[
  {
    "task_id": "J2_structural_shortcuts_000476",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 5091?",
    "correct_answer": "50904909",
    "ns_solution_with_error": "Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 50904910",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9999 * 5091?\n\nSolution: Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 50904910"
  },
  {
    "task_id": "J2_landmark_comparison_000673",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 26% of 16520 greater than 4299?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 16520 = 4130.\nApproximation gives: 2147",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 26% of 16520 greater than 4299?\n\nSolution: Using Use 25% as landmark: 25% of 16520 = 4130.\nApproximation gives: 2147"
  },
  {
    "task_id": "J2_equation_reasoning_000722",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  2196 × (3976 + 6567) = 2196 × ___ + 2196 × 6567",
    "correct_answer": "3976",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 4174",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  2196 × (3976 + 6567) = 2196 × ___ + 2196 × 6567\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 4174"
  },
  {
    "task_id": "J2_structural_shortcuts_000466",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 10001 * 9495?",
    "correct_answer": "94959495",
    "ns_solution_with_error": "Using Use (10000+1)*m = 10000*m + 1*m.\nApproximation gives: 99707469",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 10001 * 9495?\n\nSolution: Using Use (10000+1)*m = 10000*m + 1*m.\nApproximation gives: 99707469"
  },
  {
    "task_id": "J2_relative_distance_000510",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 4794/9750 or 4219/8289?",
    "correct_answer": "4219/8289",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 4794/9750 or 4219/8289?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0"
  },
  {
    "task_id": "J2_compatible_numbers_000630",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 5090 × 1947.",
    "correct_answer": "9910230",
    "ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9910228",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 5090 × 1947.\n\nSolution: Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9910228"
  },
  {
    "task_id": "J2_equation_reasoning_000747",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  5045 × (9819 + 3109) = 5045 × ___ + 5045 × 3109",
    "correct_answer": "9819",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 19638",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  5045 × (9819 + 3109) = 5045 × ___ + 5045 × 3109\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 19638"
  },
  {
    "task_id": "J2_cancellation_identity_000563",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 6144 + 3597 - 3599",
    "correct_answer": "6142",
    "ns_solution_with_error": "Using Near-cancellation: 3597 - 3599 = -2, so answer ≈ 6144 + -2.\nApproximation gives: 6449",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 6144 + 3597 - 3599\n\nSolution: Using Near-cancellation: 3597 - 3599 = -2, so answer ≈ 6144 + -2.\nApproximation gives: 6449"
  },
  {
    "task_id": "J2_relative_distance_000549",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 1237/2527 or 1278/2528?",
    "correct_answer": "1278/2528",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 1237/2527 or 1278/2528?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1"
  },
  {
    "task_id": "J2_structural_shortcuts_000473",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 10002 * 8558?",
    "correct_answer": "85597116",
    "ns_solution_with_error": "Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 171194232",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 10002 * 8558?\n\nSolution: Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 171194232"
  },
  {
    "task_id": "J2_magnitude_estimation_000432",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10100 * 10200?",
    "correct_answer": "103020000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 108171000",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10100 * 10200?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 108171000"
  },
  {
    "task_id": "J2_option_elimination_000777",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 7521 × 4423?",
    "correct_answer": "33265383",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 33265380",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 7521 × 4423?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 33265380"
  },
  {
    "task_id": "J2_landmark_comparison_000652",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 9% of 48380 greater than 22179?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 10% as landmark: 10% of 48380 = 4838.\nApproximation gives: 4357",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 9% of 48380 greater than 22179?\n\nSolution: Using Use 10% as landmark: 10% of 48380 = 4838.\nApproximation gives: 4357"
  },
  {
    "task_id": "J2_magnitude_estimation_000406",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9900 * 9800?",
    "correct_answer": "97020000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 97020001",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 9900 * 9800?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 97020001"
  },
  {
    "task_id": "J2_equation_reasoning_000728",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  6981 × 2792 × 3660 = ___ × 3660 × 6981",
    "correct_answer": "2792",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2992",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  6981 × 2792 × 3660 = ___ × 3660 × 6981\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2992"
  },
  {
    "task_id": "J2_compatible_numbers_000618",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 2540 × 3676.",
    "correct_answer": "9337040",
    "ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 9347040",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 2540 × 3676.\n\nSolution: Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 9347040"
  },
  {
    "task_id": "J2_magnitude_estimation_000439",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 10200?",
    "correct_answer": "104040000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 208080000",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10200 * 10200?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 208080000"
  },
  {
    "task_id": "J2_compatible_numbers_000651",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 2548 × 3929.",
    "correct_answer": "10011092",
    "ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 10511646",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 2548 × 3929.\n\nSolution: Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 10511646"
  },
  {
    "task_id": "J2_option_elimination_000767",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 6918 × 8652?",
    "correct_answer": "59854536",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 56861810",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 6918 × 8652?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 56861810"
  },
  {
    "task_id": "J2_option_elimination_000765",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 1104 × 5487?",
    "correct_answer": "6057648",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 12115296",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 1104 × 5487?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 12115296"
  },
  {
    "task_id": "J2_relative_distance_000509",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 2166/4399 or 1489/2922?",
    "correct_answer": "1489/2922",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 2166/4399 or 1489/2922?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1"
  },
  {
    "task_id": "J2_equation_reasoning_000751",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  6818 × (3906 + 8051) = 6818 × ___ + 6818 × 8051",
    "correct_answer": "3906",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 4101",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  6818 × (3906 + 8051) = 6818 × ___ + 6818 × 8051\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 4101"
  },
  {
    "task_id": "J2_cancellation_identity_000557",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 6268 + 4816 - 4818",
    "correct_answer": "6266",
    "ns_solution_with_error": "Using Near-cancellation: 4816 - 4818 = -2, so answer ≈ 6268 + -2.\nApproximation gives: 6579",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 6268 + 4816 - 4818\n\nSolution: Using Near-cancellation: 4816 - 4818 = -2, so answer ≈ 6268 + -2.\nApproximation gives: 6579"
  },
  {
    "task_id": "J2_structural_shortcuts_000457",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 2376?",
    "correct_answer": "23757624",
    "ns_solution_with_error": "Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 22569743",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9999 * 2376?\n\nSolution: Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 22569743"
  },
  {
    "task_id": "J2_magnitude_estimation_000411",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10100 * 10200?",
    "correct_answer": "103020000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 103020002",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10100 * 10200?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 103020002"
  },
  {
    "task_id": "J2_structural_shortcuts_000463",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 10002 * 7974?",
    "correct_answer": "79755948",
    "ns_solution_with_error": "Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 79755148",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 10002 * 7974?\n\nSolution: Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 79755148"
  },
  {
    "task_id": "J2_magnitude_estimation_000447",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9900 * 9900?",
    "correct_answer": "98010000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 196020000",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 196020000"
  },
  {
    "task_id": "J2_equation_reasoning_000732",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  1558 × 4896 × 3652 = ___ × 3652 × 1558",
    "correct_answer": "4896",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 9792",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  1558 × 4896 × 3652 = ___ × 3652 × 1558\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 9792"
  },
  {
    "task_id": "J2_option_elimination_000775",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 5559 × 9837?",
    "correct_answer": "54683883",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 57418077",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 5559 × 9837?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 57418077"
  },
  {
    "task_id": "J2_compatible_numbers_000611",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 1273 × 7425.",
    "correct_answer": "9452025",
    "ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 9452023",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 1273 × 7425.\n\nSolution: Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 9452023"
  },
  {
    "task_id": "J2_cancellation_identity_000579",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 1817 + 5124 - 5125",
    "correct_answer": "1816",
    "ns_solution_with_error": "Using Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1.\nApproximation gives: 908",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 1817 + 5124 - 5125\n\nSolution: Using Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1.\nApproximation gives: 908"
  },
  {
    "task_id": "J2_structural_shortcuts_000496",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 3721?",
    "correct_answer": "37202558",
    "ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 18601279",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9998 * 3721?\n\nSolution: Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 18601279"
  },
  {
    "task_id": "J2_landmark_comparison_000686",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 10% of 85760 greater than 36782?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 10% as landmark: 10% of 85760 = 8576.\nApproximation gives: 8148",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 10% of 85760 greater than 36782?\n\nSolution: Using Use 10% as landmark: 10% of 85760 = 8576.\nApproximation gives: 8148"
  },
  {
    "task_id": "J2_landmark_comparison_000661",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 27% of 97500 greater than 21848?",
    "correct_answer": "Yes",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 97500 = 24375.\nApproximation gives: 25009",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 27% of 97500 greater than 21848?\n\nSolution: Using Use 25% as landmark: 25% of 97500 = 24375.\nApproximation gives: 25009"
  },
  {
    "task_id": "J2_relative_distance_000513",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 884/1785 or 1924/3797?",
    "correct_answer": "1924/3797",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 5",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 884/1785 or 1924/3797?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 5"
  },
  {
    "task_id": "J2_compatible_numbers_000640",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 1228 × 7243.",
    "correct_answer": "8894404",
    "ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 4447202",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 1228 × 7243.\n\nSolution: Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 4447202"
  },
  {
    "task_id": "J2_landmark_comparison_000691",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 25% of 89710 greater than 36335?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 89710 = 22427.\nApproximation gives: 23548",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 25% of 89710 greater than 36335?\n\nSolution: Using Use 25% as landmark: 25% of 89710 = 22427.\nApproximation gives: 23548"
  },
  {
    "task_id": "J2_equation_reasoning_000724",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  7951 × 5441 × 4817 = ___ × 4817 × 7951",
    "correct_answer": "5441",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 5438",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  7951 × 5441 × 4817 = ___ × 4817 × 7951\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 5438"
  },
  {
    "task_id": "J2_cancellation_identity_000568",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 9227 + 8064 - 8063",
    "correct_answer": "9228",
    "ns_solution_with_error": "Using Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1.\nApproximation gives: 9225",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 9227 + 8064 - 8063\n\nSolution: Using Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1.\nApproximation gives: 9225"
  },
  {
    "task_id": "J2_relative_distance_000519",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 1536/3087 or 3213/6322?",
    "correct_answer": "3213/6322",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 1536/3087 or 3213/6322?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0"
  },
  {
    "task_id": "J2_cancellation_identity_000565",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 2712 + 6582 - 6583",
    "correct_answer": "2711",
    "ns_solution_with_error": "Using Near-cancellation: 6582 - 6583 = -1, so answer ≈ 2712 + -1.\nApproximation gives: 4711",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 2712 + 6582 - 6583\n\nSolution: Using Near-cancellation: 6582 - 6583 = -1, so answer ≈ 2712 + -1.\nApproximation gives: 4711"
  },
  {
    "task_id": "J2_landmark_comparison_000683",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 27% of 87480 greater than 24547?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 87480 = 21870.\nApproximation gives: 11809",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 27% of 87480 greater than 24547?\n\nSolution: Using Use 25% as landmark: 25% of 87480 = 21870.\nApproximation gives: 11809"
  },
  {
    "task_id": "J2_relative_distance_000534",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 4320/8812 or 1806/3591?",
    "correct_answer": "1806/3591",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 4320/8812 or 1806/3591?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1"
  },
  {
    "task_id": "J2_magnitude_estimation_000409",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 10100?",
    "correct_answer": "103020000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 103320000",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10200 * 10100?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 103320000"
  },
  {
    "task_id": "J2_cancellation_identity_000596",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 9205 + 6773 - 6772",
    "correct_answer": "9206",
    "ns_solution_with_error": "Using Near-cancellation: 6773 - 6772 = 1, so answer ≈ 9205 + 1.\nApproximation gives: 9306",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 9205 + 6773 - 6772\n\nSolution: Using Near-cancellation: 6773 - 6772 = 1, so answer ≈ 9205 + 1.\nApproximation gives: 9306"
  },
  {
    "task_id": "J2_structural_shortcuts_000470",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 7447?",
    "correct_answer": "74455106",
    "ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 148910212",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9998 * 7447?\n\nSolution: Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 148910212"
  },
  {
    "task_id": "J2_structural_shortcuts_000474",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 5819?",
    "correct_answer": "58184181",
    "ns_solution_with_error": "Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 29092090",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9999 * 5819?\n\nSolution: Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 29092090"
  },
  {
    "task_id": "J2_option_elimination_000781",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 1459 × 1977?",
    "correct_answer": "2884443",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 3884443",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 1459 × 1977?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 3884443"
  },
  {
    "task_id": "J2_structural_shortcuts_000475",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 9721?",
    "correct_answer": "97190558",
    "ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 102050085",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9998 * 9721?\n\nSolution: Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 102050085"
  },
  {
    "task_id": "J2_landmark_comparison_000665",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 27% of 34690 greater than 11606?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 34690 = 8672.\nApproximation gives: 2366",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 27% of 34690 greater than 11606?\n\nSolution: Using Use 25% as landmark: 25% of 34690 = 8672.\nApproximation gives: 2366"
  },
  {
    "task_id": "J2_magnitude_estimation_000446",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10100 * 9900?",
    "correct_answer": "99990000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 99990020",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 99990020"
  },
  {
    "task_id": "J2_landmark_comparison_000679",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 48% of 63500 greater than 24915?",
    "correct_answer": "Yes",
    "ns_solution_with_error": "Using Use 50% as landmark: 50% of 63500 = 31750.\nApproximation gives: 30477",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 48% of 63500 greater than 24915?\n\nSolution: Using Use 50% as landmark: 50% of 63500 = 31750.\nApproximation gives: 30477"
  },
  {
    "task_id": "J2_structural_shortcuts_000499",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 1050?",
    "correct_answer": "10497900",
    "ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 10497901",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9998 * 1050?\n\nSolution: Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 10497901"
  },
  {
    "task_id": "J2_option_elimination_000771",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 5562 × 7803?",
    "correct_answer": "43400286",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 41230272",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 5562 × 7803?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 41230272"
  },
  {
    "task_id": "J2_magnitude_estimation_000419",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10100 * 10100?",
    "correct_answer": "102010000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 102210000",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10100 * 10100?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 102210000"
  },
  {
    "task_id": "J2_equation_reasoning_000737",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  6741 × 2155 × 4707 = ___ × 4707 × 6741",
    "correct_answer": "2155",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2048",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  6741 × 2155 × 4707 = ___ × 4707 × 6741\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2048"
  },
  {
    "task_id": "J2_cancellation_identity_000578",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 5722 + 2063 - 2062",
    "correct_answer": "5723",
    "ns_solution_with_error": "Using Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1.\nApproximation gives: 5724",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 5722 + 2063 - 2062\n\nSolution: Using Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1.\nApproximation gives: 5724"
  },
  {
    "task_id": "J2_equation_reasoning_000736",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  3230 × (5915 + 1005) = 3230 × ___ + 3230 × 1005",
    "correct_answer": "5915",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2957",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  3230 × (5915 + 1005) = 3230 × ___ + 3230 × 1005\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2957"
  },
  {
    "task_id": "J2_structural_shortcuts_000481",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 4811?",
    "correct_answer": "48100378",
    "ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 48100398",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9998 * 4811?\n\nSolution: Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 48100398"
  },
  {
    "task_id": "J2_magnitude_estimation_000433",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 9800?",
    "correct_answer": "99960000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 94962000",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 94962000"
  },
  {
    "task_id": "J2_relative_distance_000547",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 1518/3038 or 3432/6744?",
    "correct_answer": "3432/6744",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 1518/3038 or 3432/6744?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0"
  },
  {
    "task_id": "J2_cancellation_identity_000567",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 4064 + 5375 - 5377",
    "correct_answer": "4062",
    "ns_solution_with_error": "Using Near-cancellation: 5375 - 5377 = -2, so answer ≈ 4064 + -2.\nApproximation gives: 4262",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 4064 + 5375 - 5377\n\nSolution: Using Near-cancellation: 5375 - 5377 = -2, so answer ≈ 4064 + -2.\nApproximation gives: 4262"
  },
  {
    "task_id": "J2_equation_reasoning_000702",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  8731 × 2490 × 7066 = ___ × 7066 × 8731",
    "correct_answer": "2490",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2614",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  8731 × 2490 × 7066 = ___ × 7066 × 8731\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2614"
  },
  {
    "task_id": "J2_option_elimination_000801",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 2531 × 7515?",
    "correct_answer": "19020465",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 9510232",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 2531 × 7515?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 9510232"
  },
  {
    "task_id": "J2_option_elimination_000794",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 2277 × 4068?",
    "correct_answer": "9262836",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 8799695",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 2277 × 4068?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 8799695"
  },
  {
    "task_id": "J2_cancellation_identity_000585",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 4359 + 9463 - 9464",
    "correct_answer": "4358",
    "ns_solution_with_error": "Using Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1.\nApproximation gives: 8716",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 4359 + 9463 - 9464\n\nSolution: Using Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1.\nApproximation gives: 8716"
  },
  {
    "task_id": "J2_compatible_numbers_000623",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 4966 × 1988.",
    "correct_answer": "9872408",
    "ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 19744816",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 4966 × 1988.\n\nSolution: Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 19744816"
  },
  {
    "task_id": "J2_relative_distance_000520",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 4625/9376 or 2049/4061?",
    "correct_answer": "2049/4061",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 4625/9376 or 2049/4061?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0"
  },
  {
    "task_id": "J2_relative_distance_000501",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 3746/7556 or 1181/2333?",
    "correct_answer": "1181/2333",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: -4",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 3746/7556 or 1181/2333?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: -4"
  },
  {
    "task_id": "J2_compatible_numbers_000638",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 2548 × 3929.",
    "correct_answer": "10011092",
    "ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 10011093",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 2548 × 3929.\n\nSolution: Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 10011093"
  },
  {
    "task_id": "J2_compatible_numbers_000608",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 5009 × 1968.",
    "correct_answer": "9857712",
    "ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 10350597",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 5009 × 1968.\n\nSolution: Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 10350597"
  },
  {
    "task_id": "J2_landmark_comparison_000659",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 10% of 71650 greater than 29517?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 10% as landmark: 10% of 71650 = 7165.\nApproximation gives: 7166",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 10% of 71650 greater than 29517?\n\nSolution: Using Use 10% as landmark: 10% of 71650 = 7165.\nApproximation gives: 7166"
  },
  {
    "task_id": "J2_structural_shortcuts_000471",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 7041?",
    "correct_answer": "70395918",
    "ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 70395915",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9998 * 7041?\n\nSolution: Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 70395915"
  },
  {
    "task_id": "J2_relative_distance_000523",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 1473/2971 or 843/1672?",
    "correct_answer": "843/1672",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 1473/2971 or 843/1672?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0"
  },
  {
    "task_id": "J2_magnitude_estimation_000422",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9800 * 10200?",
    "correct_answer": "99960000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 94962000",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 9800 * 10200?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 94962000"
  },
  {
    "task_id": "J2_cancellation_identity_000591",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 8528 + 3299 - 3298",
    "correct_answer": "8529",
    "ns_solution_with_error": "Using Near-cancellation: 3299 - 3298 = 1, so answer ≈ 8528 + 1.\nApproximation gives: 17058",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 8528 + 3299 - 3298\n\nSolution: Using Near-cancellation: 3299 - 3298 = 1, so answer ≈ 8528 + 1.\nApproximation gives: 17058"
  },
  {
    "task_id": "J2_equation_reasoning_000738",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  4804 + 8180 = ___ + 5895",
    "correct_answer": "7089",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 7092",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  4804 + 8180 = ___ + 5895\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 7092"
  },
  {
    "task_id": "J2_landmark_comparison_000663",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 10% of 75230 greater than 17577?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 10% as landmark: 10% of 75230 = 7523.\nApproximation gives: 7147",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 10% of 75230 greater than 17577?\n\nSolution: Using Use 10% as landmark: 10% of 75230 = 7523.\nApproximation gives: 7147"
  },
  {
    "task_id": "J2_structural_shortcuts_000484",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 10001 * 4007?",
    "correct_answer": "40074007",
    "ns_solution_with_error": "Using Use (10000+1)*m = 10000*m + 1*m.\nApproximation gives: 38070307",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 10001 * 4007?\n\nSolution: Using Use (10000+1)*m = 10000*m + 1*m.\nApproximation gives: 38070307"
  },
  {
    "task_id": "J2_compatible_numbers_000619",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 1274 × 8677.",
    "correct_answer": "11054498",
    "ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 22108996",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 1274 × 8677.\n\nSolution: Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 22108996"
  },
  {
    "task_id": "J2_cancellation_identity_000558",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 3344 + 1236 - 1234",
    "correct_answer": "3346",
    "ns_solution_with_error": "Using Near-cancellation: 1236 - 1234 = 2, so answer ≈ 3344 + 2.\nApproximation gives: 3342",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 3344 + 1236 - 1234\n\nSolution: Using Near-cancellation: 1236 - 1234 = 2, so answer ≈ 3344 + 2.\nApproximation gives: 3342"
  },
  {
    "task_id": "J2_structural_shortcuts_000492",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 2912?",
    "correct_answer": "29114176",
    "ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 21114176",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 9998 * 2912?\n\nSolution: Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 21114176"
  },
  {
    "task_id": "J2_landmark_comparison_000699",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 11% of 57250 greater than 11559?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 10% as landmark: 10% of 57250 = 5725.\nApproximation gives: 6497",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 11% of 57250 greater than 11559?\n\nSolution: Using Use 10% as landmark: 10% of 57250 = 5725.\nApproximation gives: 6497"
  },
  {
    "task_id": "J2_relative_distance_000506",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 4901/9978 or 3743/7451?",
    "correct_answer": "3743/7451",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 4901/9978 or 3743/7451?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1"
  },
  {
    "task_id": "J2_option_elimination_000786",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 3972 × 8996?",
    "correct_answer": "35732112",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 37732112",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 3972 × 8996?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 37732112"
  },
  {
    "task_id": "J2_equation_reasoning_000708",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  3791 + 6639 = ___ + 3553",
    "correct_answer": "6877",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 6870",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  3791 + 6639 = ___ + 3553\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 6870"
  },
  {
    "task_id": "J2_equation_reasoning_000748",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  3807 + 1362 + ___ = 1362 + 8347 + 3807",
    "correct_answer": "8347",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 8352",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  3807 + 1362 + ___ = 1362 + 8347 + 3807\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 8352"
  },
  {
    "task_id": "J2_structural_shortcuts_000453",
    "task_type": "J2_error_detection",
    "category": "structural_shortcuts",
    "problem": "What is 10002 * 7131?",
    "correct_answer": "71324262",
    "ns_solution_with_error": "Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 71324258",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 10002 * 7131?\n\nSolution: Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 71324258"
  },
  {
    "task_id": "J2_relative_distance_000532",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 1971/3979 or 3695/7308?",
    "correct_answer": "3695/7308",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 1971/3979 or 3695/7308?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1"
  },
  {
    "task_id": "J2_compatible_numbers_000610",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 1273 × 7425.",
    "correct_answer": "9452025",
    "ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 9452028",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 1273 × 7425.\n\nSolution: Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 9452028"
  },
  {
    "task_id": "J2_magnitude_estimation_000442",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9800 * 9800?",
    "correct_answer": "96040000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 192080000",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 9800 * 9800?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 192080000"
  },
  {
    "task_id": "J2_landmark_comparison_000678",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 23% of 55000 greater than 22317?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 55000 = 13750.\nApproximation gives: 6325",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 23% of 55000 greater than 22317?\n\nSolution: Using Use 25% as landmark: 25% of 55000 = 13750.\nApproximation gives: 6325"
  },
  {
    "task_id": "J2_landmark_comparison_000660",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 27% of 31870 greater than 12925?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 31870 = 7967.\nApproximation gives: 17209",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 27% of 31870 greater than 12925?\n\nSolution: Using Use 25% as landmark: 25% of 31870 = 7967.\nApproximation gives: 17209"
  },
  {
    "task_id": "J2_equation_reasoning_000726",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  1264 + 1118 = ___ + 7226",
    "correct_answer": "-4844",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: -4854",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  1264 + 1118 = ___ + 7226\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: -4854"
  },
  {
    "task_id": "J2_relative_distance_000524",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 1837/3735 or 2765/5491?",
    "correct_answer": "2765/5491",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 1837/3735 or 2765/5491?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0"
  },
  {
    "task_id": "J2_relative_distance_000546",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 3607/7251 or 2876/5669?",
    "correct_answer": "2876/5669",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: -2",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 3607/7251 or 2876/5669?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: -2"
  },
  {
    "task_id": "J2_option_elimination_000792",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 4893 × 1523?",
    "correct_answer": "7452039",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 14904078",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 4893 × 1523?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 14904078"
  },
  {
    "task_id": "J2_cancellation_identity_000554",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 6105 + 3719 - 3720",
    "correct_answer": "6104",
    "ns_solution_with_error": "Using Near-cancellation: 3719 - 3720 = -1, so answer ≈ 6105 + -1.\nApproximation gives: 6409",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 6105 + 3719 - 3720\n\nSolution: Using Near-cancellation: 3719 - 3720 = -1, so answer ≈ 6105 + -1.\nApproximation gives: 6409"
  },
  {
    "task_id": "J2_option_elimination_000789",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 3121 × 1321?",
    "correct_answer": "4122841",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 4122838",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 3121 × 1321?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 4122838"
  },
  {
    "task_id": "J2_equation_reasoning_000717",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  6336 + 4267 = ___ + 4522",
    "correct_answer": "6081",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 3040",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  6336 + 4267 = ___ + 4522\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 3040"
  },
  {
    "task_id": "J2_relative_distance_000533",
    "task_type": "J2_error_detection",
    "category": "relative_distance",
    "problem": "Which is larger: 3415/6937 or 4397/8764?",
    "correct_answer": "4397/8764",
    "ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 5",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which is larger: 3415/6937 or 4397/8764?\n\nSolution: Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 5"
  },
  {
    "task_id": "J2_cancellation_identity_000566",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 7556 + 4084 - 4086",
    "correct_answer": "7554",
    "ns_solution_with_error": "Using Near-cancellation: 4084 - 4086 = -2, so answer ≈ 7556 + -2.\nApproximation gives: 7555",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 7556 + 4084 - 4086\n\nSolution: Using Near-cancellation: 4084 - 4086 = -2, so answer ≈ 7556 + -2.\nApproximation gives: 7555"
  },
  {
    "task_id": "J2_option_elimination_000772",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 2726 × 5890?",
    "correct_answer": "16056140",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 8028070",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 2726 × 5890?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 8028070"
  },
  {
    "task_id": "J2_landmark_comparison_000669",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 27% of 18930 greater than 6267?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 18930 = 4732.\nApproximation gives: 5116",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 27% of 18930 greater than 6267?\n\nSolution: Using Use 25% as landmark: 25% of 18930 = 4732.\nApproximation gives: 5116"
  },
  {
    "task_id": "J2_magnitude_estimation_000401",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 10100?",
    "correct_answer": "103020000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 51510000",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10200 * 10100?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 51510000"
  },
  {
    "task_id": "J2_compatible_numbers_000625",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 4910 × 1977.",
    "correct_answer": "9707070",
    "ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9221717",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 4910 × 1977.\n\nSolution: Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9221717"
  },
  {
    "task_id": "J2_cancellation_identity_000600",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 2704 + 1588 - 1586",
    "correct_answer": "2706",
    "ns_solution_with_error": "Using Near-cancellation: 1588 - 1586 = 2, so answer ≈ 2704 + 2.\nApproximation gives: 2571",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 2704 + 1588 - 1586\n\nSolution: Using Near-cancellation: 1588 - 1586 = 2, so answer ≈ 2704 + 2.\nApproximation gives: 2571"
  },
  {
    "task_id": "J2_magnitude_estimation_000426",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 9900?",
    "correct_answer": "100980000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 100980004",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10200 * 9900?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 100980004"
  },
  {
    "task_id": "J2_compatible_numbers_000648",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 2520 × 3623.",
    "correct_answer": "9129960",
    "ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 9129962",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 2520 × 3623.\n\nSolution: Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 9129962"
  },
  {
    "task_id": "J2_option_elimination_000760",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 5927 × 1249?",
    "correct_answer": "7402823",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 7402824",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 5927 × 1249?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 7402824"
  },
  {
    "task_id": "J2_equation_reasoning_000716",
    "task_type": "J2_error_detection",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  7447 + 7834 = ___ + 1092",
    "correct_answer": "14189",
    "ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 14184",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What value fills the blank?  7447 + 7834 = ___ + 1092\n\nSolution: Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 14184"
  },
  {
    "task_id": "J2_compatible_numbers_000617",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 4966 × 1988.",
    "correct_answer": "9872408",
    "ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9378788",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 4966 × 1988.\n\nSolution: Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9378788"
  },
  {
    "task_id": "J2_compatible_numbers_000633",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 4960 × 2196.",
    "correct_answer": "10892160",
    "ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 5446080",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 4960 × 2196.\n\nSolution: Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 5446080"
  },
  {
    "task_id": "J2_option_elimination_000776",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 6135 × 7717?",
    "correct_answer": "47343795",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 47343705",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 6135 × 7717?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 47343705"
  },
  {
    "task_id": "J2_magnitude_estimation_000403",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 10200?",
    "correct_answer": "104040000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 98838000",
    "error_type": "wrong_rounding",
    "error_description": "Rounded in the wrong direction",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 10200 * 10200?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 98838000"
  },
  {
    "task_id": "J2_cancellation_identity_000583",
    "task_type": "J2_error_detection",
    "category": "cancellation_identity",
    "problem": "Evaluate: 7896 + 2453 - 2454",
    "correct_answer": "7895",
    "ns_solution_with_error": "Using Near-cancellation: 2453 - 2454 = -1, so answer ≈ 7896 + -1.\nApproximation gives: 3947",
    "error_type": "wrong_operand",
    "error_description": "Applied shortcut to wrong operand",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Evaluate: 7896 + 2453 - 2454\n\nSolution: Using Near-cancellation: 2453 - 2454 = -1, so answer ≈ 7896 + -1.\nApproximation gives: 3947"
  },
  {
    "task_id": "J2_compatible_numbers_000650",
    "task_type": "J2_error_detection",
    "category": "compatible_numbers",
    "problem": "Estimate 4925 × 2150.",
    "correct_answer": "10588750",
    "ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 10588752",
    "error_type": "transcription_error",
    "error_description": "Transcription error in final answer",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Estimate 4925 × 2150.\n\nSolution: Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 10588752"
  },
  {
    "task_id": "J2_magnitude_estimation_000443",
    "task_type": "J2_error_detection",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9800 * 9800?",
    "correct_answer": "96040000",
    "ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 96040001",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Which of the following is the best estimate for 9800 * 9800?\n\nSolution: Using Round both to 10000 and multiply.\nApproximation gives: 96040001"
  },
  {
    "task_id": "J2_option_elimination_000788",
    "task_type": "J2_error_detection",
    "category": "option_elimination",
    "problem": "What is 2243 × 8255?",
    "correct_answer": "18515965",
    "ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 18515967",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: What is 2243 × 8255?\n\nSolution: Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 18515967"
  },
  {
    "task_id": "J2_landmark_comparison_000664",
    "task_type": "J2_error_detection",
    "category": "landmark_comparison",
    "problem": "Is 24% of 44600 greater than 13866?",
    "correct_answer": "No",
    "ns_solution_with_error": "Using Use 25% as landmark: 25% of 44600 = 11150.\nApproximation gives: 10707",
    "error_type": "arithmetic_slip",
    "error_description": "Arithmetic slip in the shortcut step",
    "prompt": "This solution attempts to use a number sense shortcut. Find the error and explain what went wrong.\n\nProblem: Is 24% of 44600 greater than 13866?\n\nSolution: Using Use 25% as landmark: 25% of 44600 = 11150.\nApproximation gives: 10707"
  }
]