| [ |
| { |
| "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" |
| } |
| ] |
