🧪 Math Lab 🔢 Unit 1 ✕ Unit 2 ÷ Unit 3 📊 Bar Models

✕ Unit 2: Multi-Digit Multiplication

From area models to big numbers — multiply like a pro!

🔍 2.1 — Multiplication as Comparison

MULTIPLICATIVE COMPARISON

Use multiplication to compare quantities — "times as many" means multiply!

When to use this model: Use when you see "times as many" or "times as much"
Multiply to compare: 4 × 3 = 12. Tom has 4. Sarah has 3 times as many — 12!

✏️ Practice: Comparison

1Sarah has 5 stickers. Tom has 3 times as many. How many stickers does Tom have?
🤔 Think: Tom's stickers = Sarah's × 3
Model: Multiplicative Comparison. Tom has 3 times as many as Sarah. Multiply: 5 × 3 = ?
Answer: 5 × 3 = 15 stickers
2A giraffe is 4 meters tall. A tree is 5 times as tall. How tall is the tree?
🤔 The tree's height = giraffe's height × 5
Model: Multiplicative Comparison. Multiply: 4 × 5 = ?
Answer: 4 × 5 = 20 meters
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!
Model: Area Model. 20 × 4 = 80, 3 × 4 = 12. 80 + 12 = ?
Answer: 23 × 4 = 92
245 × 6 = ?
🤔 45 = 40 + 5. Multiply each part!
Model: Area Model. 40 × 6 = 240, 5 × 6 = 30. 240 + 30 = ?
Answer: 45 × 6 = 270
378 × 9 = ?
🤔 78 = 70 + 8. 70 × 9 and 8 × 9 — then add!
Model: Area Model. 70 × 9 = 630, 8 × 9 = 72. 630 + 72 = ?
Answer: 78 × 9 = 702

🔢 2.4 — 3-Digit & 4-Digit × 1-Digit

BIG NUMBERS

The area model works the same way for larger numbers — just split into more place value parts!

When to use this model: For any multi-digit × 1-digit problem. Split the big number by place value, multiply each part, then add!
Big numbers, same idea! Just split the 3-digit (or 4-digit) number by place value and multiply each part.

✏️ Practice: Big Numbers

1234 × 5 = ?
🤔 Split 234 into 200 + 30 + 4. Multiply each part!
Model: Area Model for 3-digit × 1-digit. 200×5 + 30×5 + 4×5
Answer: 234 × 5 = 1,170
21,206 × 4 = ?
🤔 1,206 = 1,000 + 200 + 0 + 6. Multiply each part by 4!
Model: Area Model for 4-digit × 1-digit. 1,000×4 + 200×4 + 6×4
Answer: 1,206 × 4 = 4,824
33,415 × 7 = ?
🤔 3,415 = 3,000 + 400 + 10 + 5. Seven times each!
Model: Area Model for 4-digit × 1-digit. 3,000×7 + 400×7 + 10×7 + 5×7
Answer: 3,415 × 7 = 23,905

🧩 2.5 — 2-Digit × 2-Digit

2-DIGIT × 2-DIGIT

The full area model! Both numbers are split by place value — creating a 2×2 grid with four partial products.

When to use this model: For any 2-digit × 2-digit multiplication. Think FOIL: First, Outer, Inner, Last!
FOIL method: First (tens×tens), Outer (tens×ones), Inner (ones×tens), Last (ones×ones). Add all four!

✏️ Practice: 2-Digit × 2-Digit

123 × 45 = ?
🤔 FOIL: (20×40) + (20×5) + (3×40) + (3×5)
Model: FOIL Area Model. 20×40=800, 20×5=100, 3×40=120, 3×5=15. 800+100+120+15=?
Answer: 23 × 45 = 1,035
256 × 34 = ?
🤔 56 = 50 + 6, 34 = 30 + 4. Four partial products to add!
Model: FOIL Area Model. 50×30=1,500, 50×4=200, 6×30=180, 6×4=24.
Answer: 56 × 34 = 1,904
378 × 92 = ?
🤔 78 = 70 + 8, 92 = 90 + 2. Use the area model!
Model: FOIL Area Model. 70×90=6,300, 70×2=140, 8×90=720, 8×2=16.
Answer: 78 × 92 = 7,176

🧠 2.6 — Multi-Step Word Problems

WORD PROBLEMS

Real-world problems often need more than one step. Look for the hidden multiplication!

When to use this model: Read the problem carefully. Ask: "What do I know?" and "What do I need to find out?" Break it into steps!