: Make equal-sized groups
5. Verification: Always multiply quotient × divisor to check
Simple: 12 ÷ 3 = 4 (because 3 × 4 = 12)
Medium: 24 ÷ 4 = 6 (because 4 × 6 = 24)
With Remainder: 23 ÷ 5 = 4 R3 (because 5 × 4 = 20, 23-20=3)
Word Problem: 36 ÷ 6 = 6 (sharing 36 items among 6 people)
Advanced: Multi-step problems requiring multiple operations
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