{ "schemaVersion": "1.0", "moduleId": "arrays-laws-pilot", "pathways": { "arrays-laws": { "objectiveRecordIds": [ "0096-stage-3-3Ni.02", "0096-stage-3-3Ni.06", "0096-stage-4-4Ni.03", "0096-stage-5-5Ni.02", "0096-stage-6-6Ni.02" ], "minimumDistinctItems": 20, "responseType": "choice", "objectiveVerb": "understand and use the laws of arithmetic and the order of operations to simplify calculations", "items": [ { "id": "arrays-q01", "objectiveRecordIds": [ "0096-stage-3-3Ni.02" ], "prompt": "The board shows one row of 5 counters with a second row of 3 counters under it, and then the same two rows written the other way round. Which of these rules does the board show?", "data": { "family": "which-law", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "swap", "parts": [ "the top row of counters", "the bottom row of counters", "both rows joined together" ], "printed": [ "5", "3" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 5, 3 ], "ops": [ "+", "+" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": "commutative", "misconceptionDistractor": "associative", "misconceptionDistractors": [ { "value": "distributive", "code": "rule-split-as-swap", "feedback": "A split cuts one array into two parts whose counts add back to the whole. Nothing here was cut: the same counters stand the other way round, so the two numbers only changed places." }, { "value": "order of operations", "code": "law-as-grouping", "feedback": "The order of operations does not let you choose a different pair. It is the agreed rule for which pair to work out first in the sum written on the board." } ], "misconceptionMeaning": "the law was guessed from how many numbers were on the board" }, "correctAnswer": "commutative", "options": [ "commutative", "distributive", "associative", "order of operations" ], "correctIndex": 0, "difficulty": 1, "hint": "Ask what changed: the order of the numbers, the grouping of them, or was one thing cut into two?", "explanation": "Nothing was split and nothing was regrouped: the two rows just changed places, so 5 + 3 and 3 + 5 are the same total. Changing the order of the numbers is the commutative law.", "misconceptionCode": "rule-counted-numbers" }, { "id": "arrays-q02", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows 3 rows of 6 counters, and beside them the same counters arranged the other way round. Which of these rules does the board show?", "data": { "family": "which-law", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "array", "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" ], "printed": [], "rows": 3, "cols": 6, "split": null, "turned": true, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": "commutative", "misconceptionDistractor": "distributive", "misconceptionDistractors": [ { "value": "associative", "code": "rule-counted-numbers", "feedback": "Do not choose by how many numerals are written on the board. Ask what happened to the objects: did they change places, did one of them get cut, or was a different pair done first?" }, { "value": "order of operations", "code": "law-as-grouping", "feedback": "The order of operations does not let you choose a different pair. It is the agreed rule for which pair to work out first in the sum written on the board." } ], "misconceptionMeaning": "a turn was read as a split", "total": 18 }, "correctAnswer": "commutative", "options": [ "associative", "commutative", "distributive", "order of operations" ], "correctIndex": 1, "difficulty": 1, "hint": "Ask what changed: the order of the numbers, the grouping of them, or was one thing cut into two?", "explanation": "The turned array has 6 rows of 3 instead of 3 rows of 6, and the same counters, so 3 × 6 = 6 × 3. Only the order of the two numbers changed, which is the commutative law.", "misconceptionCode": "rule-split-as-swap" }, { "id": "arrays-q03", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows an array of 4 rows of 5 counters cut by one dashed line. Which of these rules does the board show?", "data": { "family": "which-law", "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "figure": "array", "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" ], "printed": [], "rows": 4, "cols": 5, "split": 3, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": "distributive", "misconceptionDistractor": "associative", "misconceptionDistractors": [ { "value": "commutative", "code": "rule-swapped-not-grouped", "feedback": "Nothing swapped places: the three numbers are still in the same order with the same signs. The hoop moved, which changes only which pair is done first. That is the associative law." }, { "value": "order of operations", "code": "law-as-grouping", "feedback": "The order of operations does not let you choose a different pair. It is the agreed rule for which pair to work out first in the sum written on the board." } ], "misconceptionMeaning": "the law was guessed from how many numbers were on the board", "total": 20 }, "correctAnswer": "distributive", "options": [ "commutative", "order of operations", "distributive", "associative" ], "correctIndex": 2, "difficulty": 2, "hint": "Ask what changed: the order of the numbers, the grouping of them, or was one thing cut into two?", "explanation": "One array became two: 4 × 5 = 12 + 8, which is 4 × 3 + 4 × 2. The multiplier was shared out over a split, which is the distributive law.", "misconceptionCode": "rule-counted-numbers" }, { "id": "arrays-q04", "objectiveRecordIds": [ "0096-stage-3-3Ni.02" ], "prompt": "The board shows three numbers in a row with a hoop round two of them. Which rule lets you move this hoop to the other pair without changing the total?", "data": { "family": "which-law", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "6", "4", "8", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 6, 4, 8 ], "ops": [ "+", "+" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": "associative", "misconceptionDistractor": "commutative", "misconceptionDistractors": [ { "value": "distributive", "code": "rule-hoop-as-split", "feedback": "A hoop cuts nothing. It only shows which two numbers to work out first. With only + signs, or only \\u00d7 signs, moving it leaves the answer the same. A split cuts an array into two parts that add back to the whole." }, { "value": "order of operations", "code": "law-as-grouping", "feedback": "The order of operations does not let you choose a different pair. It is the agreed rule for which pair to work out first in the sum written on the board." } ], "misconceptionMeaning": "a new grouping was read as the numbers swapping places", "chainText": "6 + (4 + 8)", "hoopValue": 12, "conventionValue": 18, "naiveValue": 18, "firstStep": "6 + 4" }, "correctAnswer": "associative", "options": [ "distributive", "order of operations", "commutative", "associative" ], "correctIndex": 3, "difficulty": 2, "hint": "Ask what changed: the order of the numbers, the grouping of them, or was one thing cut into two?", "explanation": "The hoop does 4 + 8 first, which is 6 + (4 + 8) = 18. The same three numbers in the same order with the other pair done first read (6 + 4) + 8, and that also comes to 18. Only the grouping changed, not the order of the numbers and not the signs, which is the associative law.", "misconceptionCode": "rule-swapped-not-grouped" }, { "id": "arrays-q05", "objectiveRecordIds": [ "0096-stage-4-4Ni.03" ], "prompt": "The board shows three numbers in a row with a hoop round two of them. Which rule lets you move this hoop to the other pair without changing the total?", "data": { "family": "which-law", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "2", "5", "9", "×", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 2, 5, 9 ], "ops": [ "×", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": "associative", "misconceptionDistractor": "distributive", "misconceptionDistractors": [ { "value": "commutative", "code": "rule-swapped-not-grouped", "feedback": "Nothing swapped places: the three numbers are still in the same order with the same signs. The hoop moved, which changes only which pair is done first. That is the associative law." }, { "value": "order of operations", "code": "law-as-grouping", "feedback": "The order of operations does not let you choose a different pair. It is the agreed rule for which pair to work out first in the sum written on the board." } ], "misconceptionMeaning": "a hoop was read as cutting the array into parts", "chainText": "(2 × 5) × 9", "hoopValue": 10, "conventionValue": 90, "naiveValue": 90, "firstStep": "2 × 5" }, "correctAnswer": "associative", "options": [ "associative", "distributive", "commutative", "order of operations" ], "correctIndex": 0, "difficulty": 3, "hint": "Ask what changed: the order of the numbers, the grouping of them, or was one thing cut into two?", "explanation": "The hoop does 2 × 5 first, which is (2 × 5) × 9 = 90. The same three numbers in the same order with the other pair done first read 2 × (5 × 9), and that also comes to 90. Only the grouping changed, not the order of the numbers and not the signs, which is the associative law.", "misconceptionCode": "rule-hoop-as-split" }, { "id": "arrays-q06", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The board shows three numbers and two signs written with no brackets at all. Which of these tells you what to work out first?", "data": { "family": "which-law", "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "4", "2", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 4, 2 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": "order of operations", "misconceptionDistractor": "associative", "misconceptionDistractors": [ { "value": "commutative", "code": "rule-swapped-not-grouped", "feedback": "Nothing swapped places: the three numbers are still in the same order with the same signs. The hoop moved, which changes only which pair is done first. That is the associative law." }, { "value": "distributive", "code": "rule-split-as-swap", "feedback": "A split cuts one array into two parts whose counts add back to the whole. Nothing here was cut: the same counters stand the other way round, so the two numbers only changed places." } ], "misconceptionMeaning": "the agreement about what to do first was read as a licence to re-group", "chainText": "3 + 4 × 2", "hoopValue": null, "conventionValue": 11, "naiveValue": 14, "firstStep": "4 × 2" }, "correctAnswer": "order of operations", "options": [ "commutative", "order of operations", "associative", "distributive" ], "correctIndex": 1, "difficulty": 4, "hint": "Ask what changed: the order of the numbers, the grouping of them, or was one thing cut into two?", "explanation": "Neither order nor grouping was changed here: the question is which part to do FIRST in an expression written without brackets, and that is the order of operations. Inside 3 + 4 × 2 the × comes first.", "misconceptionCode": "law-as-grouping" }, { "id": "arrays-q07", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows the same counters arranged two different ways, one turned the other way round. In the turned arrangement, how many counters are in each row?", "data": { "family": "turn-rows", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "array", "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" ], "printed": [], "rows": 3, "cols": 6, "split": null, "turned": true, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 4, "probeLabel": "the array after it is turned the other way round", "rule": null, "misconceptionDistractor": "6", "misconceptionDistractors": [ { "value": "18", "code": "counted-all-not-one-row", "feedback": "That is every counter on the board. The question asks for ONE row of the turned array: put your pencil along a single row and count only those." }, { "value": "9", "code": "add-instead-of-multiply", "feedback": "That adds the number of rows and the number in each row. Rows and columns count different things: to count the counters, multiply the two." } ], "misconceptionMeaning": "the number of rows after the turn was given instead of the counters in a row", "total": 18 }, "correctAnswer": "3", "options": [ "18", "6", "3", "9" ], "correctIndex": 2, "difficulty": 1, "hint": "Count the counters along one row of the turned array. Turning never adds or removes a counter.", "explanation": "The turned array has 6 rows, and each of those rows holds the 3 counters that used to make a column, so the answer is 3. The total did not change, which is why 3 × 6 and 6 × 3 are equal.", "misconceptionCode": "turned-rows-for-counters" }, { "id": "arrays-q08", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows the same counters arranged two different ways, one turned the other way round. In the turned arrangement, how many counters are in each row?", "data": { "family": "turn-rows", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "array", "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" ], "printed": [], "rows": 2, "cols": 8, "split": null, "turned": true, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 4, "probeLabel": "the array after it is turned the other way round", "rule": null, "misconceptionDistractor": "8", "misconceptionDistractors": [ { "value": "16", "code": "counted-all-not-one-row", "feedback": "That is every counter on the board. The question asks for ONE row of the turned array: put your pencil along a single row and count only those." }, { "value": "10", "code": "add-instead-of-multiply", "feedback": "That adds the number of rows and the number in each row. Rows and columns count different things: to count the counters, multiply the two." } ], "misconceptionMeaning": "the number of rows after the turn was given instead of the counters in a row", "total": 16 }, "correctAnswer": "2", "options": [ "16", "8", "10", "2" ], "correctIndex": 3, "difficulty": 1, "hint": "Count the counters along one row of the turned array. Turning never adds or removes a counter.", "explanation": "The turned array has 8 rows, and each of those rows holds the 2 counters that used to make a column, so the answer is 2. The total did not change, which is why 2 × 8 and 8 × 2 are equal.", "misconceptionCode": "turned-rows-for-counters" }, { "id": "arrays-q09", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows the same counters arranged two different ways, one turned the other way round. In the turned arrangement, how many counters are in each row?", "data": { "family": "turn-rows", "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "figure": "array", "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" ], "printed": [], "rows": 4, "cols": 5, "split": null, "turned": true, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 4, "probeLabel": "the array after it is turned the other way round", "rule": null, "misconceptionDistractor": "5", "misconceptionDistractors": [ { "value": "20", "code": "counted-all-not-one-row", "feedback": "That is every counter on the board. The question asks for ONE row of the turned array: put your pencil along a single row and count only those." }, { "value": "9", "code": "add-instead-of-multiply", "feedback": "That adds the number of rows and the number in each row. Rows and columns count different things: to count the counters, multiply the two." } ], "misconceptionMeaning": "the number of rows after the turn was given instead of the counters in a row", "total": 20 }, "correctAnswer": "4", "options": [ "4", "20", "9", "5" ], "correctIndex": 0, "difficulty": 2, "hint": "Count the counters along one row of the turned array. Turning never adds or removes a counter.", "explanation": "The turned array has 5 rows, and each of those rows holds the 4 counters that used to make a column, so the answer is 4. The total did not change, which is why 4 × 5 and 5 × 4 are equal.", "misconceptionCode": "turned-rows-for-counters" }, { "id": "arrays-q10", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows the same counters arranged two different ways, one turned the other way round. In the turned arrangement, how many counters are in each row?", "data": { "family": "turn-rows", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "array", "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" ], "printed": [], "rows": 5, "cols": 4, "split": null, "turned": true, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 4, "probeLabel": "the array after it is turned the other way round", "rule": null, "misconceptionDistractor": "4", "misconceptionDistractors": [ { "value": "20", "code": "counted-all-not-one-row", "feedback": "That is every counter on the board. The question asks for ONE row of the turned array: put your pencil along a single row and count only those." }, { "value": "9", "code": "add-instead-of-multiply", "feedback": "That adds the number of rows and the number in each row. Rows and columns count different things: to count the counters, multiply the two." } ], "misconceptionMeaning": "the number of rows after the turn was given instead of the counters in a row", "total": 20 }, "correctAnswer": "5", "options": [ "20", "5", "9", "4" ], "correctIndex": 1, "difficulty": 2, "hint": "Count the counters along one row of the turned array. Turning never adds or removes a counter.", "explanation": "The turned array has 4 rows, and each of those rows holds the 5 counters that used to make a column, so the answer is 5. The total did not change, which is why 5 × 4 and 4 × 5 are equal.", "misconceptionCode": "turned-rows-for-counters" }, { "id": "arrays-q11", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows a set of counters arranged in equal rows and columns. How many counters are there altogether?", "data": { "family": "array-total", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "array", "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" ], "printed": [], "rows": 3, "cols": 6, "split": null, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 0, "probeLabel": "all the counters on the board", "rule": null, "misconceptionDistractor": "9", "misconceptionDistractors": [ { "value": "3", "code": "counted-rows-not-counters", "feedback": "You counted the rows. The counters are what the question asks for, and one row holds more than one of them." }, { "value": "6", "code": "counted-columns-not-counters", "feedback": "You counted the columns. Each column is one counter per row, so count the counters inside one row instead." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 18 }, "correctAnswer": "18", "options": [ "3", "9", "18", "6" ], "correctIndex": 2, "difficulty": 1, "hint": "Count one row, then count how many rows there are, and multiply those two numbers.", "explanation": "There are 3 rows of 6, so 3 × 6 = 18. Adding 3 and 6 counts rows and columns once each, which is not the same thing as counting the counters.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q12", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows a seed tray arranged in equal rows and columns. How many seeds are there altogether?", "data": { "family": "array-total", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "array", "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" ], "printed": [], "rows": 5, "cols": 4, "split": null, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 0, "probeLabel": "all the counters on the board", "rule": null, "misconceptionDistractor": "9", "misconceptionDistractors": [ { "value": "5", "code": "counted-rows-not-counters", "feedback": "You counted the rows. The counters are what the question asks for, and one row holds more than one of them." }, { "value": "4", "code": "counted-columns-not-counters", "feedback": "You counted the columns. Each column is one counter per row, so count the counters inside one row instead." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 20 }, "correctAnswer": "20", "options": [ "5", "9", "4", "20" ], "correctIndex": 3, "difficulty": 1, "hint": "Count one row, then count how many rows there are, and multiply those two numbers.", "explanation": "There are 5 rows of 4, so 5 × 4 = 20. Adding 5 and 4 counts rows and columns once each, which is not the same thing as counting the counters.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q13", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows a strip of tiles on a floor arranged in equal rows and columns. How many tiles are there altogether?", "data": { "family": "array-total", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "array", "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" ], "printed": [], "rows": 4, "cols": 4, "split": null, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 0, "probeLabel": "all the counters on the board", "rule": null, "misconceptionDistractor": "8", "misconceptionDistractors": [ { "value": "4", "code": "counted-rows-not-counters", "feedback": "You counted the rows. The counters are what the question asks for, and one row holds more than one of them." }, { "value": "12", "code": "missed-one-row", "feedback": "One whole row is missing from that count. Count the rows first, then the counters in one row, and multiply." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 16 }, "correctAnswer": "16", "options": [ "16", "4", "12", "8" ], "correctIndex": 0, "difficulty": 2, "hint": "Count one row, then count how many rows there are, and multiply those two numbers.", "explanation": "There are 4 rows of 4, so 4 × 4 = 16. Adding 4 and 4 counts rows and columns once each, which is not the same thing as counting the counters.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q14", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "The board shows a set of book shelves arranged in equal rows and columns. How many books are there altogether?", "data": { "family": "array-total", "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "figure": "array", "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" ], "printed": [], "rows": 5, "cols": 3, "split": null, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 0, "probeLabel": "all the counters on the board", "rule": null, "misconceptionDistractor": "8", "misconceptionDistractors": [ { "value": "5", "code": "counted-rows-not-counters", "feedback": "You counted the rows. The counters are what the question asks for, and one row holds more than one of them." }, { "value": "3", "code": "counted-columns-not-counters", "feedback": "You counted the columns. Each column is one counter per row, so count the counters inside one row instead." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 15 }, "correctAnswer": "15", "options": [ "5", "15", "3", "8" ], "correctIndex": 1, "difficulty": 2, "hint": "Count one row, then count how many rows there are, and multiply those two numbers.", "explanation": "There are 5 rows of 3, so 5 × 3 = 15. Adding 5 and 3 counts rows and columns once each, which is not the same thing as counting the counters.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q15", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "An array of counters is cut by one dashed line into two parts, and the ringed part is the block on the left of the line. How many counters are in the ringed part?", "data": { "family": "count-parts", "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "figure": "array", "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" ], "printed": [], "rows": 4, "cols": 5, "split": 3, "turned": false, "side": "left", "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 2, "probeLabel": "the counters on the left of the dashed line", "rule": null, "misconceptionDistractor": "7", "misconceptionDistractors": [ { "value": "20", "code": "counted-the-whole-array", "feedback": "That is the whole array. The hoop marks one part of it, so count the counters in that part only." }, { "value": "8", "code": "counted-the-other-part", "feedback": "That is the part on the other side of the dashed line. Read which side the hoop is on and count that side." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 20 }, "correctAnswer": "12", "options": [ "20", "8", "12", "7" ], "correctIndex": 2, "difficulty": 2, "hint": "The ringed part is its own smaller array: rows times columns for that part only.", "explanation": "The ringed part is 4 rows of 3, which is 4 × 3 = 12 counters. The other part holds 8, and the two parts together make the whole array of 20.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q16", "objectiveRecordIds": [ "0096-stage-3-3Ni.06" ], "prompt": "An array of counters is cut by one dashed line into two parts, and the ringed part is the block on the right of the line. How many counters are in the ringed part?", "data": { "family": "count-parts", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "array", "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" ], "printed": [], "rows": 3, "cols": 6, "split": 4, "turned": false, "side": "right", "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 3, "probeLabel": "the counters on the right of the dashed line", "rule": null, "misconceptionDistractor": "5", "misconceptionDistractors": [ { "value": "18", "code": "counted-the-whole-array", "feedback": "That is the whole array. The hoop marks one part of it, so count the counters in that part only." }, { "value": "12", "code": "counted-the-other-part", "feedback": "That is the part on the other side of the dashed line. Read which side the hoop is on and count that side." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 18 }, "correctAnswer": "6", "options": [ "18", "12", "5", "6" ], "correctIndex": 3, "difficulty": 2, "hint": "The ringed part is its own smaller array: rows times columns for that part only.", "explanation": "The ringed part is 3 rows of 2, which is 3 × 2 = 6 counters. The other part holds 12, and the two parts together make the whole array of 18.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q17", "objectiveRecordIds": [ "0096-stage-3-3Ni.06", "0096-stage-4-4Ni.03" ], "prompt": "An array of counters is cut by one dashed line into two parts, and the ringed part is the block on the left of the line. How many counters are in the ringed part?", "data": { "family": "count-parts", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "array", "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" ], "printed": [], "rows": 5, "cols": 4, "split": 1, "turned": false, "side": "left", "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 2, "probeLabel": "the counters on the left of the dashed line", "rule": null, "misconceptionDistractor": "6", "misconceptionDistractors": [ { "value": "20", "code": "counted-the-whole-array", "feedback": "That is the whole array. The hoop marks one part of it, so count the counters in that part only." }, { "value": "15", "code": "counted-the-other-part", "feedback": "That is the part on the other side of the dashed line. Read which side the hoop is on and count that side." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 20 }, "correctAnswer": "5", "options": [ "5", "20", "15", "6" ], "correctIndex": 0, "difficulty": 2, "hint": "The ringed part is its own smaller array: rows times columns for that part only.", "explanation": "The ringed part is 5 rows of 1, which is 5 × 1 = 5 counters. The other part holds 15, and the two parts together make the whole array of 20.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q18", "objectiveRecordIds": [ "0096-stage-3-3Ni.06", "0096-stage-5-5Ni.02" ], "prompt": "An array of counters is cut by one dashed line into two parts, and the ringed part is the block on the right of the line. How many counters are in the ringed part?", "data": { "family": "count-parts", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "array", "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" ], "printed": [], "rows": 2, "cols": 9, "split": 4, "turned": false, "side": "right", "terms": null, "ops": null, "hoop": null, "strip": null, "probe": 3, "probeLabel": "the counters on the right of the dashed line", "rule": null, "misconceptionDistractor": "7", "misconceptionDistractors": [ { "value": "18", "code": "counted-the-whole-array", "feedback": "That is the whole array. The hoop marks one part of it, so count the counters in that part only." }, { "value": "8", "code": "counted-the-other-part", "feedback": "That is the part on the other side of the dashed line. Read which side the hoop is on and count that side." } ], "misconceptionMeaning": "rows and columns were added instead of multiplied", "total": 18 }, "correctAnswer": "10", "options": [ "7", "10", "18", "8" ], "correctIndex": 1, "difficulty": 3, "hint": "The ringed part is its own smaller array: rows times columns for that part only.", "explanation": "The ringed part is 2 rows of 5, which is 2 × 5 = 10 counters. The other part holds 8, and the two parts together make the whole array of 18.", "misconceptionCode": "add-instead-of-multiply" }, { "id": "arrays-q19", "objectiveRecordIds": [ "0096-stage-5-5Ni.02" ], "prompt": "The sentence on the board is true. What number goes in the box marked with a question mark?", "data": { "family": "missing-side", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "strip", "parts": [ "the whole sentence", "the left-hand side of the sentence", "the right-hand side of the sentence", "the box marked with a question mark" ], "printed": [ "7", "×", "9", "=", "7", "×", "5", "+", "7", "×", "?" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": "7 × 9 = 7 × 5 + 7 × ?", "probe": 3, "probeLabel": "the box marked with a question mark", "rule": null, "misconceptionDistractor": "2", "misconceptionDistractors": [ { "value": "7", "code": "answered-with-the-number-of-groups", "feedback": "That is how MANY groups there are, not how many are in each one. The blank box is a number of counters in a group." }, { "value": "5", "code": "answered-with-the-known-part", "feedback": "That number is already written on the board. The box is the part the sentence has not told you yet." } ], "misconceptionMeaning": "the number of rows was subtracted instead of the part already taken" }, "correctAnswer": "4", "options": [ "2", "7", "4", "5" ], "correctIndex": 2, "difficulty": 3, "hint": "The two split parts have to add back up to the whole number of columns on the left.", "explanation": "7 groups of 9 were split into 7 groups of 5 and 7 groups of something else, so the box holds 9 − 5 = 4. Check it on the array: 7 × 5 + 7 × 4 = 35 + 28 = 63.", "misconceptionCode": "subtract-wrong-side" }, { "id": "arrays-q20", "objectiveRecordIds": [ "0096-stage-5-5Ni.02" ], "prompt": "The sentence on the board is true. What number goes in the box marked with a question mark?", "data": { "family": "missing-side", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "strip", "parts": [ "the whole sentence", "the left-hand side of the sentence", "the right-hand side of the sentence", "the box marked with a question mark" ], "printed": [ "6", "×", "7", "=", "6", "×", "2", "+", "6", "×", "?" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": "6 × 7 = 6 × 2 + 6 × ?", "probe": 3, "probeLabel": "the box marked with a question mark", "rule": null, "misconceptionDistractor": "1", "misconceptionDistractors": [ { "value": "6", "code": "answered-with-the-number-of-groups", "feedback": "That is how MANY groups there are, not how many are in each one. The blank box is a number of counters in a group." }, { "value": "2", "code": "answered-with-the-known-part", "feedback": "That number is already written on the board. The box is the part the sentence has not told you yet." } ], "misconceptionMeaning": "the number of rows was subtracted instead of the part already taken" }, "correctAnswer": "5", "options": [ "1", "6", "2", "5" ], "correctIndex": 3, "difficulty": 3, "hint": "The two split parts have to add back up to the whole number of columns on the left.", "explanation": "6 groups of 7 were split into 6 groups of 2 and 6 groups of something else, so the box holds 7 − 2 = 5. Check it on the array: 6 × 2 + 6 × 5 = 12 + 30 = 42.", "misconceptionCode": "subtract-wrong-side" }, { "id": "arrays-q21", "objectiveRecordIds": [ "0096-stage-5-5Ni.02" ], "prompt": "The sentence on the board is true. What number goes in the box marked with a question mark?", "data": { "family": "missing-side", "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "figure": "strip", "parts": [ "the whole sentence", "the left-hand side of the sentence", "the right-hand side of the sentence", "the box marked with a question mark" ], "printed": [ "5", "×", "9", "=", "5", "×", "2", "+", "5", "×", "?" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": null, "ops": null, "hoop": null, "strip": "5 × 9 = 5 × 2 + 5 × ?", "probe": 3, "probeLabel": "the box marked with a question mark", "rule": null, "misconceptionDistractor": "4", "misconceptionDistractors": [ { "value": "5", "code": "answered-with-the-number-of-groups", "feedback": "That is how MANY groups there are, not how many are in each one. The blank box is a number of counters in a group." }, { "value": "2", "code": "answered-with-the-known-part", "feedback": "That number is already written on the board. The box is the part the sentence has not told you yet." } ], "misconceptionMeaning": "the number of rows was subtracted instead of the part already taken" }, "correctAnswer": "7", "options": [ "7", "5", "2", "4" ], "correctIndex": 0, "difficulty": 2, "hint": "The two split parts have to add back up to the whole number of columns on the left.", "explanation": "5 groups of 9 were split into 5 groups of 2 and 5 groups of something else, so the box holds 9 − 2 = 7. Check it on the array: 5 × 2 + 5 × 7 = 10 + 35 = 45.", "misconceptionCode": "subtract-wrong-side" }, { "id": "arrays-q22", "objectiveRecordIds": [ "0096-stage-3-3Ni.02", "0096-stage-5-5Ni.02" ], "prompt": "Three numbers are to be worked out in the order shown, and nothing is hooped yet. Which two numbers do you work out first to make this easier to do in your head?", "data": { "family": "easier-first", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "8", "17", "3", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 8, 17, 3 ], "ops": [ "+", "+" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "8 + 17", "misconceptionDistractors": [ { "value": "8 + 3", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "8 + 17 + 3", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the first pair was chosen because it comes first, not because it is friendly", "chainText": "8 + 17 + 3", "hoopValue": null, "conventionValue": 28, "naiveValue": 28, "firstStep": "8 + 17" }, "correctAnswer": "17 + 3", "options": [ "8 + 17", "17 + 3", "8 + 3", "8 + 17 + 3" ], "correctIndex": 1, "difficulty": 3, "hint": "Look for the pair that makes a multiple of 10, or a 10 or 20 you can multiply by.", "explanation": "17 + 3 makes 20, which is a friendly number, and then the remaining number is easy to add or multiply. Doing 8 + 17 first makes 25, which leaves the awkward step still to do. Re-grouping like this is the associative law, and the total cannot change.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-q23", "objectiveRecordIds": [ "0096-stage-3-3Ni.02", "0096-stage-5-5Ni.02" ], "prompt": "Three numbers are to be worked out in the order shown, and nothing is hooped yet. Which two numbers do you work out first to make this easier to do in your head?", "data": { "family": "easier-first", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "25", "6", "4", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 25, 6, 4 ], "ops": [ "+", "+" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "25 + 6", "misconceptionDistractors": [ { "value": "25 + 4", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "25 + 6 + 4", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the first pair was chosen because it comes first, not because it is friendly", "chainText": "25 + 6 + 4", "hoopValue": null, "conventionValue": 35, "naiveValue": 35, "firstStep": "25 + 6" }, "correctAnswer": "6 + 4", "options": [ "25 + 6", "25 + 4", "6 + 4", "25 + 6 + 4" ], "correctIndex": 2, "difficulty": 3, "hint": "Look for the pair that makes a multiple of 10, or a 10 or 20 you can multiply by.", "explanation": "6 + 4 makes 10, which is a friendly number, and then the remaining number is easy to add or multiply. Doing 25 + 6 first makes 31, which leaves the awkward step still to do. Re-grouping like this is the associative law, and the total cannot change.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-q24", "objectiveRecordIds": [ "0096-stage-5-5Ni.02", "0096-stage-3-3Ni.02" ], "prompt": "Three numbers are to be worked out in the order shown, and nothing is hooped yet. Which two numbers do you work out first to make this easier to do in your head?", "data": { "family": "easier-first", "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "8", "12", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 8, 12 ], "ops": [ "+", "+" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "3 + 8", "misconceptionDistractors": [ { "value": "3 + 12", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "3 + 8 + 12", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the first pair was chosen because it comes first, not because it is friendly", "chainText": "3 + 8 + 12", "hoopValue": null, "conventionValue": 23, "naiveValue": 23, "firstStep": "3 + 8" }, "correctAnswer": "8 + 12", "options": [ "3 + 12", "3 + 8", "3 + 8 + 12", "8 + 12" ], "correctIndex": 3, "difficulty": 4, "hint": "Look for the pair that makes a multiple of 10, or a 10 or 20 you can multiply by.", "explanation": "8 + 12 makes 20, which is a friendly number, and then the remaining number is easy to add or multiply. Doing 3 + 8 first makes 11, which leaves the awkward step still to do. Re-grouping like this is the associative law, and the total cannot change.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-q25", "objectiveRecordIds": [ "0096-stage-4-4Ni.03", "0096-stage-5-5Ni.02" ], "prompt": "Three numbers are to be worked out in the order shown, and nothing is hooped yet. Which two numbers do you work out first to make this easier to do in your head?", "data": { "family": "easier-first", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "7", "5", "2", "×", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 7, 5, 2 ], "ops": [ "×", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "7 × 5", "misconceptionDistractors": [ { "value": "7 × 2", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "7 × 5 × 2", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the first pair was chosen because it comes first, not because it is friendly", "chainText": "7 × 5 × 2", "hoopValue": null, "conventionValue": 70, "naiveValue": 70, "firstStep": "7 × 5" }, "correctAnswer": "5 × 2", "options": [ "5 × 2", "7 × 5", "7 × 2", "7 × 5 × 2" ], "correctIndex": 0, "difficulty": 3, "hint": "Look for the pair that makes a multiple of 10, or a 10 or 20 you can multiply by.", "explanation": "5 × 2 makes 10, which is a friendly number, and then the remaining number is easy to add or multiply. Doing 7 × 5 first makes 35, which leaves the awkward step still to do. Re-grouping like this is the associative law, and the total cannot change.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-q26", "objectiveRecordIds": [ "0096-stage-4-4Ni.03", "0096-stage-5-5Ni.02" ], "prompt": "Three numbers are to be worked out in the order shown, and nothing is hooped yet. Which two numbers do you work out first to make this easier to do in your head?", "data": { "family": "easier-first", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "7", "2", "5", "×", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 7, 2, 5 ], "ops": [ "×", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "7 × 2", "misconceptionDistractors": [ { "value": "7 × 5", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "7 × 2 × 5", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the first pair was chosen because it comes first, not because it is friendly", "chainText": "7 × 2 × 5", "hoopValue": null, "conventionValue": 70, "naiveValue": 70, "firstStep": "7 × 2" }, "correctAnswer": "2 × 5", "options": [ "7 × 2", "2 × 5", "7 × 5", "7 × 2 × 5" ], "correctIndex": 1, "difficulty": 3, "hint": "Look for the pair that makes a multiple of 10, or a 10 or 20 you can multiply by.", "explanation": "2 × 5 makes 10, which is a friendly number, and then the remaining number is easy to add or multiply. Doing 7 × 2 first makes 14, which leaves the awkward step still to do. Re-grouping like this is the associative law, and the total cannot change.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-q27", "objectiveRecordIds": [ "0096-stage-3-3Ni.02", "0096-stage-5-5Ni.02" ], "prompt": "Three numbers are to be worked out in the order shown, and nothing is hooped yet. Which two numbers do you work out first to make this easier to do in your head?", "data": { "family": "easier-first", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "16", "5", "25", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 16, 5, 25 ], "ops": [ "+", "+" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "16 + 5", "misconceptionDistractors": [ { "value": "16 + 25", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "16 + 5 + 25", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the first pair was chosen because it comes first, not because it is friendly", "chainText": "16 + 5 + 25", "hoopValue": null, "conventionValue": 46, "naiveValue": 46, "firstStep": "16 + 5" }, "correctAnswer": "5 + 25", "options": [ "16 + 25", "16 + 5", "5 + 25", "16 + 5 + 25" ], "correctIndex": 2, "difficulty": 4, "hint": "Look for the pair that makes a multiple of 10, or a 10 or 20 you can multiply by.", "explanation": "5 + 25 makes 30, which is a friendly number, and then the remaining number is easy to add or multiply. Doing 16 + 5 first makes 21, which leaves the awkward step still to do. Re-grouping like this is the associative law, and the total cannot change.", "misconceptionCode": "group-no-friendly-total" }, { "id": "arrays-q28", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "Three numbers and two signs are written with no brackets. Which calculation is done first, following the usual agreement about the order?", "data": { "family": "order-first-step", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "4", "2", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 4, 2 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "3 + 4", "misconceptionDistractors": [ { "value": "3 + 2", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "3 + 4 × 2", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "3 + 4 × 2", "hoopValue": null, "conventionValue": 11, "naiveValue": 14, "firstStep": "4 × 2" }, "correctAnswer": "4 × 2", "options": [ "3 + 2", "3 + 4", "3 + 4 × 2", "4 × 2" ], "correctIndex": 3, "difficulty": 4, "hint": "Multiplication and division come before addition and subtraction, whatever position they sit in.", "explanation": "4 × 2 is done first, because × has priority over +, so it is done first even though it sits on the right. Doing 3 + 4 first is the mistake this item is about: it gives (3 + 4) × 2 instead of 3 + (4 × 2). The order is an agreement about one expression, not a licence to re-arrange it.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-q29", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "Three numbers and two signs are written with no brackets. Which calculation is done first, following the usual agreement about the order?", "data": { "family": "order-first-step", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "2", "6", "3", "+", "÷" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 2, 6, 3 ], "ops": [ "+", "÷" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "2 + 6", "misconceptionDistractors": [ { "value": "2 + 3", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "2 + 6 ÷ 3", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "2 + 6 ÷ 3", "hoopValue": null, "conventionValue": 4, "naiveValue": null, "firstStep": "6 ÷ 3" }, "correctAnswer": "6 ÷ 3", "options": [ "6 ÷ 3", "2 + 3", "2 + 6", "2 + 6 ÷ 3" ], "correctIndex": 0, "difficulty": 4, "hint": "Multiplication and division come before addition and subtraction, whatever position they sit in.", "explanation": "6 ÷ 3 is done first, because ÷ has priority over +, so it is done first even though it sits on the right. Doing 2 + 6 first is the mistake this item is about: it gives (2 + 6) ÷ 3 instead of 2 + (6 ÷ 3). The order is an agreement about one expression, not a licence to re-arrange it.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-q30", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "Three numbers and two signs are written with no brackets. Which calculation is done first, following the usual agreement about the order?", "data": { "family": "order-first-step", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "9", "2", "3", "−", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 9, 2, 3 ], "ops": [ "−", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "9 − 2", "misconceptionDistractors": [ { "value": "9 − 3", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "9 − 2 × 3", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "9 − 2 × 3", "hoopValue": null, "conventionValue": 3, "naiveValue": 21, "firstStep": "2 × 3" }, "correctAnswer": "2 × 3", "options": [ "9 − 3", "2 × 3", "9 − 2", "9 − 2 × 3" ], "correctIndex": 1, "difficulty": 4, "hint": "Multiplication and division come before addition and subtraction, whatever position they sit in.", "explanation": "2 × 3 is done first, because × has priority over −, so it is done first even though it sits on the right. Doing 9 − 2 first is the mistake this item is about: it gives (9 − 2) × 3 instead of 9 − (2 × 3). The order is an agreement about one expression, not a licence to re-arrange it.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-q31", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "Three numbers and two signs are written with no brackets. Which calculation is done first, following the usual agreement about the order?", "data": { "family": "order-first-step", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "4", "2", "+", "−" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 4, 2 ], "ops": [ "+", "−" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "4 − 2", "misconceptionDistractors": [ { "value": "3 + 2", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "3 + 4 − 2", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the right-hand pair was done first although both signs have equal priority", "chainText": "3 + 4 − 2", "hoopValue": null, "conventionValue": 5, "naiveValue": 5, "firstStep": "3 + 4" }, "correctAnswer": "3 + 4", "options": [ "3 + 2", "4 − 2", "3 + 4", "3 + 4 − 2" ], "correctIndex": 2, "difficulty": 4, "hint": "Multiplication and division come before addition and subtraction, whatever position they sit in.", "explanation": "3 + 4 is done first, because + and − have the same priority, so the pair on the left is done first. Doing 4 − 2 first is the mistake this item is about: it gives 3 + (4 − 2) instead of (3 + 4) − 2. The order is an agreement about one expression, not a licence to re-arrange it.", "misconceptionCode": "same-precedence-right-first" }, { "id": "arrays-q32", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "Three numbers and two signs are written with no brackets. Which calculation is done first, following the usual agreement about the order?", "data": { "family": "order-first-step", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "12", "4", "5", "÷", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 12, 4, 5 ], "ops": [ "÷", "+" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "4 + 5", "misconceptionDistractors": [ { "value": "12 ÷ 5", "code": "hooped-the-ends", "feedback": "Those two numbers do not touch on the board, so no hoop can go round them. A hoop covers two neighbours." }, { "value": "12 ÷ 4 + 5", "code": "worked-all-three", "feedback": "That is the whole line at once. The question asks which TWO are done first, so name the pair." } ], "misconceptionMeaning": "the pair without priority was done first because it looked easier to start", "chainText": "12 ÷ 4 + 5", "hoopValue": null, "conventionValue": 8, "naiveValue": null, "firstStep": "12 ÷ 4" }, "correctAnswer": "12 ÷ 4", "options": [ "12 ÷ 5", "4 + 5", "12 ÷ 4 + 5", "12 ÷ 4" ], "correctIndex": 3, "difficulty": 4, "hint": "Multiplication and division come before addition and subtraction, whatever position they sit in.", "explanation": "12 ÷ 4 is done first, because ÷ has priority over +, so it is done first wherever it sits in the line. Doing 4 + 5 first is the mistake this item is about: it gives 12 ÷ (4 + 5) instead of (12 ÷ 4) + 5. The order is an agreement about one expression, not a licence to re-arrange it.", "misconceptionCode": "priority-inverted" }, { "id": "arrays-q33", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The expression on the board is worked out following the usual agreement about the order. What is its value?", "data": { "family": "order-value", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "4", "2", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 4, 2 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "14", "misconceptionDistractors": [ { "value": "9", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "8", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "3 + 4 × 2", "hoopValue": null, "conventionValue": 11, "naiveValue": 14, "firstStep": "4 × 2" }, "correctAnswer": "11", "options": [ "11", "9", "14", "8" ], "correctIndex": 0, "difficulty": 4, "hint": "Do the part with priority first, write down what it makes, then do the other sign.", "explanation": "Do 4 × 2 first, which makes 8, then the other sign, giving 11. Working strictly from the left gives 14 instead, which is why brackets matter.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-q34", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The expression on the board is worked out following the usual agreement about the order. What is its value?", "data": { "family": "order-value", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "4", "6", "2", "+", "÷" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 4, 6, 2 ], "ops": [ "+", "÷" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "5", "misconceptionDistractors": [ { "value": "12", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "3", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "4 + 6 ÷ 2", "hoopValue": null, "conventionValue": 7, "naiveValue": 5, "firstStep": "6 ÷ 2" }, "correctAnswer": "7", "options": [ "12", "7", "5", "3" ], "correctIndex": 1, "difficulty": 4, "hint": "Do the part with priority first, write down what it makes, then do the other sign.", "explanation": "Do 6 ÷ 2 first, which makes 3, then the other sign, giving 7. Working strictly from the left gives 5 instead, which is why brackets matter.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-q35", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The expression on the board is worked out following the usual agreement about the order. What is its value?", "data": { "family": "order-value", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "5", "2", "4", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 5, 2, 4 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "28", "misconceptionDistractors": [ { "value": "11", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "8", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "5 + 2 × 4", "hoopValue": null, "conventionValue": 13, "naiveValue": 28, "firstStep": "2 × 4" }, "correctAnswer": "13", "options": [ "11", "28", "13", "8" ], "correctIndex": 2, "difficulty": 4, "hint": "Do the part with priority first, write down what it makes, then do the other sign.", "explanation": "Do 2 × 4 first, which makes 8, then the other sign, giving 13. Working strictly from the left gives 28 instead, which is why brackets matter.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-q36", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The expression on the board is worked out following the usual agreement about the order. What is its value?", "data": { "family": "order-value", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "7", "2", "3", "−", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 7, 2, 3 ], "ops": [ "−", "×" ], "hoop": null, "strip": null, "probe": null, "probeLabel": null, "rule": null, "misconceptionDistractor": "15", "misconceptionDistractors": [ { "value": "12", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "6", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "7 − 2 × 3", "hoopValue": null, "conventionValue": 1, "naiveValue": 15, "firstStep": "2 × 3" }, "correctAnswer": "1", "options": [ "12", "15", "6", "1" ], "correctIndex": 3, "difficulty": 4, "hint": "Do the part with priority first, write down what it makes, then do the other sign.", "explanation": "Do 2 × 3 first, which makes 6, then the other sign, giving 1. Working strictly from the left gives 15 instead, which is why brackets matter.", "misconceptionCode": "left-to-right-order" }, { "id": "arrays-q37", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The hoop shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "5", "4", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 5, 4 ], "ops": [ "+", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": null, "misconceptionDistractor": "23", "misconceptionDistractors": [ { "value": "8", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the hoop. The third number is still outside it, and the question asks for the whole expression." }, { "value": "12", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "(3 + 5) × 4", "hoopValue": 8, "conventionValue": 23, "naiveValue": 32, "firstStep": "5 × 4" }, "correctAnswer": "32", "options": [ "32", "8", "23", "12" ], "correctIndex": 0, "difficulty": 4, "hint": "Work the numbers inside the hoop before you touch the third number.", "explanation": "The hoop makes (3 + 5) × 4, so 3 + 5 is done first and the value is 32. Without the hoop the same numbers give 23, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "arrays-q38", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The hoop shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "4", "2", "7", "×", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 4, 2, 7 ], "ops": [ "×", "+" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": null, "misconceptionDistractor": "15", "misconceptionDistractors": [ { "value": "9", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the hoop. The third number is still outside it, and the question asks for the whole expression." }, { "value": "13", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "4 × (2 + 7)", "hoopValue": 9, "conventionValue": 15, "naiveValue": 36, "firstStep": "4 × 2" }, "correctAnswer": "36", "options": [ "9", "36", "15", "13" ], "correctIndex": 1, "difficulty": 4, "hint": "Work the numbers inside the hoop before you touch the third number.", "explanation": "The hoop makes 4 × (2 + 7), so 2 + 7 is done first and the value is 36. Without the hoop the same numbers give 15, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "arrays-q39", "objectiveRecordIds": [ "0096-stage-6-6Ni.02" ], "prompt": "The hoop shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "9", "4", "2", "−", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 9, 4, 2 ], "ops": [ "−", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": null, "misconceptionDistractor": "1", "misconceptionDistractors": [ { "value": "5", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the hoop. The third number is still outside it, and the question asks for the whole expression." }, { "value": "15", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "(9 − 4) × 2", "hoopValue": 5, "conventionValue": 1, "naiveValue": 10, "firstStep": "4 × 2" }, "correctAnswer": "10", "options": [ "5", "1", "10", "15" ], "correctIndex": 2, "difficulty": 4, "hint": "Work the numbers inside the hoop before you touch the third number.", "explanation": "The hoop makes (9 − 4) × 2, so 9 − 4 is done first and the value is 10. Without the hoop the same numbers give 1, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "arrays-q40", "objectiveRecordIds": [ "0096-stage-3-3Ni.02" ], "prompt": "The ringed hoop joins two of the numbers. What does the calculation inside the hoop make?", "data": { "family": "group-total", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "8", "17", "3", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 8, 17, 3 ], "ops": [ "+", "+" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": null, "misconceptionDistractor": "28", "misconceptionDistractors": [ { "value": "8", "code": "answered-with-the-outside-number", "feedback": "That number is outside the hoop. Only the two numbers the hoop covers are worked out for this answer." }, { "value": "25", "code": "hooped-the-other-pair", "feedback": "That is the other pair's total. Read which two numbers the hoop actually covers and work out those." } ], "misconceptionMeaning": "all three numbers were worked out when only the hooped pair was asked for", "chainText": "8 + (17 + 3)", "hoopValue": 20, "conventionValue": 28, "naiveValue": 28, "firstStep": "8 + 17" }, "correctAnswer": "20", "options": [ "8", "25", "28", "20" ], "correctIndex": 3, "difficulty": 2, "hint": "Only the two numbers inside the hoop count for this answer.", "explanation": "Inside the hoop is 17 + 3, which makes 20. The third number is not in the hoop, so it is not counted yet; the whole expression comes to 28.", "misconceptionCode": "group-whole-chain" }, { "id": "arrays-q41", "objectiveRecordIds": [ "0096-stage-3-3Ni.02" ], "prompt": "The ringed hoop joins two of the numbers. What does the calculation inside the hoop make?", "data": { "family": "group-total", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "6", "25", "4", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 6, 25, 4 ], "ops": [ "+", "+" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": null, "misconceptionDistractor": "35", "misconceptionDistractors": [ { "value": "4", "code": "answered-with-the-outside-number", "feedback": "That number is outside the hoop. Only the two numbers the hoop covers are worked out for this answer." }, { "value": "29", "code": "hooped-the-other-pair", "feedback": "That is the other pair's total. Read which two numbers the hoop actually covers and work out those." } ], "misconceptionMeaning": "all three numbers were worked out when only the hooped pair was asked for", "chainText": "(6 + 25) + 4", "hoopValue": 31, "conventionValue": 35, "naiveValue": 35, "firstStep": "6 + 25" }, "correctAnswer": "31", "options": [ "31", "4", "29", "35" ], "correctIndex": 0, "difficulty": 2, "hint": "Only the two numbers inside the hoop count for this answer.", "explanation": "Inside the hoop is 6 + 25, which makes 31. The third number is not in the hoop, so it is not counted yet; the whole expression comes to 35.", "misconceptionCode": "group-whole-chain" }, { "id": "arrays-q42", "objectiveRecordIds": [ "0096-stage-4-4Ni.03" ], "prompt": "The ringed hoop joins two of the numbers. What does the calculation inside the hoop make?", "data": { "family": "group-total", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "2", "5", "9", "×", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 2, 5, 9 ], "ops": [ "×", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": null, "misconceptionDistractor": "90", "misconceptionDistractors": [ { "value": "9", "code": "answered-with-the-outside-number", "feedback": "That number is outside the hoop. Only the two numbers the hoop covers are worked out for this answer." }, { "value": "45", "code": "hooped-the-other-pair", "feedback": "That is the other pair's total. Read which two numbers the hoop actually covers and work out those." } ], "misconceptionMeaning": "all three numbers were worked out when only the hooped pair was asked for", "chainText": "(2 × 5) × 9", "hoopValue": 10, "conventionValue": 90, "naiveValue": 90, "firstStep": "2 × 5" }, "correctAnswer": "10", "options": [ "9", "10", "45", "90" ], "correctIndex": 1, "difficulty": 2, "hint": "Only the two numbers inside the hoop count for this answer.", "explanation": "Inside the hoop is 2 × 5, which makes 10. The third number is not in the hoop, so it is not counted yet; the whole expression comes to 90.", "misconceptionCode": "group-whole-chain" }, { "id": "arrays-q43", "objectiveRecordIds": [ "0096-stage-3-3Ni.02", "0096-stage-5-5Ni.02" ], "prompt": "The ringed hoop joins two of the numbers. What does the calculation inside the hoop make?", "data": { "family": "group-total", "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "figure": "chain", "parts": [ "the three numbers", "the hoop and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "7", "5", "9", "+", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 7, 5, 9 ], "ops": [ "+", "+" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the hoop and the two numbers inside it", "rule": null, "misconceptionDistractor": "21", "misconceptionDistractors": [ { "value": "7", "code": "answered-with-the-outside-number", "feedback": "That number is outside the hoop. Only the two numbers the hoop covers are worked out for this answer." }, { "value": "12", "code": "hooped-the-other-pair", "feedback": "That is the other pair's total. Read which two numbers the hoop actually covers and work out those." } ], "misconceptionMeaning": "all three numbers were worked out when only the hooped pair was asked for", "chainText": "7 + (5 + 9)", "hoopValue": 14, "conventionValue": 21, "naiveValue": 21, "firstStep": "7 + 5" }, "correctAnswer": "14", "options": [ "21", "7", "14", "12" ], "correctIndex": 2, "difficulty": 3, "hint": "Only the two numbers inside the hoop count for this answer.", "explanation": "Inside the hoop is 5 + 9, which makes 14. The third number is not in the hoop, so it is not counted yet; the whole expression comes to 21.", "misconceptionCode": "group-whole-chain" } ] }, "brackets-order": { "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "minimumDistinctItems": 20, "responseType": "choice", "objectiveVerb": "understand that brackets can be used to alter the order of operations", "items": [ { "id": "brackets-q01", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The bracket shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "2", "3", "4", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 2, 3, 4 ], "ops": [ "+", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "14", "misconceptionDistractors": [ { "value": "5", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the bracket. The third number is still outside it, and the question asks for the whole expression." }, { "value": "9", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "(2 + 3) × 4", "hoopValue": 5, "conventionValue": 14, "naiveValue": 20, "firstStep": "3 × 4" }, "correctAnswer": "20", "options": [ "20", "5", "14", "9" ], "correctIndex": 0, "difficulty": 1, "hint": "Work the two numbers inside the bracket first, then do the sign that is left outside it.", "explanation": "The bracket makes (2 + 3) × 4, so 2 + 3 is done first and the value is 20. Without the bracket the same numbers give 14, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "brackets-q02", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The bracket shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "4", "2", "×", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 4, 2 ], "ops": [ "×", "+" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "14", "misconceptionDistractors": [ { "value": "6", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the bracket. The third number is still outside it, and the question asks for the whole expression." }, { "value": "9", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "3 × (4 + 2)", "hoopValue": 6, "conventionValue": 14, "naiveValue": 18, "firstStep": "3 × 4" }, "correctAnswer": "18", "options": [ "6", "18", "14", "9" ], "correctIndex": 1, "difficulty": 1, "hint": "Work the two numbers inside the bracket first, then do the sign that is left outside it.", "explanation": "The bracket makes 3 × (4 + 2), so 4 + 2 is done first and the value is 18. Without the bracket the same numbers give 14, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "brackets-q03", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The bracket shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "10", "3", "2", "−", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 10, 3, 2 ], "ops": [ "−", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "4", "misconceptionDistractors": [ { "value": "7", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the bracket. The third number is still outside it, and the question asks for the whole expression." }, { "value": "15", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "(10 − 3) × 2", "hoopValue": 7, "conventionValue": 4, "naiveValue": 14, "firstStep": "3 × 2" }, "correctAnswer": "14", "options": [ "7", "15", "14", "4" ], "correctIndex": 2, "difficulty": 2, "hint": "Work the two numbers inside the bracket first, then do the sign that is left outside it.", "explanation": "The bracket makes (10 − 3) × 2, so 10 − 3 is done first and the value is 14. Without the bracket the same numbers give 4, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "brackets-q04", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The bracket shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "7", "2", "3", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 7, 2, 3 ], "ops": [ "+", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "13", "misconceptionDistractors": [ { "value": "9", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the bracket. The third number is still outside it, and the question asks for the whole expression." }, { "value": "12", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "(7 + 2) × 3", "hoopValue": 9, "conventionValue": 13, "naiveValue": 27, "firstStep": "2 × 3" }, "correctAnswer": "27", "options": [ "9", "12", "13", "27" ], "correctIndex": 3, "difficulty": 2, "hint": "Work the two numbers inside the bracket first, then do the sign that is left outside it.", "explanation": "The bracket makes (7 + 2) × 3, so 7 + 2 is done first and the value is 27. Without the bracket the same numbers give 13, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "brackets-q05", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The bracket shows which two numbers are worked out first. What is the value of the whole expression worked out that way?", "data": { "family": "bracket-value", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "3", "8", "2", "×", "−" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 3, 8, 2 ], "ops": [ "×", "−" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "22", "misconceptionDistractors": [ { "value": "6", "code": "answered-with-the-hoop-only", "feedback": "That is the value inside the bracket. The third number is still outside it, and the question asks for the whole expression." }, { "value": "13", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." } ], "misconceptionMeaning": "the bracket drawn on the board was skipped and the usual order used instead", "chainText": "3 × (8 − 2)", "hoopValue": 6, "conventionValue": 22, "naiveValue": 18, "firstStep": "3 × 8" }, "correctAnswer": "18", "options": [ "18", "22", "6", "13" ], "correctIndex": 0, "difficulty": 3, "hint": "Work the two numbers inside the bracket first, then do the sign that is left outside it.", "explanation": "The bracket makes 3 × (8 − 2), so 8 − 2 is done first and the value is 18. Without the bracket the same numbers give 22, so this bracket has changed the answer.", "misconceptionCode": "bracket-ignored" }, { "id": "brackets-q06", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Three numbers and two signs are written with no brackets at all. Working in the usual order, what is the value of the line?", "data": { "family": "no-bracket-value", "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "8", "6", "2", "+", "÷" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 8, 6, 2 ], "ops": [ "+", "÷" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "7", "misconceptionDistractors": [ { "value": "16", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "3", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "8 + 6 ÷ 2", "hoopValue": null, "conventionValue": 11, "naiveValue": 7, "firstStep": "6 ÷ 2" }, "correctAnswer": "11", "options": [ "16", "11", "3", "7" ], "correctIndex": 1, "difficulty": 2, "hint": "Work the multiplication or division first, whatever position it sits in, then the other sign.", "explanation": "There is no bracket, so the usual order decides: ÷ has priority over +, so it is done first wherever it sits in the line. That makes 6 ÷ 2 first, which gives 3, and the whole line is 11. Working from the left instead gives 7, which is what a bracket round the first pair would force.", "misconceptionCode": "left-to-right-order" }, { "id": "brackets-q07", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Three numbers and two signs are written with no brackets at all. Working in the usual order, what is the value of the line?", "data": { "family": "no-bracket-value", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "10", "6", "2", "+", "÷" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 10, 6, 2 ], "ops": [ "+", "÷" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "8", "misconceptionDistractors": [ { "value": "18", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "3", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "10 + 6 ÷ 2", "hoopValue": null, "conventionValue": 13, "naiveValue": 8, "firstStep": "6 ÷ 2" }, "correctAnswer": "13", "options": [ "18", "3", "13", "8" ], "correctIndex": 2, "difficulty": 2, "hint": "Work the multiplication or division first, whatever position it sits in, then the other sign.", "explanation": "There is no bracket, so the usual order decides: ÷ has priority over +, so it is done first wherever it sits in the line. That makes 6 ÷ 2 first, which gives 3, and the whole line is 13. Working from the left instead gives 8, which is what a bracket round the first pair would force.", "misconceptionCode": "left-to-right-order" }, { "id": "brackets-q08", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Three numbers and two signs are written with no brackets at all. Working in the usual order, what is the value of the line?", "data": { "family": "no-bracket-value", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "6", "2", "4", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 6, 2, 4 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "32", "misconceptionDistractors": [ { "value": "12", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "8", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "6 + 2 × 4", "hoopValue": null, "conventionValue": 14, "naiveValue": 32, "firstStep": "2 × 4" }, "correctAnswer": "14", "options": [ "32", "12", "8", "14" ], "correctIndex": 3, "difficulty": 3, "hint": "Work the multiplication or division first, whatever position it sits in, then the other sign.", "explanation": "There is no bracket, so the usual order decides: × has priority over +, so it is done first wherever it sits in the line. That makes 2 × 4 first, which gives 8, and the whole line is 14. Working from the left instead gives 32, which is what a bracket round the first pair would force.", "misconceptionCode": "left-to-right-order" }, { "id": "brackets-q09", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Three numbers and two signs are written with no brackets at all. Working in the usual order, what is the value of the line?", "data": { "family": "no-bracket-value", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "9", "2", "4", "−", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 9, 2, 4 ], "ops": [ "−", "×" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "28", "misconceptionDistractors": [ { "value": "15", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "8", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "9 − 2 × 4", "hoopValue": null, "conventionValue": 1, "naiveValue": 28, "firstStep": "2 × 4" }, "correctAnswer": "1", "options": [ "1", "28", "15", "8" ], "correctIndex": 0, "difficulty": 3, "hint": "Work the multiplication or division first, whatever position it sits in, then the other sign.", "explanation": "There is no bracket, so the usual order decides: × has priority over −, so it is done first wherever it sits in the line. That makes 2 × 4 first, which gives 8, and the whole line is 1. Working from the left instead gives 28, which is what a bracket round the first pair would force.", "misconceptionCode": "left-to-right-order" }, { "id": "brackets-q10", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "Three numbers and two signs are written with no brackets at all. Working in the usual order, what is the value of the line?", "data": { "family": "no-bracket-value", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "8", "3", "2", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 8, 3, 2 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "22", "misconceptionDistractors": [ { "value": "13", "code": "added-all-numbers", "feedback": "Every number was added, whatever the signs said. Read the signs on the board again: a minus or a times changes what you do." }, { "value": "6", "code": "answered-with-the-first-step-only", "feedback": "That is what the first step makes. The question asks for the value of the whole line, so do the other sign as well." } ], "misconceptionMeaning": "the calculation was worked from the left regardless of the signs", "chainText": "8 + 3 × 2", "hoopValue": null, "conventionValue": 14, "naiveValue": 22, "firstStep": "3 × 2" }, "correctAnswer": "14", "options": [ "13", "14", "22", "6" ], "correctIndex": 1, "difficulty": 4, "hint": "Work the multiplication or division first, whatever position it sits in, then the other sign.", "explanation": "There is no bracket, so the usual order decides: × has priority over +, so it is done first wherever it sits in the line. That makes 3 × 2 first, which gives 6, and the whole line is 14. Working from the left instead gives 22, which is what a bracket round the first pair would force.", "misconceptionCode": "left-to-right-order" }, { "id": "brackets-q11", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The board shows three numbers and two signs with no brackets. Where would you put a pair of brackets to make the value 18?", "data": { "family": "bracket-place", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "4", "2", "3", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 4, 2, 3 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "round the last two numbers", "misconceptionDistractors": [ { "value": "round the first and last numbers", "code": "bracketed-the-ends", "feedback": "Those two numbers do not touch on the board, so no bracket can hold them together. A bracket goes round two neighbours." }, { "value": "round all three numbers", "code": "bracketed-all-three", "feedback": "A bracket holds two numbers, not three. Choose which adjacent pair it should cover and leave the third number outside it." } ], "misconceptionMeaning": "the bracket was put round the other pair, although only one pair makes the target", "chainText": "4 + 2 × 3", "hoopValue": null, "conventionValue": 10, "naiveValue": 18, "firstStep": "2 × 3" }, "correctAnswer": "round the first two numbers", "options": [ "round the first and last numbers", "round all three numbers", "round the first two numbers", "round the last two numbers" ], "correctIndex": 2, "difficulty": 2, "hint": "Try both pairs on the numbers: work each pair out, finish the line, and see which reading gives the target.", "explanation": "The target is 18, and only one of the two pairs makes it. Working out 4 + 2 first gives (4 + 2) × 3 = 18, so the bracket goes round the first two numbers. The other pair makes 4 + (2 × 3) = 10, which is not the target.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-q12", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The board shows three numbers and two signs with no brackets. Where would you put a pair of brackets to make the value 40?", "data": { "family": "bracket-place", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "6", "2", "5", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 6, 2, 5 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "round the last two numbers", "misconceptionDistractors": [ { "value": "round the first and last numbers", "code": "bracketed-the-ends", "feedback": "Those two numbers do not touch on the board, so no bracket can hold them together. A bracket goes round two neighbours." }, { "value": "round all three numbers", "code": "bracketed-all-three", "feedback": "A bracket holds two numbers, not three. Choose which adjacent pair it should cover and leave the third number outside it." } ], "misconceptionMeaning": "the bracket was put round the other pair, although only one pair makes the target", "chainText": "6 + 2 × 5", "hoopValue": null, "conventionValue": 16, "naiveValue": 40, "firstStep": "2 × 5" }, "correctAnswer": "round the first two numbers", "options": [ "round the first and last numbers", "round all three numbers", "round the last two numbers", "round the first two numbers" ], "correctIndex": 3, "difficulty": 2, "hint": "Try both pairs on the numbers: work each pair out, finish the line, and see which reading gives the target.", "explanation": "The target is 40, and only one of the two pairs makes it. Working out 6 + 2 first gives (6 + 2) × 5 = 40, so the bracket goes round the first two numbers. The other pair makes 6 + (2 × 5) = 16, which is not the target.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-q13", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The board shows three numbers and two signs with no brackets. Where would you put a pair of brackets to make the value 20?", "data": { "family": "bracket-place", "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "4", "3", "2", "×", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 4, 3, 2 ], "ops": [ "×", "+" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "round the first two numbers", "misconceptionDistractors": [ { "value": "round the first and last numbers", "code": "bracketed-the-ends", "feedback": "Those two numbers do not touch on the board, so no bracket can hold them together. A bracket goes round two neighbours." }, { "value": "round all three numbers", "code": "bracketed-all-three", "feedback": "A bracket holds two numbers, not three. Choose which adjacent pair it should cover and leave the third number outside it." } ], "misconceptionMeaning": "the bracket was put round the other pair, although only one pair makes the target", "chainText": "4 × 3 + 2", "hoopValue": null, "conventionValue": 14, "naiveValue": 20, "firstStep": "4 × 3" }, "correctAnswer": "round the last two numbers", "options": [ "round the last two numbers", "round the first two numbers", "round the first and last numbers", "round all three numbers" ], "correctIndex": 0, "difficulty": 3, "hint": "Try both pairs on the numbers: work each pair out, finish the line, and see which reading gives the target.", "explanation": "The target is 20, and only one of the two pairs makes it. Working out 3 + 2 first gives 4 × (3 + 2) = 20, so the bracket goes round the last two numbers. The other pair makes (4 × 3) + 2 = 14, which is not the target.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-q14", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The board shows three numbers and two signs with no brackets. Where would you put a pair of brackets to make the value 54?", "data": { "family": "bracket-place", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "7", "2", "6", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 7, 2, 6 ], "ops": [ "+", "×" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "round the last two numbers", "misconceptionDistractors": [ { "value": "round the first and last numbers", "code": "bracketed-the-ends", "feedback": "Those two numbers do not touch on the board, so no bracket can hold them together. A bracket goes round two neighbours." }, { "value": "round all three numbers", "code": "bracketed-all-three", "feedback": "A bracket holds two numbers, not three. Choose which adjacent pair it should cover and leave the third number outside it." } ], "misconceptionMeaning": "the bracket was put round the other pair, although only one pair makes the target", "chainText": "7 + 2 × 6", "hoopValue": null, "conventionValue": 19, "naiveValue": 54, "firstStep": "2 × 6" }, "correctAnswer": "round the first two numbers", "options": [ "round the last two numbers", "round the first two numbers", "round the first and last numbers", "round all three numbers" ], "correctIndex": 1, "difficulty": 3, "hint": "Try both pairs on the numbers: work each pair out, finish the line, and see which reading gives the target.", "explanation": "The target is 54, and only one of the two pairs makes it. Working out 7 + 2 first gives (7 + 2) × 6 = 54, so the bracket goes round the first two numbers. The other pair makes 7 + (2 × 6) = 19, which is not the target.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-q15", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "The board shows three numbers and two signs with no brackets. Where would you put a pair of brackets to make the value 35?", "data": { "family": "bracket-place", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "5", "9", "2", "×", "−" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 5, 9, 2 ], "ops": [ "×", "−" ], "hoop": null, "strip": null, "probe": 0, "probeLabel": "the three numbers", "rule": null, "misconceptionDistractor": "round the first two numbers", "misconceptionDistractors": [ { "value": "round the first and last numbers", "code": "bracketed-the-ends", "feedback": "Those two numbers do not touch on the board, so no bracket can hold them together. A bracket goes round two neighbours." }, { "value": "round all three numbers", "code": "bracketed-all-three", "feedback": "A bracket holds two numbers, not three. Choose which adjacent pair it should cover and leave the third number outside it." } ], "misconceptionMeaning": "the bracket was put round the other pair, although only one pair makes the target", "chainText": "5 × 9 − 2", "hoopValue": null, "conventionValue": 43, "naiveValue": 35, "firstStep": "5 × 9" }, "correctAnswer": "round the last two numbers", "options": [ "round the first and last numbers", "round the first two numbers", "round the last two numbers", "round all three numbers" ], "correctIndex": 2, "difficulty": 4, "hint": "Try both pairs on the numbers: work each pair out, finish the line, and see which reading gives the target.", "explanation": "The target is 35, and only one of the two pairs makes it. Working out 9 − 2 first gives 5 × (9 − 2) = 35, so the bracket goes round the last two numbers. The other pair makes (5 × 9) − 2 = 43, which is not the target.", "misconceptionCode": "bracketed-the-wrong-pair" }, { "id": "brackets-q16", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "A pair of brackets is drawn round two of the numbers. How much does the value change when that pair is worked out first? Give the size of the change, not its direction.", "data": { "family": "bracket-change", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "2", "4", "5", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 2, 4, 5 ], "ops": [ "+", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "0", "misconceptionDistractors": [ { "value": "30", "code": "answered-with-the-bracket-value", "feedback": "That is the value of the whole line with the bracket. The question asks how far the value moved, so subtract the usual-order value." }, { "value": "22", "code": "answered-with-the-unbracketed-value", "feedback": "That is the value in the usual order, without the bracket. The question asks how far the value moved, so subtract it from the bracketed value." } ], "misconceptionMeaning": "the bracket was treated as decoration, so no change was reported", "chainText": "(2 + 4) × 5", "hoopValue": 6, "conventionValue": 22, "naiveValue": 30, "firstStep": "4 × 5" }, "correctAnswer": "8", "options": [ "0", "30", "22", "8" ], "correctIndex": 3, "difficulty": 3, "hint": "Work the line twice, once with the bracket and once in the usual order, then compare the two values.", "explanation": "With the bracket, (2 + 4) × 5 comes to 30. Without it the usual order gives 2 + (4 × 5) = 22. The value moved from 22 to 30, a change of 8.", "misconceptionCode": "bracket-changes-nothing" }, { "id": "brackets-q17", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "A pair of brackets is drawn round two of the numbers. How much does the value change when that pair is worked out first? Give the size of the change, not its direction.", "data": { "family": "bracket-change", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "9", "5", "3", "×", "−" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 9, 5, 3 ], "ops": [ "×", "−" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "0", "misconceptionDistractors": [ { "value": "18", "code": "answered-with-the-bracket-value", "feedback": "That is the value of the whole line with the bracket. The question asks how far the value moved, so subtract the usual-order value." }, { "value": "42", "code": "answered-with-the-unbracketed-value", "feedback": "That is the value in the usual order, without the bracket. The question asks how far the value moved, so subtract it from the bracketed value." } ], "misconceptionMeaning": "the bracket was treated as decoration, so no change was reported", "chainText": "9 × (5 − 3)", "hoopValue": 2, "conventionValue": 42, "naiveValue": 18, "firstStep": "9 × 5" }, "correctAnswer": "24", "options": [ "24", "0", "18", "42" ], "correctIndex": 0, "difficulty": 3, "hint": "Work the line twice, once with the bracket and once in the usual order, then compare the two values.", "explanation": "With the bracket, 9 × (5 − 3) comes to 18. Without it the usual order gives (9 × 5) − 3 = 42. The value moved from 42 to 18, a change of 24.", "misconceptionCode": "bracket-changes-nothing" }, { "id": "brackets-q18", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "A pair of brackets is drawn round two of the numbers. How much does the value change when that pair is worked out first? Give the size of the change, not its direction.", "data": { "family": "bracket-change", "context": { "who": "a sheet of stickers", "thing": "stickers", "noun": "sticker", "plural": "stickers" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "6", "4", "3", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 6, 4, 3 ], "ops": [ "+", "×" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "0", "misconceptionDistractors": [ { "value": "30", "code": "answered-with-the-bracket-value", "feedback": "That is the value of the whole line with the bracket. The question asks how far the value moved, so subtract the usual-order value." }, { "value": "18", "code": "answered-with-the-unbracketed-value", "feedback": "That is the value in the usual order, without the bracket. The question asks how far the value moved, so subtract it from the bracketed value." } ], "misconceptionMeaning": "the bracket was treated as decoration, so no change was reported", "chainText": "(6 + 4) × 3", "hoopValue": 10, "conventionValue": 18, "naiveValue": 30, "firstStep": "4 × 3" }, "correctAnswer": "12", "options": [ "30", "12", "0", "18" ], "correctIndex": 1, "difficulty": 4, "hint": "Work the line twice, once with the bracket and once in the usual order, then compare the two values.", "explanation": "With the bracket, (6 + 4) × 3 comes to 30. Without it the usual order gives 6 + (4 × 3) = 18. The value moved from 18 to 30, a change of 12.", "misconceptionCode": "bracket-changes-nothing" }, { "id": "brackets-q19", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "A pair of brackets is drawn round two of the numbers. How much does the value change when that pair is worked out first? Give the size of the change, not its direction.", "data": { "family": "bracket-change", "context": { "who": "a seed tray", "thing": "seeds in a seed tray", "noun": "seed", "plural": "seeds" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "4", "9", "2", "×", "−" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 4, 9, 2 ], "ops": [ "×", "−" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "0", "misconceptionDistractors": [ { "value": "28", "code": "answered-with-the-bracket-value", "feedback": "That is the value of the whole line with the bracket. The question asks how far the value moved, so subtract the usual-order value." }, { "value": "34", "code": "answered-with-the-unbracketed-value", "feedback": "That is the value in the usual order, without the bracket. The question asks how far the value moved, so subtract it from the bracketed value." } ], "misconceptionMeaning": "the bracket was treated as decoration, so no change was reported", "chainText": "4 × (9 − 2)", "hoopValue": 7, "conventionValue": 34, "naiveValue": 28, "firstStep": "4 × 9" }, "correctAnswer": "6", "options": [ "28", "0", "6", "34" ], "correctIndex": 2, "difficulty": 4, "hint": "Work the line twice, once with the bracket and once in the usual order, then compare the two values.", "explanation": "With the bracket, 4 × (9 − 2) comes to 28. Without it the usual order gives (4 × 9) − 2 = 34. The value moved from 34 to 28, a change of 6.", "misconceptionCode": "bracket-changes-nothing" }, { "id": "brackets-q20", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "A pair of brackets is drawn round two of the numbers. Does working out that pair first change the value of the line?", "data": { "family": "bracket-effect", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "6", "5", "4", "+", "−" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 6, 5, 4 ], "ops": [ "+", "−" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "It gets bigger", "misconceptionDistractors": [ { "value": "It gets smaller", "code": "bracket-smaller-assumed", "feedback": "Do not assume the direction. Work the line with the bracket, then without it, and compare the two values." }, { "value": "It cannot be worked out", "code": "bracket-unworkable", "feedback": "This line can be worked out: every pair on the board gives a whole number. Try the bracket on the other pair, or read the usual order again." } ], "misconceptionMeaning": "the bracket was assumed to change the value without working either reading out", "chainText": "(6 + 5) − 4", "hoopValue": 11, "conventionValue": 7, "naiveValue": 7, "firstStep": "6 + 5" }, "correctAnswer": "It stays the same", "options": [ "It gets bigger", "It gets smaller", "It cannot be worked out", "It stays the same" ], "correctIndex": 3, "difficulty": 3, "hint": "Ask which pair the usual order does first. If the bracket sits on that pair, it changes nothing.", "explanation": "The bracket is round 6 + 5, and that is the pair the usual order already does first, so (6 + 5) − 4 = 7 either way. A bracket only changes the value when it moves the first step to the other pair.", "misconceptionCode": "bracket-always-changes" }, { "id": "brackets-q21", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "A pair of brackets is drawn round two of the numbers. Does working out that pair first change the value of the line?", "data": { "family": "bracket-effect", "context": { "who": "a set of book shelves", "thing": "books on shelves", "noun": "book", "plural": "books" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "8", "4", "2", "×", "÷" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 8, 4, 2 ], "ops": [ "×", "÷" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "It gets bigger", "misconceptionDistractors": [ { "value": "It gets smaller", "code": "bracket-smaller-assumed", "feedback": "Do not assume the direction. Work the line with the bracket, then without it, and compare the two values." }, { "value": "It cannot be worked out", "code": "bracket-unworkable", "feedback": "This line can be worked out: every pair on the board gives a whole number. Try the bracket on the other pair, or read the usual order again." } ], "misconceptionMeaning": "the bracket was assumed to change the value without working either reading out", "chainText": "(8 × 4) ÷ 2", "hoopValue": 32, "conventionValue": 16, "naiveValue": 16, "firstStep": "8 × 4" }, "correctAnswer": "It stays the same", "options": [ "It stays the same", "It gets smaller", "It gets bigger", "It cannot be worked out" ], "correctIndex": 0, "difficulty": 4, "hint": "Ask which pair the usual order does first. If the bracket sits on that pair, it changes nothing.", "explanation": "The bracket is round 8 × 4, and that is the pair the usual order already does first, so (8 × 4) ÷ 2 = 16 either way. A bracket only changes the value when it moves the first step to the other pair.", "misconceptionCode": "bracket-always-changes" }, { "id": "brackets-q22", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "A pair of brackets is drawn round two of the numbers. Does working out that pair first change the value of the line?", "data": { "family": "bracket-effect", "context": { "who": "a strip of tiles on a floor", "thing": "tiles", "noun": "tile", "plural": "tiles" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "7", "5", "3", "+", "−" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 7, 5, 3 ], "ops": [ "+", "−" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "It gets bigger", "misconceptionDistractors": [ { "value": "It gets smaller", "code": "bracket-smaller-assumed", "feedback": "Do not assume the direction. Work the line with the bracket, then without it, and compare the two values." }, { "value": "It cannot be worked out", "code": "bracket-unworkable", "feedback": "This line can be worked out: every pair on the board gives a whole number. Try the bracket on the other pair, or read the usual order again." } ], "misconceptionMeaning": "the bracket was assumed to change the value without working either reading out", "chainText": "(7 + 5) − 3", "hoopValue": 12, "conventionValue": 9, "naiveValue": 9, "firstStep": "7 + 5" }, "correctAnswer": "It stays the same", "options": [ "It gets smaller", "It stays the same", "It gets bigger", "It cannot be worked out" ], "correctIndex": 1, "difficulty": 4, "hint": "Ask which pair the usual order does first. If the bracket sits on that pair, it changes nothing.", "explanation": "The bracket is round 7 + 5, and that is the pair the usual order already does first, so (7 + 5) − 3 = 9 either way. A bracket only changes the value when it moves the first step to the other pair.", "misconceptionCode": "bracket-always-changes" }, { "id": "brackets-q23", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "What does the calculation inside the bracket make?", "data": { "family": "bracket-first-value", "context": { "who": "a set of counters", "thing": "counters", "noun": "counter", "plural": "counters" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "4", "5", "3", "+", "×" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 4, 5, 3 ], "ops": [ "+", "×" ], "hoop": 1, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "19", "misconceptionDistractors": [ { "value": "4", "code": "answered-with-the-outside-number", "feedback": "That number is outside the bracket. Only the two numbers the bracket covers are worked out for this answer." }, { "value": "9", "code": "bracketed-the-other-pair", "feedback": "That is what the other pair makes. Read which two numbers sit inside the bracket and work out those." } ], "misconceptionMeaning": "all three numbers were worked out when only the hooped pair was asked for", "chainText": "4 + (5 × 3)", "hoopValue": 15, "conventionValue": 19, "naiveValue": 27, "firstStep": "5 × 3" }, "correctAnswer": "15", "options": [ "4", "19", "15", "9" ], "correctIndex": 2, "difficulty": 1, "hint": "Only the two numbers inside the bracket are worked out for this answer.", "explanation": "Inside the bracket is 5 × 3, which makes 15. The third number sits outside the bracket and is not worked out yet; the whole line comes to 19.", "misconceptionCode": "group-whole-chain" }, { "id": "brackets-q24", "objectiveRecordIds": [ "0096-stage-6-6Ni.03" ], "prompt": "What does the calculation inside the bracket make?", "data": { "family": "bracket-first-value", "context": { "who": "a classroom of chairs", "thing": "chairs", "noun": "chair", "plural": "chairs" }, "figure": "chain", "parts": [ "the three numbers", "the bracket and the two numbers inside it", "the first number", "the last number", "the signs between the numbers" ], "printed": [ "6", "3", "4", "×", "+" ], "rows": null, "cols": null, "split": null, "turned": false, "side": null, "terms": [ 6, 3, 4 ], "ops": [ "×", "+" ], "hoop": 0, "strip": null, "probe": 1, "probeLabel": "the bracket and the two numbers inside it", "rule": null, "misconceptionDistractor": "22", "misconceptionDistractors": [ { "value": "4", "code": "answered-with-the-outside-number", "feedback": "That number is outside the bracket. Only the two numbers the bracket covers are worked out for this answer." }, { "value": "7", "code": "bracketed-the-other-pair", "feedback": "That is what the other pair makes. Read which two numbers sit inside the bracket and work out those." } ], "misconceptionMeaning": "all three numbers were worked out when only the hooped pair was asked for", "chainText": "(6 × 3) + 4", "hoopValue": 18, "conventionValue": 22, "naiveValue": 42, "firstStep": "6 × 3" }, "correctAnswer": "18", "options": [ "4", "7", "22", "18" ], "correctIndex": 3, "difficulty": 2, "hint": "Only the two numbers inside the bracket are worked out for this answer.", "explanation": "Inside the bracket is 6 × 3, which makes 18. The third number sits outside the bracket and is not worked out yet; the whole line comes to 22.", "misconceptionCode": "group-whole-chain" } ] } } }