// Numbas version: finer_feedback_settings
{"name": "Addition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Addition", "tags": ["adding", "Addition", "addition", "algorithms", "plus"], "metadata": {"description": "<p>Natural numbers addition algorithm. 2 and 3 digit numbers. Carrying.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write the following questions down on paper and evaluate them without using a calculator.</p>\n<p>If you are unsure of how to do&nbsp;a question, click on <em>Show steps</em> to see the full working. Then, once you understand how to do the question, click on <em>Try another question like this one</em> to start again.</p>", "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": "<p>$\\var{b2digit}+\\var{b3digit} = $&nbsp;[[0]]</p>", "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": "<p>Generally, we set up $\\var{b2digit}+\\var{b3digit}$ with the <em>ones</em> and the <em>tens</em>&nbsp;columns lined up vertically:</p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td></td>\n<td>$\\var{bdigs[1]}$</td>\n<td>$\\var{bdigs[0]}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bdigs[4]}$</td>\n<td>$\\var{bdigs[3]}$</td>\n<td>$\\var{bdigs[2]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>$\\phantom{0}$</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now&nbsp;we add the digits in the <g class=\"gr_ gr_25 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"25\" data-gr-id=\"25\">ones</g> column.</p>\n<p><span data-jme-visible=\"bunitsumtensdigit=0\">This results in&nbsp;$\\var{bunitsum}$ and so&nbsp;we place $\\var{bunitsumlastdigit}$ under the line in the ones column. </span></p>\n<p><span data-jme-visible=\"bunitsumtensdigit=1\">This results in&nbsp;$\\var{bunitsum}$ and so&nbsp;we place $\\var{bunitsumlastdigit}$ under the line in the <g class=\"gr_ gr_28 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"28\" data-gr-id=\"28\">ones</g> column and carry the $1$ into the tens column.&nbsp;</span></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td></td>\n<td><span data-jme-visible=\"bunitsumtensdigit=1\">$\\overset{\\color{red}1}{\\var{bdigs[1]}}$</span> <span data-jme-visible=\"bunitsumtensdigit=0\">$\\overset{\\phantom{0}}{\\var{bdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bdigs[4]}$</td>\n<td>$\\var{bdigs[3]}$</td>\n<td>$\\var{bdigs[2]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{bUnitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we add the digits in the tens column.</p>\n<p><span data-jme-visible=\"btencarry=0\">This results in&nbsp;$\\var{bTenSum}$ and so we place $\\var{bTenSumlastdigit}$ under the line in the tens column.</span></p>\n<p><span data-jme-visible=\"btencarry=1\">This results in&nbsp;$\\var{bTenSum}$ and so we place $\\var{bTenSumlastdigit}$ under the line in the tens column and carry the $1$ into the hundreds column.</span></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td><span data-jme-visible=\"btencarry=1\">${\\overset{\\color{red}1}{\\phantom{0}}}$</span> <span data-jme-visible=\"btencarry=0\">$\\phantom{0}$</span></td>\n<td><span data-jme-visible=\"bunitsumtensdigit=1\">$\\overset{1}{\\var{bdigs[1]}}$</span> <span data-jme-visible=\"bunitsumtensdigit=0\">$\\overset{\\phantom{0}}{\\var{bdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bdigs[4]}$</td>\n<td>$\\var{bdigs[3]}$</td>\n<td>$\\var{bdigs[2]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{bTenSumlastdigit}}$</td>\n<td>${\\var{bUnitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we add the digits in the hundreds column.</p>\n<p><span data-jme-visible=\"btencarry=0\">This is simply $\\var{bdigs[4]}$ so we place&nbsp;$\\var{bdigs[4]}$ under the line in the hundreds column.</span></p>\n<p><span data-jme-visible=\"btencarry=1\">This is $\\var{bsumhun}$ so we place&nbsp;$\\var{bsumhun}$ under the line in the hundreds column.</span></p>\n<p><span data-jme-visible=\"bans&gt;999\">This is $\\var{bsumhun}$ so we place&nbsp;$\\var{bsumhun}$ under the line so that its rightmost digit is in the hundreds column.</span></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td><span data-jme-visible=\"btencarry=1\">$\\overset{1}{\\phantom{0}}$</span> <span data-jme-visible=\"btencarry=0\">$\\phantom{0}$</span></td>\n<td><span data-jme-visible=\"bunitsumtensdigit=1\">$\\overset{1}{\\var{bdigs[1]}}$</span> <span data-jme-visible=\"bunitsumtensdigit=0\">$\\overset{\\phantom{0}}{\\var{bdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bdigs[4]}$</td>\n<td>$\\var{bdigs[3]}$</td>\n<td>$\\var{bdigs[2]}$</td>\n<td></td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"bsumhuncarry=0\">$\\phantom{\\var{bsumhuncarry}}$</span> <span data-jme-visible=\"bsumhuncarry=1\">$\\color{red}{\\var{bsumhuncarry}}$</span></td>\n<td>$\\color{red}{\\var{bsumhunlastdigit}}$</td>\n<td>$\\var{bTenSumlastdigit}$</td>\n<td>${\\var{bUnitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p>The answer is therefore $\\var{bans}$.</p>"}], "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": "<p>$\\var{threedigit1}+\\var{threedigit2} = $&nbsp;[[0]]</p>", "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": "<p>Generally&nbsp;we set up $\\var{threedigit1}+\\var{threedigit2}$&nbsp;with the <em>ones,&nbsp;</em><em>tens</em> and&nbsp;<em>hundreds</em>&nbsp;columns lined up vertically:</p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>$\\var{cdigs[2]}$</td>\n<td>$\\var{cdigs[1]}$</td>\n<td>$\\var{cdigs[0]}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>$\\phantom{0}$</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now&nbsp;we add the digits in the ones column.</p>\n<p><span data-jme-visible=\"cunitsumtensdigit=0\">This results in&nbsp;$\\var{cunitsum}$ and so&nbsp;we place $\\var{cunitsumlastdigit}$ under the line in the ones column. </span></p>\n<p><span data-jme-visible=\"cunitsumtensdigit=1\">This results in&nbsp;$\\var{cunitsum}$ and so&nbsp;we place $\\var{cunitsumlastdigit}$ under the line in the ones column and carry the $1$ into the tens column.&nbsp;</span></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$</td>\n<td><span data-jme-visible=\"cunitcarry=1\">$\\overset{\\color{red}1}{\\var{cdigs[1]}}$</span> <span data-jme-visible=\"cunitcarry=0\">$\\overset{\\phantom{0}}{\\var{cdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{cunitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we add the digits in the tens column.</p>\n<p><span data-jme-visible=\"ctencarry=0\">This results in&nbsp;$\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in the tens column.</span></p>\n<p><span data-jme-visible=\"ctencarry=1\">This results in&nbsp;$\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in the tens column and carry the $1$ into the hundreds column.</span></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td><span data-jme-visible=\"ctencarry=1\">${\\overset{\\color{red}1}{\\var{cdigs[2]}}}$</span> <span data-jme-visible=\"ctencarry=0\">$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$</span></td>\n<td><span data-jme-visible=\"cunitcarry=1\">$\\overset{1}{\\var{cdigs[1]}}$</span> <span data-jme-visible=\"cunitcarry=0\">$\\overset{\\phantom{0}}{\\var{cdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{ctenSumlastdigit}}$</td>\n<td>${\\var{cunitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we add the digits in the hundreds column.</p>\n<p><span data-jme-visible=\"cans&lt;1000\">This is $\\var{chunsum}$ so we place&nbsp;$\\var{chunsum}$ under the line in the hundreds column.</span></p>\n<p><span data-jme-visible=\"cans&gt;999\">This is $\\var{chunsum}$ so we place&nbsp;$\\var{chunsum}$ under the line so that its rightmost digit is in the hundreds column.</span></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td><span data-jme-visible=\"ctencarry=1\">$\\overset{1}{\\var{cdigs[2]}}$</span> <span data-jme-visible=\"ctencarry=0\">$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$</span></td>\n<td><span data-jme-visible=\"cunitcarry=1\">$\\overset{1}{\\var{cdigs[1]}}$</span> <span data-jme-visible=\"cunitcarry=0\">$\\overset{\\phantom{0}}{\\var{cdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"chuncarry=0\">$\\phantom{\\var{chuncarry}}$</span> <span data-jme-visible=\"chuncarry=1\">$\\color{red}{\\var{chuncarry}}$</span></td>\n<td>$\\color{red}{\\var{chunsumlastdigit}}$</td>\n<td>$\\var{ctenSumlastdigit}$</td>\n<td>${\\var{cunitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p>The answer is therefore $\\var{cans}$.</p>"}], "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", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}