5.NBT.6 • Division Dividing Whole Numbers
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Dividing Whole Numbers

How do we split large numbers into equal groups?

📚
Standard
5.NBT.6
📅
Lesson
Division
⏱️
Duration
90m

📋 Standards & Objectives

📋Common Core Standard
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
🎯Learning Objectives (SWBAT)
  • Divide multi-digit numbers by 1-digit divisors using the standard algorithm
  • Divide multi-digit numbers by 2-digit divisors using the standard algorithm
  • Use partial quotients as an alternative division strategy
  • Interpret remainders in context

🚀 Real-World Division

Division is everywhere! Think about these situations:

🍕

Pizza Party

You have 720 slices of pizza for 8 classes. How many slices does each class get?

📦

Packing Boxes

A warehouse has 2,634 items to pack into boxes of 5. How many full boxes?

💰

Saving Money

You earned $2,528 over 8 months. How much per month?

Today we'll master the tools to solve problems like these — and bigger ones!

📖 Division Vocabulary

Dividend

The number being divided (the total amount)

In 63 ÷ 5, the dividend is 63

Divisor

The number you divide by (the group size)

In 63 ÷ 5, the divisor is 5

Quotient

The answer to a division problem

In 63 ÷ 5 = 12 r3, the quotient is 12

Remainder

The amount left over after dividing evenly

In 63 ÷ 5 = 12 r3, the remainder is 3

✨ The DMSBR Algorithm

Long division follows a repeating pattern. Remember these 5 steps:

🧠 Does McDonald's Sell Burgers Raw?
➗
D
Divide
✖️
M
Multiply
➖
S
Subtract
⬇️
B
Bring Down
🔄
R
Repeat

Repeat the cycle until there are no more digits to bring down!

📌 1-Digit Division Steps

Follow DMSBR for each digit position, working left to right:

1

Divide

How many times does the divisor go into the current number? Write the digit above.

2

Multiply

Multiply the divisor by the quotient digit. Write the product below.

3

Subtract

Subtract the product from the current number. The difference must be less than the divisor.

4

Bring Down & Repeat

Bring down the next digit. Start the cycle again until no digits remain.

💡 Check: Your remainder must always be LESS than the divisor!

✏️ Problem 1

👨‍🏫 I Do • 1-Digit Divisor
2,634 ÷ 5
Divide using the standard algorithm (DMSBR)
📐 Standard Algorithm (DMSBR)
1 Divide: 5 goes into 2? No. Try 26. 5 goes into 26 → 5 times. Write 5 above. Multiply: 5 × 5 = 25. Subtract: 26 − 25 = 1. D·M·S
2 Bring down the 3 → 13. Divide: 5 into 13 → 2 times. Multiply: 5 × 2 = 10. Subtract: 13 − 10 = 3. B·D·M·S
3 Bring down the 4 → 34. Divide: 5 into 34 → 6 times. Multiply: 5 × 6 = 30. Subtract: 34 − 30 = 4. No more digits! Remainder
✓ Answer
2,634 ÷ 5 = 526 R4

✏️ Problem 2

👨‍🏫 I Do • 1-Digit Divisor
4,587 ÷ 7
Divide using the standard algorithm (DMSBR)
📐 Standard Algorithm (DMSBR)
1 Divide: 7 into 4? No. Try 45. 7 into 45 → 6 times. Write 6 above. Multiply: 7 × 6 = 42. Subtract: 45 − 42 = 3. D·M·S
2 Bring down the 8 → 38. Divide: 7 into 38 → 5 times. Multiply: 7 × 5 = 35. Subtract: 38 − 35 = 3. B·D·M·S
3 Bring down the 7 → 37. Divide: 7 into 37 → 5 times. Multiply: 7 × 5 = 35. Subtract: 37 − 35 = 2. Done! Remainder
✓ Answer
4,587 ÷ 7 = 655 R2

✏️ Problem 3

👥 We Do • 1-Digit Divisor
9,137 ÷ 4
Let's solve this together! Follow along on your packet.
📐 Standard Algorithm (DMSBR)
1 Divide: 4 into 9 → 2 times. Multiply: 4 × 2 = 8. Subtract: 9 − 8 = 1. D·M·S
2 Bring down the 1 → 11. Divide: 4 into 11 → 2 times. Multiply: 4 × 2 = 8. Subtract: 11 − 8 = 3. B·D·M·S
3 Bring down the 3 → 33. Divide: 4 into 33 → 8 times. Multiply: 4 × 8 = 32. Subtract: 33 − 32 = 1. B·D·M·S
4 Bring down the 7 → 17. Divide: 4 into 17 → 4 times. Multiply: 4 × 4 = 16. Subtract: 17 − 16 = 1. Done! R1
✓ Answer
9,137 ÷ 4 = 2,284 R1

✏️ Problem 4

👥 We Do • 1-Digit Divisor
8,025 ÷ 6
Work with your partner. What's your first step?
📐 Standard Algorithm (DMSBR)
1 Divide: 6 into 8 → 1 time. Multiply: 6 × 1 = 6. Subtract: 8 − 6 = 2. D·M·S
2 Bring down the 0 → 20. Divide: 6 into 20 → 3 times. Multiply: 6 × 3 = 18. Subtract: 20 − 18 = 2. B·D·M·S
3 Bring down the 2 → 22. Divide: 6 into 22 → 3 times. Multiply: 6 × 3 = 18. Subtract: 22 − 18 = 4. B·D·M·S
4 Bring down the 5 → 45. Divide: 6 into 45 → 7 times. Multiply: 6 × 7 = 42. Subtract: 45 − 42 = 3. Done! R3
✓ Answer
8,025 ÷ 6 = 1,337 R3

✏️ Problem 5

✏️ You Do • 1-Digit Divisor
5,672 ÷ 8
Try this one on your own! Use DMSBR.
📐 Standard Algorithm (DMSBR)
1 Divide: 8 into 5? No. Try 56. 8 into 56 → 7 times. Multiply: 8 × 7 = 56. Subtract: 56 − 56 = 0. D·M·S
2 Bring down the 7 → 07. Divide: 8 into 7 → 0 times. Write 0! Multiply: 8 × 0 = 0. Subtract: 7 − 0 = 7. B·D·M·S
3 Bring down the 2 → 72. Divide: 8 into 72 → 9 times. Multiply: 8 × 9 = 72. Subtract: 72 − 72 = 0. No remainder! R0
✓ Answer
5,672 ÷ 8 = 709

✏️ Problem 6

✏️ You Do • 1-Digit Divisor
7,841 ÷ 3
Show all your work! Remember to check — is the remainder less than 3?
📐 Standard Algorithm (DMSBR)
1 Divide: 3 into 7 → 2 times. Multiply: 3 × 2 = 6. Subtract: 7 − 6 = 1. D·M·S
2 Bring down the 8 → 18. Divide: 3 into 18 → 6 times. Multiply: 3 × 6 = 18. Subtract: 18 − 18 = 0. B·D·M·S
3 Bring down the 4 → 04. Divide: 3 into 4 → 1 time. Multiply: 3 × 1 = 3. Subtract: 4 − 3 = 1. B·D·M·S
4 Bring down the 1 → 11. Divide: 3 into 11 → 3 times. Multiply: 3 × 3 = 9. Subtract: 11 − 9 = 2. Done! 2 < 3 ✓ R2
✓ Answer
7,841 ÷ 3 = 2,613 R2

💬 Turn & Talk

🗣️Partner Discussion

Think about the DMSBR steps...

  • Which step do you think is the trickiest? Why?
  • What happens if you pick a quotient digit that's too big? Too small?
  • How do you check your answer when you're done?

💡 Check strategy: Multiply your quotient × divisor, then add the remainder. You should get back the dividend!

✨ 2-Digit Divisors

Dividing by 2-digit numbers uses the same DMSBR steps — but the "Divide" step is harder!

✅

What's the Same

Same DMSBR cycle: Divide, Multiply, Subtract, Bring Down, Repeat

⚡

What's Different

You need to estimate each quotient digit. Use compatible numbers to guess!

🔑 Estimation Trick

Round the divisor to the nearest ten, then use that to estimate. For example: 43 rounds to 40, so for 43│255, think "40 × ? ≈ 255" → try 6. Then check: 43 × 6 = 258. Too big! Try 5: 43 × 5 = 215. ✓

📌 2-Digit Division Steps

📋 Updated Procedure for 2-Digit Divisors
1
Estimate the quotient digit
Round the divisor to the nearest ten. Use multiplication facts to estimate.
2
Multiply to check
Multiply divisor × your estimate. If the product is too big, try one less.
3
Subtract
Subtract the product. The difference MUST be less than the divisor.
4
Bring Down & Repeat
Bring down the next digit and start the cycle again.

✏️ Problem 7

👨‍🏫 I Do • 2-Digit Divisor
2,554 ÷ 43
Divide using the standard algorithm with estimation
📐 Standard Algorithm with Estimation
1 Divide: 43 into 25? No. Try 255. Round 43 → 40. Think: 40 × ? ≈ 255. Try 6: 43 × 6 = 258. Too big! Try 5: 43 × 5 = 215. ✓ D·M
2 Subtract: 255 − 215 = 40. Check: 40 < 43 ✓. Bring down the 4 → 404. S·B
3 Divide: 43 into 404. Think: 40 × ? ≈ 404. Try 9: 43 × 9 = 387. Check: 387 ≤ 404 ✓. Subtract: 404 − 387 = 17. D·M·S
4 No more digits to bring down. Remainder: 17. Check: 17 < 43 ✓ R17
✓ Answer
2,554 ÷ 43 = 59 R17

✏️ Problem 8

👨‍🏫 I Do • 2-Digit Divisor
628 ÷ 24
Shorter dividend — same process!
📐 Standard Algorithm with Estimation
1 Divide: 24 into 62. Round 24 → 25. Think: 25 × ? ≈ 62. Try 2: 24 × 2 = 48. Check: 48 ≤ 62 ✓. Subtract: 62 − 48 = 14. D·M·S
2 Bring down the 8 → 148. Divide: 24 into 148. Think: 25 × ? ≈ 148. Try 6: 24 × 6 = 144. Check: 144 ≤ 148 ✓. B·D·M
3 Subtract: 148 − 144 = 4. No more digits. Remainder: 4. Check: 4 < 24 ✓ R4
✓ Answer
628 ÷ 24 = 26 R4

✏️ Problem 9

👥 We Do • 2-Digit Divisor
2,170 ÷ 29
Let's solve this together! Round 29 to what number?
📐 Standard Algorithm with Estimation
1 Divide: 29 into 21? No. Try 217. Round 29 → 30. Think: 30 × ? ≈ 217. Try 7: 29 × 7 = 203. Check: 203 ≤ 217 ✓. D·M
2 Subtract: 217 − 203 = 14. Bring down the 0 → 140. S·B
3 Divide: 29 into 140. Think: 30 × ? ≈ 140. Try 4: 29 × 4 = 116. Check: 116 ≤ 140 ✓. Subtract: 140 − 116 = 24. D·M·S
4 No more digits. Remainder: 24. Check: 24 < 29 ✓ R24
✓ Answer
2,170 ÷ 29 = 74 R24

✏️ Problem 10

👥 We Do • 2-Digit Divisor
3,109 ÷ 35
Work with your partner. Estimate first!
📐 Standard Algorithm with Estimation
1 Divide: 35 into 31? No. Try 310. Round 35 → 35. Think: 35 × ? ≈ 310. Try 8: 35 × 8 = 280. Check: 280 ≤ 310 ✓. (Try 9: 35 × 9 = 315, too big!) D·M
2 Subtract: 310 − 280 = 30. Bring down the 9 → 309. S·B
3 Divide: 35 into 309. Try 8: 35 × 8 = 280. Check: 280 ≤ 309 ✓. Subtract: 309 − 280 = 29. D·M·S
4 No more digits. Remainder: 29. Check: 29 < 35 ✓ R29
✓ Answer
3,109 ÷ 35 = 88 R29

✏️ Problem 11

✏️ You Do • 2-Digit Divisor
1,836 ÷ 27
Try this one independently! Estimate each quotient digit.
📐 Standard Algorithm with Estimation
1 Divide: 27 into 18? No. Try 183. Round 27 → 30. Think: 30 × ? ≈ 183. Try 6: 27 × 6 = 162. Check: 162 ≤ 183 ✓. D·M
2 Subtract: 183 − 162 = 21. Bring down the 6 → 216. S·B
3 Divide: 27 into 216. Try 8: 27 × 8 = 216. Exact! Subtract: 216 − 216 = 0. No remainder! R0
✓ Answer
1,836 ÷ 27 = 68

✏️ Problem 12

✏️ You Do • 2-Digit Divisor
4,297 ÷ 53
Show your estimation work! Round 53 to help you divide.
📐 Standard Algorithm with Estimation
1 Divide: 53 into 42? No. Try 429. Round 53 → 50. Think: 50 × ? ≈ 429. Try 8: 53 × 8 = 424. Check: 424 ≤ 429 ✓. D·M
2 Subtract: 429 − 424 = 5. Bring down the 7 → 57. S·B
3 Divide: 53 into 57. Try 1: 53 × 1 = 53. Check: 53 ≤ 57 ✓. Subtract: 57 − 53 = 4. D·M·S
4 No more digits. Remainder: 4. Check: 4 < 53 ✓ R4
✓ Answer
4,297 ÷ 53 = 81 R4

✨ Partial Quotients Method

Another way to divide! Instead of going digit by digit, subtract friendly chunks.

🧱

The Big Idea

Subtract large, easy-to-multiply chunks from the dividend. Keep going until you can't subtract anymore!

➕

Add Up the Chunks

Each chunk is a "partial quotient." Add all the partial quotients together for your final answer!

💡 Why Use Partial Quotients?

You get to choose your own "friendly" numbers! Use multiples of 10, 100, or whatever you're comfortable with. There's no wrong chunk — just faster and slower paths!

📌 Partial Quotients Steps

📋 How to Use Partial Quotients
1
Pick a friendly chunk
Ask: "How many groups of [divisor] can I easily take out?" Use multiples of 10 or 100.
2
Subtract the chunk
Multiply divisor × chunk, then subtract from what's left. Write the chunk to the side.
3
Repeat
Keep subtracting chunks until the remaining amount is less than the divisor.
4
Add the partial quotients
Add all your chunks together. That sum is your quotient! What's left over is the remainder.

✏️ Problem 13

👨‍🏫 I Do • Partial Quotients
4,587 ÷ 7
Solve using partial quotients — subtract friendly chunks!
🧱 Partial Quotients
1 Start with 4,587. Take out 600 groups of 7: 7 × 600 = 4,200. Subtract: 4,587 − 4,200 = 387. Write 600 to the side.
2 Now we have 387. Take out 50 groups of 7: 7 × 50 = 350. Subtract: 387 − 350 = 37. Write 50 to the side.
3 Now we have 37. Take out 5 groups of 7: 7 × 5 = 35. Subtract: 37 − 35 = 2. Write 5 to the side. 2 < 7, so we stop.
4 Add the partial quotients: 600 + 50 + 5 = 655. Remainder: 2.
✓ Answer
4,587 ÷ 7 = 655 R2

✏️ Problem 14

👨‍🏫 I Do • Partial Quotients
3,826 ÷ 7
Watch how I choose my friendly chunks
🧱 Partial Quotients
1 Start with 3,826. Take out 500 groups of 7: 7 × 500 = 3,500. Subtract: 3,826 − 3,500 = 326. Write 500.
2 Now we have 326. Take out 40 groups of 7: 7 × 40 = 280. Subtract: 326 − 280 = 46. Write 40.
3 Now we have 46. Take out 6 groups of 7: 7 × 6 = 42. Subtract: 46 − 42 = 4. Write 6. 4 < 7, stop!
4 Add the partial quotients: 500 + 40 + 6 = 546. Remainder: 4.
✓ Answer
3,826 ÷ 7 = 546 R4

✏️ Problem 15

👥 We Do • Partial Quotients
5,423 ÷ 6
Let's solve together! What chunks would you pick?
🧱 Partial Quotients
1 Start with 5,423. Take out 900 groups of 6: 6 × 900 = 5,400. Subtract: 5,423 − 5,400 = 23. Write 900.
2 Now we have 23. Take out 3 groups of 6: 6 × 3 = 18. Subtract: 23 − 18 = 5. Write 3. 5 < 6, stop!
3 Add the partial quotients: 900 + 3 = 903. Remainder: 5.
✓ Answer
5,423 ÷ 6 = 903 R5

✏️ Problem 16

👥 We Do • Partial Quotients (2-Digit)
2,819 ÷ 32
Partial quotients works great with 2-digit divisors too!
🧱 Partial Quotients
1 Start with 2,819. Take out 80 groups of 32: 32 × 80 = 2,560. Subtract: 2,819 − 2,560 = 259. Write 80.
2 Now we have 259. Take out 8 groups of 32: 32 × 8 = 256. Subtract: 259 − 256 = 3. Write 8. 3 < 32, stop!
3 Add the partial quotients: 80 + 8 = 88. Remainder: 3.
✓ Answer
2,819 ÷ 32 = 88 R3

✏️ Problem 17

✏️ You Do • Partial Quotients
3,748 ÷ 5
Choose your own friendly chunks! There's no wrong way.
🧱 Partial Quotients
1 Start with 3,748. Take out 700 groups of 5: 5 × 700 = 3,500. Subtract: 3,748 − 3,500 = 248. Write 700.
2 Now we have 248. Take out 40 groups of 5: 5 × 40 = 200. Subtract: 248 − 200 = 48. Write 40.
3 Now we have 48. Take out 9 groups of 5: 5 × 9 = 45. Subtract: 48 − 45 = 3. Write 9. 3 < 5, stop!
4 Add the partial quotients: 700 + 40 + 9 = 749. Remainder: 3.
✓ Answer
3,748 ÷ 5 = 749 R3

✏️ Problem 18

✏️ You Do • Partial Quotients (2-Digit)
1,973 ÷ 24
Use partial quotients with a 2-digit divisor. Pick friendly chunks!
🧱 Partial Quotients
1 Start with 1,973. Take out 80 groups of 24: 24 × 80 = 1,920. Subtract: 1,973 − 1,920 = 53. Write 80.
2 Now we have 53. Take out 2 groups of 24: 24 × 2 = 48. Subtract: 53 − 48 = 5. Write 2. 5 < 24, stop!
3 Add the partial quotients: 80 + 2 = 82. Remainder: 5.
✓ Answer
1,973 ÷ 24 = 82 R5

🏆 Challenge Problem

🏆 Challenge • Multi-Step
9,577 ÷ 47
A big 4-digit dividend with a 2-digit divisor — can you conquer it?
📐 Standard Algorithm
1 Divide: 47 into 95. Round 47 → 50. Think: 50 × 2 = 100 (too big). Try 2: 47 × 2 = 94. Check: 94 ≤ 95 ✓. Subtract: 95 − 94 = 1. D·M·S
2 Bring down the 7 → 17. Divide: 47 into 17 → 0 times. Write 0 in the quotient! Subtract: 17 − 0 = 17. B·D·M·S
3 Bring down the 7 → 177. Divide: 47 into 177. Try 3: 47 × 3 = 141. Check: 141 ≤ 177 ✓. (Try 4: 47 × 4 = 188, too big!) Subtract: 177 − 141 = 36. B·D·M·S
4 No more digits. Remainder: 36. Check: 36 < 47 ✓. Don't forget the 0 in the middle of 203! R36
✓ Answer
9,577 ÷ 47 = 203 R36

📝 Word Problem

👥 We Do • Applied Problem
A school fundraiser earned $2,528 over 8 months. If they earned the same amount each month, how much did they earn per month?
Set up the division, then solve!
📐 Set Up & Solve
1 Set up: $2,528 ÷ 8. The total ($2,528) is the dividend. The number of months (8) is the divisor.
2 Divide: 8 into 25 → 3. Multiply: 8 × 3 = 24. Subtract: 25 − 24 = 1. Bring down 2 → 12. 8 into 12 → 1. Multiply: 8 × 1 = 8. Subtract: 12 − 8 = 4.
3 Bring down 8 → 48. 8 into 48 → 6. Multiply: 8 × 6 = 48. Subtract: 48 − 48 = 0. No remainder!
4 Answer the question: They earned $316 per month. Check: $316 × 8 = $2,528 ✓
✓ Answer
$2,528 ÷ 8 = $316 per month

💬 Turn & Talk

🗣️Partner Discussion

Standard Algorithm vs. Partial Quotients

  • Which strategy do you like better? Why?
  • When might partial quotients be easier than the standard algorithm?
  • When might the standard algorithm be faster?

💡 Both strategies give the same answer! The standard algorithm is usually faster once you master it. Partial quotients is great when you're still learning, or when the divisor is tricky.

📌 Key Takeaways

🔑
DMSBR — Divide, Multiply, Subtract, Bring Down, Repeat. This cycle is the heart of the standard algorithm.
🎯
Estimation is key for 2-digit divisors. Round the divisor to the nearest 10 to help you estimate each quotient digit.
🧱
Partial quotients is an alternative strategy. Subtract friendly chunks, then add them up at the end.
✅
Always check: your remainder must be less than the divisor. Verify with multiplication: quotient × divisor + remainder = dividend.

🎫 Exit Ticket

Solve these on your own. Show your work!

Problem 1

6,453 ÷ 9

1-digit divisor

Problem 2

1,748 ÷ 23

2-digit divisor

Problem 3

4,235 ÷ 8

Choose any method!

📝 Answers: (1) 717 R0  |  (2) 76 R0  |  (3) 529 R3

Great Work! 🎉

You now have THREE powerful division strategies in your toolbox!

📐
Strategy 1
Standard Algorithm (1-digit)
🔍
Strategy 2
Standard Algorithm (2-digit)
🧱
Strategy 3
Partial Quotients