Multi-Digit Multiplication Mastery

Algorithms, Place Value Steps & Speed Strategies

Grade 4 • Math

Page 1 of 4

Name:

Date:

⏱️ Study & Goal: Under 6 Mins / Sheet

Score:

📌 Skill 1: Multiplying Thousands by 1-Digit (4-Digit × 1-Digit)

To multiply a 4-digit number by a single digit, multiply from right to left (Ones → Tens → Hundreds → Thousands). Always remember to add any regrouped digits (carries)!

6,130 × 6 ──────── 36,780

• Step 1 (Ones): 6 × 0 = 0 (write 0)
• Step 2 (Tens): 6 × 3 = 18 (write 8, carry 1 to hundreds)
• Step 3 (Hundreds): (6 × 1) + 1 = 7 (write 7)
• Step 4 (Thousands): 6 × 6 = 36 (write 36) → Final Product: 36,780

📌 Skill 2: Multiplying by 2 Digits (3-Digit × 2-Digit) with Partial Products

Multiplying by 2 digits requires calculating two partial products and adding them together. Never forget the zero placeholder!

348 × 95 ──────── 1,740 ← (348 × 5) + 31,320 ← (348 × 90) ──────── 33,060

• Line 1 (Multiply by Ones Digit 5): 348 × 5 = 1,740
• Line 2 (Multiply by Tens Digit 9): Write a 0 in the ones place first because 9 is in the tens place (90). Then 348 × 9 = 3,132 with the zero becomes 31,320.
• Line 3 (Add the Partial Products): 1,740 + 31,320 = 33,060.

⚡ Speed & Mastery Golden Rules:
1. Keep Columns Aligned: Keeping digits in neat vertical columns prevents accidental addition mistakes.
2. Watch the Zero in 2-Digit Multiplication: When moving to the second line, write the 0 placeholder first before multiplying!

Speed Sprint 1: Thousands by 1-Digit

Focus: 4-Digit by 1-Digit Fluency & Regrouping

Grade 4 • Math

Page 2 of 4

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Start Time:

End Time:

Score: / 12

Sprint 1 Multiply each 4-digit number. Show your regrouped digits (carries) neatly above each place value. Work as quickly and accurately as possible!

6,130
× 6

4,825
× 7

3,094
× 8

5,241
× 4

7,516
× 5

8,409
× 9

2,673
× 8

9,350
× 3

1,784
× 6

6,408
× 7

4,296
× 5

8,172
× 9

💡 Pro-Tip for Zeros: When multiplying across a zero digit (like 3,094 × 8), remember 8 × 0 = 0, then add your regrouped tens!

Speed Sprint 2: Multiplying by 2 Digits

Focus: 3-Digit by 2-Digit Partial Products & Alignment

Grade 4 • Math

Page 3 of 4

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Start Time:

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Sprint 2 Find the partial products for each problem. Write the zero placeholder in line 2, then add to find the final product.

348
× 95

(×5) ________
(×90) _______0

________

426
× 34

(×4) ________
(×30) _______0

________

582
× 47

(×7) ________
(×40) _______0

________

275
× 63

(×3) ________
(×60) _______0

________

619
× 28

(×8) ________
(×20) _______0

________

734
× 52

(×2) ________
(×50) _______0

________

845
× 36

(×6) ________
(×30) _______0

________

409
× 75

(×5) ________
(×70) _______0

________

⚠️ Check Your Place Value: Make sure the tens partial product has its 0 placeholder aligned under the ones digit before adding!

Answer Key & Scoring Guide

Complete Solutions, Partial Products & Speed Diagnostic

Grade 4 • Math

Page 4 of 4

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Total Score: / 20

🔑 Page 2: Sprint 1 (4-Digit × 1-Digit)

1. 6,130 × 6 = 36,780
2. 4,825 × 7 = 33,775
3. 3,094 × 8 = 24,752
4. 5,241 × 4 = 20,964
5. 7,516 × 5 = 37,580
6. 8,409 × 9 = 75,681
7. 2,673 × 8 = 21,384
8. 9,350 × 3 = 28,050
9. 1,784 × 6 = 10,704
10. 6,408 × 7 = 44,856
11. 4,296 × 5 = 21,480
12. 8,172 × 9 = 73,548

🔑 Page 3: Sprint 2 (3-Digit × 2-Digit)

1. 348 × 95: 1,740 + 31,320 = 33,060
2. 426 × 34: 1,704 + 12,780 = 14,484
3. 582 × 47: 4,074 + 23,280 = 27,354
4. 275 × 63: 825 + 16,500 = 17,325
5. 619 × 28: 4,952 + 12,380 = 17,332
6. 734 × 52: 1,468 + 36,700 = 38,168
7. 845 × 36: 5,070 + 25,350 = 30,420
8. 409 × 75: 2,045 + 28,630 = 30,675

⏱️ Speed & Accuracy Mastery Benchmarks

🏆 Math Olympian
Under 5 mins / sprint
18 – 20 Correct (Speed Master)

👍 Proficient Multiplier
5 – 8 mins / sprint
14 – 17 Correct (Solid Accuracy)

📖 Practice Needed
Over 8 mins / sprint
0 – 13 Correct (Review Carries)

💡 Diagnostic Guide for Tutors & Parents:
• Error in Row 2 of 2-Digit Math? The student likely forgot the zero placeholder in the ones column.
• Error with numbers containing zeros (like 3,094 × 8 or 409 × 75)? Emphasize that zero times any number is zero, but carried numbers must be added to that zero!