3Lily has 7 books. Leo has 6 times as many books. How many books does Leo have?
🤔 Compare Lily and Leo — who has more?
Model: Multiplicative Comparison. 7 × 6 = ?
Answer: 7 × 6 = 42 books
🔢 2.2 — Multiplying by 10, 100, 1,000
PLACE VALUE PATTERNS
When you multiply by 10, 100, or 1,000, digits shift left — zeros fill the empty places!
When to use this model: Any time you multiply a whole number by a power of 10 — the digits just shift left!
Thousands
Hundreds
Tens
Ones
0
0
0
5
5
Each ×10 shifts digits one place left. 5 × 10 = 50. The 5 moved from Ones to Tens!
✏️ Practice: Place Value Patterns
147 × 100 = ?
🤔 Think about digit shifting. Which places shift?
Model: Place Value Shift. 47 × 100 shifts the digits two places left. The 7 moves to the hundreds place!
Answer: 47 × 100 = 4,700
28 × 1,000 = ?
🤔 How many places does 1,000 shift the digits?
Model: Place Value Shift. 1,000 = 10 × 10 × 10 — that's three shifts left!
Answer: 8 × 1,000 = 8,000
363 × 10 = ?
🤔 Each ×10 shifts one place. What's 63 × 10?
Model: Place Value Shift. 63 × 10 — the 3 shifts from Ones to Tens, the 6 shifts from Tens to Hundreds.
Answer: 63 × 10 = 630
📐 2.3 — 2-Digit × 1-Digit (Area Model)
AREA MODEL
Split a 2-digit number by place value (tens + ones), multiply each part, then add them up!
When to use this model: The area model breaks big numbers into friendly parts. It's the key to understanding WHY multi-digit multiplication works!
How the area model works: The 2-digit number is split into tens and ones. Each part is multiplied by the single digit, then the partial products are added together.
✏️ Practice: 2-Digit × 1-Digit
123 × 4 = ?
🤔 Split 23 into 20 and 3. Multiply each by 4, then add!