{"id": "math-v1-A1-R3-133df093", "split": "train", "topic": "A", "concept_id": "A1", "prereqs": [], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A1-R3-add-carry", "params": {}, "text": "Compute 266 + 482.", "options": null}, "ground_truth": {"answer": 748, "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA01", "text": "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.", "final_answer": 648}], "feedback": [{"for_attempt": 0, "text": "When you added the tens, did you notice that the result was over 10? What do you think happens to the extra 10 when you're adding?"}], "solution": {"steps": ["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."], "final_answer": 748}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 1, "gen_attempt": 0, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}
{"id": "math-v1-A2-R3-87cfbe93", "split": "train", "topic": "A", "concept_id": "A2", "prereqs": ["A1"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A2-R3-subtract-borrow", "params": {}, "text": "Compute 496 − 109.", "options": null}, "ground_truth": {"answer": 387, "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA02", "text": "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.", "final_answer": 393}, {"misconception_id": "MA03", "text": "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.", "final_answer": 397}], "feedback": [{"for_attempt": 0, "text": "When subtracting, do we always subtract the smaller number from the larger one, or does the order of the numbers matter? Can you check with a simpler example like 12 − 9?"}, {"for_attempt": 1, "text": "When you borrowed from the tens column, did you remember to reduce the tens digit by 1? How does borrowing affect the digits in each column?"}], "solution": {"steps": ["Ones: borrow, 16 − 9 = 7", "Tens: (9 − 1 = 8 after the earlier borrow) 8 − 0 = 8", "Hundreds: 4 − 1 = 3", "So, 496 − 109 = 387"], "final_answer": 387}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 2, "gen_attempt": 0, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}
{"id": "math-v1-A3-R3-4b9b2ab3", "split": "train", "topic": "A", "concept_id": "A3", "prereqs": ["A1"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A3-R3-multiply-two-digit", "params": {}, "text": "Compute 83 × 71.", "options": null}, "ground_truth": {"answer": 5893, "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA04", "text": "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.", "final_answer": 664}], "feedback": [{"for_attempt": 0, "text": "When you multiply by the tens digit, do you remember to shift the place value? How would that change your calculation?"}], "solution": {"steps": ["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."], "final_answer": 5893}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 2, "gen_attempt": 2, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}
{"id": "math-v1-A4-R2-13473d44", "split": "train", "topic": "A", "concept_id": "A4", "prereqs": ["A1", "A3"], "rung": "R2", "difficulty": "easy", "problem": {"template_id": "A4-R2-which-first", "params": {}, "text": "In the expression 25 − 6 × 7, which operation should be done first?", "options": ["A) 6 × 7, because multiplication comes before addition and subtraction.", "B) 25 − 6, because we always work from left to right."]}, "ground_truth": {"answer": "A", "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA05", "text": "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.", "final_answer": "B"}], "feedback": [{"for_attempt": 0, "text": "What do the order of operations (PEMDAS) tell us about multiplication and subtraction?"}], "solution": {"steps": ["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."], "final_answer": "A"}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 1, "gen_attempt": 0, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}
{"id": "math-v1-A5-R3-20854100", "split": "train", "topic": "A", "concept_id": "A5", "prereqs": ["A2"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A5-R3-add-negatives", "params": {}, "text": "Compute (−10) + (−9).", "options": null}, "ground_truth": {"answer": -19, "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA06", "text": "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.", "final_answer": 19}], "feedback": [{"for_attempt": 0, "text": "Can you give an example where adding two negative numbers results in a positive number? How does that affect the idea that two negatives make a positive in addition?"}], "solution": {"steps": ["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."], "final_answer": -19}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 3, "gen_attempt": 0, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}
{"id": "math-v1-A6-R3-11517438", "split": "train", "topic": "A", "concept_id": "A6", "prereqs": ["A3", "A5"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "A6-R3-multiply-negatives", "params": {}, "text": "Compute (−8) × (−2).", "options": null}, "ground_truth": {"answer": 16, "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA08", "text": "I think when I multiply two negative numbers, the answer should be negative. So, (−8) × (−2) should be −16.", "final_answer": -16}], "feedback": [{"for_attempt": 0, "text": "Why do you think the product of two negative numbers should be negative? Can you think of a situation where multiplying two negatives would give you a positive?"}], "solution": {"steps": ["To solve (−8) × (−2), remember that the product of two negative numbers is positive.", "So, we can rewrite it as 8 × 2 = 16."], "final_answer": 16}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 2, "gen_attempt": 0, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}
{"id": "math-v1-B1-R3-2106807f", "split": "train", "topic": "B", "concept_id": "B1", "prereqs": ["A4"], "rung": "R3", "difficulty": "medium", "problem": {"template_id": "B1-R3-evaluate-coefficient", "params": {}, "text": "Evaluate 7x + 1 when x = 5.", "options": null}, "ground_truth": {"answer": 36, "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA09", "text": "I plugged x = 5 into 7x + 1. Since 7x means joining 7 and 5, I got 75 + 1, which equals 76.", "final_answer": 76}], "feedback": [{"for_attempt": 0, "text": "When you see 7x, what does it actually mean? Can you check by substituting x = 1? What do you get for 7x + 1?"}], "solution": {"steps": ["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."], "final_answer": 36}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 1, "gen_attempt": 0, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}
{"id": "math-v1-B2-R2-4a7f3441", "split": "train", "topic": "B", "concept_id": "B2", "prereqs": ["B1"], "rung": "R2", "difficulty": "easy", "problem": {"template_id": "B2-R2-can-combine", "params": {}, "text": "Can 5x + 9 be simplified to a single term?", "options": ["A) No. 5x and 9 are unlike terms, so 5x + 9 is already as simple as it gets.", "B) Yes, it simplifies to 14x."]}, "ground_truth": {"answer": "A", "unit": null, "tolerance_rel": 0}, "attempts": [{"misconception_id": "MA11", "text": "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.", "final_answer": "B"}], "feedback": [{"for_attempt": 0, "text": "When you combine terms, do the variables have to be the same? Can you add a number without a variable to a term with a variable?"}], "solution": {"steps": ["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."], "final_answer": "A"}, "provenance": {"generator": "mlx-community/Qwen2.5-32B-Instruct-4bit", "template_version": "0.1.0-spec", "seed": 3, "gen_attempt": 0, "checks": {"V2": "pass", "V3": "pass", "V4": "pass", "V5": "pass", "V6": "pass", "V9": "pass", "V10": "pass", "V11": "pass", "V7": "pass"}, "human_review": {"reviewed": false, "verdict": null}}}