✖️ Multiplication - Grade 3
What is Multiplication?
Multiplication is repeated addition! It's a faster way to add the same number many times.
\(\text{Factor} \times \text{Factor} = \text{Product}\)
📝 Multiplication Sentences
What is a Multiplication Sentence?
A multiplication sentence is a complete math statement showing multiplication!
Parts of a Multiplication Sentence:
- 🔵 First Factor - First number being multiplied
- 🔵 Multiplication Sign (×) - Shows we're multiplying
- 🔵 Second Factor - Second number being multiplied
- 🔵 Equal Sign (=) - Means "is equal to"
- 🔵 Product - The answer
Examples:
Example 1: \(7 \times 8 = 56\)
Read as: "Seven times eight equals fifty-six"
Example 2: \(3 \times 12 = 36\)
Read as: "Three times twelve equals thirty-six"
Example 3: \(9 \times 5 = 45\)
Read as: "Nine times five equals forty-five"
0️⃣ Multiply Numbers Ending in Zeros
The Zero Trick!
Step 1: Ignore the zeros and multiply
Step 2: Count ALL the zeros from both numbers
Step 3: Add those zeros to your answer!
Examples:
Example 1: One Number with Zeros
Problem: \(6 \times 40\)
Step 1: Ignore the zero: \(6 \times 4 = 24\)
Step 2: Count zeros: 40 has 1 zero
Step 3: Add 1 zero to 24
Answer: \(6 \times 40 = 240\) ✓
Example 2: Both Numbers with Zeros
Problem: \(50 \times 300\)
Step 1: Ignore zeros: \(5 \times 3 = 15\)
Step 2: Count zeros: 50 has 1 zero + 300 has 2 zeros = 3 zeros total
Step 3: Add 3 zeros to 15
Answer: \(50 \times 300 = 15,000\) ✓
Example 3: Large Numbers
Problem: \(7 \times 2,000\)
Step 1: Ignore zeros: \(7 \times 2 = 14\)
Step 2: Count zeros: 2,000 has 3 zeros
Step 3: Add 3 zeros to 14
Answer: \(7 \times 2,000 = 14,000\) ✓
Key Formula:
\(\text{Non-zero digits} \times \underbrace{0...0}_{\text{n zeros}} = \text{Product} \times 10^n\)
📊 Multiplication Input/Output Tables
What is an Input/Output Table?
A table that uses a multiplication rule to turn input numbers into output numbers!
\(\text{Output} = \text{Input} \times \text{Rule}\)
Example:
Rule: Multiply by 4
Input | Rule | Output |
---|---|---|
3 | × 4 | 12 |
5 | × 4 | 20 |
7 | × 4 | 28 |
9 | × 4 | 36 |
🔢 Multiply 1-Digit × 2-Digit Numbers
Steps to Multiply:
- Write numbers vertically (align by place value)
- Multiply ones digit first
- Regroup if needed (carry)
- Multiply tens digit
- Add carried number
- Write the final answer
Example: \(4 \times 23\)
23
× 4
-------
Step 1 - Ones: \(4 \times 3 = 12\)
Write 2, carry 1
Step 2 - Tens: \(4 \times 2 = 8\)
Add carried 1: \(8 + 1 = 9\)
Answer: \(4 \times 23 = 92\) ✓
1
23
× 4
-------
92
🔢🔢 Multiply 1-Digit × 3-Digit Numbers
Same Steps, More Digits!
- Multiply ones digit
- Multiply tens digit (add any carried number)
- Multiply hundreds digit (add any carried number)
- Write your answer
Example: \(3 \times 246\)
246
× 3
--------
Step 1 - Ones: \(3 \times 6 = 18\)
Write 8, carry 1
Step 2 - Tens: \(3 \times 4 = 12\)
Add carried 1: \(12 + 1 = 13\)
Write 3, carry 1
Step 3 - Hundreds: \(3 \times 2 = 6\)
Add carried 1: \(6 + 1 = 7\)
Answer: \(3 \times 246 = 738\) ✓
11
246
× 3
--------
738
📦 Box Multiplication Method
What is Box Multiplication?
The box method uses boxes to organize multiplication by breaking numbers into place values!
Steps:
- Write numbers in expanded form
- Draw a box grid (rows × columns)
- Multiply each box (row number × column number)
- Add all the products in the boxes
Example: \(23 \times 4\)
Step 1: Expanded form: \(23 = 20 + 3\)
Step 2: Draw box (1 row × 2 columns):
20 | 3 | |
---|---|---|
4 | \(80\) | \(12\) |
Step 3: Multiply each box:
• \(4 \times 20 = 80\)
• \(4 \times 3 = 12\)
Step 4: Add the products:
\(80 + 12 = 92\)
Answer: \(23 \times 4 = 92\) ✓
⚡ Lattice Multiplication Method
What is Lattice Multiplication?
The lattice method uses a grid with diagonals to multiply! It's like a puzzle!
Steps:
- Draw a grid (columns = digits of first number, rows = digits of second number)
- Draw diagonals in each box (top-right to bottom-left)
- Write numbers along top and right side
- Multiply and fill boxes (tens digit above diagonal, ones below)
- Add along diagonals from right to left
- Read answer down the left and across the bottom
Example: \(23 \times 4\)
Step 1-3: Draw grid (2 columns × 1 row), add diagonals, write 2 and 3 on top, 4 on right
Step 4: Fill boxes:
• Box 1: \(2 \times 4 = 08\) → write 0 above diagonal, 8 below
• Box 2: \(3 \times 4 = 12\) → write 1 above diagonal, 2 below
Visual representation:
2 3
┌───┬───┐
│0 /│1 /│
4 │ / 8│ /2│
└───┴───┘
9 2
Step 5: Add diagonals:
• Right diagonal: just 2
• Middle diagonal: \(8 + 1 = 9\)
• Left diagonal: just 0
Step 6: Read answer: 0-9-2
Answer: \(23 \times 4 = 92\) ✓
📖 Multiplication Word Problems
Key Words for Multiplication:
- ✓ Times - multiply
- ✓ Each - multiply
- ✓ Per - multiply
- ✓ Groups of - multiply
- ✓ Total - find the product
- ✓ Altogether - find the product
- ✓ Array - rows × columns
Steps to Solve:
- Read carefully
- Find the numbers
- Look for multiplication key words
- Decide what to multiply
- Write the multiplication sentence
- Solve
- Check - does your answer make sense?
Examples:
Problem 1: Equal Groups
Sarah has 6 bags of marbles. Each bag contains 8 marbles. How many marbles does Sarah have in total?
Step 1: Numbers: 6 bags, 8 marbles each
Step 2: Key word: "each" → Multiply!
Step 3: \(6 \times 8 = ?\)
Step 4: \(6 \times 8 = 48\)
Answer: Sarah has 48 marbles. ✓
Problem 2: Array Problem
A theater has 12 rows of seats. Each row has 25 seats. How many seats are there in total?
Step 1: Numbers: 12 rows, 25 seats per row
Step 2: Key word: "Each row" → Multiply!
Step 3: \(12 \times 25 = ?\)
Step 4: \(12 \times 25 = 300\)
Answer: There are 300 seats in total. ✓
❓ Word Problems: Find the Missing Factor
What is a Missing Factor Problem?
You know the product and one factor, but need to find the other factor!
If \(a \times ? = c\), then \(? = c \div a\)
Key Words:
- ✓ "How many groups?"
- ✓ "How many in each group?"
- ✓ "How many times?"
- ✓ "What number multiplied by...?"
Example:
Tom has 56 cookies. He wants to put them equally into bags with 8 cookies in each bag. How many bags does he need?
What we know:
• Total cookies: 56
• Cookies per bag: 8
• Number of bags: ?
Multiplication sentence:
\(? \times 8 = 56\)
Solution:
\(56 \div 8 = 7\)
Answer: Tom needs 7 bags. ✓
📝 Important Formulas Summary
Basic Multiplication:
\(\text{Factor} \times \text{Factor} = \text{Product}\)
Numbers Ending in Zeros:
Multiply non-zero digits, then add all zeros
\(30 \times 400 = (3 \times 4) \times 10^{1+2} = 12,000\)
Finding Missing Factor:
If \(a \times b = c\), then:
\(b = c \div a\) or \(a = c \div b\)
Commutative Property:
\(a \times b = b \times a\)
(Order doesn't matter!)
Distributive Property (Box Method):
\(a \times (b + c) = (a \times b) + (a \times c)\)
💡 Quick Learning Tips
- ✓ Line up numbers by place value when multiplying vertically
- ✓ For numbers ending in zeros: multiply non-zeros first, then add zeros
- ✓ Use the box method to organize larger multiplications
- ✓ Try lattice multiplication if you like visual methods
- ✓ Always carry when products are 10 or more
- ✓ In word problems, look for key multiplication words
- ✓ To find missing factors, use division
- ✓ Check your answer by using a different method
- ✓ Practice with input/output tables to see patterns
- ✓ Draw pictures to help understand word problems
- ✓ Remember: multiplication is faster than repeated addition!
- ✓ Use estimation to check if your answer makes sense