| {"id": "math-v1-A1-R3-133df093-a0", "prompt": "Compute 266 + 482.", "chosen": "First, I added the ones: 6 + 2 = 8, and wrote down 8. Next, I added the tens: 6 + 8 = 14, wrote down 4, and carried over 1. Then, I added the hundreds: 2 + 4 + 1 = 7, and wrote down 7. So, the answer is 748.", "rejected": "First, I added the ones: 6 + 2 = 8, and wrote down 8. Next, I added the tens: 6 + 8 = 14, and wrote down 4. Finally, I added the hundreds: 2 + 4 = 6, and wrote down 6. So, I got 648.", "rejected_misconception_id": "MA01"} | |
| {"id": "math-v1-A2-R3-87cfbe93-a0", "prompt": "Compute 496 − 109.", "chosen": "Ones: borrow, 16 − 9 = 7. Tens: (9 − 1 = 8 after the earlier borrow) 8 − 0 = 8. Hundreds: 4 − 1 = 3. So, 496 − 109 = 387.", "rejected": "I subtracted the smaller digit from the larger in each column. Ones: 9 − 6 = 3. Tens: 9 − 0 = 9. Hundreds: 4 − 1 = 3. So, the answer is 393.", "rejected_misconception_id": "MA02"} | |
| {"id": "math-v1-A2-R3-87cfbe93-a1", "prompt": "Compute 496 − 109.", "chosen": "Ones: borrow, 16 − 9 = 7. Tens: (9 − 1 = 8 after the earlier borrow) 8 − 0 = 8. Hundreds: 4 − 1 = 3. So, 496 − 109 = 387.", "rejected": "I borrowed in the ones place and added 10, so 16 − 9 = 7. In the tens, 9 − 0 = 9. In the hundreds, 4 − 1 = 3. So, the answer is 397.", "rejected_misconception_id": "MA03"} | |
| {"id": "math-v1-A3-R3-4b9b2ab3-a0", "prompt": "Compute 83 × 71.", "chosen": "First, I multiplied 83 by 1, which gives 83. Then, I multiplied 83 by 70, which gives 5810. Next, I added 83 and 5810, which gives 5893. So, the final answer is 5893.", "rejected": "I started by multiplying 83 by 1, which gives 83. Then, I multiplied 83 by 7, which gives 581. Finally, I added 83 and 581 to get 664.", "rejected_misconception_id": "MA04"} | |
| {"id": "math-v1-A4-R2-13473d44-a0", "prompt": "In the expression 25 − 6 × 7, which operation should be done first?\nA) 6 × 7, because multiplication comes before addition and subtraction.\nB) 25 − 6, because we always work from left to right.", "chosen": "First, handle multiplication before subtraction according to the order of operations. Calculate 6 × 7 to get 42, then subtract this from 25. The correct answer is A.", "rejected": "I always do operations from left to right, so I'll start with 25 − 6 first. Then I'll move on to the rest. So I pick B.", "rejected_misconception_id": "MA05"} | |
| {"id": "math-v1-A5-R3-20854100-a0", "prompt": "Compute (−10) + (−9).", "chosen": "Start with (−10) + (−9). Adding two negative numbers means moving further to the left on the number line. So, (−10) + (−9) = −19. The final answer is −19.", "rejected": "I think when you add two negative numbers, the negatives cancel out and you get a positive. So, (−10) + (−9) should be the same as 10 + 9, which gives me 19.", "rejected_misconception_id": "MA06"} | |
| {"id": "math-v1-A6-R3-11517438-a0", "prompt": "Compute (−8) × (−2).", "chosen": "To solve (−8) × (−2), remember that the product of two negative numbers is positive. So, we can rewrite it as 8 × 2 = 16.", "rejected": "I think when I multiply two negative numbers, the answer should be negative. So, (−8) × (−2) should be −16.", "rejected_misconception_id": "MA08"} | |
| {"id": "math-v1-B1-R3-2106807f-a0", "prompt": "Evaluate 7x + 1 when x = 5.", "chosen": "Replace x with 5 in 7x + 1, we get 7 × 5 + 1. First, compute 7 × 5, which equals 35. Then, add 1 to 35, resulting in 36. The final answer is 36.", "rejected": "I plugged x = 5 into 7x + 1. Since 7x means joining 7 and 5, I got 75 + 1, which equals 76.", "rejected_misconception_id": "MA09"} | |
| {"id": "math-v1-B2-R2-4a7f3441-a0", "prompt": "Can 5x + 9 be simplified to a single term?\nA) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.\nB) Yes, it simplifies to 14x.", "chosen": "5x and 9 are unlike terms because one has a variable and the other does not. Unlike terms cannot be combined into a single term. Therefore, 5x + 9 cannot be simplified further. The correct answer is A.", "rejected": "I think 5x + 9 can be simplified to 14x because I add the number 9 to the coefficient 5 and then put the x at the end. So I pick B.", "rejected_misconception_id": "MA11"} | |