🧠 Part 1: Problem Solving Questions

🎯 Part 2: More Problem Solving

📋 Answer Sheet

1. Jake's answer should be 157,015. He likely made an error in place value or addition of partial products.

2. Disagree. Example: 1,000 × 10 = 10,000 (5 digits). The product can be 5 or 6 digits.

3. True. This demonstrates the commutative property of multiplication.

4. Sometimes. Depends on the specific numbers (e.g., 1,000 × 10 = 10,000 < 100,000).

5. 1,275 × 38 = 48,450 tickets

6. 1,235 × 78 = 96,330 (arrange smallest digits first for minimum product)

7. Incorrect. 4,567 × 29 = 132,443 should be 132,443. Need to check calculation.

8. Agree. 25 = 100 ÷ 4, so multiplying by 25 equals multiplying by 100 then dividing by 4.

9. True. Both equal 120,000 (commutative and associative properties).

10. Always. 2,500 ends in two zeros, 36 has no trailing zeros, so product keeps the two zeros.

11. 2,847 × 52 = 148,044 widgets

12. 9,864 × 21 = 207,144 (arrange largest digits first for maximum product)

13. Correct answer is 305,505. Need to verify Tom's working method.

14. Disagree. This only works for single digits (e.g., 3 × 11 = 33). For larger numbers, it's more complex.

15. False. 1,999 × 50 ≈ 2,000 × 50 = 100,000, while 2,000 × 49 = 98,000. First is larger.