⚡ Division Fluency - Grade 3
What is Division Fluency?
Division fluency means knowing division facts quickly and accurately without counting!
By the end of Grade 3, you should know all division facts from memory! Remember: If you know multiplication, you know division! 🎯
📌 Division Facts: 2, 3, 4, 5, 10
Why Learn These First?
These are the foundation facts - the easiest division facts to learn!
- ✓ ÷2: Find half
- ✓ ÷5: Dividends end in 0 or 5
- ✓ ÷10: Remove a zero
- ✓ ÷3 & ÷4: Use multiplication facts!
Quick Reference Table
| Dividend | ÷2 | ÷3 | ÷4 | ÷5 | ÷10 |
|---|---|---|---|---|---|
| 10 | 5 | — | — | 2 | 1 |
| 20 | 10 | — | 5 | 4 | 2 |
| 30 | 15 | 10 | — | 6 | 3 |
| 40 | 20 | — | 10 | 8 | 4 |
| 50 | 25 | — | — | 10 | 5 |
| 60 | 30 | 20 | 15 | 12 | 6 |
📌 Division Facts: 6, 7, 8, 9
The Trickier Facts
These facts are harder, but use related multiplication facts to help!
Quick Reference Table
| Dividend | ÷6 | ÷7 | ÷8 | ÷9 |
|---|---|---|---|---|
| 18 | 3 | — | — | 2 |
| 24 | 4 | — | 3 | — |
| 36 | 6 | — | — | 4 |
| 42 | 7 | 6 | — | — |
| 54 | 9 | — | — | 6 |
| 63 | — | 9 | — | 7 |
| 72 | — | — | 9 | 8 |
✓✗ True or False Practice
What is True or False?
Look at a division sentence and decide if it's TRUE (correct) or FALSE (incorrect)!
Examples
Example 1:
Question: \(20 \div 4 = 5\) - True or False?
Think: Does \(20 \div 4\) really equal \(5\)?
Check with multiplication: \(4 \times 5 = 20\) ✓
Answer: TRUE!
Example 2:
Question: \(42 \div 6 = 8\) - True or False?
Think: Does \(42 \div 6\) equal \(8\)?
Check: \(6 \times 8 = 48\), not \(42\)!
Correct answer: \(42 \div 6 = 7\)
Answer: FALSE!
Strategy:
💡 Use multiplication to check! Multiply the quotient by the divisor to see if you get the dividend!
🔢 Sorting Division Facts
What is Sorting?
Sorting means organizing division facts into groups based on certain rules!
Ways to Sort
1. Sort by Divisor
Group all facts with the same divisor together
÷5 group: \(10÷5, 15÷5, 20÷5, 25÷5...\)
÷7 group: \(14÷7, 21÷7, 28÷7, 35÷7...\)
2. Sort by Quotient
Group facts with quotients in certain ranges
Quotient 1-5: \(6÷2, 12÷3, 20÷5...\)
Quotient 6-10: \(42÷6, 56÷8, 63÷9...\)
3. Sort by Dividend Range
Group by the size of the dividend
Dividends 1-30: \(12÷3, 20÷5, 24÷6...\)
Dividends 31-60: \(36÷6, 42÷7, 54÷9...\)
Dividends 61+: \(63÷7, 72÷8, 81÷9...\)
❓ Find the Missing Number
Three Types of Missing Numbers
In division, we can have three types of missing numbers!
- 🔵 Missing Dividend - The number being divided
- 🔵 Missing Divisor - The number dividing by
- 🔵 Missing Quotient - The answer
Type 1: Missing Dividend
\(? \div \text{Divisor} = \text{Quotient}\)
Formula:
\(\text{Dividend} = \text{Divisor} \times \text{Quotient}\)
Example:
Problem: \(? \div 6 = 7\)
Solution:
Multiply the divisor by the quotient:
\(6 \times 7 = 42\)
Answer: \(42 \div 6 = 7\) ✓
Type 2: Missing Divisor
\(\text{Dividend} \div ? = \text{Quotient}\)
Formula:
\(\text{Divisor} = \text{Dividend} \div \text{Quotient}\)
Example:
Problem: \(56 \div ? = 8\)
Solution:
Divide the dividend by the quotient:
\(56 \div 8 = 7\)
Answer: \(56 \div 7 = 8\) ✓
Type 3: Missing Quotient
\(\text{Dividend} \div \text{Divisor} = ?\)
This is regular division!
Just divide normally!
Example:
Problem: \(45 \div 9 = ?\)
Solution:
Think: What times 9 equals 45?
\(9 \times 5 = 45\)
Answer: \(45 \div 9 = 5\) ✓
📝 Division Sentences: True or False?
What is a Division Sentence?
A division sentence is a complete mathematical statement showing division with an equals sign!
\(\underbrace{36}_{\text{Dividend}} \div \underbrace{4}_{\text{Divisor}} = \underbrace{9}_{\text{Quotient}}\)
How to Check if a Division Sentence is True
- Look at the division sentence
- Use multiplication to check: Multiply the quotient by the divisor
- Compare: Does it equal the dividend?
- If YES = TRUE, If NO = FALSE
Examples:
Example 1: TRUE Sentence
Sentence: \(32 \div 8 = 4\)
Check: \(8 \times 4 = 32\) ✓
This matches the dividend!
Answer: TRUE!
Example 2: FALSE Sentence
Sentence: \(48 \div 6 = 9\)
Check: \(6 \times 9 = 54\) ✗
This does NOT match the dividend (48)!
Correct: \(48 \div 6 = 8\)
Answer: FALSE!
⚡ Building Division Fluency - Strategies
What is Fluency?
Fluency means being able to answer division facts:
- ✓ Quickly - Within 3 seconds
- ✓ Accurately - With the correct answer
- ✓ Automatically - Without counting
Practice Strategies
1. Use Fact Families
Learn multiplication and division together! They're related!
If \(7 \times 8 = 56\), then:
\(56 \div 7 = 8\) and \(56 \div 8 = 7\)
2. Flashcard Practice
Practice daily! Start with easier facts (÷2, ÷5, ÷10) then add harder ones!
3. True or False Games
Quickly decide if division sentences are correct. This builds fast thinking!
4. Missing Number Practice
Practice finding missing dividends, divisors, and quotients!
5. Sorting Activities
Sort division facts by divisor, quotient, or dividend range. This helps you see patterns!
6. Mixed Practice
Don't practice in order! Mix up different facts to build real fluency!
📝 Important Formulas Summary
Basic Division:
\(\text{Dividend} \div \text{Divisor} = \text{Quotient}\)
Finding Missing Dividend:
\(\text{Dividend} = \text{Divisor} \times \text{Quotient}\)
Finding Missing Divisor:
\(\text{Divisor} = \text{Dividend} \div \text{Quotient}\)
Checking Division with Multiplication:
\(\text{Quotient} \times \text{Divisor} = \text{Dividend}\)
Fact Family Relationship:
If \(a \times b = c\), then:
\(c \div a = b\) and \(c \div b = a\)
💡 Quick Learning Tips
- ✓ Practice every day for 10-15 minutes
- ✓ Start with easier divisors (2, 5, 10) then add harder ones
- ✓ If you know multiplication facts, you know division facts!
- ✓ Use fact families to see the connection
- ✓ Always check division with multiplication
- ✓ To find missing dividend: multiply divisor × quotient
- ✓ To find missing divisor: divide dividend ÷ quotient
- ✓ Practice true/false questions to build quick thinking
- ✓ Sort facts by different categories to see patterns
- ✓ Use flashcards and games to make practice fun
- ✓ Don't rush - accuracy is more important than speed at first
- ✓ A number divided by itself always equals 1
- ✓ Any number divided by 1 equals that same number
- ✓ By the end of Grade 3, aim to know all division facts from memory!