Division Steps Slide Deck Digit Detectives Math Lab
Grade 4–5 • Core Division
1-Digit Divisors Made Simple
Crack the Code of
Long Division
Master the 4-step algorithm to divide multi-digit numbers with accuracy, speed, and confidence.
D Divide
M Multiply
S Subtract
B Bring Down
Anatomy of a Division Problem
Step 01: Vocabulary Check
Quotient (The Answer)
25 R 1
Divisor 3
Dividend (Total to Share) 76
Divisor (Outside)
How many equal groups we are making (1 digit).
Dividend (Inside)
The total amount being split or shared.
Quotient (On Top)
The result: how many fit in each equal group.
Remainder (What's Left)
Leftover amount smaller than the divisor.
Golden Detective Rule: The remainder must ALWAYS be smaller than the divisor!
The DMSB Routine
Memory Trick: Does McDonald's Serve Burgers?
D
Divide
How many times does the divisor fit into the current digit?
7 ÷ 3 = 2
M
Multiply
Multiply that quotient digit by the divisor.
2 × 3 = 6
S
Subtract
Subtract to find the difference between the digits.
7 − 6 = 1
B
Bring Down
Bring down the next digit from the dividend and repeat!
Drop next digit ↓
After Bring Down: Ask yourself, is there another digit to drop?
If NO → Remaining number is your Remainder!
Model 1: 78 ÷ 3 (Clean Division)
Target Quotient: 26
2 6
3
7 8
− 6
1 8
− 1 8
0
Cycle 1 (Tens)
Divide: 3 into 7 goes 2 times.Multiply: 2 × 3 = 6 .Subtract: 7 − 6 = 1 .
Cycle 2 (Ones)
Bring Down: Drop the 8 to make 18 .Divide: 3 into 18 goes 6 times.Multiply & Subtract: 6 × 3 = 18; 18 − 18 = 0 .
Check: 26 × 3 = 78 ✓
Align each quotient digit directly above the dividend column you just divided!
Model 2: 95 ÷ 4 (With Remainder)
23 Remainder 3
2 3 R 3
4
9 5
− 8
1 5
− 1 2
3
How to Check Your Answer
(Quotient × Divisor) + Remainder = Dividend
Multiply quotient by divisor: 23 × 4 = 92
Add the remainder: 92 + 3 = 95
Matches dividend (95)! Verified.
Warning: If your remainder is 4 or higher, 4 could have gone in more times!
Always verify: Remainder (3) < Divisor (4). It passes inspection!
Partner Challenge: Try It Together
Grab your whiteboards or notebook!
Mission 1 Even Split
84 ÷ 6
How many 6s fit in 8?
Multiply and subtract.
Bring down the 4.
Hint: Quotient has 2 digits, R 0
Mission 2 Watch the Remainder
97 ÷ 5
How many 5s fit in 9?
Multiply, subtract, bring down 7.
How many 5s fit in 47?
Hint: Quotient ends with R 2
Ready for independent practice? Open your Long Division Mastery Worksheet!
Long Division Mastery Worksheet Math Mission 4th–5th Grade Operations
Digit Detectives: Long Division Mission
Solve multi-digit division problems with 1-digit divisors using the DMSB algorithm.
Name:
Date:
Class:
The DMSB Code:
D Divide (÷) → M Multiply (×) → S Subtract (−) → B Bring Down (↓)
1 Part 1: Guided Warm-Up (Keep numbers aligned in place-value columns)
Show all DMSB steps
#1. \( 72 \div 3 \) Exact
3 7 2
Quotient:
#2. \( 85 \div 4 \) With Remainder
4 8 5
Quotient:
#3. \( 96 \div 6 \) Exact
6 9 6
Quotient:
2 Part 2: Independent Practice (Check with multiplication)
Solve & verify
#4. \( 68 \div 4 \)
4 6 8
Answer:
#5. \( 87 \div 5 \)
5 8 7
Answer:
#6. \( 92 \div 3 \)
3 9 2
Answer:
Detective Checkpoint: Compare your remainder to the divisor. Remainder must be less than divisor!
Page 1 of 2
Mission Phase 2 • 3-Digit Dividends & Applications
Advanced Detective Work
Name:
3 Part 3: 3-Digit Dividends (Repeat the DMSB cycle twice)
Hundreds → Tens → Ones
#7. \( 348 \div 3 \)
3 3 4 8
Quotient:
#8. \( 476 \div 4 \)
4 4 7 6
Quotient:
#9. \( 529 \div 5 \) Watch Zero in Quotient!
5 5 2 9
Quotient:
#10. \( 734 \div 6 \)
6 7 3 4
Quotient:
4 Part 4: Real-World Case Investigation
Case Scenario: Detective Maya has 147 clues to catalog into evidence binders. Each binder holds exactly 6 clues. How many complete binders will she fill, and how many clues will be left over?
Show your calculation:
Complete binders filled:
Clues left over (remainder):
Check work: (Binders × 6) + Leftovers = 147
5 Part 5: Error Detective Challenge
Spot the Slip-Up
Leo's Flawed Work
1 4 R 5
4 ) 8 5
− 4
4 5
− 4 0
5
1. What mistake did Leo make?
2. Correct Quotient:
Digit Detectives Math Series • Long Division Mastery Page 2 of 2
Long Division Solutions Key Teacher Resource Complete Solutions & Pedagogical Guide
Long Division Mastery: Answer Key
Step-by-step worked solutions for 1-digit divisors with checking proofs.
Grade 4–5 Operations
Key Misconceptions & Facilitation Cues:
1. Remainder Size Check: Emphasize that if remainder \(\ge\) divisor, another whole group could have been extracted.
2. Place Value Alignment: Keep quotient digits strictly over the dividend digit being divided to prevent column shifts.
Part 1 & 2 Solutions: 2-Digit Dividends (Problems 1–6)
Formula: (Quotient × Divisor) + R = Dividend
#1. \( 72 \div 3 \) Q: 24
2 4
3 ) 7 2
− 6
1 2
− 1 2
0
Check: \( 24 \times 3 = 72 \) ✓
#2. \( 85 \div 4 \) Q: 21 R 1
2 1 R 1
4 ) 8 5
− 8
0 5
− 0 4
1
Check: \( (21 \times 4) + 1 = 85 \) ✓
#3. \( 96 \div 6 \) Q: 16
1 6
6 ) 9 6
− 6
3 6
− 3 6
0
Check: \( 16 \times 6 = 96 \) ✓
#4. \( 68 \div 4 \) Q: 17
1 7
4 ) 6 8
− 4
2 8
− 2 8
0
Check: \( 17 \times 4 = 68 \) ✓
#5. \( 87 \div 5 \) Q: 17 R 2
1 7 R 2
5 ) 8 7
− 5
3 7
− 3 5
2
Check: \( (17 \times 5) + 2 = 87 \) ✓
#6. \( 92 \div 3 \) Q: 30 R 2
3 0 R 2
3 ) 9 2
− 9
0 2
− 0 0
2
Check: \( (30 \times 3) + 2 = 92 \) ✓
Teacher Guide & Solutions • Page 1: 2-Digit Focus Page 1 of 2
Solutions Key Phase 2 • 3-Digit Dividends & Applications
Advanced Problems (7–12)
Scoring Total: 100 Points
Part 3 Solutions: 3-Digit Dividends (Problems 7–10)
#7. \( 348 \div 3 \) Q: 116
1 1 6
3 ) 3 4 8
− 3
0 4
− 3
1 8
− 1 8
0
Check: \( 116 \times 3 = 348 \) ✓
#8. \( 476 \div 4 \) Q: 119
1 1 9
4 ) 4 7 6
− 4
0 7
− 4
3 6
− 3 6
0
Check: \( 119 \times 4 = 476 \) ✓
#9. \( 529 \div 5 \) Q: 105 R 4
1 0 5 R 4
5 ) 5 2 9
− 5
0 2
− 0
2 9
− 2 5
4
Critical Note: 5 into 2 goes 0 times in tens place!
#10. \( 734 \div 6 \) Q: 122 R 2
1 2 2 R 2
6 ) 7 3 4
− 6
1 3
− 1 2
1 4
− 1 2
2
Check: \( (122 \times 6) + 2 = 734 \) ✓
Part 4: Word Problem Key (\( 147 \div 6 \))
\( 147 \div 6 = \mathbf{24 \text{ R } 3} \)
• Complete binders filled: 24 binders
• Leftover clues: 3 clues
Check: \( (24 \times 6) + 3 = 144 + 3 = 147 \) clues total.
Part 5: Error Detective Analysis
Leo's Mistake: In the first step, Leo divided \( 8 \div 4 \) and said it goes 1 time instead of 2. This left a remainder of 4 (equal to the divisor!). His final remainder of 5 is greater than the divisor (4), violating the fundamental division rule.
Correct Quotient: 21 R 1
Scoring Guide (100 Points Total)
Problems 1–6: 8 pts each (48 pts). Award 4 pts for correct DMSB steps, 4 pts for quotient.
Problems 7–10: 8 pts each (32 pts). Look for zero placeholder in Problem 9.
Part 4 Word Problem: 10 pts. (5 pts for calculation, 5 pts for interpreting quotient vs remainder).
Part 5 Error Analysis: 10 pts. (5 pts for identifying remainder flaw, 5 pts for correct solution).
Teacher Guide & Solutions • Page 2: Advanced & Rubric Page 2 of 2
