📊 Key Multiplication Facts:

🔑 Basic Formula:

Product = Factor 1 × Factor 2

🔍 Strategy:

📐 Formulas:

If a × ? = b, then ? = b ÷ a

Missing Factor = Product ÷ Known Factor

📝 Comparison Language:

• "times as many" → multiplication
• "3 times as many" → multiply by 3
• "twice as much" → multiply by 2

✏️ Example:

📝 Steps:

1. Write the larger number on top, 1-digit number below
2. Start from ONES place, multiply and write result
3. If product ≥ 10, carry the tens digit
4. Move to TENS, multiply and add carry
5. Continue for all place values

✏️ Examples:

2-digit:  23 × 4 = 92
3-digit:  345 × 6 = 2,070
4-digit:  4,567 × 7 = 31,969
                

🔢 Pattern Examples:

📐 Rule:

When multiplying by 10, add one zero
When multiplying by 100, add two zeros
When multiplying by 1000, add three zeros

📐 Six Properties:

📝 Steps to Estimate:

1. Round each factor to nearest 10, 100, or 1000
2. Multiply the rounded numbers
3. Write answer with ≈ (approximately equals)

✏️ Examples:

📝 Steps:

1. Write numbers in expanded form
2. Draw a box/grid based on digits
3. Multiply each part and fill boxes
4. Add all box values together

✏️ Example: 23 × 15

📝 Steps:

1. Draw grid with rows and columns for digits
2. Draw diagonals in each box (top-right to bottom-left)
3. Multiply digits, write tens above diagonal, ones below
4. Add along diagonals from right to left
5. Carry if needed, write answer from top to bottom

💡 Key Points:

• Great for visual learners
• Reduces carrying errors
• Works for any size numbers

📝 Steps:

1. Write numbers vertically, align right
2. Multiply by ONES digit of bottom number
3. Multiply by TENS digit (write result one place left)
4. Add the two partial products

✏️ Example: 34 × 26

      3 4
    × 2 6
    ______
    2 0 4  (34 × 6)
  6 8 0    (34 × 20)
  ______
  8 8 4
                

🎯 Strategy:

1. Look at target product
2. Find factor pairs of the target
3. Check if both factors are in the given set
4. Use estimation to eliminate unlikely pairs

✏️ Example:

📝 Steps (same as 2-digit × 2-digit):

1. Multiply by ones digit of multiplier
2. Multiply by tens digit (shift one place left)
3. Add partial products

✏️ Example: 234 × 23

      2 3 4
    ×   2 3
    ________
      7 0 2  (234 × 3)
  4 6 8 0    (234 × 20)
  ________
  5 3 8 2
                

📝 Steps:

1. Ignore all zeros temporarily
2. Multiply the non-zero digits
3. Count total zeros from both numbers
4. Add that many zeros to your answer

✏️ Examples:

📝 Strategy:

1. Look for pairs that are easy to multiply
2. Look for pairs that make 10, 100, etc.
3. Multiply two factors first
4. Multiply result by third factor

✏️ Examples:

📐 Formula:

a × b × c = (a × b) × c = a × (b × c)