{ "schemaVersion": "1.0", "moduleId": "calculator-use-0580-pilot", "status": "prototype-scenarios", "pathways": { "enter-it-right": { "objectiveCode": "C1.14-1,2 / E1.14-1,2", "learnerAction": "Enter the calculation on the bench calculator with a correct key sequence.", "objectiveVerbs": [ "use a calculator efficiently", "enter values appropriately on a calculator" ], "responseType": "model-construction", "scenarios": [ { "id": "ent-mission-01", "objectiveRecordIds": [ "0580-core-C1.14-1", "0580-core-C1.14-2", "0580-extended-E1.14-1", "0580-extended-E1.14-2" ], "prompt": "Work out (7.35 + 2.65) ÷ (4 − 2.75). Press the keys on the bench calculator, then =.", "model": { "kind": "fraction", "slipValues": [ { "value": "5.2625", "code": "cu-brackets-missing" }, { "value": "-0.25", "code": "cu-brackets-missing" }, { "value": "9", "code": "cu-arithmetic" } ], "calc": "( 7.35 + 2.65 ) ÷ ( 4 − 2.75 )", "keys": [ "(", "7", ".", "3", "5", "+", "2", ".", "6", "5", ")", "÷", "(", "4", "−", "2", ".", "7", "5", ")", "=" ], "wrongKeys": [ "7", ".", "3", "5", "+", "2", ".", "6", "5", "÷", "4", "−", "2", ".", "7", "5", "=" ] }, "expected": { "answer": "8" }, "hint": "Plan the sequence first: brackets around every long numerator and denominator; the root or power covers only its bracket; (−) makes a negative base; ×10^x enters standard form in one piece. Check: estimate the size before you trust the display.", "misconceptionCode": "cu-brackets-missing" }, { "id": "ent-mission-02", "objectiveRecordIds": [ "0580-core-C1.14-1", "0580-core-C1.14-2", "0580-extended-E1.14-1", "0580-extended-E1.14-2" ], "prompt": "Work out √(12.96 + 23.04). Press the keys on the bench calculator, then =.", "model": { "kind": "root", "slipValues": [ { "value": "26.64", "code": "cu-root-scope" }, { "value": "8.4", "code": "cu-root-scope" }, { "value": "7", "code": "cu-arithmetic" } ], "calc": "√ ( 12.96 + 23.04 )", "keys": [ "√", "1", "2", ".", "9", "6", "+", "2", "3", ".", "0", "4", ")", "=" ], "wrongKeys": [ "√", "1", "2", ".", "9", "6", ")", "+", "2", "3", ".", "0", "4", "=" ] }, "expected": { "answer": "6" }, "hint": "Plan the sequence first: brackets around every long numerator and denominator; the root or power covers only its bracket; (−) makes a negative base; ×10^x enters standard form in one piece. Check: estimate the size before you trust the display.", "misconceptionCode": "cu-root-scope" }, { "id": "ent-mission-03", "objectiveRecordIds": [ "0580-core-C1.14-1", "0580-core-C1.14-2", "0580-extended-E1.14-1", "0580-extended-E1.14-2" ], "prompt": "Work out (−4.5)². Press the keys on the bench calculator, then =.", "model": { "kind": "negative-power", "slipValues": [ { "value": "-20.25", "code": "cu-minus-power" }, { "value": "-9", "code": "cu-minus-power" }, { "value": "21.25", "code": "cu-arithmetic" } ], "calc": "( (−) 4.5 ) x²", "keys": [ "(", "(−)", "4", ".", "5", ")", "x²", "=" ], "wrongKeys": [ "−", "4", ".", "5", "x²", "=" ] }, "expected": { "answer": "20.25" }, "hint": "Plan the sequence first: brackets around every long numerator and denominator; the root or power covers only its bracket; (−) makes a negative base; ×10^x enters standard form in one piece. Check: estimate the size before you trust the display.", "misconceptionCode": "cu-minus-power" }, { "id": "ent-mission-04", "objectiveRecordIds": [ "0580-core-C1.14-1", "0580-core-C1.14-2", "0580-extended-E1.14-1", "0580-extended-E1.14-2" ], "prompt": "Work out 2.4 × 10⁶ ÷ (9.6 × 10⁻³). Press the keys on the bench calculator, then =.", "model": { "kind": "std-entry", "slipValues": [ { "value": "250", "code": "cu-fraction-chain" }, { "value": "250000", "code": "cu-e-notation" }, { "value": "2500000000", "code": "cu-arithmetic" } ], "calc": "2.4 ×10^x 6 ÷ ( 9.6 ×10^x (−) 3 )", "keys": [ "2", ".", "4", "EXP", "6", "÷", "(", "9", ".", "6", "EXP", "(−)", "3", ")", "=" ], "wrongKeys": [ "2", ".", "4", "EXP", "6", "÷", "9", ".", "6", "×", "1", "0", "^", "(−)", "3", "=" ] }, "expected": { "answer": "250000000" }, "hint": "Plan the sequence first: brackets around every long numerator and denominator; the root or power covers only its bracket; (−) makes a negative base; ×10^x enters standard form in one piece. Check: estimate the size before you trust the display.", "misconceptionCode": "cu-fraction-chain" }, { "id": "ent-mission-05", "objectiveRecordIds": [ "0580-core-C1.14-1", "0580-core-C1.14-2", "0580-extended-E1.14-1", "0580-extended-E1.14-2" ], "prompt": "Work out 2½ × 3.6. Press the keys on the bench calculator, then =.", "model": { "kind": "mixed-number", "slipValues": [ { "value": "3.6", "code": "cu-mixed-number" }, { "value": "3.8", "code": "cu-mixed-number" }, { "value": "12.6", "code": "cu-arithmetic" } ], "calc": "( 2 + 1 ÷ 2 ) × 3.6", "keys": [ "(", "2", "+", "1", "÷", "2", ")", "×", "3", ".", "6", "=" ], "wrongKeys": [ "2", "×", "(", "1", "÷", "2", ")", "×", "3", ".", "6", "=" ] }, "expected": { "answer": "9" }, "hint": "Plan the sequence first: brackets around every long numerator and denominator; the root or power covers only its bracket; (−) makes a negative base; ×10^x enters standard form in one piece. Check: estimate the size before you trust the display.", "misconceptionCode": "cu-mixed-number" } ] }, "read-the-display": { "objectiveCode": "C1.14-3 / E1.14-3", "learnerAction": "Interpret the calculator display as a number, rounded as asked.", "objectiveVerbs": [ "interpret the calculator display appropriately" ], "responseType": "model-construction", "scenarios": [ { "id": "rea-mission-01", "objectiveRecordIds": [ "0580-core-C1.14-3", "0580-extended-E1.14-3" ], "prompt": "The display shows 2.46E9. Type the number it means.", "model": { "kind": "e-notation", "slipValues": [ { "value": "3299.26", "code": "cu-e-notation" }, { "value": "22.14", "code": "cu-e-notation" }, { "value": "246000000", "code": "cu-arithmetic" } ], "display": "2.46E9" }, "expected": { "answer": "2460000000" }, "hint": "Read the display as mathematics: E means × 10^, the stacked mark is a fraction bar (a over b is a/b), a mixed display is a + b/c. Round only at the end, from the first non-zero digit.", "misconceptionCode": "cu-e-notation" }, { "id": "rea-mission-02", "objectiveRecordIds": [ "0580-core-C1.14-3", "0580-extended-E1.14-3" ], "prompt": "The display shows 7/16 as a fraction. Type the value as a decimal.", "model": { "kind": "fraction-display", "slipValues": [ { "value": "7.16", "code": "cu-fraction-display" }, { "value": "112", "code": "cu-fraction-display" }, { "value": "0.5", "code": "cu-arithmetic" } ], "display": "7⌘16" }, "expected": { "answer": "0.4375" }, "hint": "Read the display as mathematics: E means × 10^, the stacked mark is a fraction bar (a over b is a/b), a mixed display is a + b/c. Round only at the end, from the first non-zero digit.", "misconceptionCode": "cu-fraction-display" }, { "id": "rea-mission-03", "objectiveRecordIds": [ "0580-core-C1.14-3", "0580-extended-E1.14-3" ], "prompt": "The display shows 5 3/8 as a mixed fraction. Type the value as a decimal.", "model": { "kind": "mixed-display", "slipValues": [ { "value": "1.875", "code": "cu-fraction-display" }, { "value": "5.3", "code": "cu-fraction-display" }, { "value": "6.375", "code": "cu-arithmetic" } ], "display": "5⌘3⌘8" }, "expected": { "answer": "5.375" }, "hint": "Read the display as mathematics: E means × 10^, the stacked mark is a fraction bar (a over b is a/b), a mixed display is a + b/c. Round only at the end, from the first non-zero digit.", "misconceptionCode": "cu-fraction-display" }, { "id": "rea-mission-04", "objectiveRecordIds": [ "0580-core-C1.14-3", "0580-extended-E1.14-3" ], "prompt": "The display shows 0.046193. Type the value rounded to 3 significant figures.", "model": { "kind": "rounding", "slipValues": [ { "value": "0.0461", "code": "cu-rounding" }, { "value": "0.046", "code": "cu-rounding" }, { "value": "0.46193", "code": "cu-arithmetic" } ], "display": "0.046193", "sf": 3 }, "expected": { "answer": "0.0462" }, "hint": "Read the display as mathematics: E means × 10^, the stacked mark is a fraction bar (a over b is a/b), a mixed display is a + b/c. Round only at the end, from the first non-zero digit.", "misconceptionCode": "cu-rounding" }, { "id": "rea-mission-05", "objectiveRecordIds": [ "0580-core-C1.14-3", "0580-extended-E1.14-3" ], "prompt": "The display shows −4.8E−3. Type the number it means.", "model": { "kind": "negative-e", "slipValues": [ { "value": "0.0048", "code": "cu-sign-lost" }, { "value": "-0.00048", "code": "cu-e-notation" }, { "value": "-0.048", "code": "cu-arithmetic" } ], "display": "−4.8E−3" }, "expected": { "answer": "-0.0048" }, "hint": "Read the display as mathematics: E means × 10^, the stacked mark is a fraction bar (a over b is a/b), a mixed display is a + b/c. Round only at the end, from the first non-zero digit.", "misconceptionCode": "cu-sign-lost" } ] } } }