A single question which asks you to round to the nearest ten, hundred or thousand.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"number": {"name": "number", "group": "Ungrouped variables", "definition": "random(10*seed..50*seed except 10*seed..50*seed#seed)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "tonearest(number, seed)\n", "description": "", "templateType": "anything", "can_override": false}, "digit_to_the_right": {"name": "digit_to_the_right", "group": "Ungrouped variables", "definition": "mod(floor(10*number/seed),10)\n//(mod(number,seed)-mod(number, seed/10))/(seed/10)\n//floor(lastdigits/(seed/10))", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "Ungrouped variables", "definition": "random(10,100,1000)", "description": "", "templateType": "anything", "can_override": false}, "direction": {"name": "direction", "group": "Ungrouped variables", "definition": "if(digit_to_the_right<5,'down', 'up')", "description": "", "templateType": "anything", "can_override": false}, "seedtext": {"name": "seedtext", "group": "Ungrouped variables", "definition": "switch(seed=10, 'ten', seed=100, 'hundred', seed=1000, 'thousand', 'error')", "description": "", "templateType": "anything", "can_override": false}, "less_greater": {"name": "less_greater", "group": "Ungrouped variables", "definition": "if(digit_to_the_right<5,'less than', 'greater than or equal to')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["seed", "seedtext", "number", "digit_to_the_right", "direction", "less_greater", "ans"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\var{number}$ rounded to the nearest {seedtext} is [[0]].
\n\n", "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": "When we are rounding we look at the first digit that we might discard. If it is $5$ or greater we round up. If it is less than $5$ we round down.
\n\nTo round $\\var{number}$ to the nearest {seedtext}, we look to the right of the {seedtext}s column and see the digit $\\var{digit_to_the_right}$.
\nSince $\\var{digit_to_the_right}$ is {less_greater} $5$ we round {direction} to $\\var{ans}$.
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"}, "functions": {}, "variables": {"ok": {"group": "Ungrouped variables", "name": "ok", "definition": "shuffle(2..9)", "templateType": "anything", "description": ""}, "r": {"group": "Ungrouped variables", "name": "r", "definition": "ok[0..4]", "templateType": "anything", "description": ""}, "c": {"group": "Ungrouped variables", "name": "c", "definition": "ok[4..8]", "templateType": "anything", "description": ""}}, "ungrouped_variables": ["ok", "r", "c"], "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "", "variable_groups": [], "tags": [], "parts": [{"unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "extendBaseMarkingAlgorithm": true, "prompt": "\n| $\\large\\times$ | \n$\\large\\var{c[0]}$ | \n$\\large\\var{c[1]}$ | \n$\\large\\var{c[2]}$ | \n$\\large\\var{c[3]}$ | \n
| $\\large\\var{r[0]}$ | \n[[0]] | \n[[1]] | \n[[2]] | \n[[3]] | \n
| $\\large\\var{r[1]}$ | \n[[4]] | \n[[5]] | \n[[6]] | \n[[7]] | \n
| $\\large\\var{r[2]}$ | \n[[8]] | \n[[9]] | \n[[10]] | \n[[11]] | \n
| $\\large\\var{r[3]}$ | \n[[12]] | \n[[13]] | \n[[14]] | \n[[15]] | \n
Memorising as many of the times tables as possible is really helpful for lots of things in mathematics.
\nIf you can't memorise them, for some of the times tables there are little tricks you can use to work them out (sometimes quickly, sometimes slowly).
\nIf you are stuck on a times table, just for practice see if you can work it out in more than one way.
", "unitTests": [], "scripts": {}}]}], "statement": "Complete this random selection of times tables. If you cannot recall the answer, try to work it out!
\nFor more practice, click 'Try another question like this one'.
", "rulesets": {}, "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "Units: converting between centimetres and metres", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "advice": "Write the following questions down on paper and evaluate them without using a calculator.
\nIf you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.
", "variables": {"P1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "prefix[RP1[1]]", "description": "", "name": "P1"}, "prefix": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[[\"c\",10^(-2),\"centi\",-2],[\"\",1,\"the base unit, \",0]]", "description": "", "name": "prefix"}, "mult": {"group": "Ungrouped variables", "templateType": "anything", "definition": "shuffle([random(3..191 except 100),random(0.1..2.9#0.01 except [1,2])])", "description": "", "name": "mult"}, "ansb": {"group": "Ungrouped variables", "templateType": "anything", "definition": "precround(mult[1]*10^(P2[3]-P3[3]),0)", "description": "", "name": "ansb"}, "bpowerdiff": {"group": "Ungrouped variables", "templateType": "anything", "definition": "P2[3]-P3[3]", "description": "", "name": "bpowerdiff"}, "RP1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[0,1]", "description": "random pair 1 - designed to be increasing
", "name": "RP1"}, "RP2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[1,0]", "description": "random pair 2 - designed to be decreasing
", "name": "RP2"}, "P0": {"group": "Ungrouped variables", "templateType": "anything", "definition": "prefix[RP1[0]]", "description": "", "name": "P0"}, "P3": {"group": "Ungrouped variables", "templateType": "anything", "definition": "prefix[RP2[1]]", "description": "", "name": "P3"}, "ansa": {"group": "Ungrouped variables", "templateType": "anything", "definition": "precround(mult[0]*10^(P0[3]-P1[3]),P1[3]-P0[3]+2)", "description": "", "name": "ansa"}, "random_order": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[0,1]", "description": "", "name": "random_order"}, "P2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "prefix[RP2[0]]", "description": "", "name": "P2"}, "apowerdiff": {"group": "Ungrouped variables", "templateType": "anything", "definition": "P1[3]-P0[3]", "description": "", "name": "apowerdiff"}, "units": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[[\"m\",\"metres\"]]", "description": "", "name": "units"}}, "statement": "Write the following questions down on paper and evaluate them without using a calculator.
\nIf you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.
", "parts": [{"variableReplacements": [], "prompt": "$\\var{mult[0]}\\, \\text{cm} =$ [[0]] $\\text{m}$
\n", "stepsPenalty": "1", "showCorrectAnswer": true, "steps": [{"variableReplacements": [], "prompt": "The scaling factor between {P0[2]} and {P1[2]} is $10^\\var{apowerdiff}=\\simplify{10^{apowerdiff}}$.
\nWhen converting from {P0[2]+units[0][1]} to {P1[2]+units[0][1]} the units are getting larger and so the the number will have to get smaller. That is, we will divide by $\\simplify{10^{apowerdiff}}$ to convert from {P0[2]+units[0][1]} to {P1[2]+units[0][1]}. Recall dividing by $\\simplify{10^{apowerdiff}}$ is simply moving the decimal place to the left $\\var{apowerdiff}$ places in order to make the number smaller.
\nIf this doesn't make sense to you consider a simpler example. $5$ one-dollar coins is the same amount of money as $1$ five-dollar note. As the units get bigger you need less of them to have the same amount of money. In this example the scaling factor would be $5$ since the size of the units increases by a factor of $5$ and the number of units decreases by a factor of $5$. Now, say we had $20$ one-dollar coins and we wanted to convert this to five-dollar notes, we would calculate $20\\div 5$ which equals $4$ and therefore we would get $4$ five-dollar notes.
\nTherefore, \\begin{align}\\var{mult[0]} \\,\\var{P0[0]}\\var{units[0][0]}&=\\left(\\var{mult[0]} \\div\\simplify{10^{P1[3]-P0[3]}} \\right)\\,\\var{P1[0]}\\var{units[0][0]}\\\\&=\\var{ansa}\\,\\var{P1[0]}\\var{units[0][0]}.\\end{align}
\n\n\n", "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "information", "unitTests": [], "customMarkingAlgorithm": "", "scripts": {}}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "strictPrecision": false, "marks": 1, "showFeedbackIcon": true, "minValue": "{ansa}", "type": "numberentry", "unitTests": [], "allowFractions": false, "precisionType": "sigfig", "scripts": {}, "mustBeReducedPC": 0, "precision": "4", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "maxValue": "{ansa}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0}], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "sortAnswers": false, "type": "gapfill", "unitTests": [], "scripts": {}}, {"variableReplacements": [], "prompt": "$\\var{mult[1]} \\,\\text{m} =$ [[0]] $\\text{cm}$
", "stepsPenalty": "1", "showCorrectAnswer": true, "steps": [{"variableReplacements": [], "prompt": "The scaling factor between {P2[2]} and {P3[2]} is $10^\\var{bpowerdiff}=\\simplify{10^{bpowerdiff}}$.
\nWhen converting from {P2[2]+units[0][1]} to {P3[2]+units[0][1]} the units are getting smaller and so the the number will have to get bigger. That is, we will multiply by $\\simplify{10^{bpowerdiff}}$ to convert from {P2[2]+units[0][1]} to {P3[2]+units[0][1]}. Recall multiplying by $\\simplify{10^{bpowerdiff}}$ is simply moving the decimal place to the right $\\var{bpowerdiff}$ places in order to make the number larger.
\nIf this doesn't make sense to you consider a simpler example. $1$ five-dollar note is the same amount of money as $5$ one-dollar coins. As the units get smaller you need more of them to have the same amount of money. In this example the scaling factor would be $5$ since the size of the units decreases by a factor of $5$ and the number of units increases by a factor of $5$. Now, say we had $4$ five-dollar notes and we wanted to convert this to one-dollar coins, we would calculate $4\\times 5$ which equals $20$ and therefore we would get $20$ one-dollar coins.
\nTherefore, \\begin{align}\\var{mult[1]} \\,\\var{P2[0]}\\var{units[0][0]}&=\\left(\\var{mult[1]} \\times\\simplify{10^{bpowerdiff}} \\right)\\,\\var{P3[0]}\\var{units[0][0]}\\\\&=\\var{ansb}\\,\\var{P3[0]}\\var{units[0][0]}.\\end{align}
\n\n", "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "information", "unitTests": [], "customMarkingAlgorithm": "", "scripts": {}}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "strictPrecision": false, "marks": 1, "showFeedbackIcon": true, "minValue": "{ansb}", "type": "numberentry", "unitTests": [], "allowFractions": false, "precisionType": "sigfig", "scripts": {}, "mustBeReducedPC": 0, "precision": "4", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "maxValue": "{ansb}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0}], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "sortAnswers": false, "type": "gapfill", "unitTests": [], "scripts": {}}], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "variable_groups": [], "metadata": {"description": "\nConverting between metres (m) and centimetres (cm).
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "tags": [], "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["prefix", "units", "mult", "random_order", "RP1", "RP2", "P0", "P1", "P2", "P3", "ansa", "apowerdiff", "ansb", "bpowerdiff"], "functions": {}, "type": "question"}]}], "metadata": {"description": "A test of basic questions - imported into Moodle", "licence": "Creative Commons Attribution 4.0 International"}, "timing": {"allowPause": true, "timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}}, "duration": 0, "contributors": [{"name": "University_of_London Worldwide", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3624/"}], "extensions": [], "custom_part_types": [], "resources": []}