➗ Division - Grade 3
Master Division Skills!
In Grade 3, we learn to use division tables, solve word problems, and discover divisibility rules that make division easier!
📋 Complete the Division Table
What is a Division Table?
A division table shows all the division facts for a specific divisor. It helps you learn and memorize division facts quickly!
\(\text{Dividend} \div \text{Divisor} = \text{Quotient}\)
Example: Division Table for 3
| Division Problem | Answer |
|---|---|
| \(3 \div 3\) | 1 |
| \(6 \div 3\) | 2 |
| \(9 \div 3\) | 3 |
| \(12 \div 3\) | 4 |
| \(15 \div 3\) | 5 |
| \(18 \div 3\) | 6 |
| \(21 \div 3\) | 7 |
| \(24 \div 3\) | 8 |
| \(27 \div 3\) | 9 |
| \(30 \div 3\) | 10 |
How to Complete a Division Table
- Look at the divisor (the number you're dividing by)
- Use multiplication facts to help! If \(3 \times 4 = 12\), then \(12 \div 3 = 4\)
- Skip count by the divisor to find dividends
- Fill in the quotients (answers)
💡 Tip: Knowing your multiplication facts makes completing division tables easy!
📊 Division Input/Output Tables
What is an Input/Output Table?
An input/output table uses a division rule to turn input numbers into output numbers!
\(\text{Output} = \text{Input} \div \text{Rule}\)
Example 1: Rule - Divide by 5
| Input | Rule | Output |
|---|---|---|
| 15 | ÷ 5 | 3 |
| 25 | ÷ 5 | 5 |
| 35 | ÷ 5 | 7 |
| 40 | ÷ 5 | 8 |
How to Use Input/Output Tables
- Find the rule (what division operation to use)
- Take each input number
- Divide by the rule number
- Write the answer in the output column
Example: If Input = 24 and Rule = ÷ 6
Then Output = \(24 \div 6 = 4\)
📖 Division Word Problems
Key Words for Division
- ✓ Share equally - divide
- ✓ Split into groups - divide
- ✓ Divide - division
- ✓ Each - divide
- ✓ Per - divide
- ✓ How many groups? - divide
- ✓ How many in each group? - divide
Steps to Solve Division Word Problems
- Read the problem carefully
- Find the numbers
- Look for division key words
- Decide what to divide
- Write the division sentence
- Solve and find the answer
- Check - does your answer make sense?
Example Problems
Problem 1: Equal Sharing
Sarah has 24 cookies. She wants to share them equally among 6 friends. How many cookies does each friend get?
Step 1: Numbers: 24 cookies, 6 friends
Step 2: Key words: "share equally" → Divide!
Step 3: Division sentence: \(24 \div 6 = ?\)
Step 4: \(24 \div 6 = 4\)
Answer: Each friend gets 4 cookies. ✓
Problem 2: Equal Groups
A teacher has 48 pencils. She puts 8 pencils in each box. How many boxes does she need?
Step 1: Numbers: 48 pencils, 8 pencils per box
Step 2: Key words: "in each box" → Divide!
Step 3: Division sentence: \(48 \div 8 = ?\)
Step 4: \(48 \div 8 = 6\)
Answer: She needs 6 boxes. ✓
Problem 3: Array Problem
There are 35 students in a classroom. They sit in 5 equal rows. How many students are in each row?
Step 1: Numbers: 35 students, 5 rows
Step 2: Key words: "in each row" → Divide!
Step 3: Division sentence: \(35 \div 5 = ?\)
Step 4: \(35 \div 5 = 7\)
Answer: There are 7 students in each row. ✓
🎯 Divisibility Rules for 2, 5, and 10
What are Divisibility Rules?
Divisibility rules are shortcuts that help you tell if a number can be divided evenly by another number without actually dividing!
Just look at the last digit(s) of the number!
Rule for Divisibility by 2
A number is divisible by 2 if the last digit is EVEN
(0, 2, 4, 6, or 8)
Examples:
- 24 → Last digit is 4 (even) → Divisible by 2 ✓
- 138 → Last digit is 8 (even) → Divisible by 2 ✓
- 57 → Last digit is 7 (odd) → NOT divisible by 2 ✗
- 100 → Last digit is 0 (even) → Divisible by 2 ✓
Rule for Divisibility by 5
A number is divisible by 5 if the last digit is 0 or 5
Examples:
- 35 → Last digit is 5 → Divisible by 5 ✓
- 120 → Last digit is 0 → Divisible by 5 ✓
- 87 → Last digit is 7 → NOT divisible by 5 ✗
- 245 → Last digit is 5 → Divisible by 5 ✓
Rule for Divisibility by 10
A number is divisible by 10 if the last digit is 0
Examples:
- 50 → Last digit is 0 → Divisible by 10 ✓
- 370 → Last digit is 0 → Divisible by 10 ✓
- 95 → Last digit is 5 → NOT divisible by 10 ✗
- 1,000 → Last digit is 0 → Divisible by 10 ✓
Practice: Check Divisibility
| Number | Divisible by 2? | Divisible by 5? | Divisible by 10? |
|---|---|---|---|
| 42 | ✓ (ends in 2) | ✗ | ✗ |
| 75 | ✗ | ✓ (ends in 5) | ✗ |
| 90 | ✓ (ends in 0) | ✓ (ends in 0) | ✓ (ends in 0) |
| 63 | ✗ | ✗ | ✗ |
| 140 | ✓ (ends in 0) | ✓ (ends in 0) | ✓ (ends in 0) |
Quick Summary:
- 🔹 Divisible by 2: Last digit is 0, 2, 4, 6, or 8
- 🔹 Divisible by 5: Last digit is 0 or 5
- 🔹 Divisible by 10: Last digit is 0
💡 Notice: Numbers ending in 0 are divisible by 2, 5, AND 10!
📝 Important Formulas Summary
Basic Division:
\(\text{Dividend} \div \text{Divisor} = \text{Quotient}\)
Input/Output Table:
\(\text{Output} = \text{Input} \div \text{Rule}\)
Checking Division with Multiplication:
\(\text{Quotient} \times \text{Divisor} = \text{Dividend}\)
💡 Quick Learning Tips
- ✓ Practice completing division tables to memorize division facts
- ✓ Use multiplication to check your division answers
- ✓ In word problems, look for key words like "share," "each," "groups"
- ✓ Draw pictures to understand word problems better
- ✓ Divisibility by 2: Look for even numbers (0, 2, 4, 6, 8)
- ✓ Divisibility by 5: Numbers end in 0 or 5
- ✓ Divisibility by 10: Numbers must end in 0
- ✓ Input/output tables show patterns in division
- ✓ Always check if your answer makes sense in word problems
- ✓ Practice with real objects to understand equal sharing
- ✓ Numbers ending in 0 are special - divisible by 2, 5, AND 10!
- ✓ Master your multiplication tables - they help with division!