Partial Quotients Steps:
1. Pick a "friendly" multiple of the divisor (use 10×, 20×, 30× etc.)
2. Subtract that amount from the dividend
3. Write the multiplier on the right side
4. Repeat until the remainder is less than the divisor
5. Add up all the partial quotients = your answer!
Example: 156 ÷ 12 → take out 10 groups (120), then 3 groups (36) → 10 + 3 = 13
Multi-Digit Division with 2-Digit Divisors
Partial Quotients Method
📚
Subject
Math
⏱️
Duration
50+ min
🎯
Standard
5.NBT.B.6
📋 Standards & Objectives
📜Standards
5.NBT.B.6Find 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.
5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction. (Spiral Review)
🎯SWBAT
- Divide multi-digit numbers by 2-digit divisors using partial quotients
- Build and use a multiplication helper chart to find "friendly" multiples of the divisor
- Use estimation to check whether a quotient is reasonable
- Verify a division answer by multiplying the quotient back by the divisor
🔥 Spiral Warm-Up
Review: Fraction Multiplication
Solve:
34 × 25 = ?
Multiply numerators: 3 × 2 = 6
Multiply denominators: 4 × 5 = 20
Simplify: 620 ÷ 22 = 310
34 × 25 = 310
🔥 Spiral Warm-Up
Review: Fraction of a Set
There are 28 students in Ms. Hall's class. 37 of them are wearing sneakers. How many students are wearing sneakers?
What does "of" mean in math? Multiply!
37 × 28 = 3 × 287 = 847
84 ÷ 7 = 12
12 students are wearing sneakers
🚀 The Big Question
Can you solve this?
🎈 Water Balloon Fight! 🎈
Ms. Hall's class found 2,498 water balloons for a water balloon fight. There are 28 students in the class.
How many balloons does each student get?
Could you do this in your head? 🤔
Probably not — and that's okay! Today we learn a strategy for dividing BIG numbers by 2-digit divisors.
💡 By the end of this lesson, you WILL be able to solve this.
💡 SBA Tip #5
💡 Show Your Work on Division
SBA division problems almost always say "show your work." Partial quotients earn you credit even if your final answer has a small error. Write your steps. Don't try to do 2,498 ÷ 28 in your head on the test.
How to use it: When you see "show your work" on a constructed response, write each step of partial quotients — the scorer gives points for the process, not just the answer.
📖 Key Vocabulary
📝Partial Quotients
A division strategy where you subtract "friendly" multiples of the divisor one chunk at a time, then add up all the chunks to get the quotient.
To solve 156 ÷ 12, you might subtract 10 groups of 12 (= 120), then 3 groups of 12 (= 36). The partial quotients are 10 and 3. Add them: 10 + 3 = 13.
With partial quotients, different students can use different chunk sizes and still get the same answer!
📝Quotient
The answer to a division problem. It tells you how many groups you made, or how many are in each group.
In 156 ÷ 12 = 13, the quotient is 13.
You can check a quotient by multiplying it back by the divisor: 13 × 12 = 156. ✓
📝Divisor
The number you are dividing BY. It tells you the size of each group (or how many groups to make).
In 2,498 ÷ 28, the divisor is 28 — we're splitting 2,498 into groups of 28.
Before dividing, build a multiplication helper chart for your divisor so you know its "friendly" multiples.
📝Remainder
The amount left over after dividing when the divisor doesn't go in evenly. It must be less than the divisor.
If you divide 100 ÷ 12, you get 8 groups of 12 (= 96) with a remainder of 4.
If your remainder is bigger than the divisor, you're not done dividing yet!
👨🏫 I Do: What Are Partial Quotients?
A strategy for BIG division
The Big Idea
Instead of dividing everything at once, we subtract "friendly" chunks of the divisor — one piece at a time. Then we add up all the chunks to get the quotient.
Think of it like unloading a truck:
You don't carry ALL the boxes at once. You carry as many as you can, set them down, go back for more, and keep going until the truck is empty.
Then count how many trips you made!
👨🏫 I Do: 156 ÷ 12
Partial Quotients — Scaffold Format
156 ÷ 12 = ?
1
How many 12s can I easily take out? 10 × 12 = 120
2
Subtract: 156 − 120 = 36 left
3
How many more 12s? 3 × 12 = 36
4
Subtract: 36 − 36 = 0 left
5
Add partial quotients: 10 + 3 = 13
156 ÷ 12 = 13
Scaffold Format
12 ) 156
−120 → 10
36
−36 → 3
0
= 13
📓 Write This Down
Write this in your notebook!
Key Terms
Partial Quotients
Scaffold
Notes
🛠️ Build a Multiplication Helper
Your secret weapon for division
Before you divide, build a list of "friendly" multiples of the divisor!
Multiples of 24
1 × 24 = 24
2 × 24 = 48
5 × 24 = 120
10 × 24 = 240 ⭐
20 × 24 = 480 ⭐
30 × 24 = 720 ⭐
⭐ The tens multiples (10×, 20×, 30×) are the most useful — they're your biggest "chunks" for partial quotients.
📝 Write this chart on your paper BEFORE you start dividing.
💡 You only need the multiples that are LESS than your dividend.
✅ Quick Check
In partial quotients, what do you do with the chunks you subtract?
👍 Add them up 👎 Multiply them together
👍 Add them up! That's why they're called partial quotients — each chunk is part of the full answer.
👨🏫 I Do: 888 ÷ 24
Bigger numbers, same strategy
888 ÷ 24 = ?
1
Start big: 30 × 24 = 720
2
888 − 720 = 168 left
3
Next chunk: 7 × 24 = 168
4
168 − 168 = 0 left
5
Add partial quotients: 30 + 7 = 37
888 ÷ 24 = 37
Scaffold
24 ) 888
−720 → 30
168
−168 → 7
0
= 37
👨🏫 Same Problem, Different Chunks
888 ÷ 24 — another way
What if a student used different "friendly" multiples? Let's see!
Ethan's Way
24 ) 888
−720 → 30
168
−168 → 7
0
= 37 ✓
Fae's Way
24 ) 888
−480 → 20
408
−240 → 10
168
−120 → 5
48
−48 → 2
0
= 37 ✓
Both are correct! Bigger chunks = fewer steps, but any "friendly" multiple works.
👨🏫 I Do: 1,424 ÷ 89
4-digit dividend!
1,424 ÷ 89 = ?
1
Big chunk: 10 × 89 = 890
2
1,424 − 890 = 534 left
3
Next: 5 × 89 = 445
4
534 − 445 = 89 left
5
Last chunk: 1 × 89 = 89
6
89 − 89 = 0 left
7
Add: 10 + 5 + 1 = 16
1,424 ÷ 89 = 16
Scaffold
89 ) 1424
−890 → 10
534
−445 → 5
89
−89 → 1
0
= 16
🎯 Estimation Check
Does your answer make sense?
Before you divide, ESTIMATE!
Round the dividend and divisor to "friendly" numbers, then divide in your head.
888 ÷ 24
Round: 900 ÷ 25 ≈ 36
Our answer was 37. Close to 36? Yes! ✓
1,424 ÷ 89
Round: 1,400 ÷ 90 ≈ about 15–16
Our answer was 16. Makes sense? Yes! ✓
If your answer is WAY off from your estimate, go back and check your subtraction!
🔄 What We Learned → What's Next
✅ What we just learned:
Partial quotients — subtract "friendly" multiples, then add up the chunks. Different chunk sizes = same answer. Always estimate to check!
⏭️ What's next:
Now it's YOUR turn to try it — but don't worry, we'll do the first ones together.
👥 We Do: 672 ÷ 32
Let's solve this together!
672 ÷ 32 = ?
First: Build your multiplication helper for 32!
1
Big chunk: 20 × 32 = 640
2
672 − 640 = 32 left
3
One more group: 1 × 32 = 32
4
32 − 32 = 0 left
5
Add: 20 + 1 = 21
672 ÷ 32 = 21
Scaffold
32 ) 672
−640 → 20
32
−32 → 1
0
= 21
👥 We Do: 945 ÷ 45
Try the first steps on your own, then we'll check!
945 ÷ 45 = ?
1
Start: 20 × 45 = 900
2
945 − 900 = 45 left
3
One more: 1 × 45 = 45
4
45 − 45 = 0
5
Add: 20 + 1 = 21
945 ÷ 45 = 21
Scaffold
45 ) 945
−900 → 20
45
−45 → 1
0
= 21
👥 We Do: Word Problem
Apply partial quotients to a real situation
A school is buying calculators that cost $18 each. They have $540. How many calculators can they buy?
Set up: 540 ÷ 18 = ?
Big chunk: 20 × 18 = 360
540 − 360 = 180 left
Next: 10 × 18 = 180
180 − 180 = 0
Add: 20 + 10 = 30
They can buy 30 calculators.
💬 Turn & Talk
🤔Discuss with a Partner
Eli says 756 ÷ 18 = 42.
How can you check his answer WITHOUT dividing?
Sentence starter: "I can check by ___"
Multiply back: 42 × 18 = 756 ✓
If quotient × divisor = dividend, the answer is correct!
🎯 Wrong Answer Analysis
Marcus vs. Tina — Who's right?
Problem: 756 ÷ 18
Marcus's Work
18 ) 756
−360 → 20
396
−360 → 20
36
−36 → 2
0
Answer: 42
Tina's Work
18 ) 756
−72 → 4
36
Answer: 4 R 36
"I'm done — I can't take out any more!"
Marcus is right! Tina stopped too early.
Tina's remainder (36) is bigger than the divisor (18). That means she can still take out more groups!
Rule: You're NOT done until the remainder is LESS than the divisor.
📓 Write This Down
Write this in your notebook!
Key Terms
Remainder Rule
Check Your Work
Notes
When are you DONE dividing?
When the remainder is LESS than the divisor.
If remainder ≥ divisor → keep going!
How to check your answer:
Quotient × Divisor = Dividend
Example: 42 × 18 = 756 ✓
When the remainder is LESS than the divisor.
If remainder ≥ divisor → keep going!
How to check your answer:
Quotient × Divisor = Dividend
Example: 42 × 18 = 756 ✓
🔄 Your Turn!
Time to fly solo! 🚀
Remember your steps:
1
Build your multiplication helper chart
2
Pick a "friendly" multiple and subtract
3
Repeat until remainder < divisor
4
Add up all partial quotients
5
Estimate to check!
🔍 You Try #1: 576 ÷ 24
Show your work using partial quotients!
576 ÷ 24 = ?
1
20 × 24 = 480
2
576 − 480 = 96
3
4 × 24 = 96
4
96 − 96 = 0
5
Add: 20 + 4 = 24
576 ÷ 24 = 24
Scaffold
24 ) 576
−480 → 20
96
−96 → 4
0
= 24
🔍 You Try #2: 1,350 ÷ 54
Show your work!
1,350 ÷ 54 = ?
1
20 × 54 = 1,080
2
1,350 − 1,080 = 270
3
5 × 54 = 270
4
270 − 270 = 0
5
Add: 20 + 5 = 25
1,350 ÷ 54 = 25
Scaffold
54 ) 1350
−1080 → 20
270
−270 → 5
0
= 25
🎈 You Try #3: The Balloon Problem!
Remember the hook? NOW you can solve it!
2,498 balloons ÷ 28 students = ?
1
80 × 28 = 2,240
2
2,498 − 2,240 = 258
3
9 × 28 = 252
4
258 − 252 = 6 left (6 < 28 ✓)
5
Add: 80 + 9 = 89 R 6
Each student gets 89 balloons (with 6 left over)!
Scaffold
28 ) 2498
−2240 → 80
258
−252 → 9
6
= 89 R 6
🔍 You Try #4: Word Problem
Apply partial quotients to a real situation
A factory makes 1,152 pencils per day. They pack them in boxes of 36. How many full boxes can they fill?
Set up: 1,152 ÷ 36 = ?
30 × 36 = 1,080
1,152 − 1,080 = 72
2 × 36 = 72
72 − 72 = 0
Add: 30 + 2 = 32
They can fill 32 full boxes.
🎯 SBA Spotlight
Multiple Choice — Estimation
Which is the BEST estimate for 1,847 ÷ 31?
Aabout 6
❌ Way too small. 6 × 31 = 186 — that's nowhere near 1,847.
B✅ about 60
✅ Round: 1,800 ÷ 30 = 60. This is the best estimate!
Cabout 600
❌ Too big. 600 × 31 = 18,600 — way more than 1,847.
Dabout 6,000
❌ WAY too big. Use rounding to eliminate obviously wrong options.
💡 Strategy: Round to "friendly" numbers, then divide in your head to eliminate wrong choices.
🎯 SBA Spotlight
Constructed Response — Show Your Work
Use partial quotients to solve 2,835 ÷ 63.
Show every step of your work AND write a sentence explaining why your answer is reasonable.
63 ) 2835
−2520 → 40 (40 × 63 = 2,520)
315
−315 → 5 (5 × 63 = 315)
0
= 45
2,835 ÷ 63 = 45
Reasonableness check: 3,000 ÷ 60 = 50. My answer of 45 is close to 50, so it is reasonable. ✓
📓 Summary Note
Write 1 Sentence
In the bottom of your notebook page, write one sentence explaining what you learned today about dividing big numbers with 2-digit divisors.
Sentence starter: "Today I learned that partial quotients work by ___"
🎫 Exit Ticket
Show what you know — 4 questions!
1️⃣Partial Quotients
756 ÷ 18 = ?
Show your work using partial quotients!
40×18=720, 756−720=36, 2×18=36, 36−36=0
40+2 = 42
2️⃣Partial Quotients
1,008 ÷ 42 = ?
Show your work!
20×42=840, 1008−840=168, 4×42=168, 168−168=0
20+4 = 24
3️⃣SBA — Multiple Choice + Work
What is 2,835 ÷ 63?
A) 35 B) 45 C) 55 D) 450
Circle answer AND show partial quotients work!
40×63=2520, 2835−2520=315, 5×63=315, 0 left
40+5 = B) 45
4️⃣🔄 Spiral Review
56 × 34 = ?
Simplify your answer!
5×36×4 = 1524 = 58