Basic Math

Multiplication | Third Grade

✖️ 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

InputRuleOutput
3× 412
5× 420
7× 428
9× 436

🔢 Multiply 1-Digit × 2-Digit Numbers

Steps to Multiply:

  1. Write numbers vertically (align by place value)
  2. Multiply ones digit first
  3. Regroup if needed (carry)
  4. Multiply tens digit
  5. Add carried number
  6. 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!

  1. Multiply ones digit
  2. Multiply tens digit (add any carried number)
  3. Multiply hundreds digit (add any carried number)
  4. 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:

  1. Write numbers in expanded form
  2. Draw a box grid (rows × columns)
  3. Multiply each box (row number × column number)
  4. 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):

203
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:

  1. Draw a grid (columns = digits of first number, rows = digits of second number)
  2. Draw diagonals in each box (top-right to bottom-left)
  3. Write numbers along top and right side
  4. Multiply and fill boxes (tens digit above diagonal, ones below)
  5. Add along diagonals from right to left
  6. 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:

  1. Read carefully
  2. Find the numbers
  3. Look for multiplication key words
  4. Decide what to multiply
  5. Write the multiplication sentence
  6. Solve
  7. 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
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