Use fact families and check your work.
Advanced Division: Division involving larger numbers up to 144 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 12 equals 144?"
12 × ? = 144
We know: 12 × 12 = 144
If 12 × 12 = 144, then 144 ÷ 12 = 12
144 ÷ 12 = 12 because 12 × 12 = 144.
• Multiplication-Division Connection: If a × b = c, then c ÷ a = b
• Fact Families: 12, 12, and 144 form a fact family
• Verification: 12 × 12 = 144 ✓
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 108.
Think of the 9 times table: 9 × 12 = 108
If 9 × 12 = 108, then 108 ÷ 9 = 12
108 ÷ 9 = 12 because 9 × 12 = 108.
• Pattern Recognition: 108 is in the 9 times table
• Division Verification: 12 × 9 = 108 ✓
• 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.
144 ÷ 8 = 18 toys per hour
108 ÷ 18 = 6 hours needed
18 toys/hour × 6 hours = 108 toys ✓
144 ÷ 8 = 18 and 108 ÷ 6 = 18 ✓
The factory produces 18 toys per hour, and it would take 6 hours to produce 108 toys.
• Order of Operations: Solve in the logical sequence
• Multi-Step Problem Solving: Break into smaller problems
• Rate Problems: Find the unit rate first
Dividend: The number being divided
Divisor: The number we divide by
Quotient: The result of division
Fact Family: Related multiplication and division facts
- 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 |
|---|---|---|
| 12 ÷ 12 | 1 | 1 × 12 = 12 |
| 24 ÷ 12 | 2 | 2 × 12 = 24 |
| 36 ÷ 12 | 3 | 3 × 12 = 36 |
| 48 ÷ 12 | 4 | 4 × 12 = 48 |
| 60 ÷ 12 | 5 | 5 × 12 = 60 |
| 72 ÷ 12 | 6 | 6 × 12 = 72 |
| 84 ÷ 12 | 7 | 7 × 12 = 84 |
| 96 ÷ 12 | 8 | 8 × 12 = 96 |
| 108 ÷ 12 | 9 | 9 × 12 = 108 |
| 120 ÷ 12 | 10 | 10 × 12 = 120 |
| 132 ÷ 12 | 11 | 11 × 12 = 132 |
| 144 ÷ 12 | 12 | 12 × 12 = 144 |
• Dividing by 12 gives one-twelfth of the original number
• These facts are essential for mastering division up to 144
• 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 |
| 99 ÷ 9 | 11 | 11 × 9 = 99 |
| 108 ÷ 9 | 12 | 12 × 9 = 108 |
| 117 ÷ 9 | 13 | 13 × 9 = 117 |
| 126 ÷ 9 | 14 | 14 × 9 = 126 |
| 135 ÷ 9 | 15 | 15 × 9 = 135 |
| 144 ÷ 9 | 16 | 16 × 9 = 144 |
• 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
• 144 is the largest perfect square in our range (12²)
Questions & Answers
Question: How can I help my students understand the connection between multiplication and division up to 144? 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: 12 × 12 = 144
- Show how it creates two division facts: 144 ÷ 12 = 12 and 144 ÷ 12 = 12
- Use visual models: 12 rows of 12 dots = 144 dots total
- Then ask: "If I have 144 dots and want 12 rows, how many in each row?" (144 ÷ 12 = 12)
- Or: "If I have 144 dots and want 12 in each row, how many rows?" (144 ÷ 12 = 12)
Concrete examples work best: "I have 144 cookies and 12 friends. How many does each friend get?" versus "I have 144 cookies and want to give 12 to each friend. How many friends can I feed?"
Question: Why do we need to learn division facts up to 144? That seems like a lot of numbers!
Answer: Learning division facts up to 144 is important because:
- 144 is 12 × 12, so it covers all multiplication tables up to 12
- These facts help solve larger division problems quickly
- They prepare you for more advanced math in later grades
- Many real-world problems involve numbers in this range
- Knowing these facts builds confidence and mental math skills
Think of it as building a strong foundation for future math success!
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 144 cookies and want to put 12 in each bag - how many bags?" (144 ÷ 12 = 12 bags)
Division Facts Mastery Progress Chart
Division Facts Up To 144 - Complete Summary
Advanced Division: Division involving numbers up to 144 that require knowledge of multiplication tables.
Dividend: The number being divided.
Divisor: The number we divide by.
Quotient: The result of division.
Fact Family: A set of related multiplication and division facts using the same numbers.
Perfect Squares: Numbers like 144 (12²) that result from multiplying a number by itself.
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
Perfect Squares: 144 = 12², so 144 ÷ 12 = 12
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 quotient × divisor to check
Simple: 12 ÷ 3 = 4 (basic fact)
Medium: 72 ÷ 8 = 9 (intermediate fact)
Advanced: 144 ÷ 12 = 12 (perfect square)
Complex: 108 ÷ 9 = 12 (advanced fact)
Application: Word 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
Look for Patterns: Notice relationships in division facts
Perfect Squares: 144 ÷ 12 = 12, 121 ÷ 11 = 11, etc.
Confusing Dividend/Divisor: Pay attention to which number is being divided
Not Checking: Always verify your answer by multiplying back
Mixing Operations: Be careful to identify whether to multiply or divide
Perfect Square Confusion: Remember that √144 = 12, so 144÷12 = 12
Large Number Overwhelm: Break problems into smaller, manageable parts