// Numbas version: exam_results_page_options
{"name": "Proportional reasoning - bagel baking (6)", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Proportional reasoning - bagel baking (6)", "tags": ["LANTITE"], "metadata": {"description": "<p>Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given the number of bagels baked, in a number of hours, and need to calculate the number baked per half-hour. There are 6 different versions of this question.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>{name1} baked&nbsp; $\\var{bagels}$&nbsp; bagels in {a_or_an}&nbsp; $\\var{hours}$ - hour shift.</p>", "advice": "<p>Did you estimate the answer before working it out? Did you immediately eliminate one answer because it was obviously too big?</p>\n<p><strong>You could</strong> then solve this problem by testing each of the remaining answers to see which one works. If you are not confident with division, you may prefer this method for this question.</p>\n<p>If you do it this way, you could double each answer to get the number of bagels baked in one hour, then multiply by the number of hours to see if you get the total number of bagels,&nbsp; $\\var{bagels}$.</p>\n<p>$\\var{bagels/hours*2} \\times 2 = \\var{bagels/hours*4}$&nbsp; then&nbsp; $\\var{bagels/hours*4} \\times \\var{hours} = \\var{bagels*4}$. This is not correct, as it should be&nbsp; $\\var{bagels}$.</p>\n<p>$\\var{bagels/hours} \\times 2 = \\var{bagels/hours*2}$&nbsp; then&nbsp; $\\var{bagels/hours*2} \\times \\var{hours} = \\var{bagels*2}$. This is not correct, as it should be&nbsp; $\\var{bagels}$.</p>\n<p>$\\var{answer} \\times 2 = \\var{answer*2}$&nbsp; then&nbsp; $\\var{answer*2} \\times \\var{hours} = \\var{bagels}$. This option is correct.</p>\n<p><strong>Alternatively</strong>, you could divide the total number of bagels baked by the number of hours, then halve this number to get the quantity of bagels baked each half-hour.</p>\n<p>$\\var{bagels} \\div \\var{hours} = \\var{bagels/hours}$&nbsp; bagels baked in one hour.</p>\n<p>$\\var{bagels/hours} \\div 2 = \\var{answer}$&nbsp; bagels baked in half an hour.</p>\n<p>{name1} baked&nbsp; $\\var{answer}$&nbsp; bagels on average each half-hour.</p>", "rulesets": {}, "extensions": ["random_person"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n_bagels": {"name": "n_bagels", "group": "Ungrouped variables", "definition": "[2000,1000,1200,960,750,840]", "description": "<p>The list containing the numbers of bagels.</p>", "templateType": "anything", "can_override": false}, "n_hours": {"name": "n_hours", "group": "Ungrouped variables", "definition": "[8,4,8,6,5,6]", "description": "<p>The list containing the numbers of hours.</p>", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0 .. 5#1)", "description": "<p>The index to select the position in the list.</p>", "templateType": "randrange", "can_override": false}, "bagels": {"name": "bagels", "group": "Ungrouped variables", "definition": "n_bagels[index]", "description": "<p>The randomly selected number of bagels.</p>", "templateType": "anything", "can_override": false}, "hours": {"name": "hours", "group": "Ungrouped variables", "definition": "n_hours[index]", "description": "<p>The number of hours that corresponds to the number of bagels.</p>", "templateType": "anything", "can_override": false}, "a_an": {"name": "a_an", "group": "Ungrouped variables", "definition": "[\"an\",\"a\",\"an\",\"a\",\"a\",\"a\"]", "description": "<p>The list containing the correct word - \"a\" or \"an\".</p>", "templateType": "anything", "can_override": false}, "a_or_an": {"name": "a_or_an", "group": "Ungrouped variables", "definition": "a_an[index]", "description": "<p>The word \"a\" or \"an\" that corresponds to the number of hours.</p>", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "bagels/(hours*2)", "description": "<p>The answer to the question.</p>", "templateType": "anything", "can_override": false}, "person": {"name": "person", "group": "Ungrouped variables", "definition": "random_person()", "description": "", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "person[\"name\"]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n_bagels", "n_hours", "a_an", "index", "bagels", "hours", "a_or_an", "answer", "person", "name1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "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>How many bagels did {name1} bake on average each half-hour?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["$\\var{answer}$", "$\\var{(bagels)/(hours)}$", "$\\var{(bagels*2)/(hours)}$", "$\\var{bagels*hours}$"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done - you are correct!", "Have you worked out the number each half-hour, or each hour?", "You need to multiply by 1/2, not divide by 1/2 to get the number in a half-hour.", "You need to divide the number of bagels by the number of hours, not multiply."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}