// Numbas version: exam_results_page_options {"name": "Scaling one number into another", "metadata": {"description": "
A quick practice set of problems for education students to take in preparation for their numeracy test.
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\nBased on the Australian Core Skills Framework - numeracy - level 3 - personal and community sample activity:Accurately measures a range of quantities to follow a recipe or operating instructions
incorporating making a product of a smaller or larger size than specified, e.g. follows a recipe
for six people and can adjust it to cater for 24 people
Has an annoying plural issue
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "The following are the ingredients from a recipe that makes 12 {food}.
\n\n\n \n 1 1/2 cups milk \n | \n2 1/4 cups self-raising flour 3/4 cup caster sugar 1 egg 1/2 cup vegetable oil 3/4 cup milk | \n
If you wanted to make {new_amount[0]} {food}, how many {worded_ingredient[0]} would you need?
", "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": "The recipe tells us that for 12 {food} we need $\\simplify[fractionNumbers]{{worded_ingredient[1]}}$ {worded_ingredient[0]}. Since we were asked about making $\\var{new_amount[0]}$ {food} and $\\simplify[fractionNumbers]{{new_amount[0]}/12={scaling_factor}}$, we have been asked about making {new_amount[1]} the number contained in the recipe. So we will need $\\simplify[fractionNumbers]{{scaling_factor}}\\times \\simplify[fractionNumbers]{{worded_ingredient[1]}={ans}}$ {worded_ingredient[0]}.
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\nInstead of using that stepping-stone of going to $1$ first, we can multiply by a fraction equivalent to the above division and multiplication. That is,
\n$\\var{c}\\times $ [[2]] $= \\var{d}$.
", "stepsPenalty": "3", "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": "We want to know what number to multiply $\\var{c}$ by in order to get the number $\\var{d}$.
\nWe can think of this as stretching/scaling $\\var{c}$ by a scaling factor to get the number $\\var{d}$.
\nWe can find this scaling factor by using the unitary method:
\nThis two-step process called the unitary method is used in many places (such as rates, ratios and percentages).
\nInstead of using that stepping-stone of going to $1$ first, we can multiply by a fraction equivalent to the above division and multiplication. That is,
\n$\\var{c}\\times \\frac{\\var{d}}{\\var{c}}= \\var{d}$.
\nNotice how multiplying by a number less than $1$ results in a smaller number.
"}], "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": "{c}", "maxValue": "{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{d}", "maxValue": "{d}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{d/c}", "maxValue": "{d/c}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "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": "We can turn the number $\\var{n}$ into the number $\\var{m}$ by multiplying (or scaling) by [[0]].
\nWe want to know what number to multiply $\\var{n}$ by in order to get the number $\\var{m}$.
\nWe can think of this as stretching/scaling $\\var{n}$ by a scaling factor to get the number $\\var{m}$.
\nWe can find this scaling factor by using the unitary method:
\nThis two-step process called the unitary method is used in many places (such as rates, ratios and percentages).
\nInstead of using that stepping-stone of going to $1$ first, we can multiply by a fraction equivalent to the above division and multiplication. That is,
\n$\\var{n}\\times \\frac{\\var{m}}{\\var{n}}= \\var{m}$.
\nNotice how multiplying by a number less than $1$ results in a smaller number.
\n