Even & Odd Patterns with LARGE Numbers

📚 Grade 3
📂 Operations & Algebraic Thinking (OA)
⏱️ 15 minutes
❓ 20 Questions
Common Core Standards:
3.OA.C.7: Fluently multiply within 100
3.OA.D.9: Identify arithmetic patterns
3.NBT.A.3: Multiply one-digit whole numbers by multiples of 10
Name: _______________________ Date: _______________________ Score: _______ / 20

📖 You DON'T Need to Multiply!

The BEST part about even and odd patterns? They work with ANY numbers - even HUGE ones!

You can check if 847 × 926 = 784,322 is correct WITHOUT doing the multiplication!

Remember the Even & Odd Rules:
• Even × Even = Even (The answer MUST be even)
• Even × Odd = Even (The answer MUST be even)
• Odd × Even = Even (The answer MUST be even)
• Odd × Odd = Odd (The answer MUST be odd)

⭐ KEY TAKEAWAYS:
• Notice the pattern: If at least ONE number is even, the answer MUST be even.
• Only when BOTH numbers are odd will the answer be odd!

How to Check BIG Numbers:
• Only look at the LAST DIGIT to tell if a number is even or odd
• 847 ends in 7 (odd), so 847 is ODD
• 926 ends in 6 (even), so 926 is EVEN
• Odd × Even = Even, so the answer MUST end in an even digit (0, 2, 4, 6, or 8)
• 784,322 ends in 2 (even) ✓ This could be correct!

DON'T multiply the big numbers - just check the pattern!

💡 Worked Examples

Study these examples carefully before starting the practice questions.

Example 1

Problem: Is this answer possible? 348 × 527 = 183,396

We DON'T multiply! Just check: 348 ends in 8 (even), 527 ends in 7 (odd). Even × Odd = Even. The answer 183,396 ends in 6 (even). ✓ This COULD be correct!

  1. Look at last digit of 348: it's 8, so 348 is EVEN
  2. Look at last digit of 527: it's 7, so 527 is ODD
  3. Even × Odd = EVEN (rule)
  4. Check answer: 183,396 ends in 6, which is EVEN ✓

Answer: Yes, this could be correct! (Even × Odd = Even)

Example 2

Problem: Is this answer possible? 825 × 493 = 406,826

Check the pattern: 825 ends in 5 (odd), 493 ends in 3 (odd). Odd × Odd = Odd. But 406,826 ends in 6 (even). ✗ This is DEFINITELY WRONG!

  1. Look at last digit of 825: it's 5, so 825 is ODD
  2. Look at last digit of 493: it's 3, so 493 is ODD
  3. Odd × Odd = ODD (rule)
  4. Check answer: 406,826 ends in 6, which is EVEN ✗

Answer: No, this is definitely wrong! (Odd × Odd must be Odd, not Even)

Example 3

Problem: Is this answer possible? 6,842 × 5,719 = 39,127,198

Even with REALLY big numbers: 6,842 ends in 2 (even), 5,719 ends in 9 (odd). Even × Odd = Even. 39,127,198 ends in 8 (even). ✓ This passes the check!

  1. Last digit of 6,842 is 2 → EVEN
  2. Last digit of 5,719 is 9 → ODD
  3. Even × Odd = EVEN
  4. 39,127,198 ends in 8 → EVEN ✓

Answer: Yes, this could be correct! (Even × Odd = Even)

✏️ Practice Questions

Solve each problem. Show your work in the space provided.

1. Is 12,483 even or odd? (Hint: Look at the last digit!)
2. Is 1,847 even or odd? (Hint: Look at the last digit!)
3. Is 5,926 even or odd? (Hint: Look at the last digit!)
4. Is 8,750 even or odd? (Hint: Look at the last digit!)
5. Is 23,491 even or odd? (Hint: Look at the last digit!)
6. What will 1,642 × 3,891 be: Even or Odd?
A) Even     B) Odd
7. What will 348 × 527 be: Even or Odd?
A) Even     B) Odd
8. What will 9,263 × 7,185 be: Even or Odd?
A) Even     B) Odd
9. What will 825 × 493 be: Even or Odd?
A) Even     B) Odd
10. What will 5,777 × 8,444 be: Even or Odd?
A) Even     B) Odd
11. Is this answer possible? 246 × 357 = 87,842
12. Is this answer possible? 1,428 × 2,650 = 3,784,200
13. Is this answer possible? 9,999 × 7,777 = 77,762,226
14. Is this answer possible? 835 × 729 = 608,715
15. Is this answer possible? 5,318 × 4,927 = 26,202,087
16. Is this answer possible? 6,245 × 3,817 = 23,836,564
17. Is this answer possible? 847 × 926 = 784,321
18. Which answer is IMPOSSIBLE based on even/odd rules? Problem: 576 × 834
A) 480,384     B) 480,385     C) 480,386     D) 480,388
19. Which answer is IMPOSSIBLE based on even/odd rules? Problem: 8,624 × 5,931
A) 51,149,142     B) 51,149,144     C) 51,149,145     D) 51,149,146
20. Which answer is IMPOSSIBLE based on even/odd rules? Problem: 1,247 × 3,851
A) 4,801,496     B) 4,801,497     C) 4,801,498     D) 4,801,499
Generated on November 17, 2025 | Math Practice Curriculum - Grade 3
Created by Naveen Ede