{ "schemaVersion": "1.0", "moduleId": "bounds-estimation-0580-pilot", "pathways": { "accuracy-and-bounds": { "objectiveRecordIds": [ "0580-core-C1.9-2", "0580-extended-E1.9-2", "0580-core-C1.10-section", "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "minimumDistinctItems": 20, "responseType": "choice", "objectiveVerb": "treat a rounded value as the band of values it really is", "items": [ { "id": "bounds-q01", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A strip of tape is shown as 4.6 cm, with the whole band of lengths that read that way drawn under it and both of its ends marked. Use that band: how wide is it, from end to end?", "data": { "family": "band-width", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": false }, "misconceptionDistractor": "0.05 cm" }, "correctAnswer": "0.1 cm", "options": [ "0.1 cm", "4.55 cm", "4.65 cm", "0.05 cm" ], "correctIndex": 0, "difficulty": 1, "hint": "Measure from one end of the drawn band to the other, not from the middle to an end.", "explanation": "The band runs from 4.55 cm to 4.65 cm, so from end to end it is 0.1 cm wide. Half of that, 0.05 cm, is how far each end sits from the reading.", "misconceptionCode": "width-is-half-step" }, { "id": "bounds-q02", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A metal rod is shown as 3 cm, with the whole band of lengths that read that way drawn under it and both of its ends marked. Use that band: how wide is it, from end to end?", "data": { "family": "band-width", "meas": "rod", "object": "metal rod", "unit": "cm", "reading": 3, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 2.75, 3.25 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": false }, "misconceptionDistractor": "0.25 cm" }, "correctAnswer": "0.5 cm", "options": [ "2.75 cm", "0.5 cm", "3.25 cm", "0.25 cm" ], "correctIndex": 1, "difficulty": 1, "hint": "Measure from one end of the drawn band to the other, not from the middle to an end.", "explanation": "The band runs from 2.75 cm to 3.25 cm, so from end to end it is 0.5 cm wide. Half of that, 0.25 cm, is how far each end sits from the reading.", "misconceptionCode": "width-is-half-step" }, { "id": "bounds-q03", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A piece of wire is shown as 34 cm, with the whole band of lengths that read that way drawn under it and both of its ends marked. Use that band: how wide is it, from end to end?", "data": { "family": "band-width", "meas": "wire", "object": "piece of wire", "unit": "cm", "reading": 34, "step": 1, "accuracy": "2 significant figures", "band": [ 33.5, 34.5 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": false }, "misconceptionDistractor": "0.5 cm" }, "correctAnswer": "1 cm", "options": [ "33.5 cm", "34.5 cm", "1 cm", "0.5 cm" ], "correctIndex": 2, "difficulty": 1, "hint": "Measure from one end of the drawn band to the other, not from the middle to an end.", "explanation": "The band runs from 33.5 cm to 34.5 cm, so from end to end it is 1 cm wide. Half of that, 0.5 cm, is how far each end sits from the reading.", "misconceptionCode": "width-is-half-step" }, { "id": "bounds-q04", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A pencil is shown as 12.4 cm, with the band of lengths that read that way drawn under it and both of its ends marked. Use that band: how far does it reach from the reading to one of its ends?", "data": { "family": "band-half", "meas": "pencil", "object": "pencil", "unit": "cm", "reading": 12.4, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 12.35, 12.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": false }, "misconceptionDistractor": "0.1 cm" }, "correctAnswer": "0.05 cm", "options": [ "12.35 cm", "12.45 cm", "0.1 cm", "0.05 cm" ], "correctIndex": 3, "difficulty": 1, "hint": "The distance from the reading to one end is half of what you are asked for.", "explanation": "The two ends are 0.1 cm apart and the reading is in the middle, so the band reaches 0.05 cm from the reading to either end.", "misconceptionCode": "half-step-is-whole" }, { "id": "bounds-q05", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A wooden plank is shown as 8.5 cm, with the band of lengths that read that way drawn under it and both of its ends marked. Use that band: how far does it reach from the reading to one of its ends?", "data": { "family": "band-half", "meas": "plank", "object": "wooden plank", "unit": "cm", "reading": 8.5, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 8.25, 8.75 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": false }, "misconceptionDistractor": "0.5 cm" }, "correctAnswer": "0.25 cm", "options": [ "0.25 cm", "8.25 cm", "8.75 cm", "0.5 cm" ], "correctIndex": 0, "difficulty": 1, "hint": "The distance from the reading to one end is half of what you are asked for.", "explanation": "The two ends are 0.5 cm apart and the reading is in the middle, so the band reaches 0.25 cm from the reading to either end.", "misconceptionCode": "half-step-is-whole" }, { "id": "bounds-q06", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A caterpillar is shown as 3.4 cm, with the band of lengths that read that way drawn under it and both of its ends marked. Use that band: how far does it reach from the reading to one of its ends?", "data": { "family": "band-half", "meas": "worm", "object": "caterpillar", "unit": "cm", "reading": 3.4, "step": 0.1, "accuracy": "2 significant figures", "band": [ 3.35, 3.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": false }, "misconceptionDistractor": "0.1 cm" }, "correctAnswer": "0.05 cm", "options": [ "3.35 cm", "0.05 cm", "3.45 cm", "0.1 cm" ], "correctIndex": 1, "difficulty": 1, "hint": "The distance from the reading to one end is half of what you are asked for.", "explanation": "The two ends are 0.1 cm apart and the reading is in the middle, so the band reaches 0.05 cm from the reading to either end.", "misconceptionCode": "half-step-is-whole" }, { "id": "bounds-q07", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "Every length from 4.55 cm up to but not including 4.65 cm reads the same way on the bench. What did the strip of tape read?", "data": { "family": "reading-from-band", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": false, "accuracy": false }, "misconceptionDistractor": "0.1 cm" }, "correctAnswer": "4.6 cm", "options": [ "4.55 cm", "4.65 cm", "4.6 cm", "0.1 cm" ], "correctIndex": 2, "difficulty": 2, "hint": "The reading is the number the whole band is built around: it sits in the middle.", "explanation": "The reading is in the middle of the band: halfway from 4.55 cm to 4.65 cm is 4.6 cm. The whole band is 0.1 cm wide, which is the accuracy, so an end is not the reading.", "misconceptionCode": "step-is-reading" }, { "id": "bounds-q08", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "Every length from 12.35 cm up to but not including 12.45 cm reads the same way on the bench. What did the pencil read?", "data": { "family": "reading-from-band", "meas": "pencil", "object": "pencil", "unit": "cm", "reading": 12.4, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 12.35, 12.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": false, "accuracy": false }, "misconceptionDistractor": "0.1 cm" }, "correctAnswer": "12.4 cm", "options": [ "12.35 cm", "12.45 cm", "0.1 cm", "12.4 cm" ], "correctIndex": 3, "difficulty": 2, "hint": "The reading is the number the whole band is built around: it sits in the middle.", "explanation": "The reading is in the middle of the band: halfway from 12.35 cm to 12.45 cm is 12.4 cm. The whole band is 0.1 cm wide, which is the accuracy, so an end is not the reading.", "misconceptionCode": "step-is-reading" }, { "id": "bounds-q09", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "Every length from 2.75 cm up to but not including 3.25 cm reads the same way on the bench. What did the metal rod read?", "data": { "family": "reading-from-band", "meas": "rod", "object": "metal rod", "unit": "cm", "reading": 3, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 2.75, 3.25 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": false, "accuracy": false }, "misconceptionDistractor": "0.5 cm" }, "correctAnswer": "3 cm", "options": [ "3 cm", "2.75 cm", "3.25 cm", "0.5 cm" ], "correctIndex": 0, "difficulty": 2, "hint": "The reading is the number the whole band is built around: it sits in the middle.", "explanation": "The reading is in the middle of the band: halfway from 2.75 cm to 3.25 cm is 3 cm. The whole band is 0.5 cm wide, which is the accuracy, so an end is not the reading.", "misconceptionCode": "step-is-reading" }, { "id": "bounds-q10", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "Every length from 8.25 cm up to but not including 8.75 cm reads the same way on the bench. What did the wooden plank read?", "data": { "family": "reading-from-band", "meas": "plank", "object": "wooden plank", "unit": "cm", "reading": 8.5, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 8.25, 8.75 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": false, "accuracy": false }, "misconceptionDistractor": "0.5 cm" }, "correctAnswer": "8.5 cm", "options": [ "8.25 cm", "8.5 cm", "8.75 cm", "0.5 cm" ], "correctIndex": 1, "difficulty": 2, "hint": "The reading is the number the whole band is built around: it sits in the middle.", "explanation": "The reading is in the middle of the band: halfway from 8.25 cm to 8.75 cm is 8.5 cm. The whole band is 0.5 cm wide, which is the accuracy, so an end is not the reading.", "misconceptionCode": "step-is-reading" }, { "id": "bounds-q11", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "Every length from 3.35 cm up to but not including 3.45 cm reads the same way on the bench. What did the caterpillar read?", "data": { "family": "reading-from-band", "meas": "worm", "object": "caterpillar", "unit": "cm", "reading": 3.4, "step": 0.1, "accuracy": "2 significant figures", "band": [ 3.35, 3.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": false, "accuracy": false }, "misconceptionDistractor": "0.1 cm" }, "correctAnswer": "3.4 cm", "options": [ "3.35 cm", "3.45 cm", "3.4 cm", "0.1 cm" ], "correctIndex": 2, "difficulty": 2, "hint": "The reading is the number the whole band is built around: it sits in the middle.", "explanation": "The reading is in the middle of the band: halfway from 3.35 cm to 3.45 cm is 3.4 cm. The whole band is 0.1 cm wide, which is the accuracy, so an end is not the reading.", "misconceptionCode": "step-is-reading" }, { "id": "bounds-q12", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "Every length from 33.5 cm up to but not including 34.5 cm reads the same way on the bench. What did the piece of wire read?", "data": { "family": "reading-from-band", "meas": "wire", "object": "piece of wire", "unit": "cm", "reading": 34, "step": 1, "accuracy": "2 significant figures", "band": [ 33.5, 34.5 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": false, "accuracy": false }, "misconceptionDistractor": "1 cm" }, "correctAnswer": "34 cm", "options": [ "33.5 cm", "34.5 cm", "1 cm", "34 cm" ], "correctIndex": 3, "difficulty": 2, "hint": "The reading is the number the whole band is built around: it sits in the middle.", "explanation": "The reading is in the middle of the band: halfway from 33.5 cm to 34.5 cm is 34 cm. The whole band is 1 cm wide, which is the accuracy, so an end is not the reading.", "misconceptionCode": "step-is-reading" }, { "id": "bounds-q13", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A strip of tape is shown as 4.6 cm measured to the nearest 0.1 cm. What is its upper bound, in cm?", "data": { "family": "upper-bound", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "4.7 cm" }, "correctAnswer": "4.65 cm", "options": [ "4.65 cm", "4.55 cm", "4.6 cm", "4.7 cm" ], "correctIndex": 0, "difficulty": 2, "hint": "The band reaches only half the accuracy each side of the reading, not the whole of it.", "explanation": "Measured to the nearest 0.1 cm means every length from 4.55 cm up to but not including 4.65 cm reads as 4.6 cm, so the band reaches 0.05 cm each side of the reading. 4.65 cm is the upper bound: the real length is less than this, and a length of exactly 4.65 cm would read as 4.7 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q14", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A pencil is shown as 12.4 cm measured to the nearest 0.1 cm. What is its upper bound, in cm?", "data": { "family": "upper-bound", "meas": "pencil", "object": "pencil", "unit": "cm", "reading": 12.4, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 12.35, 12.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "12.5 cm" }, "correctAnswer": "12.45 cm", "options": [ "12.35 cm", "12.45 cm", "12.4 cm", "12.5 cm" ], "correctIndex": 1, "difficulty": 2, "hint": "The band reaches only half the accuracy each side of the reading, not the whole of it.", "explanation": "Measured to the nearest 0.1 cm means every length from 12.35 cm up to but not including 12.45 cm reads as 12.4 cm, so the band reaches 0.05 cm each side of the reading. 12.45 cm is the upper bound: the real length is less than this, and a length of exactly 12.45 cm would read as 12.4 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q15", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A metal rod is shown as 3 cm measured to the nearest 0.5 cm. What is its upper bound, in cm?", "data": { "family": "upper-bound", "meas": "rod", "object": "metal rod", "unit": "cm", "reading": 3, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 2.75, 3.25 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "3.5 cm" }, "correctAnswer": "3.25 cm", "options": [ "2.75 cm", "3 cm", "3.25 cm", "3.5 cm" ], "correctIndex": 2, "difficulty": 2, "hint": "The band reaches only half the accuracy each side of the reading, not the whole of it.", "explanation": "Measured to the nearest 0.5 cm means every length from 2.75 cm up to but not including 3.25 cm reads as 3 cm, so the band reaches 0.25 cm each side of the reading. 3.25 cm is the upper bound: the real length is less than this, and a length of exactly 3.25 cm would read as 3.5 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q16", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A wooden plank is shown as 8.5 cm measured to the nearest 0.5 cm. What is its upper bound, in cm?", "data": { "family": "upper-bound", "meas": "plank", "object": "wooden plank", "unit": "cm", "reading": 8.5, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 8.25, 8.75 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "9 cm" }, "correctAnswer": "8.75 cm", "options": [ "8.25 cm", "8.5 cm", "9 cm", "8.75 cm" ], "correctIndex": 3, "difficulty": 2, "hint": "The band reaches only half the accuracy each side of the reading, not the whole of it.", "explanation": "Measured to the nearest 0.5 cm means every length from 8.25 cm up to but not including 8.75 cm reads as 8.5 cm, so the band reaches 0.25 cm each side of the reading. 8.75 cm is the upper bound: the real length is less than this, and a length of exactly 8.75 cm would read as 9 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q17", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A caterpillar is shown as 3.4 cm measured to 2 significant figures. What is its upper bound, in cm?", "data": { "family": "upper-bound", "meas": "worm", "object": "caterpillar", "unit": "cm", "reading": 3.4, "step": 0.1, "accuracy": "2 significant figures", "band": [ 3.35, 3.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "3.5 cm" }, "correctAnswer": "3.45 cm", "options": [ "3.45 cm", "3.35 cm", "3.4 cm", "3.5 cm" ], "correctIndex": 0, "difficulty": 3, "hint": "The band reaches only half the accuracy each side of the reading, not the whole of it.", "explanation": "Measured to 2 significant figures means every length from 3.35 cm up to but not including 3.45 cm reads as 3.4 cm, so the band reaches 0.05 cm each side of the reading. 3.45 cm is the upper bound: the real length is less than this, and a length of exactly 3.45 cm would read as 3.5 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q18", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A piece of wire is shown as 34 cm measured to 2 significant figures. What is its upper bound, in cm?", "data": { "family": "upper-bound", "meas": "wire", "object": "piece of wire", "unit": "cm", "reading": 34, "step": 1, "accuracy": "2 significant figures", "band": [ 33.5, 34.5 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "35 cm" }, "correctAnswer": "34.5 cm", "options": [ "33.5 cm", "34.5 cm", "34 cm", "35 cm" ], "correctIndex": 1, "difficulty": 3, "hint": "The band reaches only half the accuracy each side of the reading, not the whole of it.", "explanation": "Measured to 2 significant figures means every length from 33.5 cm up to but not including 34.5 cm reads as 34 cm, so the band reaches 0.5 cm each side of the reading. 34.5 cm is the upper bound: the real length is less than this, and a length of exactly 34.5 cm would read as 35 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q19", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A strip of tape is shown as 4.6 cm measured to the nearest 0.1 cm. What is its lower bound, in cm?", "data": { "family": "lower-bound", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "4.5 cm" }, "correctAnswer": "4.55 cm", "options": [ "4.65 cm", "4.6 cm", "4.55 cm", "4.5 cm" ], "correctIndex": 2, "difficulty": 2, "hint": "Start at the reading and take away half the accuracy, not the whole of it.", "explanation": "Measured to the nearest 0.1 cm means every length from 4.55 cm up to but not including 4.65 cm reads as 4.6 cm, so the band reaches 0.05 cm each side of the reading. 4.55 cm is the lower bound: the real length is at least this, and a length of exactly 4.55 cm really does read as 4.6 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q20", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A pencil is shown as 12.4 cm measured to the nearest 0.1 cm. What is its lower bound, in cm?", "data": { "family": "lower-bound", "meas": "pencil", "object": "pencil", "unit": "cm", "reading": 12.4, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 12.35, 12.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "12.3 cm" }, "correctAnswer": "12.35 cm", "options": [ "12.45 cm", "12.4 cm", "12.3 cm", "12.35 cm" ], "correctIndex": 3, "difficulty": 2, "hint": "Start at the reading and take away half the accuracy, not the whole of it.", "explanation": "Measured to the nearest 0.1 cm means every length from 12.35 cm up to but not including 12.45 cm reads as 12.4 cm, so the band reaches 0.05 cm each side of the reading. 12.35 cm is the lower bound: the real length is at least this, and a length of exactly 12.35 cm really does read as 12.4 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q21", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A metal rod is shown as 3 cm measured to the nearest 0.5 cm. What is its lower bound, in cm?", "data": { "family": "lower-bound", "meas": "rod", "object": "metal rod", "unit": "cm", "reading": 3, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 2.75, 3.25 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "2.5 cm" }, "correctAnswer": "2.75 cm", "options": [ "2.75 cm", "3.25 cm", "3 cm", "2.5 cm" ], "correctIndex": 0, "difficulty": 2, "hint": "Start at the reading and take away half the accuracy, not the whole of it.", "explanation": "Measured to the nearest 0.5 cm means every length from 2.75 cm up to but not including 3.25 cm reads as 3 cm, so the band reaches 0.25 cm each side of the reading. 2.75 cm is the lower bound: the real length is at least this, and a length of exactly 2.75 cm really does read as 3 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q22", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A wooden plank is shown as 8.5 cm measured to the nearest 0.5 cm. What is its lower bound, in cm?", "data": { "family": "lower-bound", "meas": "plank", "object": "wooden plank", "unit": "cm", "reading": 8.5, "step": 0.5, "accuracy": "the nearest 0.5 cm", "band": [ 8.25, 8.75 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "8 cm" }, "correctAnswer": "8.25 cm", "options": [ "8.75 cm", "8.25 cm", "8.5 cm", "8 cm" ], "correctIndex": 1, "difficulty": 2, "hint": "Start at the reading and take away half the accuracy, not the whole of it.", "explanation": "Measured to the nearest 0.5 cm means every length from 8.25 cm up to but not including 8.75 cm reads as 8.5 cm, so the band reaches 0.25 cm each side of the reading. 8.25 cm is the lower bound: the real length is at least this, and a length of exactly 8.25 cm really does read as 8.5 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q23", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A caterpillar is shown as 3.4 cm measured to 2 significant figures. What is its lower bound, in cm?", "data": { "family": "lower-bound", "meas": "worm", "object": "caterpillar", "unit": "cm", "reading": 3.4, "step": 0.1, "accuracy": "2 significant figures", "band": [ 3.35, 3.45 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "3.3 cm" }, "correctAnswer": "3.35 cm", "options": [ "3.45 cm", "3.4 cm", "3.35 cm", "3.3 cm" ], "correctIndex": 2, "difficulty": 3, "hint": "Start at the reading and take away half the accuracy, not the whole of it.", "explanation": "Measured to 2 significant figures means every length from 3.35 cm up to but not including 3.45 cm reads as 3.4 cm, so the band reaches 0.05 cm each side of the reading. 3.35 cm is the lower bound: the real length is at least this, and a length of exactly 3.35 cm really does read as 3.4 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q24", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A piece of wire is shown as 34 cm measured to 2 significant figures. What is its lower bound, in cm?", "data": { "family": "lower-bound", "meas": "wire", "object": "piece of wire", "unit": "cm", "reading": 34, "step": 1, "accuracy": "2 significant figures", "band": [ 33.5, 34.5 ], "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": false, "ends": false, "reading": true, "accuracy": true }, "misconceptionDistractor": "33 cm" }, "correctAnswer": "33.5 cm", "options": [ "34.5 cm", "34 cm", "33 cm", "33.5 cm" ], "correctIndex": 3, "difficulty": 3, "hint": "Start at the reading and take away half the accuracy, not the whole of it.", "explanation": "Measured to 2 significant figures means every length from 33.5 cm up to but not including 34.5 cm reads as 34 cm, so the band reaches 0.5 cm each side of the reading. 33.5 cm is the lower bound: the real length is at least this, and a length of exactly 33.5 cm really does read as 34 cm.", "misconceptionCode": "bound-whole-step" }, { "id": "bounds-q25", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A strip of tape is shown as 4.6 cm measured to the nearest 0.1 cm. Could its real length have been exactly 4.55 cm?", "data": { "family": "possible-value", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": 4.55, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": true }, "misconceptionDistractor": "yes, the band reaches 4.65 cm and that end counts too" }, "correctAnswer": "yes, it rounds to 4.6 cm, the reading", "options": [ "yes, it rounds to 4.6 cm, the reading", "no, it rounds to 4.7 cm, one step above the reading", "no, it rounds to 4.5 cm, one step below the reading", "yes, the band reaches 4.65 cm and that end counts too" ], "correctIndex": 0, "difficulty": 3, "hint": "Round the value the way the bench did and see which reading it lands on.", "explanation": "4.55 cm rounded to the nearest 0.1 cm is 4.5 cm. The band holds every length from 4.55 cm up to but not including 4.65 cm, so 4.55 cm is a length that really would read this way — the answer is yes.", "misconceptionCode": "upper-end-included" }, { "id": "bounds-q26", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A strip of tape is shown as 4.6 cm measured to the nearest 0.1 cm. Could its real length have been exactly 4.62 cm?", "data": { "family": "possible-value", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": 4.62, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": true }, "misconceptionDistractor": "yes, the band reaches 4.65 cm and that end counts too" }, "correctAnswer": "yes, it rounds to 4.6 cm, the reading", "options": [ "no, it rounds to 4.7 cm, one step above the reading", "yes, it rounds to 4.6 cm, the reading", "no, it rounds to 4.5 cm, one step below the reading", "yes, the band reaches 4.65 cm and that end counts too" ], "correctIndex": 1, "difficulty": 3, "hint": "Round the value the way the bench did and see which reading it lands on.", "explanation": "4.62 cm rounded to the nearest 0.1 cm is 4.6 cm. The band holds every length from 4.55 cm up to but not including 4.65 cm, so 4.62 cm is a length that really would read this way — the answer is yes.", "misconceptionCode": "upper-end-included" }, { "id": "bounds-q27", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A strip of tape is shown as 4.6 cm measured to the nearest 0.1 cm. Could its real length have been exactly 4.65 cm?", "data": { "family": "possible-value", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": 4.65, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": true }, "misconceptionDistractor": "yes, the band reaches 4.65 cm and that end counts too" }, "correctAnswer": "no, it rounds to 4.7 cm, one step above the reading", "options": [ "yes, it rounds to 4.6 cm, the reading", "no, it rounds to 4.5 cm, one step below the reading", "no, it rounds to 4.7 cm, one step above the reading", "yes, the band reaches 4.65 cm and that end counts too" ], "correctIndex": 2, "difficulty": 3, "hint": "Round the value the way the bench did and see which reading it lands on.", "explanation": "4.65 cm rounded to the nearest 0.1 cm is 4.7 cm. The band holds every length from 4.55 cm up to but not including 4.65 cm, so 4.65 cm is not a length that reads this way — the answer is no.", "misconceptionCode": "upper-end-included" }, { "id": "bounds-q28", "objectiveRecordIds": [ "0580-core-C1.10-section", "0580-extended-E1.10-1" ], "prompt": "A strip of tape is shown as 4.6 cm measured to the nearest 0.1 cm. Could its real length have been exactly 4.5 cm?", "data": { "family": "possible-value", "meas": "tape", "object": "strip of tape", "unit": "cm", "reading": 4.6, "step": 0.1, "accuracy": "the nearest 0.1 cm", "band": [ 4.55, 4.65 ], "probe": 4.5, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": null, "view": { "band": true, "ends": true, "reading": true, "accuracy": true }, "misconceptionDistractor": "yes, the band reaches 4.65 cm and that end counts too" }, "correctAnswer": "no, it rounds to 4.5 cm, one step below the reading", "options": [ "yes, it rounds to 4.6 cm, the reading", "no, it rounds to 4.7 cm, one step above the reading", "yes, the band reaches 4.65 cm and that end counts too", "no, it rounds to 4.5 cm, one step below the reading" ], "correctIndex": 3, "difficulty": 3, "hint": "Round the value the way the bench did and see which reading it lands on.", "explanation": "4.5 cm rounded to the nearest 0.1 cm is 4.5 cm. The band holds every length from 4.55 cm up to but not including 4.65 cm, so 4.5 cm is not a length that reads this way — the answer is no.", "misconceptionCode": "upper-end-included" }, { "id": "bounds-q29", "objectiveRecordIds": [ "0580-core-C1.9-2", "0580-extended-E1.9-2" ], "prompt": "A learner multiplies the tape's 4.6 cm by the pencil's 12.4 cm to find an area. They round each number to 1 significant figure and get 50 cm². How does the exact answer compare with that?", "data": { "family": "estimate-compare", "meas": null, "object": "two numbers rounded to 1 significant figure", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": "4.6 × 12.4", "rough": 50.0, "exact": 57.04, "answerUnit": "cm²", "combine": null, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "there is no way to compare the estimate with the exact answer" }, "correctAnswer": "the exact answer is bigger than the estimate", "options": [ "the exact answer is bigger than the estimate", "the exact answer is smaller than the estimate", "the exact answer is the same as the estimate", "there is no way to compare the estimate with the exact answer" ], "correctIndex": 0, "difficulty": 4, "hint": "Work out the exact answer, or say which way each number moved when it was rounded — and remember a smaller number does not always make the answer smaller.", "explanation": "Rounding gives 4.6 cm to 5 cm and 12.4 cm to 10 cm, so the estimate is 50 cm² while the exact answer is 57.04 cm² — the exact answer is bigger than the estimate. Say which way each number moved before you guess which way the answer moved.", "misconceptionCode": "estimate-direction-guessed" }, { "id": "bounds-q30", "objectiveRecordIds": [ "0580-core-C1.9-2", "0580-extended-E1.9-2" ], "prompt": "A learner multiplies the plank's 8.5 cm by the rod's 3 cm to find an area. They round each number to 1 significant figure and get 27 cm². How does the exact answer compare with that?", "data": { "family": "estimate-compare", "meas": null, "object": "two numbers rounded to 1 significant figure", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": "8.5 × 3", "rough": 27.0, "exact": 25.5, "answerUnit": "cm²", "combine": null, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "there is no way to compare the estimate with the exact answer" }, "correctAnswer": "the exact answer is smaller than the estimate", "options": [ "the exact answer is bigger than the estimate", "the exact answer is smaller than the estimate", "the exact answer is the same as the estimate", "there is no way to compare the estimate with the exact answer" ], "correctIndex": 1, "difficulty": 4, "hint": "Work out the exact answer, or say which way each number moved when it was rounded — and remember a smaller number does not always make the answer smaller.", "explanation": "Rounding gives 8.5 cm to 9 cm and 3 cm unchanged, so the estimate is 27 cm² while the exact answer is 25.5 cm² — the exact answer is smaller than the estimate. Say which way each number moved before you guess which way the answer moved.", "misconceptionCode": "estimate-direction-guessed" }, { "id": "bounds-q31", "objectiveRecordIds": [ "0580-core-C1.9-2", "0580-extended-E1.9-2" ], "prompt": "A learner divides the wire's 34 cm by the caterpillar's 3.4 cm to count how many caterpillars reach along it. They round each number to 1 significant figure and get 10. How does the exact answer compare with that?", "data": { "family": "estimate-compare", "meas": null, "object": "two numbers rounded to 1 significant figure", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": "34 ÷ 3.4", "rough": 10.0, "exact": 10.0, "answerUnit": "", "combine": null, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "there is no way to compare the estimate with the exact answer" }, "correctAnswer": "the exact answer is the same as the estimate", "options": [ "the exact answer is bigger than the estimate", "the exact answer is smaller than the estimate", "the exact answer is the same as the estimate", "there is no way to compare the estimate with the exact answer" ], "correctIndex": 2, "difficulty": 4, "hint": "Work out the exact answer, or say which way each number moved when it was rounded — and remember a smaller number does not always make the answer smaller.", "explanation": "Rounding gives 34 cm to 30 cm and 3.4 cm to 3 cm, so the estimate is 10 while the exact answer is 10 — the exact answer is the same as the estimate. Say which way each number moved before you guess which way the answer moved.", "misconceptionCode": "estimate-direction-guessed" }, { "id": "bounds-q32", "objectiveRecordIds": [ "0580-core-C1.9-2", "0580-extended-E1.9-2" ], "prompt": "A learner subtracts the tape's 4.6 cm from the pencil's 12.4 cm. They round each number to 1 significant figure and get 5 cm. How does the exact answer compare with that?", "data": { "family": "estimate-compare", "meas": null, "object": "two numbers rounded to 1 significant figure", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": "12.4 − 4.6", "rough": 5.0, "exact": 7.800000000000001, "answerUnit": "cm", "combine": null, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "there is no way to compare the estimate with the exact answer" }, "correctAnswer": "the exact answer is bigger than the estimate", "options": [ "the exact answer is smaller than the estimate", "the exact answer is the same as the estimate", "there is no way to compare the estimate with the exact answer", "the exact answer is bigger than the estimate" ], "correctIndex": 3, "difficulty": 4, "hint": "Work out the exact answer, or say which way each number moved when it was rounded — and remember a smaller number does not always make the answer smaller.", "explanation": "Rounding gives 12.4 cm to 10 cm and 4.6 cm to 5 cm, so the estimate is 5 cm while the exact answer is 7.8 cm — the exact answer is bigger than the estimate. Say which way each number moved before you guess which way the answer moved.", "misconceptionCode": "estimate-direction-guessed" }, { "id": "bounds-q33", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A rectangle has its length read as 7 cm to the nearest 1 cm and its width read as 3 cm to the nearest 1 cm. What is the upper bound of the area these measurements allow, in cm²?", "data": { "family": "result-bound", "meas": null, "object": "rectangle", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "area", "op": "×", "want": "area", "who": "rectangle", "label": "cm²", "dp": null, "slot": "ub", "pair": [ 7.5, 3.5 ], "a": { "who": "length", "reading": 7.0, "step": 1.0, "unit": " cm", "lb": 6.5, "ub": 7.5 }, "b": { "who": "width", "reading": 3.0, "step": 1.0, "unit": " cm", "lb": 2.5, "ub": 3.5 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "21 cm²" }, "correctAnswer": "26.25 cm²", "options": [ "26.25 cm²", "16.25 cm²", "18.75 cm²", "21 cm²" ], "correctIndex": 0, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The length is somewhere from 6.5 cm up to but not including 7.5 cm, and the width from 2.5 cm up to but not including 3.5 cm. So the upper bound of the area pairs the biggest end of the length with the biggest end of the width: 7.5 cm × 3.5 cm = 26.25 cm². The area takes its upper bound when both sides are at their biggest end, and its lower bound when both are at their smallest. The result can be any value below this but never exactly it, because each side's band stops short of its upper end.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q34", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A rectangle has its length read as 7 cm to the nearest 1 cm and its width read as 3 cm to the nearest 1 cm. What is the lower bound of the area these measurements allow, in cm²?", "data": { "family": "result-bound", "meas": null, "object": "rectangle", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "area", "op": "×", "want": "area", "who": "rectangle", "label": "cm²", "dp": null, "slot": "lb", "pair": [ 6.5, 2.5 ], "a": { "who": "length", "reading": 7.0, "step": 1.0, "unit": " cm", "lb": 6.5, "ub": 7.5 }, "b": { "who": "width", "reading": 3.0, "step": 1.0, "unit": " cm", "lb": 2.5, "ub": 3.5 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "21 cm²" }, "correctAnswer": "16.25 cm²", "options": [ "26.25 cm²", "16.25 cm²", "18.75 cm²", "21 cm²" ], "correctIndex": 1, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The length is somewhere from 6.5 cm up to but not including 7.5 cm, and the width from 2.5 cm up to but not including 3.5 cm. So the lower bound of the area pairs the smallest end of the length with the smallest end of the width: 6.5 cm × 2.5 cm = 16.25 cm². The area takes its upper bound when both sides are at their biggest end, and its lower bound when both are at their smallest. The result can be this, because each side's band includes its lower end.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q35", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A rectangle has its length read as 7 cm to the nearest 1 cm and its width read as 3 cm to the nearest 1 cm. A learner worked out 7.5 cm × 2.5 cm. What area does that give, in cm²?", "data": { "family": "result-bound", "meas": null, "object": "rectangle", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "area", "op": "×", "want": "area", "who": "rectangle", "label": "cm²", "dp": null, "slot": "mixA", "pair": [ 7.5, 2.5 ], "a": { "who": "length", "reading": 7.0, "step": 1.0, "unit": " cm", "lb": 6.5, "ub": 7.5 }, "b": { "who": "width", "reading": 3.0, "step": 1.0, "unit": " cm", "lb": 2.5, "ub": 3.5 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "21 cm²" }, "correctAnswer": "18.75 cm²", "options": [ "26.25 cm²", "16.25 cm²", "18.75 cm²", "21 cm²" ], "correctIndex": 2, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The length is somewhere from 6.5 cm up to but not including 7.5 cm, and the width from 2.5 cm up to but not including 3.5 cm. 7.5 cm × 2.5 cm = 18.75 cm², which pairs the biggest end of the length with the smallest end of the width. That is neither end of the area's band: the area takes its upper bound when both sides are at their biggest end, and its lower bound when both are at their smallest, and working at the readings gives 7 × 3 instead of the ends.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q36", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A rectangle has its length read as 7 cm to the nearest 1 cm and its width read as 3 cm to the nearest 1 cm. A learner worked out 6.5 cm × 3.5 cm. What area does that give, in cm²?", "data": { "family": "result-bound", "meas": null, "object": "rectangle", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "area", "op": "×", "want": "area", "who": "rectangle", "label": "cm²", "dp": null, "slot": "mixB", "pair": [ 6.5, 3.5 ], "a": { "who": "length", "reading": 7.0, "step": 1.0, "unit": " cm", "lb": 6.5, "ub": 7.5 }, "b": { "who": "width", "reading": 3.0, "step": 1.0, "unit": " cm", "lb": 2.5, "ub": 3.5 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "21 cm²" }, "correctAnswer": "22.75 cm²", "options": [ "26.25 cm²", "16.25 cm²", "21 cm²", "22.75 cm²" ], "correctIndex": 3, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The length is somewhere from 6.5 cm up to but not including 7.5 cm, and the width from 2.5 cm up to but not including 3.5 cm. 6.5 cm × 3.5 cm = 22.75 cm², which pairs the smallest end of the length with the biggest end of the width. That is neither end of the area's band: the area takes its upper bound when both sides are at their biggest end, and its lower bound when both are at their smallest, and working at the readings gives 7 × 3 instead of the ends.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q37", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A pair of strips is compared: the longer strip reads 8.5 cm to the nearest 0.5 cm and the shorter strip reads 4.6 cm to the nearest 0.1 cm. What is the upper bound of the difference in length these measurements allow, in cm?", "data": { "family": "result-bound", "meas": null, "object": "pair of strips", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "difference", "op": "−", "want": "difference in length", "who": "pair of strips", "label": "cm", "dp": null, "slot": "ub", "pair": [ 8.75, 4.55 ], "a": { "who": "longer strip", "reading": 8.5, "step": 0.5, "unit": " cm", "lb": 8.25, "ub": 8.75 }, "b": { "who": "shorter strip", "reading": 4.6, "step": 0.1, "unit": " cm", "lb": 4.55, "ub": 4.65 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "3.9 cm" }, "correctAnswer": "4.2 cm", "options": [ "4.2 cm", "3.6 cm", "4.1 cm", "3.9 cm" ], "correctIndex": 0, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The longer strip is somewhere from 8.25 cm up to but not including 8.75 cm, and the shorter strip from 4.55 cm up to but not including 4.65 cm. So the upper bound of the difference in length pairs the biggest end of the longer strip with the smallest end of the shorter strip: 8.75 cm − 4.55 cm = 4.2 cm. The difference in length takes its upper bound when the longer strip is at its biggest end and the shorter at its smallest, and its lower bound the other way round. The result can be any value below this but never exactly it, because each side's band stops short of its upper end.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q38", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A pair of strips is compared: the longer strip reads 8.5 cm to the nearest 0.5 cm and the shorter strip reads 4.6 cm to the nearest 0.1 cm. What is the lower bound of the difference in length these measurements allow, in cm?", "data": { "family": "result-bound", "meas": null, "object": "pair of strips", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "difference", "op": "−", "want": "difference in length", "who": "pair of strips", "label": "cm", "dp": null, "slot": "lb", "pair": [ 8.25, 4.65 ], "a": { "who": "longer strip", "reading": 8.5, "step": 0.5, "unit": " cm", "lb": 8.25, "ub": 8.75 }, "b": { "who": "shorter strip", "reading": 4.6, "step": 0.1, "unit": " cm", "lb": 4.55, "ub": 4.65 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "3.9 cm" }, "correctAnswer": "3.6 cm", "options": [ "4.2 cm", "3.6 cm", "4.1 cm", "3.9 cm" ], "correctIndex": 1, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The longer strip is somewhere from 8.25 cm up to but not including 8.75 cm, and the shorter strip from 4.55 cm up to but not including 4.65 cm. So the lower bound of the difference in length pairs the smallest end of the longer strip with the biggest end of the shorter strip: 8.25 cm − 4.65 cm = 3.6 cm. The difference in length takes its upper bound when the longer strip is at its biggest end and the shorter at its smallest, and its lower bound the other way round. The result can be this, because each side's band includes its lower end.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q39", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A pair of strips is compared: the longer strip reads 8.5 cm to the nearest 0.5 cm and the shorter strip reads 4.6 cm to the nearest 0.1 cm. A learner worked out 8.75 cm − 4.65 cm. What difference in length does that give, in cm?", "data": { "family": "result-bound", "meas": null, "object": "pair of strips", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "difference", "op": "−", "want": "difference in length", "who": "pair of strips", "label": "cm", "dp": null, "slot": "mixA", "pair": [ 8.75, 4.65 ], "a": { "who": "longer strip", "reading": 8.5, "step": 0.5, "unit": " cm", "lb": 8.25, "ub": 8.75 }, "b": { "who": "shorter strip", "reading": 4.6, "step": 0.1, "unit": " cm", "lb": 4.55, "ub": 4.65 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "3.9 cm" }, "correctAnswer": "4.1 cm", "options": [ "4.2 cm", "3.6 cm", "4.1 cm", "3.9 cm" ], "correctIndex": 2, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The longer strip is somewhere from 8.25 cm up to but not including 8.75 cm, and the shorter strip from 4.55 cm up to but not including 4.65 cm. 8.75 cm − 4.65 cm = 4.1 cm, which pairs the biggest end of the longer strip with the biggest end of the shorter strip. That is neither end of the difference in length's band: the difference in length takes its upper bound when the longer strip is at its biggest end and the shorter at its smallest, and its lower bound the other way round, and working at the readings gives 8.5 − 4.6 instead of the ends.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q40", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A pair of strips is compared: the longer strip reads 8.5 cm to the nearest 0.5 cm and the shorter strip reads 4.6 cm to the nearest 0.1 cm. A learner worked out 8.25 cm − 4.55 cm. What difference in length does that give, in cm?", "data": { "family": "result-bound", "meas": null, "object": "pair of strips", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "difference", "op": "−", "want": "difference in length", "who": "pair of strips", "label": "cm", "dp": null, "slot": "mixB", "pair": [ 8.25, 4.55 ], "a": { "who": "longer strip", "reading": 8.5, "step": 0.5, "unit": " cm", "lb": 8.25, "ub": 8.75 }, "b": { "who": "shorter strip", "reading": 4.6, "step": 0.1, "unit": " cm", "lb": 4.55, "ub": 4.65 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "3.9 cm" }, "correctAnswer": "3.7 cm", "options": [ "4.2 cm", "3.6 cm", "3.9 cm", "3.7 cm" ], "correctIndex": 3, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The longer strip is somewhere from 8.25 cm up to but not including 8.75 cm, and the shorter strip from 4.55 cm up to but not including 4.65 cm. 8.25 cm − 4.55 cm = 3.7 cm, which pairs the smallest end of the longer strip with the smallest end of the shorter strip. That is neither end of the difference in length's band: the difference in length takes its upper bound when the longer strip is at its biggest end and the shorter at its smallest, and its lower bound the other way round, and working at the readings gives 8.5 − 4.6 instead of the ends.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q41", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A sprint on the stopwatch is timed: the distance reads 20 m to the nearest 1 m and the time reads 3 s to the nearest 0.5 s. What is the upper bound of the average speed these measurements allow, in m/s?", "data": { "family": "result-bound", "meas": null, "object": "sprint on the stopwatch", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "rate", "op": "÷", "want": "average speed", "who": "sprint on the stopwatch", "label": "m/s", "dp": 2, "slot": "ub", "pair": [ 20.5, 2.75 ], "a": { "who": "distance", "reading": 20.0, "step": 1.0, "unit": " m", "lb": 19.5, "ub": 20.5 }, "b": { "who": "time", "reading": 3.0, "step": 0.5, "unit": " s", "lb": 2.75, "ub": 3.25 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "6.67 m/s" }, "correctAnswer": "7.45 m/s", "options": [ "7.45 m/s", "6.00 m/s", "6.31 m/s", "6.67 m/s" ], "correctIndex": 0, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The distance is somewhere from 19.5 m up to but not including 20.5 m, and the time from 2.75 s up to but not including 3.25 s. So the upper bound of the average speed pairs the biggest end of the distance with the smallest end of the time: 20.5 m ÷ 2.75 s = 7.45 m/s. The average speed takes its upper bound when the distance is at its biggest end and the time at its smallest, and its lower bound the other way round. The result can be any value below this but never exactly it, because each side's band stops short of its upper end.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q42", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A sprint on the stopwatch is timed: the distance reads 20 m to the nearest 1 m and the time reads 3 s to the nearest 0.5 s. What is the lower bound of the average speed these measurements allow, in m/s?", "data": { "family": "result-bound", "meas": null, "object": "sprint on the stopwatch", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "rate", "op": "÷", "want": "average speed", "who": "sprint on the stopwatch", "label": "m/s", "dp": 2, "slot": "lb", "pair": [ 19.5, 3.25 ], "a": { "who": "distance", "reading": 20.0, "step": 1.0, "unit": " m", "lb": 19.5, "ub": 20.5 }, "b": { "who": "time", "reading": 3.0, "step": 0.5, "unit": " s", "lb": 2.75, "ub": 3.25 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "6.67 m/s" }, "correctAnswer": "6.00 m/s", "options": [ "7.45 m/s", "6.00 m/s", "6.31 m/s", "6.67 m/s" ], "correctIndex": 1, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The distance is somewhere from 19.5 m up to but not including 20.5 m, and the time from 2.75 s up to but not including 3.25 s. So the lower bound of the average speed pairs the smallest end of the distance with the biggest end of the time: 19.5 m ÷ 3.25 s = 6.00 m/s. The average speed takes its upper bound when the distance is at its biggest end and the time at its smallest, and its lower bound the other way round. The result can be this, because each side's band includes its lower end.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q43", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A sprint on the stopwatch is timed: the distance reads 20 m to the nearest 1 m and the time reads 3 s to the nearest 0.5 s. A learner worked out 20.5 m ÷ 3.25 s. What average speed does that give, in m/s?", "data": { "family": "result-bound", "meas": null, "object": "sprint on the stopwatch", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "rate", "op": "÷", "want": "average speed", "who": "sprint on the stopwatch", "label": "m/s", "dp": 2, "slot": "mixA", "pair": [ 20.5, 3.25 ], "a": { "who": "distance", "reading": 20.0, "step": 1.0, "unit": " m", "lb": 19.5, "ub": 20.5 }, "b": { "who": "time", "reading": 3.0, "step": 0.5, "unit": " s", "lb": 2.75, "ub": 3.25 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "6.67 m/s" }, "correctAnswer": "6.31 m/s", "options": [ "7.45 m/s", "6.00 m/s", "6.31 m/s", "6.67 m/s" ], "correctIndex": 2, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The distance is somewhere from 19.5 m up to but not including 20.5 m, and the time from 2.75 s up to but not including 3.25 s. 20.5 m ÷ 3.25 s = 6.31 m/s, which pairs the biggest end of the distance with the biggest end of the time. That is neither end of the average speed's band: the average speed takes its upper bound when the distance is at its biggest end and the time at its smallest, and its lower bound the other way round, and working at the readings gives 20 ÷ 3 instead of the ends.", "misconceptionCode": "result-used-readings" }, { "id": "bounds-q44", "objectiveRecordIds": [ "0580-extended-E1.10-1", "0580-extended-E1.10-2" ], "prompt": "A sprint on the stopwatch is timed: the distance reads 20 m to the nearest 1 m and the time reads 3 s to the nearest 0.5 s. A learner worked out 19.5 m ÷ 2.75 s. What average speed does that give, in m/s?", "data": { "family": "result-bound", "meas": null, "object": "sprint on the stopwatch", "unit": "cm", "reading": null, "step": null, "accuracy": null, "band": null, "probe": null, "calc": null, "rough": null, "exact": null, "answerUnit": null, "combine": { "scene": "rate", "op": "÷", "want": "average speed", "who": "sprint on the stopwatch", "label": "m/s", "dp": 2, "slot": "mixB", "pair": [ 19.5, 2.75 ], "a": { "who": "distance", "reading": 20.0, "step": 1.0, "unit": " m", "lb": 19.5, "ub": 20.5 }, "b": { "who": "time", "reading": 3.0, "step": 0.5, "unit": " s", "lb": 2.75, "ub": 3.25 } }, "view": { "band": false, "ends": false, "reading": false, "accuracy": false }, "misconceptionDistractor": "6.67 m/s" }, "correctAnswer": "7.09 m/s", "options": [ "7.45 m/s", "6.00 m/s", "6.67 m/s", "7.09 m/s" ], "correctIndex": 3, "difficulty": 4, "hint": "Pair the two bands end by end: the answer is not the calculation done at the readings.", "explanation": "The distance is somewhere from 19.5 m up to but not including 20.5 m, and the time from 2.75 s up to but not including 3.25 s. 19.5 m ÷ 2.75 s = 7.09 m/s, which pairs the smallest end of the distance with the smallest end of the time. That is neither end of the average speed's band: the average speed takes its upper bound when the distance is at its biggest end and the time at its smallest, and its lower bound the other way round, and working at the readings gives 20 ÷ 3 instead of the ends.", "misconceptionCode": "result-used-readings" } ] } } }