Kiddie Blocks PH
Tutorial Center • Project 8, Quezon City

Long Division Mastery & Fluency

DMSB Algorithm, Estimation & Place Value Regrouping
Grade 4 • Math
Page 1 of 4
Name:
Date:
⏱️ Study & Goal: Under 8 Mins / Practice Sheet
Score:
📌 The 4-Step Long Division Cycle: DMSB

Remember: Does McDonald's Serve Burgers? (Divide → Multiply → Subtract → Bring Down → Repeat or Remainder).

1437 r 1 ┌────── 4 │ 5749 - 4 ─── 17 - 16 ──── 14 - 12 ──── 29 - 28 ──── 1
• Step 1 (Thousands): 5 ÷ 4 = 1. Multiply: 1 × 4 = 4. Subtract: 5 - 4 = 1. Bring down 7 → 17.
• Step 2 (Hundreds): 17 ÷ 4 = 4. Multiply: 4 × 4 = 16. Subtract: 17 - 16 = 1. Bring down 4 → 14.
• Step 3 (Tens): 14 ÷ 4 = 3. Multiply: 3 × 4 = 12. Subtract: 14 - 12 = 2. Bring down 9 → 29.
• Step 4 (Ones): 29 ÷ 4 = 7. Multiply: 7 × 4 = 28. Subtract: 29 - 28 = 1 (Remainder).
• Check: (Quotient × Divisor) + Remainder = (1,437 × 4) + 1 = 5,748 + 1 = 5,749 ✔️
📌 Skill 2: Dividing by 2-Digit Numbers using Compatible Estimation

To divide by a 2-digit number (like 26), round the divisor to the nearest 10 (26 rounds to 30) to estimate each quotient digit quickly!

33 r 16 ┌───── 26 │ 874 - 78 ──── 94 - 78 ──── 16
• Estimate Digit 1: 26 doesn't fit into 8. Look at 87. Round 26 to 30. How many 30s in 87? About 3. Test: 3 × 26 = 78. Subtract: 87 - 78 = 9. Bring down 4 → 94.
• Estimate Digit 2: How many 30s in 94? About 3. Test: 3 × 26 = 78. Subtract: 94 - 78 = 16.
• Remainder Check: 16 is less than 26 (R < D). Quotient = 33 r 16.
• Check: (33 × 26) + 16 = 858 + 16 = 874 ✔️
⚡ Long Division Golden Rules:
1. Remainder Rule: The remainder must ALWAYS be strictly less than the divisor (R < D). If R ≥ D, your quotient digit was too small!
2. Don't Forget the Zero in Quotients: If a divisor does not go into a brought-down number (e.g., 3 ÷ 8 = 0), you MUST write a 0 in the quotient before bringing down the next digit!
BOOST MATH CONFIDENCE! ENROLL YOUR CHILD IN PERSONALIZED TUTORIALS AT PROJECT 8, QC!
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Kiddie Blocks PH
Tutorial Center • Project 8, Quezon City

Sprint 1: 3- to 4-Digit by 1-Digit Divisors

Focus: Division Fluency With & Without Regrouping
Grade 4 • Math
Page 2 of 4
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Score: / 12
Sprint 1 Divide using DMSB. Write the quotient on the top line. Write the remainder (if any) with "r". Show your subtraction work!
⭐ PART A: Exact Quotients (Without Remainder) Items 1 – 6
1
3
639
2
4
848
3
2
4,826
4
3
9,630
5
5
5,505
6
4
8,488
⚡ PART B: With Regrouping & Remainders Items 7 – 12
7
4
758
8
7
946
9
6
3,485
10
5
6,149
11
8
8,372
12
9
5,723
💡 Pro-Tip for Zero Quotients: In Problem 11 (8,372 ÷ 8), after 8 ÷ 8 = 1, bringing down 3 gives 3 ÷ 8 = 0. Write a 0 in the hundreds place! Quotient is 1,046 r 4 (not 146).
BOOST MATH CONFIDENCE! ENROLL YOUR CHILD IN PERSONALIZED TUTORIALS AT PROJECT 8, QC!
📍 Tandang Sora Ave., Project 8, Quezon City | 📞 09540351970 | 🌐 kiddieblocks.com | facebook.com/kiddieblocksph
Kiddie Blocks PH
Tutorial Center • Project 8, Quezon City

Sprint 2: 2- to 3-Digit by 2-Digit Divisors

Focus: Estimating Quotients & Multi-Step Division
Grade 4 • Math
Page 3 of 4
Name:
Start:
End:
Score: / 8
Sprint 2 Estimate using compatible tens, divide, and fill in the Quotient and Remainder. Complete the quick check equation!
⭐ PART A: Exact Quotients (Without Remainder) Items 1 – 4
1
21
84
Quotient:
Remainder:
Check: (__ × 21) + __ = 84
2
32
96
Quotient:
Remainder:
Check: (__ × 32) + __ = 96
3
12
432
Quotient:
Remainder:
Check: (__ × 12) + __ = 432
4
25
675
Quotient:
Remainder:
Check: (__ × 25) + __ = 675
⚡ PART B: With Regrouping & Remainders Items 5 – 8
5
14
95
Quotient:
Remainder:
Check: (__ × 14) + __ = 95
6
15
528
Quotient:
Remainder:
Check: (__ × 15) + __ = 528
7
23
749
Quotient:
Remainder:
Check: (__ × 23) + __ = 749
8
26
874
Quotient:
Remainder:
Check: (__ × 26) + __ = 874
⚠️ Check Your Remainder: Always verify that your remainder is strictly smaller than your divisor (R < D), then confirm using (Quotient × Divisor) + Remainder = Dividend!
BOOST MATH CONFIDENCE! ENROLL YOUR CHILD IN PERSONALIZED TUTORIALS AT PROJECT 8, QC!
📍 Tandang Sora Ave., Project 8, Quezon City | 📞 09540351970 | 🌐 kiddieblocks.com | facebook.com/kiddieblocksph
Kiddie Blocks PH
Tutorial Center • Project 8, Quezon City

Answer Key & Scoring Guide

Complete Solutions, Verification Checks & Diagnostic Guide
Grade 4 • Math
Page 4 of 4
Student Name:
Evaluation Date:
Total Score: / 20
🔑 Page 2: Sprint 1 (1-Digit Divisors)
Part A: Exact Quotients
1. 639 ÷ 3 = 213 (213 × 3 = 639)
2. 848 ÷ 4 = 212 (212 × 4 = 848)
3. 4,826 ÷ 2 = 2,413 (2,413 × 2 = 4,826)
4. 9,630 ÷ 3 = 3,210 (3,210 × 3 = 9,630)
5. 5,505 ÷ 5 = 1,101 (1,101 × 5 = 5,505)
6. 8,488 ÷ 4 = 2,122 (2,122 × 4 = 8,488)
Part B: With Regrouping & Remainders
7. 758 ÷ 4 = 189 r 2 (189 × 4 + 2 = 758)
8. 946 ÷ 7 = 135 r 1 (135 × 7 + 1 = 946)
9. 3,485 ÷ 6 = 580 r 5 (580 × 6 + 5 = 3,485)
10. 6,149 ÷ 5 = 1,229 r 4 (1,229 × 5 + 4 = 6,149)
11. 8,372 ÷ 8 = 1,046 r 4 (1,046 × 8 + 4 = 8,372)
12. 5,723 ÷ 9 = 635 r 8 (635 × 9 + 8 = 5,723)
🔑 Page 3: Sprint 2 (2-Digit Divisors)
Part A: Exact Quotients
1. 84 ÷ 21 = Q: 4, R: 0 (4 × 21 = 84)
2. 96 ÷ 32 = Q: 3, R: 0 (3 × 32 = 96)
3. 432 ÷ 12 = Q: 36, R: 0 (36 × 12 = 432)
4. 675 ÷ 25 = Q: 27, R: 0 (27 × 25 = 675)

Part B: With Regrouping & Remainders
5. 95 ÷ 14 = Q: 6, R: 11 (6 × 14 + 11 = 95)
6. 528 ÷ 15 = Q: 35, R: 3 (35 × 15 + 3 = 528)
7. 749 ÷ 23 = Q: 32, R: 13 (32 × 23 + 13 = 749)
8. 874 ÷ 26 = Q: 33, R: 16 (33 × 26 + 16 = 874)
⏱️ Speed & Accuracy Mastery Benchmarks
🏆 Division Master
Under 6 mins / sprint
18 – 20 Correct (Rapid & Fluent)
👍 Proficient Calculator
6 – 10 mins / sprint
14 – 17 Correct (Solid DMSB Steps)
📖 Practice Needed
Over 10 mins / sprint
0 – 13 Correct (Review Remainder & Zeroes)
💡 Diagnostic Guide for Tutors & Parents:
• Did the student omit a zero in the quotient (e.g., writing 146 instead of 1,046)? Emphasize place value alignment: every brought-down digit MUST produce a quotient digit!
• Is the remainder larger than the divisor? Remind students that R must always be strictly less than D. If R ≥ D, the quotient digit was too low.
• Difficulty with 2-digit divisors? Teach students to round the divisor to compatible tens (e.g., 23 rounds to 20; 26 rounds to 30) before testing multiples.