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Upload data/judge_j2.json with huggingface_hub
Browse files- data/judge_j2.json +1322 -0
data/judge_j2.json
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|
| 1 |
+
[
|
| 2 |
+
{
|
| 3 |
+
"task_id": "J2_structural_shortcuts_000476",
|
| 4 |
+
"task_type": "J2_error_detection",
|
| 5 |
+
"category": "structural_shortcuts",
|
| 6 |
+
"problem": "What is 9999 * 5091?",
|
| 7 |
+
"correct_answer": "50904909",
|
| 8 |
+
"ns_solution_with_error": "Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 50904910",
|
| 9 |
+
"error_type": "arithmetic_slip",
|
| 10 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 11 |
+
"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"
|
| 12 |
+
},
|
| 13 |
+
{
|
| 14 |
+
"task_id": "J2_landmark_comparison_000673",
|
| 15 |
+
"task_type": "J2_error_detection",
|
| 16 |
+
"category": "landmark_comparison",
|
| 17 |
+
"problem": "Is 26% of 16520 greater than 4299?",
|
| 18 |
+
"correct_answer": "No",
|
| 19 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 16520 = 4130.\nApproximation gives: 2147",
|
| 20 |
+
"error_type": "wrong_operand",
|
| 21 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 22 |
+
"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"
|
| 23 |
+
},
|
| 24 |
+
{
|
| 25 |
+
"task_id": "J2_equation_reasoning_000722",
|
| 26 |
+
"task_type": "J2_error_detection",
|
| 27 |
+
"category": "equation_reasoning",
|
| 28 |
+
"problem": "What value fills the blank? 2196 × (3976 + 6567) = 2196 × ___ + 2196 × 6567",
|
| 29 |
+
"correct_answer": "3976",
|
| 30 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 4174",
|
| 31 |
+
"error_type": "wrong_rounding",
|
| 32 |
+
"error_description": "Rounded in the wrong direction",
|
| 33 |
+
"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"
|
| 34 |
+
},
|
| 35 |
+
{
|
| 36 |
+
"task_id": "J2_structural_shortcuts_000466",
|
| 37 |
+
"task_type": "J2_error_detection",
|
| 38 |
+
"category": "structural_shortcuts",
|
| 39 |
+
"problem": "What is 10001 * 9495?",
|
| 40 |
+
"correct_answer": "94959495",
|
| 41 |
+
"ns_solution_with_error": "Using Use (10000+1)*m = 10000*m + 1*m.\nApproximation gives: 99707469",
|
| 42 |
+
"error_type": "wrong_rounding",
|
| 43 |
+
"error_description": "Rounded in the wrong direction",
|
| 44 |
+
"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"
|
| 45 |
+
},
|
| 46 |
+
{
|
| 47 |
+
"task_id": "J2_relative_distance_000510",
|
| 48 |
+
"task_type": "J2_error_detection",
|
| 49 |
+
"category": "relative_distance",
|
| 50 |
+
"problem": "Which is larger: 4794/9750 or 4219/8289?",
|
| 51 |
+
"correct_answer": "4219/8289",
|
| 52 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
|
| 53 |
+
"error_type": "wrong_rounding",
|
| 54 |
+
"error_description": "Rounded in the wrong direction",
|
| 55 |
+
"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"
|
| 56 |
+
},
|
| 57 |
+
{
|
| 58 |
+
"task_id": "J2_compatible_numbers_000630",
|
| 59 |
+
"task_type": "J2_error_detection",
|
| 60 |
+
"category": "compatible_numbers",
|
| 61 |
+
"problem": "Estimate 5090 × 1947.",
|
| 62 |
+
"correct_answer": "9910230",
|
| 63 |
+
"ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9910228",
|
| 64 |
+
"error_type": "arithmetic_slip",
|
| 65 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 66 |
+
"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"
|
| 67 |
+
},
|
| 68 |
+
{
|
| 69 |
+
"task_id": "J2_equation_reasoning_000747",
|
| 70 |
+
"task_type": "J2_error_detection",
|
| 71 |
+
"category": "equation_reasoning",
|
| 72 |
+
"problem": "What value fills the blank? 5045 × (9819 + 3109) = 5045 × ___ + 5045 × 3109",
|
| 73 |
+
"correct_answer": "9819",
|
| 74 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 19638",
|
| 75 |
+
"error_type": "wrong_operand",
|
| 76 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 77 |
+
"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"
|
| 78 |
+
},
|
| 79 |
+
{
|
| 80 |
+
"task_id": "J2_cancellation_identity_000563",
|
| 81 |
+
"task_type": "J2_error_detection",
|
| 82 |
+
"category": "cancellation_identity",
|
| 83 |
+
"problem": "Evaluate: 6144 + 3597 - 3599",
|
| 84 |
+
"correct_answer": "6142",
|
| 85 |
+
"ns_solution_with_error": "Using Near-cancellation: 3597 - 3599 = -2, so answer ≈ 6144 + -2.\nApproximation gives: 6449",
|
| 86 |
+
"error_type": "wrong_rounding",
|
| 87 |
+
"error_description": "Rounded in the wrong direction",
|
| 88 |
+
"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"
|
| 89 |
+
},
|
| 90 |
+
{
|
| 91 |
+
"task_id": "J2_relative_distance_000549",
|
| 92 |
+
"task_type": "J2_error_detection",
|
| 93 |
+
"category": "relative_distance",
|
| 94 |
+
"problem": "Which is larger: 1237/2527 or 1278/2528?",
|
| 95 |
+
"correct_answer": "1278/2528",
|
| 96 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
|
| 97 |
+
"error_type": "wrong_rounding",
|
| 98 |
+
"error_description": "Rounded in the wrong direction",
|
| 99 |
+
"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"
|
| 100 |
+
},
|
| 101 |
+
{
|
| 102 |
+
"task_id": "J2_structural_shortcuts_000473",
|
| 103 |
+
"task_type": "J2_error_detection",
|
| 104 |
+
"category": "structural_shortcuts",
|
| 105 |
+
"problem": "What is 10002 * 8558?",
|
| 106 |
+
"correct_answer": "85597116",
|
| 107 |
+
"ns_solution_with_error": "Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 171194232",
|
| 108 |
+
"error_type": "wrong_operand",
|
| 109 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 110 |
+
"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"
|
| 111 |
+
},
|
| 112 |
+
{
|
| 113 |
+
"task_id": "J2_magnitude_estimation_000432",
|
| 114 |
+
"task_type": "J2_error_detection",
|
| 115 |
+
"category": "magnitude_estimation",
|
| 116 |
+
"problem": "Which of the following is the best estimate for 10100 * 10200?",
|
| 117 |
+
"correct_answer": "103020000",
|
| 118 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 108171000",
|
| 119 |
+
"error_type": "wrong_rounding",
|
| 120 |
+
"error_description": "Rounded in the wrong direction",
|
| 121 |
+
"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"
|
| 122 |
+
},
|
| 123 |
+
{
|
| 124 |
+
"task_id": "J2_option_elimination_000777",
|
| 125 |
+
"task_type": "J2_error_detection",
|
| 126 |
+
"category": "option_elimination",
|
| 127 |
+
"problem": "What is 7521 × 4423?",
|
| 128 |
+
"correct_answer": "33265383",
|
| 129 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 33265380",
|
| 130 |
+
"error_type": "arithmetic_slip",
|
| 131 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 132 |
+
"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"
|
| 133 |
+
},
|
| 134 |
+
{
|
| 135 |
+
"task_id": "J2_landmark_comparison_000652",
|
| 136 |
+
"task_type": "J2_error_detection",
|
| 137 |
+
"category": "landmark_comparison",
|
| 138 |
+
"problem": "Is 9% of 48380 greater than 22179?",
|
| 139 |
+
"correct_answer": "No",
|
| 140 |
+
"ns_solution_with_error": "Using Use 10% as landmark: 10% of 48380 = 4838.\nApproximation gives: 4357",
|
| 141 |
+
"error_type": "arithmetic_slip",
|
| 142 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 143 |
+
"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"
|
| 144 |
+
},
|
| 145 |
+
{
|
| 146 |
+
"task_id": "J2_magnitude_estimation_000406",
|
| 147 |
+
"task_type": "J2_error_detection",
|
| 148 |
+
"category": "magnitude_estimation",
|
| 149 |
+
"problem": "Which of the following is the best estimate for 9900 * 9800?",
|
| 150 |
+
"correct_answer": "97020000",
|
| 151 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 97020001",
|
| 152 |
+
"error_type": "arithmetic_slip",
|
| 153 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 154 |
+
"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"
|
| 155 |
+
},
|
| 156 |
+
{
|
| 157 |
+
"task_id": "J2_equation_reasoning_000728",
|
| 158 |
+
"task_type": "J2_error_detection",
|
| 159 |
+
"category": "equation_reasoning",
|
| 160 |
+
"problem": "What value fills the blank? 6981 × 2792 × 3660 = ___ × 3660 × 6981",
|
| 161 |
+
"correct_answer": "2792",
|
| 162 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2992",
|
| 163 |
+
"error_type": "transcription_error",
|
| 164 |
+
"error_description": "Transcription error in final answer",
|
| 165 |
+
"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"
|
| 166 |
+
},
|
| 167 |
+
{
|
| 168 |
+
"task_id": "J2_compatible_numbers_000618",
|
| 169 |
+
"task_type": "J2_error_detection",
|
| 170 |
+
"category": "compatible_numbers",
|
| 171 |
+
"problem": "Estimate 2540 × 3676.",
|
| 172 |
+
"correct_answer": "9337040",
|
| 173 |
+
"ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 9347040",
|
| 174 |
+
"error_type": "transcription_error",
|
| 175 |
+
"error_description": "Transcription error in final answer",
|
| 176 |
+
"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"
|
| 177 |
+
},
|
| 178 |
+
{
|
| 179 |
+
"task_id": "J2_magnitude_estimation_000439",
|
| 180 |
+
"task_type": "J2_error_detection",
|
| 181 |
+
"category": "magnitude_estimation",
|
| 182 |
+
"problem": "Which of the following is the best estimate for 10200 * 10200?",
|
| 183 |
+
"correct_answer": "104040000",
|
| 184 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 208080000",
|
| 185 |
+
"error_type": "wrong_operand",
|
| 186 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 187 |
+
"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"
|
| 188 |
+
},
|
| 189 |
+
{
|
| 190 |
+
"task_id": "J2_compatible_numbers_000651",
|
| 191 |
+
"task_type": "J2_error_detection",
|
| 192 |
+
"category": "compatible_numbers",
|
| 193 |
+
"problem": "Estimate 2548 × 3929.",
|
| 194 |
+
"correct_answer": "10011092",
|
| 195 |
+
"ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 10511646",
|
| 196 |
+
"error_type": "wrong_rounding",
|
| 197 |
+
"error_description": "Rounded in the wrong direction",
|
| 198 |
+
"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"
|
| 199 |
+
},
|
| 200 |
+
{
|
| 201 |
+
"task_id": "J2_option_elimination_000767",
|
| 202 |
+
"task_type": "J2_error_detection",
|
| 203 |
+
"category": "option_elimination",
|
| 204 |
+
"problem": "What is 6918 × 8652?",
|
| 205 |
+
"correct_answer": "59854536",
|
| 206 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 56861810",
|
| 207 |
+
"error_type": "wrong_rounding",
|
| 208 |
+
"error_description": "Rounded in the wrong direction",
|
| 209 |
+
"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"
|
| 210 |
+
},
|
| 211 |
+
{
|
| 212 |
+
"task_id": "J2_option_elimination_000765",
|
| 213 |
+
"task_type": "J2_error_detection",
|
| 214 |
+
"category": "option_elimination",
|
| 215 |
+
"problem": "What is 1104 × 5487?",
|
| 216 |
+
"correct_answer": "6057648",
|
| 217 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 12115296",
|
| 218 |
+
"error_type": "wrong_operand",
|
| 219 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 220 |
+
"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"
|
| 221 |
+
},
|
| 222 |
+
{
|
| 223 |
+
"task_id": "J2_relative_distance_000509",
|
| 224 |
+
"task_type": "J2_error_detection",
|
| 225 |
+
"category": "relative_distance",
|
| 226 |
+
"problem": "Which is larger: 2166/4399 or 1489/2922?",
|
| 227 |
+
"correct_answer": "1489/2922",
|
| 228 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
|
| 229 |
+
"error_type": "wrong_operand",
|
| 230 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 231 |
+
"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"
|
| 232 |
+
},
|
| 233 |
+
{
|
| 234 |
+
"task_id": "J2_equation_reasoning_000751",
|
| 235 |
+
"task_type": "J2_error_detection",
|
| 236 |
+
"category": "equation_reasoning",
|
| 237 |
+
"problem": "What value fills the blank? 6818 × (3906 + 8051) = 6818 × ___ + 6818 × 8051",
|
| 238 |
+
"correct_answer": "3906",
|
| 239 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 4101",
|
| 240 |
+
"error_type": "wrong_rounding",
|
| 241 |
+
"error_description": "Rounded in the wrong direction",
|
| 242 |
+
"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"
|
| 243 |
+
},
|
| 244 |
+
{
|
| 245 |
+
"task_id": "J2_cancellation_identity_000557",
|
| 246 |
+
"task_type": "J2_error_detection",
|
| 247 |
+
"category": "cancellation_identity",
|
| 248 |
+
"problem": "Evaluate: 6268 + 4816 - 4818",
|
| 249 |
+
"correct_answer": "6266",
|
| 250 |
+
"ns_solution_with_error": "Using Near-cancellation: 4816 - 4818 = -2, so answer ≈ 6268 + -2.\nApproximation gives: 6579",
|
| 251 |
+
"error_type": "wrong_rounding",
|
| 252 |
+
"error_description": "Rounded in the wrong direction",
|
| 253 |
+
"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"
|
| 254 |
+
},
|
| 255 |
+
{
|
| 256 |
+
"task_id": "J2_structural_shortcuts_000457",
|
| 257 |
+
"task_type": "J2_error_detection",
|
| 258 |
+
"category": "structural_shortcuts",
|
| 259 |
+
"problem": "What is 9999 * 2376?",
|
| 260 |
+
"correct_answer": "23757624",
|
| 261 |
+
"ns_solution_with_error": "Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 22569743",
|
| 262 |
+
"error_type": "wrong_rounding",
|
| 263 |
+
"error_description": "Rounded in the wrong direction",
|
| 264 |
+
"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"
|
| 265 |
+
},
|
| 266 |
+
{
|
| 267 |
+
"task_id": "J2_magnitude_estimation_000411",
|
| 268 |
+
"task_type": "J2_error_detection",
|
| 269 |
+
"category": "magnitude_estimation",
|
| 270 |
+
"problem": "Which of the following is the best estimate for 10100 * 10200?",
|
| 271 |
+
"correct_answer": "103020000",
|
| 272 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 103020002",
|
| 273 |
+
"error_type": "arithmetic_slip",
|
| 274 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 275 |
+
"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"
|
| 276 |
+
},
|
| 277 |
+
{
|
| 278 |
+
"task_id": "J2_structural_shortcuts_000463",
|
| 279 |
+
"task_type": "J2_error_detection",
|
| 280 |
+
"category": "structural_shortcuts",
|
| 281 |
+
"problem": "What is 10002 * 7974?",
|
| 282 |
+
"correct_answer": "79755948",
|
| 283 |
+
"ns_solution_with_error": "Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 79755148",
|
| 284 |
+
"error_type": "transcription_error",
|
| 285 |
+
"error_description": "Transcription error in final answer",
|
| 286 |
+
"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"
|
| 287 |
+
},
|
| 288 |
+
{
|
| 289 |
+
"task_id": "J2_magnitude_estimation_000447",
|
| 290 |
+
"task_type": "J2_error_detection",
|
| 291 |
+
"category": "magnitude_estimation",
|
| 292 |
+
"problem": "Which of the following is the best estimate for 9900 * 9900?",
|
| 293 |
+
"correct_answer": "98010000",
|
| 294 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 196020000",
|
| 295 |
+
"error_type": "wrong_operand",
|
| 296 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 297 |
+
"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"
|
| 298 |
+
},
|
| 299 |
+
{
|
| 300 |
+
"task_id": "J2_equation_reasoning_000732",
|
| 301 |
+
"task_type": "J2_error_detection",
|
| 302 |
+
"category": "equation_reasoning",
|
| 303 |
+
"problem": "What value fills the blank? 1558 × 4896 × 3652 = ___ × 3652 × 1558",
|
| 304 |
+
"correct_answer": "4896",
|
| 305 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 9792",
|
| 306 |
+
"error_type": "wrong_operand",
|
| 307 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 308 |
+
"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"
|
| 309 |
+
},
|
| 310 |
+
{
|
| 311 |
+
"task_id": "J2_option_elimination_000775",
|
| 312 |
+
"task_type": "J2_error_detection",
|
| 313 |
+
"category": "option_elimination",
|
| 314 |
+
"problem": "What is 5559 × 9837?",
|
| 315 |
+
"correct_answer": "54683883",
|
| 316 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 57418077",
|
| 317 |
+
"error_type": "wrong_rounding",
|
| 318 |
+
"error_description": "Rounded in the wrong direction",
|
| 319 |
+
"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"
|
| 320 |
+
},
|
| 321 |
+
{
|
| 322 |
+
"task_id": "J2_compatible_numbers_000611",
|
| 323 |
+
"task_type": "J2_error_detection",
|
| 324 |
+
"category": "compatible_numbers",
|
| 325 |
+
"problem": "Estimate 1273 × 7425.",
|
| 326 |
+
"correct_answer": "9452025",
|
| 327 |
+
"ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 9452023",
|
| 328 |
+
"error_type": "arithmetic_slip",
|
| 329 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 330 |
+
"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"
|
| 331 |
+
},
|
| 332 |
+
{
|
| 333 |
+
"task_id": "J2_cancellation_identity_000579",
|
| 334 |
+
"task_type": "J2_error_detection",
|
| 335 |
+
"category": "cancellation_identity",
|
| 336 |
+
"problem": "Evaluate: 1817 + 5124 - 5125",
|
| 337 |
+
"correct_answer": "1816",
|
| 338 |
+
"ns_solution_with_error": "Using Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1.\nApproximation gives: 908",
|
| 339 |
+
"error_type": "wrong_operand",
|
| 340 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 341 |
+
"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"
|
| 342 |
+
},
|
| 343 |
+
{
|
| 344 |
+
"task_id": "J2_structural_shortcuts_000496",
|
| 345 |
+
"task_type": "J2_error_detection",
|
| 346 |
+
"category": "structural_shortcuts",
|
| 347 |
+
"problem": "What is 9998 * 3721?",
|
| 348 |
+
"correct_answer": "37202558",
|
| 349 |
+
"ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 18601279",
|
| 350 |
+
"error_type": "wrong_operand",
|
| 351 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 352 |
+
"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"
|
| 353 |
+
},
|
| 354 |
+
{
|
| 355 |
+
"task_id": "J2_landmark_comparison_000686",
|
| 356 |
+
"task_type": "J2_error_detection",
|
| 357 |
+
"category": "landmark_comparison",
|
| 358 |
+
"problem": "Is 10% of 85760 greater than 36782?",
|
| 359 |
+
"correct_answer": "No",
|
| 360 |
+
"ns_solution_with_error": "Using Use 10% as landmark: 10% of 85760 = 8576.\nApproximation gives: 8148",
|
| 361 |
+
"error_type": "wrong_rounding",
|
| 362 |
+
"error_description": "Rounded in the wrong direction",
|
| 363 |
+
"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"
|
| 364 |
+
},
|
| 365 |
+
{
|
| 366 |
+
"task_id": "J2_landmark_comparison_000661",
|
| 367 |
+
"task_type": "J2_error_detection",
|
| 368 |
+
"category": "landmark_comparison",
|
| 369 |
+
"problem": "Is 27% of 97500 greater than 21848?",
|
| 370 |
+
"correct_answer": "Yes",
|
| 371 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 97500 = 24375.\nApproximation gives: 25009",
|
| 372 |
+
"error_type": "wrong_rounding",
|
| 373 |
+
"error_description": "Rounded in the wrong direction",
|
| 374 |
+
"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"
|
| 375 |
+
},
|
| 376 |
+
{
|
| 377 |
+
"task_id": "J2_relative_distance_000513",
|
| 378 |
+
"task_type": "J2_error_detection",
|
| 379 |
+
"category": "relative_distance",
|
| 380 |
+
"problem": "Which is larger: 884/1785 or 1924/3797?",
|
| 381 |
+
"correct_answer": "1924/3797",
|
| 382 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 5",
|
| 383 |
+
"error_type": "arithmetic_slip",
|
| 384 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 385 |
+
"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"
|
| 386 |
+
},
|
| 387 |
+
{
|
| 388 |
+
"task_id": "J2_compatible_numbers_000640",
|
| 389 |
+
"task_type": "J2_error_detection",
|
| 390 |
+
"category": "compatible_numbers",
|
| 391 |
+
"problem": "Estimate 1228 × 7243.",
|
| 392 |
+
"correct_answer": "8894404",
|
| 393 |
+
"ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 4447202",
|
| 394 |
+
"error_type": "wrong_operand",
|
| 395 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 396 |
+
"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"
|
| 397 |
+
},
|
| 398 |
+
{
|
| 399 |
+
"task_id": "J2_landmark_comparison_000691",
|
| 400 |
+
"task_type": "J2_error_detection",
|
| 401 |
+
"category": "landmark_comparison",
|
| 402 |
+
"problem": "Is 25% of 89710 greater than 36335?",
|
| 403 |
+
"correct_answer": "No",
|
| 404 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 89710 = 22427.\nApproximation gives: 23548",
|
| 405 |
+
"error_type": "wrong_rounding",
|
| 406 |
+
"error_description": "Rounded in the wrong direction",
|
| 407 |
+
"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"
|
| 408 |
+
},
|
| 409 |
+
{
|
| 410 |
+
"task_id": "J2_equation_reasoning_000724",
|
| 411 |
+
"task_type": "J2_error_detection",
|
| 412 |
+
"category": "equation_reasoning",
|
| 413 |
+
"problem": "What value fills the blank? 7951 × 5441 × 4817 = ___ × 4817 × 7951",
|
| 414 |
+
"correct_answer": "5441",
|
| 415 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 5438",
|
| 416 |
+
"error_type": "arithmetic_slip",
|
| 417 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 418 |
+
"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"
|
| 419 |
+
},
|
| 420 |
+
{
|
| 421 |
+
"task_id": "J2_cancellation_identity_000568",
|
| 422 |
+
"task_type": "J2_error_detection",
|
| 423 |
+
"category": "cancellation_identity",
|
| 424 |
+
"problem": "Evaluate: 9227 + 8064 - 8063",
|
| 425 |
+
"correct_answer": "9228",
|
| 426 |
+
"ns_solution_with_error": "Using Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1.\nApproximation gives: 9225",
|
| 427 |
+
"error_type": "arithmetic_slip",
|
| 428 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 429 |
+
"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"
|
| 430 |
+
},
|
| 431 |
+
{
|
| 432 |
+
"task_id": "J2_relative_distance_000519",
|
| 433 |
+
"task_type": "J2_error_detection",
|
| 434 |
+
"category": "relative_distance",
|
| 435 |
+
"problem": "Which is larger: 1536/3087 or 3213/6322?",
|
| 436 |
+
"correct_answer": "3213/6322",
|
| 437 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
|
| 438 |
+
"error_type": "transcription_error",
|
| 439 |
+
"error_description": "Transcription error in final answer",
|
| 440 |
+
"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"
|
| 441 |
+
},
|
| 442 |
+
{
|
| 443 |
+
"task_id": "J2_cancellation_identity_000565",
|
| 444 |
+
"task_type": "J2_error_detection",
|
| 445 |
+
"category": "cancellation_identity",
|
| 446 |
+
"problem": "Evaluate: 2712 + 6582 - 6583",
|
| 447 |
+
"correct_answer": "2711",
|
| 448 |
+
"ns_solution_with_error": "Using Near-cancellation: 6582 - 6583 = -1, so answer ≈ 2712 + -1.\nApproximation gives: 4711",
|
| 449 |
+
"error_type": "transcription_error",
|
| 450 |
+
"error_description": "Transcription error in final answer",
|
| 451 |
+
"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"
|
| 452 |
+
},
|
| 453 |
+
{
|
| 454 |
+
"task_id": "J2_landmark_comparison_000683",
|
| 455 |
+
"task_type": "J2_error_detection",
|
| 456 |
+
"category": "landmark_comparison",
|
| 457 |
+
"problem": "Is 27% of 87480 greater than 24547?",
|
| 458 |
+
"correct_answer": "No",
|
| 459 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 87480 = 21870.\nApproximation gives: 11809",
|
| 460 |
+
"error_type": "wrong_operand",
|
| 461 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 462 |
+
"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"
|
| 463 |
+
},
|
| 464 |
+
{
|
| 465 |
+
"task_id": "J2_relative_distance_000534",
|
| 466 |
+
"task_type": "J2_error_detection",
|
| 467 |
+
"category": "relative_distance",
|
| 468 |
+
"problem": "Which is larger: 4320/8812 or 1806/3591?",
|
| 469 |
+
"correct_answer": "1806/3591",
|
| 470 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
|
| 471 |
+
"error_type": "wrong_operand",
|
| 472 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 473 |
+
"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"
|
| 474 |
+
},
|
| 475 |
+
{
|
| 476 |
+
"task_id": "J2_magnitude_estimation_000409",
|
| 477 |
+
"task_type": "J2_error_detection",
|
| 478 |
+
"category": "magnitude_estimation",
|
| 479 |
+
"problem": "Which of the following is the best estimate for 10200 * 10100?",
|
| 480 |
+
"correct_answer": "103020000",
|
| 481 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 103320000",
|
| 482 |
+
"error_type": "transcription_error",
|
| 483 |
+
"error_description": "Transcription error in final answer",
|
| 484 |
+
"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"
|
| 485 |
+
},
|
| 486 |
+
{
|
| 487 |
+
"task_id": "J2_cancellation_identity_000596",
|
| 488 |
+
"task_type": "J2_error_detection",
|
| 489 |
+
"category": "cancellation_identity",
|
| 490 |
+
"problem": "Evaluate: 9205 + 6773 - 6772",
|
| 491 |
+
"correct_answer": "9206",
|
| 492 |
+
"ns_solution_with_error": "Using Near-cancellation: 6773 - 6772 = 1, so answer ≈ 9205 + 1.\nApproximation gives: 9306",
|
| 493 |
+
"error_type": "transcription_error",
|
| 494 |
+
"error_description": "Transcription error in final answer",
|
| 495 |
+
"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"
|
| 496 |
+
},
|
| 497 |
+
{
|
| 498 |
+
"task_id": "J2_structural_shortcuts_000470",
|
| 499 |
+
"task_type": "J2_error_detection",
|
| 500 |
+
"category": "structural_shortcuts",
|
| 501 |
+
"problem": "What is 9998 * 7447?",
|
| 502 |
+
"correct_answer": "74455106",
|
| 503 |
+
"ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 148910212",
|
| 504 |
+
"error_type": "wrong_operand",
|
| 505 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 506 |
+
"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"
|
| 507 |
+
},
|
| 508 |
+
{
|
| 509 |
+
"task_id": "J2_structural_shortcuts_000474",
|
| 510 |
+
"task_type": "J2_error_detection",
|
| 511 |
+
"category": "structural_shortcuts",
|
| 512 |
+
"problem": "What is 9999 * 5819?",
|
| 513 |
+
"correct_answer": "58184181",
|
| 514 |
+
"ns_solution_with_error": "Using Use (10000-1)*m = 10000*m - 1*m.\nApproximation gives: 29092090",
|
| 515 |
+
"error_type": "wrong_operand",
|
| 516 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 517 |
+
"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"
|
| 518 |
+
},
|
| 519 |
+
{
|
| 520 |
+
"task_id": "J2_option_elimination_000781",
|
| 521 |
+
"task_type": "J2_error_detection",
|
| 522 |
+
"category": "option_elimination",
|
| 523 |
+
"problem": "What is 1459 × 1977?",
|
| 524 |
+
"correct_answer": "2884443",
|
| 525 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 3884443",
|
| 526 |
+
"error_type": "transcription_error",
|
| 527 |
+
"error_description": "Transcription error in final answer",
|
| 528 |
+
"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"
|
| 529 |
+
},
|
| 530 |
+
{
|
| 531 |
+
"task_id": "J2_structural_shortcuts_000475",
|
| 532 |
+
"task_type": "J2_error_detection",
|
| 533 |
+
"category": "structural_shortcuts",
|
| 534 |
+
"problem": "What is 9998 * 9721?",
|
| 535 |
+
"correct_answer": "97190558",
|
| 536 |
+
"ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 102050085",
|
| 537 |
+
"error_type": "wrong_rounding",
|
| 538 |
+
"error_description": "Rounded in the wrong direction",
|
| 539 |
+
"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"
|
| 540 |
+
},
|
| 541 |
+
{
|
| 542 |
+
"task_id": "J2_landmark_comparison_000665",
|
| 543 |
+
"task_type": "J2_error_detection",
|
| 544 |
+
"category": "landmark_comparison",
|
| 545 |
+
"problem": "Is 27% of 34690 greater than 11606?",
|
| 546 |
+
"correct_answer": "No",
|
| 547 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 34690 = 8672.\nApproximation gives: 2366",
|
| 548 |
+
"error_type": "transcription_error",
|
| 549 |
+
"error_description": "Transcription error in final answer",
|
| 550 |
+
"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"
|
| 551 |
+
},
|
| 552 |
+
{
|
| 553 |
+
"task_id": "J2_magnitude_estimation_000446",
|
| 554 |
+
"task_type": "J2_error_detection",
|
| 555 |
+
"category": "magnitude_estimation",
|
| 556 |
+
"problem": "Which of the following is the best estimate for 10100 * 9900?",
|
| 557 |
+
"correct_answer": "99990000",
|
| 558 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 99990020",
|
| 559 |
+
"error_type": "transcription_error",
|
| 560 |
+
"error_description": "Transcription error in final answer",
|
| 561 |
+
"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"
|
| 562 |
+
},
|
| 563 |
+
{
|
| 564 |
+
"task_id": "J2_landmark_comparison_000679",
|
| 565 |
+
"task_type": "J2_error_detection",
|
| 566 |
+
"category": "landmark_comparison",
|
| 567 |
+
"problem": "Is 48% of 63500 greater than 24915?",
|
| 568 |
+
"correct_answer": "Yes",
|
| 569 |
+
"ns_solution_with_error": "Using Use 50% as landmark: 50% of 63500 = 31750.\nApproximation gives: 30477",
|
| 570 |
+
"error_type": "arithmetic_slip",
|
| 571 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 572 |
+
"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"
|
| 573 |
+
},
|
| 574 |
+
{
|
| 575 |
+
"task_id": "J2_structural_shortcuts_000499",
|
| 576 |
+
"task_type": "J2_error_detection",
|
| 577 |
+
"category": "structural_shortcuts",
|
| 578 |
+
"problem": "What is 9998 * 1050?",
|
| 579 |
+
"correct_answer": "10497900",
|
| 580 |
+
"ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 10497901",
|
| 581 |
+
"error_type": "arithmetic_slip",
|
| 582 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 583 |
+
"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"
|
| 584 |
+
},
|
| 585 |
+
{
|
| 586 |
+
"task_id": "J2_option_elimination_000771",
|
| 587 |
+
"task_type": "J2_error_detection",
|
| 588 |
+
"category": "option_elimination",
|
| 589 |
+
"problem": "What is 5562 × 7803?",
|
| 590 |
+
"correct_answer": "43400286",
|
| 591 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 41230272",
|
| 592 |
+
"error_type": "wrong_rounding",
|
| 593 |
+
"error_description": "Rounded in the wrong direction",
|
| 594 |
+
"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"
|
| 595 |
+
},
|
| 596 |
+
{
|
| 597 |
+
"task_id": "J2_magnitude_estimation_000419",
|
| 598 |
+
"task_type": "J2_error_detection",
|
| 599 |
+
"category": "magnitude_estimation",
|
| 600 |
+
"problem": "Which of the following is the best estimate for 10100 * 10100?",
|
| 601 |
+
"correct_answer": "102010000",
|
| 602 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 102210000",
|
| 603 |
+
"error_type": "transcription_error",
|
| 604 |
+
"error_description": "Transcription error in final answer",
|
| 605 |
+
"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"
|
| 606 |
+
},
|
| 607 |
+
{
|
| 608 |
+
"task_id": "J2_equation_reasoning_000737",
|
| 609 |
+
"task_type": "J2_error_detection",
|
| 610 |
+
"category": "equation_reasoning",
|
| 611 |
+
"problem": "What value fills the blank? 6741 × 2155 × 4707 = ___ × 4707 × 6741",
|
| 612 |
+
"correct_answer": "2155",
|
| 613 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2048",
|
| 614 |
+
"error_type": "wrong_rounding",
|
| 615 |
+
"error_description": "Rounded in the wrong direction",
|
| 616 |
+
"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"
|
| 617 |
+
},
|
| 618 |
+
{
|
| 619 |
+
"task_id": "J2_cancellation_identity_000578",
|
| 620 |
+
"task_type": "J2_error_detection",
|
| 621 |
+
"category": "cancellation_identity",
|
| 622 |
+
"problem": "Evaluate: 5722 + 2063 - 2062",
|
| 623 |
+
"correct_answer": "5723",
|
| 624 |
+
"ns_solution_with_error": "Using Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1.\nApproximation gives: 5724",
|
| 625 |
+
"error_type": "arithmetic_slip",
|
| 626 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 627 |
+
"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"
|
| 628 |
+
},
|
| 629 |
+
{
|
| 630 |
+
"task_id": "J2_equation_reasoning_000736",
|
| 631 |
+
"task_type": "J2_error_detection",
|
| 632 |
+
"category": "equation_reasoning",
|
| 633 |
+
"problem": "What value fills the blank? 3230 × (5915 + 1005) = 3230 × ___ + 3230 × 1005",
|
| 634 |
+
"correct_answer": "5915",
|
| 635 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2957",
|
| 636 |
+
"error_type": "wrong_operand",
|
| 637 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 638 |
+
"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"
|
| 639 |
+
},
|
| 640 |
+
{
|
| 641 |
+
"task_id": "J2_structural_shortcuts_000481",
|
| 642 |
+
"task_type": "J2_error_detection",
|
| 643 |
+
"category": "structural_shortcuts",
|
| 644 |
+
"problem": "What is 9998 * 4811?",
|
| 645 |
+
"correct_answer": "48100378",
|
| 646 |
+
"ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 48100398",
|
| 647 |
+
"error_type": "transcription_error",
|
| 648 |
+
"error_description": "Transcription error in final answer",
|
| 649 |
+
"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"
|
| 650 |
+
},
|
| 651 |
+
{
|
| 652 |
+
"task_id": "J2_magnitude_estimation_000433",
|
| 653 |
+
"task_type": "J2_error_detection",
|
| 654 |
+
"category": "magnitude_estimation",
|
| 655 |
+
"problem": "Which of the following is the best estimate for 10200 * 9800?",
|
| 656 |
+
"correct_answer": "99960000",
|
| 657 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 94962000",
|
| 658 |
+
"error_type": "wrong_rounding",
|
| 659 |
+
"error_description": "Rounded in the wrong direction",
|
| 660 |
+
"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"
|
| 661 |
+
},
|
| 662 |
+
{
|
| 663 |
+
"task_id": "J2_relative_distance_000547",
|
| 664 |
+
"task_type": "J2_error_detection",
|
| 665 |
+
"category": "relative_distance",
|
| 666 |
+
"problem": "Which is larger: 1518/3038 or 3432/6744?",
|
| 667 |
+
"correct_answer": "3432/6744",
|
| 668 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
|
| 669 |
+
"error_type": "transcription_error",
|
| 670 |
+
"error_description": "Transcription error in final answer",
|
| 671 |
+
"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"
|
| 672 |
+
},
|
| 673 |
+
{
|
| 674 |
+
"task_id": "J2_cancellation_identity_000567",
|
| 675 |
+
"task_type": "J2_error_detection",
|
| 676 |
+
"category": "cancellation_identity",
|
| 677 |
+
"problem": "Evaluate: 4064 + 5375 - 5377",
|
| 678 |
+
"correct_answer": "4062",
|
| 679 |
+
"ns_solution_with_error": "Using Near-cancellation: 5375 - 5377 = -2, so answer ≈ 4064 + -2.\nApproximation gives: 4262",
|
| 680 |
+
"error_type": "transcription_error",
|
| 681 |
+
"error_description": "Transcription error in final answer",
|
| 682 |
+
"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"
|
| 683 |
+
},
|
| 684 |
+
{
|
| 685 |
+
"task_id": "J2_equation_reasoning_000702",
|
| 686 |
+
"task_type": "J2_error_detection",
|
| 687 |
+
"category": "equation_reasoning",
|
| 688 |
+
"problem": "What value fills the blank? 8731 × 2490 × 7066 = ___ × 7066 × 8731",
|
| 689 |
+
"correct_answer": "2490",
|
| 690 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 2614",
|
| 691 |
+
"error_type": "wrong_rounding",
|
| 692 |
+
"error_description": "Rounded in the wrong direction",
|
| 693 |
+
"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"
|
| 694 |
+
},
|
| 695 |
+
{
|
| 696 |
+
"task_id": "J2_option_elimination_000801",
|
| 697 |
+
"task_type": "J2_error_detection",
|
| 698 |
+
"category": "option_elimination",
|
| 699 |
+
"problem": "What is 2531 × 7515?",
|
| 700 |
+
"correct_answer": "19020465",
|
| 701 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 9510232",
|
| 702 |
+
"error_type": "wrong_operand",
|
| 703 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 704 |
+
"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"
|
| 705 |
+
},
|
| 706 |
+
{
|
| 707 |
+
"task_id": "J2_option_elimination_000794",
|
| 708 |
+
"task_type": "J2_error_detection",
|
| 709 |
+
"category": "option_elimination",
|
| 710 |
+
"problem": "What is 2277 × 4068?",
|
| 711 |
+
"correct_answer": "9262836",
|
| 712 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 8799695",
|
| 713 |
+
"error_type": "wrong_rounding",
|
| 714 |
+
"error_description": "Rounded in the wrong direction",
|
| 715 |
+
"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"
|
| 716 |
+
},
|
| 717 |
+
{
|
| 718 |
+
"task_id": "J2_cancellation_identity_000585",
|
| 719 |
+
"task_type": "J2_error_detection",
|
| 720 |
+
"category": "cancellation_identity",
|
| 721 |
+
"problem": "Evaluate: 4359 + 9463 - 9464",
|
| 722 |
+
"correct_answer": "4358",
|
| 723 |
+
"ns_solution_with_error": "Using Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1.\nApproximation gives: 8716",
|
| 724 |
+
"error_type": "wrong_operand",
|
| 725 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 726 |
+
"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"
|
| 727 |
+
},
|
| 728 |
+
{
|
| 729 |
+
"task_id": "J2_compatible_numbers_000623",
|
| 730 |
+
"task_type": "J2_error_detection",
|
| 731 |
+
"category": "compatible_numbers",
|
| 732 |
+
"problem": "Estimate 4966 × 1988.",
|
| 733 |
+
"correct_answer": "9872408",
|
| 734 |
+
"ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 19744816",
|
| 735 |
+
"error_type": "wrong_operand",
|
| 736 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 737 |
+
"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"
|
| 738 |
+
},
|
| 739 |
+
{
|
| 740 |
+
"task_id": "J2_relative_distance_000520",
|
| 741 |
+
"task_type": "J2_error_detection",
|
| 742 |
+
"category": "relative_distance",
|
| 743 |
+
"problem": "Which is larger: 4625/9376 or 2049/4061?",
|
| 744 |
+
"correct_answer": "2049/4061",
|
| 745 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
|
| 746 |
+
"error_type": "wrong_operand",
|
| 747 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 748 |
+
"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"
|
| 749 |
+
},
|
| 750 |
+
{
|
| 751 |
+
"task_id": "J2_relative_distance_000501",
|
| 752 |
+
"task_type": "J2_error_detection",
|
| 753 |
+
"category": "relative_distance",
|
| 754 |
+
"problem": "Which is larger: 3746/7556 or 1181/2333?",
|
| 755 |
+
"correct_answer": "1181/2333",
|
| 756 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: -4",
|
| 757 |
+
"error_type": "arithmetic_slip",
|
| 758 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 759 |
+
"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"
|
| 760 |
+
},
|
| 761 |
+
{
|
| 762 |
+
"task_id": "J2_compatible_numbers_000638",
|
| 763 |
+
"task_type": "J2_error_detection",
|
| 764 |
+
"category": "compatible_numbers",
|
| 765 |
+
"problem": "Estimate 2548 × 3929.",
|
| 766 |
+
"correct_answer": "10011092",
|
| 767 |
+
"ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 10011093",
|
| 768 |
+
"error_type": "transcription_error",
|
| 769 |
+
"error_description": "Transcription error in final answer",
|
| 770 |
+
"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"
|
| 771 |
+
},
|
| 772 |
+
{
|
| 773 |
+
"task_id": "J2_compatible_numbers_000608",
|
| 774 |
+
"task_type": "J2_error_detection",
|
| 775 |
+
"category": "compatible_numbers",
|
| 776 |
+
"problem": "Estimate 5009 × 1968.",
|
| 777 |
+
"correct_answer": "9857712",
|
| 778 |
+
"ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 10350597",
|
| 779 |
+
"error_type": "wrong_rounding",
|
| 780 |
+
"error_description": "Rounded in the wrong direction",
|
| 781 |
+
"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"
|
| 782 |
+
},
|
| 783 |
+
{
|
| 784 |
+
"task_id": "J2_landmark_comparison_000659",
|
| 785 |
+
"task_type": "J2_error_detection",
|
| 786 |
+
"category": "landmark_comparison",
|
| 787 |
+
"problem": "Is 10% of 71650 greater than 29517?",
|
| 788 |
+
"correct_answer": "No",
|
| 789 |
+
"ns_solution_with_error": "Using Use 10% as landmark: 10% of 71650 = 7165.\nApproximation gives: 7166",
|
| 790 |
+
"error_type": "transcription_error",
|
| 791 |
+
"error_description": "Transcription error in final answer",
|
| 792 |
+
"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"
|
| 793 |
+
},
|
| 794 |
+
{
|
| 795 |
+
"task_id": "J2_structural_shortcuts_000471",
|
| 796 |
+
"task_type": "J2_error_detection",
|
| 797 |
+
"category": "structural_shortcuts",
|
| 798 |
+
"problem": "What is 9998 * 7041?",
|
| 799 |
+
"correct_answer": "70395918",
|
| 800 |
+
"ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 70395915",
|
| 801 |
+
"error_type": "arithmetic_slip",
|
| 802 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 803 |
+
"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"
|
| 804 |
+
},
|
| 805 |
+
{
|
| 806 |
+
"task_id": "J2_relative_distance_000523",
|
| 807 |
+
"task_type": "J2_error_detection",
|
| 808 |
+
"category": "relative_distance",
|
| 809 |
+
"problem": "Which is larger: 1473/2971 or 843/1672?",
|
| 810 |
+
"correct_answer": "843/1672",
|
| 811 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
|
| 812 |
+
"error_type": "transcription_error",
|
| 813 |
+
"error_description": "Transcription error in final answer",
|
| 814 |
+
"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"
|
| 815 |
+
},
|
| 816 |
+
{
|
| 817 |
+
"task_id": "J2_magnitude_estimation_000422",
|
| 818 |
+
"task_type": "J2_error_detection",
|
| 819 |
+
"category": "magnitude_estimation",
|
| 820 |
+
"problem": "Which of the following is the best estimate for 9800 * 10200?",
|
| 821 |
+
"correct_answer": "99960000",
|
| 822 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 94962000",
|
| 823 |
+
"error_type": "wrong_rounding",
|
| 824 |
+
"error_description": "Rounded in the wrong direction",
|
| 825 |
+
"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"
|
| 826 |
+
},
|
| 827 |
+
{
|
| 828 |
+
"task_id": "J2_cancellation_identity_000591",
|
| 829 |
+
"task_type": "J2_error_detection",
|
| 830 |
+
"category": "cancellation_identity",
|
| 831 |
+
"problem": "Evaluate: 8528 + 3299 - 3298",
|
| 832 |
+
"correct_answer": "8529",
|
| 833 |
+
"ns_solution_with_error": "Using Near-cancellation: 3299 - 3298 = 1, so answer ≈ 8528 + 1.\nApproximation gives: 17058",
|
| 834 |
+
"error_type": "wrong_operand",
|
| 835 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 836 |
+
"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"
|
| 837 |
+
},
|
| 838 |
+
{
|
| 839 |
+
"task_id": "J2_equation_reasoning_000738",
|
| 840 |
+
"task_type": "J2_error_detection",
|
| 841 |
+
"category": "equation_reasoning",
|
| 842 |
+
"problem": "What value fills the blank? 4804 + 8180 = ___ + 5895",
|
| 843 |
+
"correct_answer": "7089",
|
| 844 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 7092",
|
| 845 |
+
"error_type": "arithmetic_slip",
|
| 846 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 847 |
+
"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"
|
| 848 |
+
},
|
| 849 |
+
{
|
| 850 |
+
"task_id": "J2_landmark_comparison_000663",
|
| 851 |
+
"task_type": "J2_error_detection",
|
| 852 |
+
"category": "landmark_comparison",
|
| 853 |
+
"problem": "Is 10% of 75230 greater than 17577?",
|
| 854 |
+
"correct_answer": "No",
|
| 855 |
+
"ns_solution_with_error": "Using Use 10% as landmark: 10% of 75230 = 7523.\nApproximation gives: 7147",
|
| 856 |
+
"error_type": "wrong_rounding",
|
| 857 |
+
"error_description": "Rounded in the wrong direction",
|
| 858 |
+
"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"
|
| 859 |
+
},
|
| 860 |
+
{
|
| 861 |
+
"task_id": "J2_structural_shortcuts_000484",
|
| 862 |
+
"task_type": "J2_error_detection",
|
| 863 |
+
"category": "structural_shortcuts",
|
| 864 |
+
"problem": "What is 10001 * 4007?",
|
| 865 |
+
"correct_answer": "40074007",
|
| 866 |
+
"ns_solution_with_error": "Using Use (10000+1)*m = 10000*m + 1*m.\nApproximation gives: 38070307",
|
| 867 |
+
"error_type": "wrong_rounding",
|
| 868 |
+
"error_description": "Rounded in the wrong direction",
|
| 869 |
+
"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"
|
| 870 |
+
},
|
| 871 |
+
{
|
| 872 |
+
"task_id": "J2_compatible_numbers_000619",
|
| 873 |
+
"task_type": "J2_error_detection",
|
| 874 |
+
"category": "compatible_numbers",
|
| 875 |
+
"problem": "Estimate 1274 × 8677.",
|
| 876 |
+
"correct_answer": "11054498",
|
| 877 |
+
"ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 22108996",
|
| 878 |
+
"error_type": "wrong_operand",
|
| 879 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 880 |
+
"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"
|
| 881 |
+
},
|
| 882 |
+
{
|
| 883 |
+
"task_id": "J2_cancellation_identity_000558",
|
| 884 |
+
"task_type": "J2_error_detection",
|
| 885 |
+
"category": "cancellation_identity",
|
| 886 |
+
"problem": "Evaluate: 3344 + 1236 - 1234",
|
| 887 |
+
"correct_answer": "3346",
|
| 888 |
+
"ns_solution_with_error": "Using Near-cancellation: 1236 - 1234 = 2, so answer ≈ 3344 + 2.\nApproximation gives: 3342",
|
| 889 |
+
"error_type": "arithmetic_slip",
|
| 890 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 891 |
+
"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"
|
| 892 |
+
},
|
| 893 |
+
{
|
| 894 |
+
"task_id": "J2_structural_shortcuts_000492",
|
| 895 |
+
"task_type": "J2_error_detection",
|
| 896 |
+
"category": "structural_shortcuts",
|
| 897 |
+
"problem": "What is 9998 * 2912?",
|
| 898 |
+
"correct_answer": "29114176",
|
| 899 |
+
"ns_solution_with_error": "Using Use (10000-2)*m = 10000*m - 2*m.\nApproximation gives: 21114176",
|
| 900 |
+
"error_type": "transcription_error",
|
| 901 |
+
"error_description": "Transcription error in final answer",
|
| 902 |
+
"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"
|
| 903 |
+
},
|
| 904 |
+
{
|
| 905 |
+
"task_id": "J2_landmark_comparison_000699",
|
| 906 |
+
"task_type": "J2_error_detection",
|
| 907 |
+
"category": "landmark_comparison",
|
| 908 |
+
"problem": "Is 11% of 57250 greater than 11559?",
|
| 909 |
+
"correct_answer": "No",
|
| 910 |
+
"ns_solution_with_error": "Using Use 10% as landmark: 10% of 57250 = 5725.\nApproximation gives: 6497",
|
| 911 |
+
"error_type": "transcription_error",
|
| 912 |
+
"error_description": "Transcription error in final answer",
|
| 913 |
+
"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"
|
| 914 |
+
},
|
| 915 |
+
{
|
| 916 |
+
"task_id": "J2_relative_distance_000506",
|
| 917 |
+
"task_type": "J2_error_detection",
|
| 918 |
+
"category": "relative_distance",
|
| 919 |
+
"problem": "Which is larger: 4901/9978 or 3743/7451?",
|
| 920 |
+
"correct_answer": "3743/7451",
|
| 921 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
|
| 922 |
+
"error_type": "wrong_operand",
|
| 923 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 924 |
+
"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"
|
| 925 |
+
},
|
| 926 |
+
{
|
| 927 |
+
"task_id": "J2_option_elimination_000786",
|
| 928 |
+
"task_type": "J2_error_detection",
|
| 929 |
+
"category": "option_elimination",
|
| 930 |
+
"problem": "What is 3972 × 8996?",
|
| 931 |
+
"correct_answer": "35732112",
|
| 932 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 37732112",
|
| 933 |
+
"error_type": "transcription_error",
|
| 934 |
+
"error_description": "Transcription error in final answer",
|
| 935 |
+
"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"
|
| 936 |
+
},
|
| 937 |
+
{
|
| 938 |
+
"task_id": "J2_equation_reasoning_000708",
|
| 939 |
+
"task_type": "J2_error_detection",
|
| 940 |
+
"category": "equation_reasoning",
|
| 941 |
+
"problem": "What value fills the blank? 3791 + 6639 = ___ + 3553",
|
| 942 |
+
"correct_answer": "6877",
|
| 943 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 6870",
|
| 944 |
+
"error_type": "transcription_error",
|
| 945 |
+
"error_description": "Transcription error in final answer",
|
| 946 |
+
"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"
|
| 947 |
+
},
|
| 948 |
+
{
|
| 949 |
+
"task_id": "J2_equation_reasoning_000748",
|
| 950 |
+
"task_type": "J2_error_detection",
|
| 951 |
+
"category": "equation_reasoning",
|
| 952 |
+
"problem": "What value fills the blank? 3807 + 1362 + ___ = 1362 + 8347 + 3807",
|
| 953 |
+
"correct_answer": "8347",
|
| 954 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 8352",
|
| 955 |
+
"error_type": "arithmetic_slip",
|
| 956 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 957 |
+
"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"
|
| 958 |
+
},
|
| 959 |
+
{
|
| 960 |
+
"task_id": "J2_structural_shortcuts_000453",
|
| 961 |
+
"task_type": "J2_error_detection",
|
| 962 |
+
"category": "structural_shortcuts",
|
| 963 |
+
"problem": "What is 10002 * 7131?",
|
| 964 |
+
"correct_answer": "71324262",
|
| 965 |
+
"ns_solution_with_error": "Using Use (10000+2)*m = 10000*m + 2*m.\nApproximation gives: 71324258",
|
| 966 |
+
"error_type": "arithmetic_slip",
|
| 967 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 968 |
+
"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"
|
| 969 |
+
},
|
| 970 |
+
{
|
| 971 |
+
"task_id": "J2_relative_distance_000532",
|
| 972 |
+
"task_type": "J2_error_detection",
|
| 973 |
+
"category": "relative_distance",
|
| 974 |
+
"problem": "Which is larger: 1971/3979 or 3695/7308?",
|
| 975 |
+
"correct_answer": "3695/7308",
|
| 976 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 1",
|
| 977 |
+
"error_type": "wrong_rounding",
|
| 978 |
+
"error_description": "Rounded in the wrong direction",
|
| 979 |
+
"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"
|
| 980 |
+
},
|
| 981 |
+
{
|
| 982 |
+
"task_id": "J2_compatible_numbers_000610",
|
| 983 |
+
"task_type": "J2_error_detection",
|
| 984 |
+
"category": "compatible_numbers",
|
| 985 |
+
"problem": "Estimate 1273 × 7425.",
|
| 986 |
+
"correct_answer": "9452025",
|
| 987 |
+
"ns_solution_with_error": "Using Round to 1250×8000 for easy mental computation.\nApproximation gives: 9452028",
|
| 988 |
+
"error_type": "arithmetic_slip",
|
| 989 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 990 |
+
"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"
|
| 991 |
+
},
|
| 992 |
+
{
|
| 993 |
+
"task_id": "J2_magnitude_estimation_000442",
|
| 994 |
+
"task_type": "J2_error_detection",
|
| 995 |
+
"category": "magnitude_estimation",
|
| 996 |
+
"problem": "Which of the following is the best estimate for 9800 * 9800?",
|
| 997 |
+
"correct_answer": "96040000",
|
| 998 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 192080000",
|
| 999 |
+
"error_type": "wrong_operand",
|
| 1000 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1001 |
+
"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"
|
| 1002 |
+
},
|
| 1003 |
+
{
|
| 1004 |
+
"task_id": "J2_landmark_comparison_000678",
|
| 1005 |
+
"task_type": "J2_error_detection",
|
| 1006 |
+
"category": "landmark_comparison",
|
| 1007 |
+
"problem": "Is 23% of 55000 greater than 22317?",
|
| 1008 |
+
"correct_answer": "No",
|
| 1009 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 55000 = 13750.\nApproximation gives: 6325",
|
| 1010 |
+
"error_type": "wrong_operand",
|
| 1011 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1012 |
+
"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"
|
| 1013 |
+
},
|
| 1014 |
+
{
|
| 1015 |
+
"task_id": "J2_landmark_comparison_000660",
|
| 1016 |
+
"task_type": "J2_error_detection",
|
| 1017 |
+
"category": "landmark_comparison",
|
| 1018 |
+
"problem": "Is 27% of 31870 greater than 12925?",
|
| 1019 |
+
"correct_answer": "No",
|
| 1020 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 31870 = 7967.\nApproximation gives: 17209",
|
| 1021 |
+
"error_type": "wrong_operand",
|
| 1022 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1023 |
+
"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"
|
| 1024 |
+
},
|
| 1025 |
+
{
|
| 1026 |
+
"task_id": "J2_equation_reasoning_000726",
|
| 1027 |
+
"task_type": "J2_error_detection",
|
| 1028 |
+
"category": "equation_reasoning",
|
| 1029 |
+
"problem": "What value fills the blank? 1264 + 1118 = ___ + 7226",
|
| 1030 |
+
"correct_answer": "-4844",
|
| 1031 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: -4854",
|
| 1032 |
+
"error_type": "transcription_error",
|
| 1033 |
+
"error_description": "Transcription error in final answer",
|
| 1034 |
+
"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"
|
| 1035 |
+
},
|
| 1036 |
+
{
|
| 1037 |
+
"task_id": "J2_relative_distance_000524",
|
| 1038 |
+
"task_type": "J2_error_detection",
|
| 1039 |
+
"category": "relative_distance",
|
| 1040 |
+
"problem": "Which is larger: 1837/3735 or 2765/5491?",
|
| 1041 |
+
"correct_answer": "2765/5491",
|
| 1042 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 0",
|
| 1043 |
+
"error_type": "wrong_rounding",
|
| 1044 |
+
"error_description": "Rounded in the wrong direction",
|
| 1045 |
+
"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"
|
| 1046 |
+
},
|
| 1047 |
+
{
|
| 1048 |
+
"task_id": "J2_relative_distance_000546",
|
| 1049 |
+
"task_type": "J2_error_detection",
|
| 1050 |
+
"category": "relative_distance",
|
| 1051 |
+
"problem": "Which is larger: 3607/7251 or 2876/5669?",
|
| 1052 |
+
"correct_answer": "2876/5669",
|
| 1053 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: -2",
|
| 1054 |
+
"error_type": "arithmetic_slip",
|
| 1055 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1056 |
+
"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"
|
| 1057 |
+
},
|
| 1058 |
+
{
|
| 1059 |
+
"task_id": "J2_option_elimination_000792",
|
| 1060 |
+
"task_type": "J2_error_detection",
|
| 1061 |
+
"category": "option_elimination",
|
| 1062 |
+
"problem": "What is 4893 × 1523?",
|
| 1063 |
+
"correct_answer": "7452039",
|
| 1064 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 14904078",
|
| 1065 |
+
"error_type": "wrong_operand",
|
| 1066 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1067 |
+
"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"
|
| 1068 |
+
},
|
| 1069 |
+
{
|
| 1070 |
+
"task_id": "J2_cancellation_identity_000554",
|
| 1071 |
+
"task_type": "J2_error_detection",
|
| 1072 |
+
"category": "cancellation_identity",
|
| 1073 |
+
"problem": "Evaluate: 6105 + 3719 - 3720",
|
| 1074 |
+
"correct_answer": "6104",
|
| 1075 |
+
"ns_solution_with_error": "Using Near-cancellation: 3719 - 3720 = -1, so answer ≈ 6105 + -1.\nApproximation gives: 6409",
|
| 1076 |
+
"error_type": "wrong_rounding",
|
| 1077 |
+
"error_description": "Rounded in the wrong direction",
|
| 1078 |
+
"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"
|
| 1079 |
+
},
|
| 1080 |
+
{
|
| 1081 |
+
"task_id": "J2_option_elimination_000789",
|
| 1082 |
+
"task_type": "J2_error_detection",
|
| 1083 |
+
"category": "option_elimination",
|
| 1084 |
+
"problem": "What is 3121 × 1321?",
|
| 1085 |
+
"correct_answer": "4122841",
|
| 1086 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 4122838",
|
| 1087 |
+
"error_type": "arithmetic_slip",
|
| 1088 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1089 |
+
"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"
|
| 1090 |
+
},
|
| 1091 |
+
{
|
| 1092 |
+
"task_id": "J2_equation_reasoning_000717",
|
| 1093 |
+
"task_type": "J2_error_detection",
|
| 1094 |
+
"category": "equation_reasoning",
|
| 1095 |
+
"problem": "What value fills the blank? 6336 + 4267 = ___ + 4522",
|
| 1096 |
+
"correct_answer": "6081",
|
| 1097 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 3040",
|
| 1098 |
+
"error_type": "wrong_operand",
|
| 1099 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1100 |
+
"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"
|
| 1101 |
+
},
|
| 1102 |
+
{
|
| 1103 |
+
"task_id": "J2_relative_distance_000533",
|
| 1104 |
+
"task_type": "J2_error_detection",
|
| 1105 |
+
"category": "relative_distance",
|
| 1106 |
+
"problem": "Which is larger: 3415/6937 or 4397/8764?",
|
| 1107 |
+
"correct_answer": "4397/8764",
|
| 1108 |
+
"ns_solution_with_error": "Using One is below 1/2, the other above; no computation needed.\nApproximation gives: 5",
|
| 1109 |
+
"error_type": "arithmetic_slip",
|
| 1110 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1111 |
+
"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"
|
| 1112 |
+
},
|
| 1113 |
+
{
|
| 1114 |
+
"task_id": "J2_cancellation_identity_000566",
|
| 1115 |
+
"task_type": "J2_error_detection",
|
| 1116 |
+
"category": "cancellation_identity",
|
| 1117 |
+
"problem": "Evaluate: 7556 + 4084 - 4086",
|
| 1118 |
+
"correct_answer": "7554",
|
| 1119 |
+
"ns_solution_with_error": "Using Near-cancellation: 4084 - 4086 = -2, so answer ≈ 7556 + -2.\nApproximation gives: 7555",
|
| 1120 |
+
"error_type": "arithmetic_slip",
|
| 1121 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1122 |
+
"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"
|
| 1123 |
+
},
|
| 1124 |
+
{
|
| 1125 |
+
"task_id": "J2_option_elimination_000772",
|
| 1126 |
+
"task_type": "J2_error_detection",
|
| 1127 |
+
"category": "option_elimination",
|
| 1128 |
+
"problem": "What is 2726 × 5890?",
|
| 1129 |
+
"correct_answer": "16056140",
|
| 1130 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 8028070",
|
| 1131 |
+
"error_type": "wrong_operand",
|
| 1132 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1133 |
+
"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"
|
| 1134 |
+
},
|
| 1135 |
+
{
|
| 1136 |
+
"task_id": "J2_landmark_comparison_000669",
|
| 1137 |
+
"task_type": "J2_error_detection",
|
| 1138 |
+
"category": "landmark_comparison",
|
| 1139 |
+
"problem": "Is 27% of 18930 greater than 6267?",
|
| 1140 |
+
"correct_answer": "No",
|
| 1141 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 18930 = 4732.\nApproximation gives: 5116",
|
| 1142 |
+
"error_type": "arithmetic_slip",
|
| 1143 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1144 |
+
"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"
|
| 1145 |
+
},
|
| 1146 |
+
{
|
| 1147 |
+
"task_id": "J2_magnitude_estimation_000401",
|
| 1148 |
+
"task_type": "J2_error_detection",
|
| 1149 |
+
"category": "magnitude_estimation",
|
| 1150 |
+
"problem": "Which of the following is the best estimate for 10200 * 10100?",
|
| 1151 |
+
"correct_answer": "103020000",
|
| 1152 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 51510000",
|
| 1153 |
+
"error_type": "wrong_operand",
|
| 1154 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1155 |
+
"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"
|
| 1156 |
+
},
|
| 1157 |
+
{
|
| 1158 |
+
"task_id": "J2_compatible_numbers_000625",
|
| 1159 |
+
"task_type": "J2_error_detection",
|
| 1160 |
+
"category": "compatible_numbers",
|
| 1161 |
+
"problem": "Estimate 4910 × 1977.",
|
| 1162 |
+
"correct_answer": "9707070",
|
| 1163 |
+
"ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9221717",
|
| 1164 |
+
"error_type": "wrong_rounding",
|
| 1165 |
+
"error_description": "Rounded in the wrong direction",
|
| 1166 |
+
"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"
|
| 1167 |
+
},
|
| 1168 |
+
{
|
| 1169 |
+
"task_id": "J2_cancellation_identity_000600",
|
| 1170 |
+
"task_type": "J2_error_detection",
|
| 1171 |
+
"category": "cancellation_identity",
|
| 1172 |
+
"problem": "Evaluate: 2704 + 1588 - 1586",
|
| 1173 |
+
"correct_answer": "2706",
|
| 1174 |
+
"ns_solution_with_error": "Using Near-cancellation: 1588 - 1586 = 2, so answer ≈ 2704 + 2.\nApproximation gives: 2571",
|
| 1175 |
+
"error_type": "wrong_rounding",
|
| 1176 |
+
"error_description": "Rounded in the wrong direction",
|
| 1177 |
+
"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"
|
| 1178 |
+
},
|
| 1179 |
+
{
|
| 1180 |
+
"task_id": "J2_magnitude_estimation_000426",
|
| 1181 |
+
"task_type": "J2_error_detection",
|
| 1182 |
+
"category": "magnitude_estimation",
|
| 1183 |
+
"problem": "Which of the following is the best estimate for 10200 * 9900?",
|
| 1184 |
+
"correct_answer": "100980000",
|
| 1185 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 100980004",
|
| 1186 |
+
"error_type": "arithmetic_slip",
|
| 1187 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1188 |
+
"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"
|
| 1189 |
+
},
|
| 1190 |
+
{
|
| 1191 |
+
"task_id": "J2_compatible_numbers_000648",
|
| 1192 |
+
"task_type": "J2_error_detection",
|
| 1193 |
+
"category": "compatible_numbers",
|
| 1194 |
+
"problem": "Estimate 2520 × 3623.",
|
| 1195 |
+
"correct_answer": "9129960",
|
| 1196 |
+
"ns_solution_with_error": "Using Round to 2500×4000 for easy mental computation.\nApproximation gives: 9129962",
|
| 1197 |
+
"error_type": "arithmetic_slip",
|
| 1198 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1199 |
+
"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"
|
| 1200 |
+
},
|
| 1201 |
+
{
|
| 1202 |
+
"task_id": "J2_option_elimination_000760",
|
| 1203 |
+
"task_type": "J2_error_detection",
|
| 1204 |
+
"category": "option_elimination",
|
| 1205 |
+
"problem": "What is 5927 × 1249?",
|
| 1206 |
+
"correct_answer": "7402823",
|
| 1207 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 7402824",
|
| 1208 |
+
"error_type": "arithmetic_slip",
|
| 1209 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1210 |
+
"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"
|
| 1211 |
+
},
|
| 1212 |
+
{
|
| 1213 |
+
"task_id": "J2_equation_reasoning_000716",
|
| 1214 |
+
"task_type": "J2_error_detection",
|
| 1215 |
+
"category": "equation_reasoning",
|
| 1216 |
+
"problem": "What value fills the blank? 7447 + 7834 = ___ + 1092",
|
| 1217 |
+
"correct_answer": "14189",
|
| 1218 |
+
"ns_solution_with_error": "Using Recognize commutativity/distributive law — matching terms cancel.\nApproximation gives: 14184",
|
| 1219 |
+
"error_type": "arithmetic_slip",
|
| 1220 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1221 |
+
"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"
|
| 1222 |
+
},
|
| 1223 |
+
{
|
| 1224 |
+
"task_id": "J2_compatible_numbers_000617",
|
| 1225 |
+
"task_type": "J2_error_detection",
|
| 1226 |
+
"category": "compatible_numbers",
|
| 1227 |
+
"problem": "Estimate 4966 × 1988.",
|
| 1228 |
+
"correct_answer": "9872408",
|
| 1229 |
+
"ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 9378788",
|
| 1230 |
+
"error_type": "wrong_rounding",
|
| 1231 |
+
"error_description": "Rounded in the wrong direction",
|
| 1232 |
+
"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"
|
| 1233 |
+
},
|
| 1234 |
+
{
|
| 1235 |
+
"task_id": "J2_compatible_numbers_000633",
|
| 1236 |
+
"task_type": "J2_error_detection",
|
| 1237 |
+
"category": "compatible_numbers",
|
| 1238 |
+
"problem": "Estimate 4960 × 2196.",
|
| 1239 |
+
"correct_answer": "10892160",
|
| 1240 |
+
"ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 5446080",
|
| 1241 |
+
"error_type": "wrong_operand",
|
| 1242 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1243 |
+
"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"
|
| 1244 |
+
},
|
| 1245 |
+
{
|
| 1246 |
+
"task_id": "J2_option_elimination_000776",
|
| 1247 |
+
"task_type": "J2_error_detection",
|
| 1248 |
+
"category": "option_elimination",
|
| 1249 |
+
"problem": "What is 6135 × 7717?",
|
| 1250 |
+
"correct_answer": "47343795",
|
| 1251 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 47343705",
|
| 1252 |
+
"error_type": "transcription_error",
|
| 1253 |
+
"error_description": "Transcription error in final answer",
|
| 1254 |
+
"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"
|
| 1255 |
+
},
|
| 1256 |
+
{
|
| 1257 |
+
"task_id": "J2_magnitude_estimation_000403",
|
| 1258 |
+
"task_type": "J2_error_detection",
|
| 1259 |
+
"category": "magnitude_estimation",
|
| 1260 |
+
"problem": "Which of the following is the best estimate for 10200 * 10200?",
|
| 1261 |
+
"correct_answer": "104040000",
|
| 1262 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 98838000",
|
| 1263 |
+
"error_type": "wrong_rounding",
|
| 1264 |
+
"error_description": "Rounded in the wrong direction",
|
| 1265 |
+
"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"
|
| 1266 |
+
},
|
| 1267 |
+
{
|
| 1268 |
+
"task_id": "J2_cancellation_identity_000583",
|
| 1269 |
+
"task_type": "J2_error_detection",
|
| 1270 |
+
"category": "cancellation_identity",
|
| 1271 |
+
"problem": "Evaluate: 7896 + 2453 - 2454",
|
| 1272 |
+
"correct_answer": "7895",
|
| 1273 |
+
"ns_solution_with_error": "Using Near-cancellation: 2453 - 2454 = -1, so answer ≈ 7896 + -1.\nApproximation gives: 3947",
|
| 1274 |
+
"error_type": "wrong_operand",
|
| 1275 |
+
"error_description": "Applied shortcut to wrong operand",
|
| 1276 |
+
"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"
|
| 1277 |
+
},
|
| 1278 |
+
{
|
| 1279 |
+
"task_id": "J2_compatible_numbers_000650",
|
| 1280 |
+
"task_type": "J2_error_detection",
|
| 1281 |
+
"category": "compatible_numbers",
|
| 1282 |
+
"problem": "Estimate 4925 × 2150.",
|
| 1283 |
+
"correct_answer": "10588750",
|
| 1284 |
+
"ns_solution_with_error": "Using Round to 5000×2000 for easy mental computation.\nApproximation gives: 10588752",
|
| 1285 |
+
"error_type": "transcription_error",
|
| 1286 |
+
"error_description": "Transcription error in final answer",
|
| 1287 |
+
"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"
|
| 1288 |
+
},
|
| 1289 |
+
{
|
| 1290 |
+
"task_id": "J2_magnitude_estimation_000443",
|
| 1291 |
+
"task_type": "J2_error_detection",
|
| 1292 |
+
"category": "magnitude_estimation",
|
| 1293 |
+
"problem": "Which of the following is the best estimate for 9800 * 9800?",
|
| 1294 |
+
"correct_answer": "96040000",
|
| 1295 |
+
"ns_solution_with_error": "Using Round both to 10000 and multiply.\nApproximation gives: 96040001",
|
| 1296 |
+
"error_type": "arithmetic_slip",
|
| 1297 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1298 |
+
"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"
|
| 1299 |
+
},
|
| 1300 |
+
{
|
| 1301 |
+
"task_id": "J2_option_elimination_000788",
|
| 1302 |
+
"task_type": "J2_error_detection",
|
| 1303 |
+
"category": "option_elimination",
|
| 1304 |
+
"problem": "What is 2243 × 8255?",
|
| 1305 |
+
"correct_answer": "18515965",
|
| 1306 |
+
"ns_solution_with_error": "Using Check trailing digit / parity / magnitude — only one option matches.\nApproximation gives: 18515967",
|
| 1307 |
+
"error_type": "arithmetic_slip",
|
| 1308 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1309 |
+
"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"
|
| 1310 |
+
},
|
| 1311 |
+
{
|
| 1312 |
+
"task_id": "J2_landmark_comparison_000664",
|
| 1313 |
+
"task_type": "J2_error_detection",
|
| 1314 |
+
"category": "landmark_comparison",
|
| 1315 |
+
"problem": "Is 24% of 44600 greater than 13866?",
|
| 1316 |
+
"correct_answer": "No",
|
| 1317 |
+
"ns_solution_with_error": "Using Use 25% as landmark: 25% of 44600 = 11150.\nApproximation gives: 10707",
|
| 1318 |
+
"error_type": "arithmetic_slip",
|
| 1319 |
+
"error_description": "Arithmetic slip in the shortcut step",
|
| 1320 |
+
"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"
|
| 1321 |
+
}
|
| 1322 |
+
]
|