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{"name": "Times tables (multiplication)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [], "tags": [], "name": "Times tables (multiplication)", "functions": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>This creates a 4x4 times table grid using numbers from 2 to 9. The step gives some advice on how to work out times tables (products, multiplications) if you can't remember them.</p>"}, "ungrouped_variables": ["ok", "r", "c"], "parts": [{"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "prompt": "<p>Memorising as many of the times tables as possible is really helpful for lots of things in mathematics.</p>\n<p>If 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).&nbsp;</p>\n<ul>\n<li>Recall that the order of multiplication is irrelevant. For example,&nbsp;$8\\times 9$ is the same as $9\\times 8$ so sometimes thinking about the multiplication in the <strong>reverse order</strong> makes it easier to recall or work out.</li>\n<li>If&nbsp;you don't know a times table but you know one <strong>'near'</strong> it, you can use that to work the unknown one out! For example, say you don't know $6\\times 7$, but you do know&nbsp;$6\\times 6=36$, then $6\\times 7$ is just one more lot of $6$,&nbsp;and so $6 \\times 7=36+6=42$.</li>\n<li>As a last resort you can always&nbsp;just use <strong>repeated addition</strong>. For example, for $8\\times 3$ you could just work out $8+8+8=16+8=24$, note this is less work than $8$ lots of $3$.</li>\n<li>Multiply by $\\bf 2$. Most people are comfortable with doubling a number. If not, just add the number to itself.</li>\n<li>Multiplying by $\\bf 3$? You could just double it and add on another lot. For example, for $3\\times 7$ you could double $7$ then add another $7$ on, $3\\times 7=14+7=21$.</li>\n<li>Multiplying by $\\bf 4$? You could just double it and then double that. For example, for $4\\times 8$ you could double $8$ and get $16$ and then double $16$ to get $32$.</li>\n<li>Multiplying by $\\bf 5$? You could just multiply by $10$ (that is add on a zero) and then halve that. For example, for $5\\times 6$ you multiply $6$ by $10$ to get $60$ and then you halve $60$&nbsp;to get $30$.&nbsp;</li>\n<li>Multiplying by $\\bf 6$? You could multiply by $5$ and then add one more lot on. For example, for $6\\times 8$ you could work out that $5\\times 8=40$ and then add on another $8$ to get $48$.</li>\n<li>Multiplying by $\\bf 7$?&nbsp;If you couldn't work it out another way, then you could&nbsp;multiply the number by $5$ and then add on the number doubled. For example, $7\\times 8=5\\times 8+2\\times 8=40+16=56$.&nbsp;&nbsp;</li>\n<li>Multiplying by $\\bf 8$? Here&nbsp;are three&nbsp;not-so-great ways (you can normally find a better way using the above tricks):\n<ul>\n<li>Double, then double, then double. For example, for $8\\times 7$, double $7$ to get $14$, double that to get $28$, then double that to get $56$.</li>\n<li>Multiply the number by $5$ and $3$ separately and then add them up. For example, for $8\\times 7$ you could do $5\\times 7=35$ and $3\\times 7=21$ and so $8\\times 7=35+21=56$.</li>\n<li>Multiply the number by $10$ and then subtract the number doubled. For example, $8\\times 7$ will be $10\\times 7-2\\times 7=70-14=56$.</li>\n</ul>\n</li>\n<li>Multiplying by $\\bf 9$? Here are two ways.&nbsp;\n<ul>\n<li>You could multiply by $10$ (that is add on a zero) and then subtract one lot. For example, $9\\times 8=10\\times 8-8=80-8=72$.&nbsp;</li>\n<li>If you are multiplying $9$&nbsp;by a number from $2$ to $10$ then take the number you are multiply by and subtract one from it, this is the start of your&nbsp;answer, then tack on whatever number makes the digits add up to&nbsp;$9$. For example, the answer to $9\\times 7$ starts the digit $6$ (one less than seven) and since $6+3=9$ the answer must be $9\\times 7=63$.&nbsp;</li>\n</ul>\n</li>\n<li>Multiply by $\\bf 10$? Just add a zero to the end of the number. For example, $10\\times 7=70$.</li>\n</ul>\n<p>If you are stuck on a times table, just for practice see if you can work it out in more than one way.</p>", "variableReplacements": [], "scripts": {}, "marks": 0}], "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacements": [], "minValue": "r[0]*c[0]", "scripts": {}, "marks": 1, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "r[0]*c[0]", "mustBeReduced": false}, {"variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "unitTests": [], "showCorrectAnswer": true, 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"showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacements": [], "minValue": "r[3]*c[1]", "scripts": {}, "marks": 1, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "r[3]*c[1]", "mustBeReduced": false}, {"variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacements": [], "minValue": "r[3]*c[2]", "scripts": {}, "marks": 1, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "r[3]*c[2]", "mustBeReduced": false}, {"variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacements": [], "minValue": "r[3]*c[3]", "scripts": {}, "marks": 1, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "correctAnswerFraction": false, "maxValue": "r[3]*c[3]", "mustBeReduced": false}], "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "scripts": {}, "stepsPenalty": "8", "type": "gapfill", "prompt": "<p></p>\n<table border=\"1\" style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$\\large\\times$</td>\n<td style=\"text-align: center;\">$\\large\\var{c[0]}$</td>\n<td style=\"text-align: center;\">$\\large\\var{c[1]}$</td>\n<td style=\"text-align: center;\">$\\large\\var{c[2]}$</td>\n<td style=\"text-align: center;\">$\\large\\var{c[3]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\large\\var{r[0]}$</td>\n<td style=\"text-align: center;\">[[0]]</td>\n<td style=\"text-align: center;\">[[1]]</td>\n<td style=\"text-align: center;\">[[2]]</td>\n<td style=\"text-align: center;\">[[3]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\large\\var{r[1]}$</td>\n<td style=\"text-align: center;\">[[4]]</td>\n<td style=\"text-align: center;\">[[5]]</td>\n<td style=\"text-align: center;\">[[6]]</td>\n<td style=\"text-align: center;\">[[7]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\large\\var{r[2]}$</td>\n<td style=\"text-align: center;\">[[8]]</td>\n<td style=\"text-align: center;\">[[9]]</td>\n<td style=\"text-align: center;\">[[10]]</td>\n<td style=\"text-align: center;\">[[11]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\large\\var{r[3]}$</td>\n<td style=\"text-align: center;\">[[12]]</td>\n<td style=\"text-align: center;\">[[13]]</td>\n<td style=\"text-align: center;\">[[14]]</td>\n<td style=\"text-align: center;\">[[15]]</td>\n</tr>\n</tbody>\n</table>"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"name": "c", "description": "", "templateType": "anything", "definition": "ok[4..8]", "group": "Ungrouped variables"}, "r": {"name": "r", "description": "", "templateType": "anything", "definition": "ok[0..4]", "group": "Ungrouped variables"}, "ok": {"name": "ok", "description": "", "templateType": "anything", "definition": "shuffle(2..9)", "group": "Ungrouped variables"}}, "extensions": [], "type": "question", "preamble": {"js": "", "css": ""}, "advice": "", "statement": "<p>Complete&nbsp;this random selection of times tables. If you cannot recall the answer, try to work it out!</p>\n<p>For more practice, click 'Try another question like this one'.</p>", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}