// Numbas version: exam_results_page_options
{"name": "Rounding and estimating calculations - painting a room", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rounding and estimating calculations - painting a room", "type": "question", "statement": "<p>{person['name']} just bought a new house. {capitalise(pronouns['their'])}&nbsp;new bedroom's wall and ceiling are currently painted white, but {pronouns['they']} would like to paint these {colour}.</p>\n<p>The dimensions of the&nbsp;floor&nbsp;are $\\var{length}\\,\\mathrm{m} \\times \\var{width}\\,\\mathrm{m}$&nbsp;and&nbsp;the room&nbsp;is&nbsp;$\\var{height}\\,\\mathrm{m}$&nbsp;high.&nbsp;</p>\n<p>{person['name']} want{verbs} to know how much paint to buy so {pronouns['they']} can paint all four walls and the ceiling {colour}.</p>", "variablesTest": {"condition": "mod(rall,15)<>0", "maxRuns": 100}, "variables": {"buckets": {"description": "", "name": "buckets", "group": "Calculations", "templateType": "anything", "definition": "ceil(rall/bucket_area)"}, "bucket_area": {"description": "<p>The area that can be painted with one bucket of paint.</p>", "name": "bucket_area", "group": "Calculations", "templateType": "anything", "definition": "15"}, "colour": {"description": "", "name": "colour", "group": "Random bits", "templateType": "anything", "definition": "random(\"green\", \"red\", \"orange\", \"yellow\", \"blue\", \"purple\", \"pink\")"}, "width": {"description": "", "name": "width", "group": "Random bits", "templateType": "anything", "definition": "random(2.50..5.00 #0.1) + random(0.01..0.09 #0.01)"}, "w": {"description": "", "name": "w", "group": "Calculations", "templateType": "anything", "definition": "ceil(width)"}, "verbs": {"description": "", "name": "verbs", "group": "Person", "templateType": "anything", "definition": "if(person['gender']='neutral','','s')"}, "height": {"description": "", "name": "height", "group": "Random bits", "templateType": "anything", "definition": "random(2.10..2.70 #0.1) + random(0.01..0.09 #0.01)"}, "h": {"description": "", "name": "h", "group": "Calculations", "templateType": "anything", "definition": "ceil(height)"}, "rall": {"description": "", "name": "rall", "group": "Calculations", "templateType": "anything", "definition": "rceiling + rwall1*2 + rwall2*2"}, "pronouns": {"description": "", "name": "pronouns", "group": "Person", "templateType": "anything", "definition": "person['pronouns']"}, "length": {"description": "", "name": "length", "group": "Random bits", "templateType": "anything", "definition": "random(3.50..8.00 #0.1) + random(0.01..0.09 #0.01)"}, "person": {"description": "", "name": "person", "group": "Person", "templateType": "anything", "definition": "random_person()"}, "rwall1": {"description": "", "name": "rwall1", "group": "Calculations", "templateType": "anything", "definition": "l*h"}, "rwall2": {"description": "", "name": "rwall2", "group": "Calculations", "templateType": "anything", "definition": "w*h"}, "rceiling": {"description": "", "name": "rceiling", "group": "Calculations", "templateType": "anything", "definition": "w*l"}, "l": {"description": "", "name": "l", "group": "Calculations", "templateType": "anything", "definition": "ceil(length)"}}, "extensions": ["random_person"], "functions": {}, "tags": ["random names", "taxonomy"], "variable_groups": [{"name": "Random bits", "variables": ["colour", "height", "width", "length"]}, {"name": "Person", "variables": ["person", "pronouns", "verbs"]}, {"name": "Calculations", "variables": ["h", "w", "l", "rwall1", "rwall2", "rceiling", "rall", "bucket_area", "buckets"]}], "parts": [{"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"scripts": {}, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "choices": ["<p>Overestimate and therefore we round each measurement up.</p>", "<p>Underestimate and therefore we round each measurement down.</p>"], "showFeedbackIcon": true, "shuffleChoices": false, "displayColumns": "1", "variableReplacements": [], "marks": 0, "matrix": ["1", 0], "showCorrectAnswer": true, "maxMarks": 0, "type": "1_n_2"}], "showFeedbackIcon": true, "prompt": "<p>Is it better to overestimate or underestimate in this situation?</p>\n<p>[[0]]<em></em></p>", "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "rall", "showFeedbackIcon": true, "minValue": "rall", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "stepsPenalty": 0, "prompt": "<p>Rounding each measurement to&nbsp;<strong>the nearest metre</strong>, estimate&nbsp;the whole area to be painted {colour}.</p>\n<p>[[0]]&nbsp;m<sup>2</sup></p>\n<p><em></em></p>", "steps": [{"scripts": {}, "variableReplacements": [], "type": "information", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>The room is {length}m long, {width}m wide, and {height}m high.</p>\n<p>Round each measurement in the direction you decided on above.&nbsp;</p>", "marks": 0}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(length)", "showFeedbackIcon": true, "prompt": "<p>Round the length&nbsp;to the nearest metre.</p>", "minValue": "ceil(length)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(width)", "showFeedbackIcon": true, "prompt": "<p>Round the width&nbsp;to the nearest metre.</p>", "minValue": "ceil(width)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(height)", "showFeedbackIcon": true, "prompt": "<p>Round the height&nbsp;to the nearest metre.</p>", "minValue": "ceil(height)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}], "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "buckets", "showFeedbackIcon": true, "minValue": "buckets", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "<p>One&nbsp;bucket of {colour} paint is enough to paint an area of 15m<sup>2</sup>. How many buckets should {person['name']}&nbsp;buy to ensure {pronouns['they']}&nbsp;{if(person['gender']='neutral','have','has')}&nbsp;enough paint?</p>\n<p>[[0]]</p>", "marks": 0}], "ungrouped_variables": [], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Estimate the number of buckets of paint to buy,&nbsp;by rounding measurements of a room up to the nearest metre and estimating the total area.</p>"}, "preamble": {"css": "", "js": ""}, "advice": "<h4>a)</h4>\n<p>It is much better to have spare&nbsp;paint than not to have enough of it. So it is&nbsp;better to overestimate the area.</p>\n<p>Therefore, we round each measurement&nbsp;<strong>up.</strong></p>\n<h4>b)</h4>\n<p>We round each of our measurements up to the nearest whole metre:</p>\n<p>Length: $\\var{length}\\,\\mathrm{m} \\approx&nbsp;\\var{l}\\,\\mathrm{m}$.</p>\n<p>Width: $\\var{width}\\,\\mathrm{m} \\approx \\var{w}\\,\\mathrm{m}$.</p>\n<p>Height: $\\var{height}\\,\\mathrm{m} \\approx \\var{h}\\,\\mathrm{m}$.</p>\n<p style=\"text-align: left;\">The total area consists of five areas: two walls of $\\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (length by height); two walls of $\\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (width by height); and a ceiling of $\\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m}$ (length by width).</p>\n<p>\\[ \\begin{align}<br/>\\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m} &amp;= \\var{l*h}\\,\\text{m}^2<br/>\\\\ \\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m} &amp;= \\var{w*h}\\,\\text{m}^2<br/>\\\\ \\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m} &amp;= \\var{l*w}\\,\\text{m}^2<br/>\\end{align}\\]</p>\n<p>Therefore, the total area {person['name']} needs to paint is</p>\n<p>\\[&nbsp;\\var{2*l*h} + \\var{2*w*h} + \\var{l*w} \\,\\mathrm{m}^2 = \\var{rall}\\,\\mathrm{m}^2 \\text{.} \\]</p>\n<h4>c)</h4>\n<p>The exact number of buckets needed is</p>\n<p>\\[\\var{rall}\\,\\text{m}^2 \\div 15\\,\\text{m}^2&nbsp;= \\var{rall/15} \\text{.}\\]</p>\n<p>{person['name']} can only buy a whole number of buckets, so {pronouns['they']}&nbsp;need{verbs} to decide between&nbsp;{buckets-1}&nbsp;and {buckets} paint buckets. As it is better to buy more paint than not buy enough, {pronouns['they']} should buy {buckets} buckets of {colour} paint.</p>", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}