// Numbas version: exam_results_page_options {"name": "Merryn's copy of Addition 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Merryn's copy of Addition 1", "tags": ["adding", "Addition", "addition", "algorithms", "plus"], "metadata": {"description": "
Natural numbers addition algorithm. 2 and 3 digit numbers. Carrying.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Write the following questions down on paper and evaluate them without using a calculator. You can use any method you wish to practice.
\nIf you click on Show steps you will see full working for the standard method. Click on Try another question like this one to get a new pair of numbers to add.
", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"chuncarry": {"name": "chuncarry", "group": "Ungrouped variables", "definition": "floor(chunsum/10)", "description": "", "templateType": "anything", "can_override": false}, "ctencarry": {"name": "ctencarry", "group": "Ungrouped variables", "definition": "floor(ctensum/10)", "description": "", "templateType": "anything", "can_override": false}, "bTenSum": {"name": "bTenSum", "group": "Ungrouped variables", "definition": "bdigs[1]+bdigs[3]+bunitsumtensdigit", "description": "", "templateType": "anything", "can_override": false}, "cunitsum": {"name": "cunitsum", "group": "Ungrouped variables", "definition": "cdigs[0]+cdigs[3]", "description": "", "templateType": "anything", "can_override": false}, "bUnitSumLastDigit": {"name": "bUnitSumLastDigit", "group": "Ungrouped variables", "definition": "mod(bunitsum,10)", "description": "", "templateType": "anything", "can_override": false}, "bunitsumtensdigit": {"name": "bunitsumtensdigit", "group": "Ungrouped variables", "definition": "floor((bunitsum)/10)", "description": "", "templateType": "anything", "can_override": false}, "bans": {"name": "bans", "group": "Ungrouped variables", "definition": "b2digit+b3digit", "description": "", "templateType": "anything", "can_override": false}, "btencarry": {"name": "btencarry", "group": "Ungrouped variables", "definition": "floor(btensum/10)", "description": "", "templateType": "anything", "can_override": false}, "bdigs": {"name": "bdigs", "group": "Ungrouped variables", "definition": "shuffle(1..9)[0..5]", "description": "", "templateType": "anything", "can_override": false}, "cunitcarry": {"name": "cunitcarry", "group": "Ungrouped variables", "definition": "floor(cunitsum/10)", "description": "", "templateType": "anything", "can_override": false}, "bunitsum": {"name": "bunitsum", "group": "Ungrouped variables", "definition": "bdigs[0]+bdigs[2]", "description": "", "templateType": "anything", "can_override": false}, "threedigit2": {"name": "threedigit2", "group": "Ungrouped variables", "definition": "cdigs[3]+cdigs[4]*10+cdigs[5]*100", "description": "", "templateType": "anything", "can_override": false}, "threedigit1": {"name": "threedigit1", "group": "Ungrouped variables", "definition": "cdigs[0]+cdigs[1]*10+cdigs[2]*100", "description": "", "templateType": "anything", "can_override": false}, "chunsumlastdigit": {"name": "chunsumlastdigit", "group": "Ungrouped variables", "definition": "mod(chunsum,10)", "description": "", "templateType": "anything", "can_override": false}, "cdigs": {"name": "cdigs", "group": "Ungrouped variables", "definition": "shuffle(3..9)", "description": "", "templateType": "anything", "can_override": false}, "b2digit": {"name": "b2digit", "group": "Ungrouped variables", "definition": "bdigs[0]+bdigs[1]*10", "description": "", "templateType": "anything", "can_override": false}, "cans": {"name": "cans", "group": "Ungrouped variables", "definition": "threedigit1+threedigit2", "description": "", "templateType": "anything", "can_override": false}, "cunitsumlastdigit": {"name": "cunitsumlastdigit", "group": "Ungrouped variables", "definition": "mod(cunitsum,10)", "description": "", "templateType": "anything", "can_override": false}, "b3digit": {"name": "b3digit", "group": "Ungrouped variables", "definition": "bdigs[2]+bdigs[3]*10+bdigs[4]*100", "description": "", "templateType": "anything", "can_override": false}, "ctensumlastdigit": {"name": "ctensumlastdigit", "group": "Ungrouped variables", "definition": "mod(ctensum,10)", "description": "", "templateType": "anything", "can_override": false}, "bsumhun": {"name": "bsumhun", "group": "Ungrouped variables", "definition": "bdigs[4]+btencarry", "description": "", "templateType": "anything", "can_override": false}, "bsumhunlastdigit": {"name": "bsumhunlastdigit", "group": "Ungrouped variables", "definition": "mod(bsumhun,10)", "description": "", "templateType": "anything", "can_override": false}, "bsumhuncarry": {"name": "bsumhuncarry", "group": "Ungrouped variables", "definition": "floor(bsumhun/10)", "description": "", "templateType": "anything", "can_override": false}, "ctensum": {"name": "ctensum", "group": "Ungrouped variables", "definition": "cdigs[1]+cdigs[4]+cunitcarry", "description": "", "templateType": "anything", "can_override": false}, "chunsum": {"name": "chunsum", "group": "Ungrouped variables", "definition": "ctencarry+cdigs[2]+cdigs[5]", "description": "", "templateType": "anything", "can_override": false}, "btensumlastdigit": {"name": "btensumlastdigit", "group": "Ungrouped variables", "definition": "mod(btensum,10)", "description": "", "templateType": "anything", "can_override": false}, "cunitsumtensdigit": {"name": "cunitsumtensdigit", "group": "Ungrouped variables", "definition": "0.1*(cunitsum-cunitsumlastdigit)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["bdigs", "b2digit", "b3digit", "bunitsum", "bUnitSumLastDigit", "bunitsumtensdigit", "bTenSum", "btensumlastdigit", "btencarry", "bsumhun", "bsumhuncarry", "bsumhunlastdigit", "bans", "cdigs", "threedigit1", "threedigit2", "cans", "cunitsum", "cunitsumlastdigit", "cunitcarry", "ctensum", "ctensumlastdigit", "ctencarry", "chunsum", "chunsumlastdigit", "chuncarry", "cunitsumtensdigit"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\var{b2digit}+\\var{b3digit} = $ [[0]]
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Generally, we set up $\\var{b2digit}+\\var{b3digit}$ with the ones and the tens columns lined up vertically:
\n\n | \n | $\\var{bdigs[1]}$ | \n$\\var{bdigs[0]}$ | \n$+$ | \n
\n | $\\var{bdigs[4]}$ | \n$\\var{bdigs[3]}$ | \n$\\var{bdigs[2]}$ | \n\n |
\n | \n | $\\phantom{0}$ | \n\n | \n |
Now we add the digits in the
This results in $\\var{bunitsum}$ and so we place $\\var{bunitsumlastdigit}$ under the line in the ones column.
\nThis results in $\\var{bunitsum}$ and so we place $\\var{bunitsumlastdigit}$ under the line in the
\n | \n | $\\overset{\\color{red}1}{\\var{bdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{bdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$ | \n$+$ | \n
\n | $\\var{bdigs[4]}$ | \n$\\var{bdigs[3]}$ | \n$\\var{bdigs[2]}$ | \n\n |
\n | \n | \n | $\\color{red}{\\var{bUnitSumLastDigit}}$ | \n\n |
Now we add the digits in the tens column.
\nThis results in $\\var{bTenSum}$ and so we place $\\var{bTenSumlastdigit}$ under the line in the tens column.
\nThis results in $\\var{bTenSum}$ and so we place $\\var{bTenSumlastdigit}$ under the line in the tens column and carry the $1$ into the hundreds column.
\n\n | ${\\overset{\\color{red}1}{\\phantom{0}}}$ $\\phantom{0}$ | \n$\\overset{1}{\\var{bdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{bdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$ | \n$+$ | \n
\n | $\\var{bdigs[4]}$ | \n$\\var{bdigs[3]}$ | \n$\\var{bdigs[2]}$ | \n\n |
\n | \n | $\\color{red}{\\var{bTenSumlastdigit}}$ | \n${\\var{bUnitSumLastDigit}}$ | \n\n |
Now we add the digits in the hundreds column.
\nThis is simply $\\var{bdigs[4]}$ so we place $\\var{bdigs[4]}$ under the line in the hundreds column.
\nThis is $\\var{bsumhun}$ so we place $\\var{bsumhun}$ under the line in the hundreds column.
\nThis is $\\var{bsumhun}$ so we place $\\var{bsumhun}$ under the line so that its rightmost digit is in the hundreds column.
\n\n | $\\overset{1}{\\phantom{0}}$ $\\phantom{0}$ | \n$\\overset{1}{\\var{bdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{bdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$ | \n$+$ | \n
\n | $\\var{bdigs[4]}$ | \n$\\var{bdigs[3]}$ | \n$\\var{bdigs[2]}$ | \n\n |
$\\phantom{\\var{bsumhuncarry}}$ $\\color{red}{\\var{bsumhuncarry}}$ | \n$\\color{red}{\\var{bsumhunlastdigit}}$ | \n$\\var{bTenSumlastdigit}$ | \n${\\var{bUnitSumLastDigit}}$ | \n\n |
The answer is therefore $\\var{bans}$.
"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "bans", "maxValue": "bans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\var{threedigit1}+\\var{threedigit2} = $ [[0]]
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Generally we set up $\\var{threedigit1}+\\var{threedigit2}$ with the ones, tens and hundreds columns lined up vertically:
\n\n | $\\var{cdigs[2]}$ | \n$\\var{cdigs[1]}$ | \n$\\var{cdigs[0]}$ | \n$+$ | \n
\n | $\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
\n | \n | $\\phantom{0}$ | \n\n | \n |
Now we add the digits in the ones column.
\nThis results in $\\var{cunitsum}$ and so we place $\\var{cunitsumlastdigit}$ under the line in the ones column.
\nThis results in $\\var{cunitsum}$ and so we place $\\var{cunitsumlastdigit}$ under the line in the ones column and carry the $1$ into the tens column.
\n\n | $\\overset{\\phantom{1}}{\\var{cdigs[2]}}$ | \n$\\overset{\\color{red}1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$ | \n$+$ | \n
\n | $\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
\n | \n | \n | $\\color{red}{\\var{cunitSumLastDigit}}$ | \n\n |
Now we add the digits in the tens column.
\nThis results in $\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in the tens column.
\nThis results in $\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in the tens column and carry the $1$ into the hundreds column.
\n\n | ${\\overset{\\color{red}1}{\\var{cdigs[2]}}}$ $\\overset{\\phantom{1}}{\\var{cdigs[2]}}$ | \n$\\overset{1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$ | \n$+$ | \n
\n | $\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
\n | \n | $\\color{red}{\\var{ctenSumlastdigit}}$ | \n${\\var{cunitSumLastDigit}}$ | \n\n |
Now we add the digits in the hundreds column.
\nThis is $\\var{chunsum}$ so we place $\\var{chunsum}$ under the line in the hundreds column.
\nThis is $\\var{chunsum}$ so we place $\\var{chunsum}$ under the line so that its rightmost digit is in the hundreds column.
\n\n | $\\overset{1}{\\var{cdigs[2]}}$ $\\overset{\\phantom{1}}{\\var{cdigs[2]}}$ | \n$\\overset{1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$ | \n$+$ | \n
\n | $\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
$\\phantom{\\var{chuncarry}}$ $\\color{red}{\\var{chuncarry}}$ | \n$\\color{red}{\\var{chunsumlastdigit}}$ | \n$\\var{ctenSumlastdigit}$ | \n${\\var{cunitSumLastDigit}}$ | \n\n |
The answer is therefore $\\var{cans}$.
"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "cans", "maxValue": "cans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}