{ "schemaVersion": "1.0", "moduleId": "arrays-laws-pilot", "status": "prototype-scenarios", "pathways": { "arrays-laws": { "objectiveCode": "3Ni", "learnerAction": "Turn the array, move the divider and slide the hoop until the arrangement matches what the goal states.", "objectiveVerbs": [ "understand the commutative and associative properties of addition", "understand and explain the commutative and distributive properties of multiplication", "understand the associative property of multiplication", "understand which law of arithmetic to apply to simplify calculations", "use knowledge of laws of arithmetic and order of operations to simplify calculations" ], "responseType": "model-construction", "scenarios": [ { "id": "arrays-mission-01", "title": "Turn the array the other way round", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "Turn the array the other way round. Goal: the same 18 counters are still on the board · there are 6 rows · there are 3 counters in each row.", "model": { "start": { "figure": "array", "rows": 3, "cols": 6, "split": null, "turned": false, "terms": null, "ops": null, "hoop": null }, "editable": [ "rows", "cols" ], "given": [], "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "parts": [ "all the counters on the board", "the dashed line that cuts the array", "the counters on the left of the dashed line", "the counters on the right of the dashed line", "the array after it is turned the other way round", "one row of counters" ], "partsKey": "array" }, "expected": { "counters-unchanged": true, "rows-are": 6, "cols-are": 3 }, "goal": { "text": "the same 18 counters are still on the board · there are 6 rows · there are 3 counters in each row", "statements": [ { "kind": "counters-unchanged", "text": "the same 18 counters are still on the board", "code": "turn-changed-total", "value": true }, { "kind": "rows-are", "text": "there are 6 rows", "code": "turned-rows-for-counters", "value": 6 }, { "kind": "cols-are", "text": "there are 3 counters in each row", "code": "turned-rows-for-counters", "value": 3 } ], "working": [ "Count the array you start with: 3 rows of 6 is 18 counters.", "Turning it makes the columns into rows, so the board has 6 rows of 3 and still totals 18." ] }, "solution": { "figure": "array", "rows": 6, "cols": 3, "split": null, "turned": false, "terms": null, "ops": null, "hoop": null }, "hint": "Drag the corner of the array until there are 6 rows, and check that no counter has been added or removed.", "misconceptionCode": "turned-rows-for-counters" }, { "id": "arrays-mission-02", "title": "Split the array so the left part has 12 counters", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "Split the array so the left part has 12 counters. Goal: the whole array is still 4 rows of 5 · the part on the left of the dashed line holds 12 counters · the part on the right holds 8 counters.", "model": { "start": { "figure": "array", "rows": 4, "cols": 5, "split": 2, "turned": false, "terms": null, "ops": null, "hoop": null }, "editable": [ "split", "rows", "cols" ], "given": [], "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "parts": [ "all the counters on the board", "the dashed line that cuts the array", "the counters on the left of the dashed line", "the counters on the right of the dashed line", "the array after it is turned the other way round", "one row of counters" ], "partsKey": "array" }, "expected": { "total-is": 20, "left-part-is": 12, "right-part-is": 8 }, "goal": { "text": "the whole array is still 4 rows of 5 · the part on the left of the dashed line holds 12 counters · the part on the right holds 8 counters", "statements": [ { "kind": "total-is", "text": "the whole array is still 4 rows of 5", "code": "split-not-whole-column", "value": 20 }, { "kind": "left-part-is", "text": "the part on the left of the dashed line holds 12 counters", "code": "split-wrong-part", "value": 12 }, { "kind": "right-part-is", "text": "the part on the right holds 8 counters", "code": "split-wrong-part", "value": 8 } ], "working": [ "The divider can only sit between whole columns, so the left part is always 4 rows of some number of columns.", "The board starts with the line after the second column, which puts 12 on the wrong side.", "12 counters is 4 rows of 3, so the divider goes after the third column and leaves 4 rows of 2 on the right." ] }, "solution": { "figure": "array", "rows": 4, "cols": 5, "split": 3, "turned": false, "terms": null, "ops": null, "hoop": null }, "hint": "Drag the dashed divider along the array until the left block holds 12 counters.", "misconceptionCode": "split-wrong-part" }, { "id": "arrays-mission-03", "title": "Hoop the pair that makes 20 in 8 + 17 + 3", "objectiveRecordIds": [ "0096-stage-3-3Ni.02", "0096-stage-5-5Ni.02" ], "prompt": "Hoop the pair that makes 20 in 8 + 17 + 3. Goal: the hoop is round the pair that is worth doing first · the pair inside the hoop makes the total that is easiest to work with.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 8, 17, 3 ], "ops": [ "+", "+" ], "hoop": null }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain" }, "expected": { "hoop-is": 1, "hoop-total-is": 20 }, "goal": { "text": "the hoop is round the pair that is worth doing first · the pair inside the hoop makes the total that is easiest to work with", "statements": [ { "kind": "hoop-is", "text": "the hoop is round the pair that is worth doing first", "code": "group-no-friendly-total", "value": 1 }, { "kind": "hoop-total-is", "text": "the pair inside the hoop makes the total that is easiest to work with", "code": "group-no-friendly-total", "value": 20 } ], "working": [ "The three numbers stay in this order, so the only choice is which pair to do first.", "17 + 3 makes 20, which is why the hoop goes round the last two numbers." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 8, 17, 3 ], "ops": [ "+", "+" ], "hoop": 1 }, "hint": "Drag the hoop to the right so it covers 17 and 3.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-mission-04", "title": "Hoop the pair that makes 10 in 2 × 5 × 9", "objectiveRecordIds": [ "0096-stage-4-4Ni.03" ], "prompt": "Hoop the pair that makes 10 in 2 × 5 × 9. Goal: the hoop is round the pair that is worth doing first · the pair inside the hoop makes the total that is easiest to work with.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 2, 5, 9 ], "ops": [ "×", "×" ], "hoop": null }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain" }, "expected": { "hoop-is": 0, "hoop-total-is": 10 }, "goal": { "text": "the hoop is round the pair that is worth doing first · the pair inside the hoop makes the total that is easiest to work with", "statements": [ { "kind": "hoop-is", "text": "the hoop is round the pair that is worth doing first", "code": "group-no-friendly-total", "value": 0 }, { "kind": "hoop-total-is", "text": "the pair inside the hoop makes the total that is easiest to work with", "code": "group-no-friendly-total", "value": 10 } ], "working": [ "Two pairs are possible: 2 × 5 or 5 × 9.", "2 × 5 makes 10, and multiplying anything by 10 is the easy step, so the hoop goes round the first pair." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 2, 5, 9 ], "ops": [ "×", "×" ], "hoop": 0 }, "hint": "Drag the hoop to the left so it covers 2 and 5.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-mission-05", "title": "Put the hoop where the multiplication comes first", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "Put the hoop where the multiplication comes first. Goal: the hoop is round the pair the usual agreement does first · the pair inside the hoop is the pair that has priority · the board's value is the value of the expression as it is written.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 3, 4, 2 ], "ops": [ "+", "×" ], "hoop": null }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain" }, "expected": { "hoop-is": 1, "first-step-is": "4 × 2", "expression-value-is": 11 }, "goal": { "text": "the hoop is round the pair the usual agreement does first · the pair inside the hoop is the pair that has priority · the board's value is the value of the expression as it is written", "statements": [ { "kind": "hoop-is", "text": "the hoop is round the pair the usual agreement does first", "code": "left-to-right-order", "value": 1 }, { "kind": "first-step-is", "text": "the pair inside the hoop is the pair that has priority", "code": "left-to-right-order", "value": "4 × 2" }, { "kind": "expression-value-is", "text": "the board's value is the value of the expression as it is written", "code": "bracket-ignored", "value": 11 } ], "working": [ "3 + 4 × 2 has no brackets, so the usual agreement decides the order: multiplication before addition.", "The multiplication is the pair on the right, so the hoop goes round 4 and 2, and 3 + 8 makes 11." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 3, 4, 2 ], "ops": [ "+", "×" ], "hoop": 1 }, "hint": "Drag the hoop over the 4 and the 2, which is the pair the agreement does first.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-mission-06", "title": "Add a bracket that changes the answer", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "Add a bracket that changes the answer. Goal: the hoop is round the pair that changes the answer · the value with the hoop differs from the value without it · the same three numbers and the same two signs are still on the board.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 9, 4, 2 ], "ops": [ "−", "×" ], "hoop": null }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain" }, "expected": { "hoop-is": 0, "expression-value-is": 10, "counters-unchanged": true }, "goal": { "text": "the hoop is round the pair that changes the answer · the value with the hoop differs from the value without it · the same three numbers and the same two signs are still on the board", "statements": [ { "kind": "hoop-is", "text": "the hoop is round the pair that changes the answer", "code": "bracket-ignored", "value": 0 }, { "kind": "expression-value-is", "text": "the value with the hoop differs from the value without it", "code": "bracket-ignored", "value": 10 }, { "kind": "counters-unchanged", "text": "the same three numbers and the same two signs are still on the board", "code": "bracket-moved-number", "value": true } ], "working": [ "Without a bracket, 9 − 4 × 2 means 9 − 8, which is 1.", "Hooping 9 − 4 first makes 5 × 2, which is 10: the numbers did not move, only the grouping did." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 9, 4, 2 ], "ops": [ "−", "×" ], "hoop": 0 }, "hint": "Drag the hoop round 9 and 4, then read the value the board gives back.", "misconceptionCode": "bracket-ignored" } ] }, "brackets-order": { "objectiveCode": "6Ni", "learnerAction": "Move the bracket between the two pairs until the line gives the value the goal asks for.", "objectiveVerbs": [ "understand that brackets can be used to alter the order of operations" ], "responseType": "model-construction", "scenarios": [ { "id": "brackets-mission-01", "title": "Bracket the pair that makes 25", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Bracket the pair that makes 25. Goal: the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 3, 2, 5 ], "ops": [ "+", "×" ], "hoop": 1 }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain-bracket" }, "expected": { "hoop-is": 0, "expression-value-is": 25, "counters-unchanged": true }, "goal": { "text": "the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board", "statements": [ { "kind": "hoop-is", "text": "the bracket is round the pair that makes the value in the title", "code": "bracketed-the-wrong-pair", "value": 0 }, { "kind": "expression-value-is", "text": "the value with the bracket is the value in the title", "code": "bracket-ignored", "value": 25 }, { "kind": "counters-unchanged", "text": "the same three numbers and the same two signs are still on the board", "code": "bracket-moved-number", "value": true } ], "working": [ "The three numbers stay in this order, so the bracket can only go round the first two or the last two.", "3 + 2 makes 5, and 5 × 5 makes 25; the other pair makes 3 + 10 = 13." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 3, 2, 5 ], "ops": [ "+", "×" ], "hoop": 0 }, "hint": "Drag the bracket round the 3 and the 2, then check the value the board gives back.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-mission-02", "title": "Bracket the pair that makes 54", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Bracket the pair that makes 54. Goal: the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 6, 4, 5 ], "ops": [ "×", "+" ], "hoop": 0 }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain-bracket" }, "expected": { "hoop-is": 1, "expression-value-is": 54, "counters-unchanged": true }, "goal": { "text": "the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board", "statements": [ { "kind": "hoop-is", "text": "the bracket is round the pair that makes the value in the title", "code": "bracketed-the-wrong-pair", "value": 1 }, { "kind": "expression-value-is", "text": "the value with the bracket is the value in the title", "code": "bracket-ignored", "value": 54 }, { "kind": "counters-unchanged", "text": "the same three numbers and the same two signs are still on the board", "code": "bracket-moved-number", "value": true } ], "working": [ "6 × 4 makes 24, and 24 + 5 makes 29; the other reading is 4 + 5 = 9, then 6 × 9 = 54." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 6, 4, 5 ], "ops": [ "×", "+" ], "hoop": 1 }, "hint": "Drag the bracket round the 4 and the 5, so the addition is done before the multiplication.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-mission-03", "title": "Bracket the pair that makes the value as large as you can", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Bracket the pair that makes the value as large as you can. Goal: the bracket is round the pair that gives the larger value · the value with the bracket is the larger of the two readings · the same three numbers and the same two signs are still on the board.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 8, 2, 5 ], "ops": [ "+", "×" ], "hoop": 1 }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain-bracket" }, "expected": { "hoop-is": 0, "expression-value-is": 50, "counters-unchanged": true }, "goal": { "text": "the bracket is round the pair that gives the larger value · the value with the bracket is the larger of the two readings · the same three numbers and the same two signs are still on the board", "statements": [ { "kind": "hoop-is", "text": "the bracket is round the pair that gives the larger value", "code": "bracketed-the-wrong-pair", "value": 0 }, { "kind": "expression-value-is", "text": "the value with the bracket is the larger of the two readings", "code": "bracket-ignored", "value": 50 }, { "kind": "counters-unchanged", "text": "the same three numbers and the same two signs are still on the board", "code": "bracket-moved-number", "value": true } ], "working": [ "Both readings are whole numbers, so work both out and compare them.", "8 + 2 makes 10, and 10 × 5 makes 50; the other reading makes 8 + 10 = 18." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 8, 2, 5 ], "ops": [ "+", "×" ], "hoop": 0 }, "hint": "Try the bracket on each pair in turn and keep the reading that gives the larger value.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-mission-04", "title": "Bracket the pair that makes 5", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Bracket the pair that makes 5. Goal: the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 12, 3, 4 ], "ops": [ "−", "+" ], "hoop": 0 }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain-bracket" }, "expected": { "hoop-is": 1, "expression-value-is": 5, "counters-unchanged": true }, "goal": { "text": "the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board", "statements": [ { "kind": "hoop-is", "text": "the bracket is round the pair that makes the value in the title", "code": "bracketed-the-wrong-pair", "value": 1 }, { "kind": "expression-value-is", "text": "the value with the bracket is the value in the title", "code": "bracket-ignored", "value": 5 }, { "kind": "counters-unchanged", "text": "the same three numbers and the same two signs are still on the board", "code": "bracket-moved-number", "value": true } ], "working": [ "12 − 3 makes 9, and 9 + 4 makes 13; 3 + 4 makes 7, and 12 − 7 makes 5." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 12, 3, 4 ], "ops": [ "−", "+" ], "hoop": 1 }, "hint": "Drag the bracket round the 3 and the 4 so the addition is done before the subtraction.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-mission-05", "title": "Bracket the pair that makes the value as small as you can", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Bracket the pair that makes the value as small as you can. Goal: the bracket is round the pair that gives the smaller value · the value with the bracket is the smaller of the two readings · the same three numbers and the same two signs are still on the board.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 11, 4, 2 ], "ops": [ "−", "×" ], "hoop": 0 }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain-bracket" }, "expected": { "hoop-is": 1, "expression-value-is": 3, "counters-unchanged": true }, "goal": { "text": "the bracket is round the pair that gives the smaller value · the value with the bracket is the smaller of the two readings · the same three numbers and the same two signs are still on the board", "statements": [ { "kind": "hoop-is", "text": "the bracket is round the pair that gives the smaller value", "code": "bracketed-the-wrong-pair", "value": 1 }, { "kind": "expression-value-is", "text": "the value with the bracket is the smaller of the two readings", "code": "bracket-ignored", "value": 3 }, { "kind": "counters-unchanged", "text": "the same three numbers and the same two signs are still on the board", "code": "bracket-moved-number", "value": true } ], "working": [ "11 − 4 makes 7, and 7 × 2 makes 14; 4 × 2 makes 8, and 11 − 8 makes 3." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 11, 4, 2 ], "ops": [ "−", "×" ], "hoop": 1 }, "hint": "Try the bracket on each pair in turn and keep the reading that gives the smaller value.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-mission-06", "title": "Bracket the pair that makes 20", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Bracket the pair that makes 20. Goal: the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board.", "model": { "start": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 3, 7, 2 ], "ops": [ "+", "×" ], "hoop": 1 }, "editable": [ "hoop" ], "given": [ "rows", "cols", "terms", "ops" ], "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "partsKey": "chain-bracket" }, "expected": { "hoop-is": 0, "expression-value-is": 20, "counters-unchanged": true }, "goal": { "text": "the bracket is round the pair that makes the value in the title · the value with the bracket is the value in the title · the same three numbers and the same two signs are still on the board", "statements": [ { "kind": "hoop-is", "text": "the bracket is round the pair that makes the value in the title", "code": "bracketed-the-wrong-pair", "value": 0 }, { "kind": "expression-value-is", "text": "the value with the bracket is the value in the title", "code": "bracket-ignored", "value": 20 }, { "kind": "counters-unchanged", "text": "the same three numbers and the same two signs are still on the board", "code": "bracket-moved-number", "value": true } ], "working": [ "3 + 7 makes 10, and 10 × 2 makes 20; the other reading is 7 × 2 = 14, then 3 + 14 = 17." ] }, "solution": { "figure": "chain", "rows": 0, "cols": 0, "split": null, "turned": false, "terms": [ 3, 7, 2 ], "ops": [ "+", "×" ], "hoop": 0 }, "hint": "Drag the bracket round the 3 and the 7 so the addition is done before the multiplication.", "misconceptionCode": "bracketed-the-wrong-pair" } ] } } }