5.NBT.5 Multiply Whole Numbers
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Multiply Whole Numbers

How can we use different strategies to multiply multi-digit numbers?

📚
Standard
NBT.5
🧮
Strategies
3
⏱️
Duration
75m

📋 Standards & Objectives

📐Standard
5.NBT.5Fluently multiply multi-digit whole numbers using the standard algorithm.
🎯SWBAT
  • Multiply by multiples of 10, 100, and 1,000
  • Use an area model to multiply 2-digit by 2-digit numbers
  • Use the standard algorithm to multiply multi-digit whole numbers
  • Estimate products to check reasonableness

💭 Real-World Hook

Where do we use multiplication in the real world?

🏟️Stadium Seating

A stadium has 48 sections with 325 seats each. How many seats total? That's 48 × 325!

🏗️Construction Project

A builder needs 36 boxes of tiles with 145 tiles per box. How many tiles? That's 36 × 145!

🎒School Supplies

The school ordered 24 packs of pencils with 50 pencils each. How many pencils? That's 24 × 50!

📚 Key Vocabulary

✖️Factor

The numbers being multiplied together. In 24 × 50, both 24 and 50 are factors.

🟰Product

The answer to a multiplication problem. In 24 × 50 = 1,200 — the product is 1,200.

🧩Partial Products

The results of multiplying by each place value separately. You add them up to get the final product.

📊Area Model

A rectangle divided into sections to show multiplication using expanded form (tens and ones).

💡 Concept: Multiples of 10

When multiplying by multiples of 10, follow this two-step pattern:

Step 1: Multiply the basic fact (non-zero digits)   Step 2: Add the zeros

Example from Packet Page 1:

4 × 80

4 × 8 = 32

Add 1 zero → 320

Example from Packet Page 1:

6 × 600

6 × 6 = 36

Add 2 zeros → 3,600

Example from Packet Page 1:

90 × 30

9 × 3 = 27

Add 2 zeros → 2,700

📏 Rule: Multiply by Multiples of 10

Use this two-step method every time you multiply by 10s, 100s, or 1,000s:

Step 1
Multiply the Basic Fact
Multiply the non-zero digits together
Step 2
Count & Add the Zeros
Count total trailing zeros in both factors, add them to the product

50 × 200 → 5 × 2 = 10 → add 3 zeros → 10,000

30 × 70 → 3 × 7 = 21 → add 2 zeros → 2,100

✏️ Problem 1

👨‍🏫 I Do • Multiples of 10
6 × 40
Multiply by a multiple of 10
💡 Multiply the Basic Fact, Then Add Zeros
1 Basic Fact: 6 × 4 = 24
2 Count the Zeros: 40 has 1 zero → Add 1 zero to 24 → 240
✓ Answer
6 × 40 = 240

✏️ Problem 2

👨‍🏫 I Do • Multiples of 10
30 × 400
Multiply by multiples of 10
💡 Multiply the Basic Fact, Then Add Zeros
1 Basic Fact: 3 × 4 = 12
2 Count the Zeros: 30 has 1 zero, 400 has 2 zeros = 3 zeros total → Add 3 zeros to 12 → 12,000
✓ Answer
30 × 400 = 12,000

✏️ Problem 3

👥 We Do • Multiples of 10
5 × 5,000
Multiply by a multiple of 10
💡 Multiply the Basic Fact, Then Add Zeros
1 Basic Fact: 5 × 5 = 25
2 Count the Zeros: 5,000 has 3 zeros → Add 3 zeros to 25 → 25,000
✓ Answer
5 × 5,000 = 25,000

✏️ Problem 4

👥 We Do • Multiples of 10
800 × 200
Multiply by multiples of 10
💡 Multiply the Basic Fact, Then Add Zeros
1 Basic Fact: 8 × 2 = 16
2 Count the Zeros: 800 has 2 zeros, 200 has 2 zeros = 4 zeros → Add 4 zeros to 16 → 160,000
✓ Answer
800 × 200 = 160,000

✏️ Problem 5

✏️ You Do • Multiples of 10
70 × 90
Multiply by multiples of 10
💡 Multiply the Basic Fact, Then Add Zeros
1 Basic Fact: 7 × 9 = 63
2 Count the Zeros: 70 has 1 zero, 90 has 1 zero = 2 zeros → Add 2 zeros to 63 → 6,300
✓ Answer
70 × 90 = 6,300

✏️ Problem 6

✏️ You Do • Multiples of 10
400 × 9
Multiply by a multiple of 10
💡 Multiply the Basic Fact, Then Add Zeros
1 Basic Fact: 4 × 9 = 36
2 Count the Zeros: 400 has 2 zeros → Add 2 zeros to 36 → 3,600
✓ Answer
400 × 9 = 3,600

💡 The Area Model

An area model breaks multiplication into smaller, easier pieces using expanded form.

Example: 23 × 36

Break each factor into tens and ones: 23 = 20 + 3 and 36 = 30 + 6

30
6
20
600
120
3
90
18

600 + 120 + 90 + 18 = 828

📏 Area Model Steps

Follow these 4 steps every time you use the area model:

1 Expand Both Factors

Break each number into place values (tens + ones).

2 Draw the Box

Create a grid with the expanded parts as headers.

3 Multiply Each Section

Find the partial product in each cell of the grid.

4 Add All Partial Products

Sum all sections for the final answer.

Quick Example: 45 × 12 = (40+5)(10+2) = 400 + 80 + 50 + 10 = 540

✏️ Problem 7

👨‍🏫 I Do • Area Model
23 × 36
Use the area model
📐 Area Model Strategy
1 Expand: 23 = 20 + 3 and 36 = 30 + 6
×
30
6
20
600
120
3
90
18
2 Multiply: 20 × 30 = 600
3 Multiply remaining: 20×6 = 120, 3×30 = 90, 3×6 = 18
4 Add partial products: 600 + 120 + 90 + 18 = 828
✓ Answer
23 × 36 = 828

✏️ Problem 8

👨‍🏫 I Do • Area Model
45 × 86
Use the area model
📐 Area Model Strategy
1 Expand: 45 = 40 + 5 and 86 = 80 + 6
×
80
6
40
3200
240
5
400
30
2 Multiply: 40 × 80 = 3200
3 Multiply remaining: 40×6 = 240, 5×80 = 400, 5×6 = 30
4 Add partial products: 3200 + 240 + 400 + 30 = 3,870
✓ Answer
45 × 86 = 3,870

✏️ Problem 9

👥 We Do • Area Model
29 × 94
Use the area model
📐 Area Model Strategy
1 Expand: 29 = 20 + 9 and 94 = 90 + 4
×
90
4
20
1800
80
9
810
36
2 Multiply: 20 × 90 = 1800
3 Multiply remaining: 20×4 = 80, 9×90 = 810, 9×4 = 36
4 Add partial products: 1800 + 80 + 810 + 36 = 2,726
✓ Answer
29 × 94 = 2,726

✏️ Problem 10

👥 We Do • Area Model
52 × 38
Use the area model
📐 Area Model Strategy
1 Expand: 52 = 50 + 2 and 38 = 30 + 8
×
30
8
50
1500
400
2
60
16
2 Multiply: 50 × 30 = 1500
3 Multiply remaining: 50×8 = 400, 2×30 = 60, 2×8 = 16
4 Add partial products: 1500 + 400 + 60 + 16 = 1,976
✓ Answer
52 × 38 = 1,976

✏️ Problem 11

🎯 You Do • Area Model
37 × 64
Use the area model
📐 Area Model Strategy
1 Expand: 37 = 30 + 7 and 64 = 60 + 4
×
60
4
30
1800
120
7
420
28
2 Multiply: 30 × 60 = 1800
3 Multiply remaining: 30×4 = 120, 7×60 = 420, 7×4 = 28
4 Add partial products: 1800 + 120 + 420 + 28 = 2,368
✓ Answer
37 × 64 = 2,368

✏️ Problem 12

🎯 You Do • Area Model
58 × 43
Use the area model
📐 Area Model Strategy
1 Expand: 58 = 50 + 8 and 43 = 40 + 3
×
40
3
50
2000
150
8
320
24
2 Multiply: 50 × 40 = 2000
3 Multiply remaining: 50×3 = 150, 8×40 = 320, 8×3 = 24
4 Add partial products: 2000 + 150 + 320 + 24 = 2,494
✓ Answer
58 × 43 = 2,494

💡 The Standard Algorithm

Multiply each place value separately, then add the partial products.

Example: 34 × 27

34
×27
238 ← 7 × 34
680 ← 20 × 34
918 ← Add

📏 Standard Algorithm Steps

Follow these 3 steps every time you use the standard algorithm:

1 Multiply by Ones

Multiply the bottom ones digit by the top factor. Write this first partial product.

2 Multiply by Tens

Add a zero placeholder, then multiply the bottom tens digit by the top factor.

3 Add Partials

Add the two partial products together for the final answer.

⚠️ Don't forget the zero placeholder when multiplying by the tens digit!

The zero holds the ones place because you're really multiplying by 20, not 2.

✏️ Problem 13

👨‍🏫 I Do • Standard Algorithm
34 × 27
Use the standard algorithm
📝 Standard Algorithm
1 Multiply by ones: 7 × 34 = 238
34
×27
2 3 8 ← 7 × 34
6 8 0 ← 20 × 34
9 1 8 ← Add
2 Multiply by tens: 20 × 34 = 680 (don't forget the zero!)
3 Add partial products: 238 + 680 = 918
✓ Answer
34 × 27 = 918

✏️ Problem 14

👨‍🏫 I Do • Standard Algorithm
634 × 27
Use the standard algorithm
📝 Standard Algorithm
1 Multiply by ones: 7 × 634 = 4,438
634
×27
4 , 4 3 8 ← 7 × 634
1 2 , 6 8 0 ← 20 × 634
1 7 , 1 1 8 ← Add
2 Multiply by tens: 20 × 634 = 12,680 (don't forget the zero!)
3 Add partial products: 4,438 + 12,680 = 17,118
✓ Answer
634 × 27 = 17,118

✏️ Problem 15

👥 We Do • Standard Algorithm
78 × 49
Use the standard algorithm
📝 Standard Algorithm
1 Multiply by ones: 9 × 78 = 702
78
×49
7 0 2 ← 9 × 78
3 , 1 2 0 ← 40 × 78
3 , 8 2 2 ← Add
2 Multiply by tens: 40 × 78 = 3,120 (don't forget the zero!)
3 Add partial products: 702 + 3,120 = 3,822
✓ Answer
78 × 49 = 3,822

✏️ Problem 16

👥 We Do • Standard Algorithm
276 × 28
Use the standard algorithm
📝 Standard Algorithm
1 Multiply by ones: 8 × 276 = 2,208
276
×28
2 , 2 0 8 ← 8 × 276
5 , 5 2 0 ← 20 × 276
7 , 7 2 8 ← Add
2 Multiply by tens: 20 × 276 = 5,520 (don't forget the zero!)
3 Add partial products: 2,208 + 5,520 = 7,728
✓ Answer
276 × 28 = 7,728

✏️ Problem 17

✏️ You Do • Standard Algorithm
63 × 85
Use the standard algorithm
📝 Standard Algorithm
1 Multiply by ones: 5 × 63 = 315
63
×85
3 1 5 ← 5 × 63
5 , 0 4 0 ← 80 × 63
5 , 3 5 5 ← Add
2 Multiply by tens: 80 × 63 = 5,040 (don't forget the zero!)
3 Add partial products: 315 + 5,040 = 5,355
✓ Answer
63 × 85 = 5,355

✏️ Problem 18

✏️ You Do • Standard Algorithm
492 × 37
Use the standard algorithm
📝 Standard Algorithm
1 Multiply by ones: 7 × 492 = 3,444
492
×37
3 , 4 4 4 ← 7 × 492
1 4 , 7 6 0 ← 30 × 492
1 8 , 2 0 4 ← Add
2 Multiply by tens: 30 × 492 = 14,760 (don't forget the zero!)
3 Add partial products: 3,444 + 14,760 = 18,204
✓ Answer
492 × 37 = 18,204

🏆 Challenge Problem

Challenge
428 × 536
3-digit × 3-digit — use the standard algorithm!
📝 Standard Algorithm (3 × 3)
1 Multiply by ones: 6 × 428 = 2,568
428
×536
2 , 5 6 8 ← 6 × 428
1 2 , 8 4 0 ← 30 × 428
2 1 4 , 0 0 0 ← 500 × 428
2 2 9 , 4 0 8 ← Add all
2 Multiply by tens: 30 × 428 = 12,840
3 Multiply by hundreds: 500 × 428 = 214,000
4 Add partial products: 2,568 + 12,840 + 214,000 = 229,408
✓ Answer
428 × 536 = 229,408

🍩 Word Problem 1

You Do
📖Read Carefully

A bakery makes 38 doughnuts per batch. They bake 12 batches every morning. How many doughnuts do they make each morning?

38 × 12
Choose any strategy you've learned!
📝 Standard Algorithm
1 Multiply by ones: 2 × 38 = 76
2 Multiply by tens: 10 × 38 = 380. Then add: 76 + 380 = 456
✓ Answer
The bakery makes 456 doughnuts each morning.

🐟 Word Problem 2

You Do
📖Read Carefully

A fish hatchery releases 56 fish into the river each week. After 87 weeks, how many fish have been released in total?

56 × 87
Choose any strategy you've learned!
📝 Standard Algorithm
1 Multiply by ones: 7 × 56 = 392
2 Multiply by tens: 80 × 56 = 4,480. Then add: 392 + 4,480 = 4,872
✓ Answer
The hatchery released 4,872 fish in total.

💬 Turn & Talk

🤔Discuss with a Partner

Talk with your partner about these questions:

1. Which strategy do you like best — multiples of 10, area model, or standard algorithm? Why?

2. When would the area model be more helpful than the standard algorithm? When would it be less helpful?

3. A student says 45 × 30 = 135. What mistake did they make? How would you help them fix it?

Tip 1: All strategies give the same answer — it's about choosing the most efficient one!

Tip 2: Area model is great for seeing partial products. Standard algorithm is faster for bigger numbers.

Tip 3: The student forgot to count the zero! 45 × 3 = 135, then add the zero → 1,350.

📝 Key Takeaways

🔟 Multiples of 10
Multiply the basic fact, then count and add the total zeros from both factors.
📊 Area Model
Expand each factor, multiply the parts in a grid, then add all partial products together.
📝 Standard Algorithm
Multiply by ones, then by tens (with a zero placeholder), then add the partial products.
🎯 Choose Wisely
All strategies give the same product — pick the one that's most efficient for the numbers!

🎫 Exit Ticket

Solve each problem on your whiteboard, then check your answers!

1️⃣Multiples of 10

50 × 700

Basic fact: 5 × 7 = 35. Count zeros: 3 total.
50 × 700 = 35,000

2️⃣Area Model or Algorithm

46 × 73

3 × 46 = 138 | 70 × 46 = 3,220
138 + 3,220 = 3,358

3️⃣Standard Algorithm

325 × 18

8 × 325 = 2,600 | 10 × 325 = 3,250
2,600 + 3,250 = 5,850

Great Work Today!

You learned 3 powerful strategies for multiplying whole numbers!

🔟
Strategy 1
10s
📊
Strategy 2
Area
📝
Strategy 3
Algo