// Numbas version: exam_results_page_options {"name": "TALMO Formative assessment talk 2022", "metadata": {"description": "

Questions shown in my presentation for the Teaching And Learning Mathematics Online session, 16th November 2022.

", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], []], "questions": [{"name": "Feedback loop: is it correct?", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "

Two parts to demonstrate kinds of feedback loop in a Numbas part: correctness, and refining an answer.

Calculate \\[ \\prod_{i=1}^5 2i \\]

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I think you added the terms, instead of multiplying them.

$\\prod$ means multiply the terms together.

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Demonstrating a kind of feedback loop in a Numbas part: you're told how close you are to the correct answer.

Find, to 3 decimal places, a root of the following function:

\\[ f(x) = \\var{expr} \\]

$x = $ [[0]]

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Demonstrating a feedback loop in a Numbas part: which of the required properties does your answer satisfy?

Write a number congruent to:

$\\var{m1} \\bmod \\var{b1}$
$\\var{m2} \\bmod \\var{b2}$
$\\var{m3} \\bmod \\var{b3}$

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The student must write a word on the given generators which is equivalent to the given word.

The generators are given as a dictionary mapping letters to permutations.

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The letters in the student's word. Any non-letter characters are removed.

", "definition": "split(replace_regex(\"[^a-z]\",\"\",lower(studentanswer),\"g\"),\"\")"}, {"name": "valid_letters", "description": "

Are all of the letters in the student's word in the generator dictionary? Fail if not.

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The permutation produced by the student's word.

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Made for my TALMO talk. This demonstrates how you can use a part with no marks as an oracle to perform calculations, to help the student check their working.

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Consider the binary tree $B_\\var{depth}$ with $2^\\var{depth}$ leaves.

{tree_diagram(depth,1..2^depth)}

In the diagram, each dashed line represents the action of swapping the two branches of the tree on either side of the line, in place.

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Generators for the isomorphism group of

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$\"+letterordinal(j)+\": \"+show(generators[j])+\"$

\")", "description": "", "templateType": "anything", "can_override": false}, "commutes": {"name": "commutes", "group": "Ungrouped variables", "definition": "matrix(\n map(map(award(1,a*b=b*a),b,generators),a,generators)\n)", "description": "

Which of the generators commute with each other? 1 if they commute, 0 otherwise.

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The names of each generator. The root node is called a, then the ones directly under it are called b and c, and so on.

", "templateType": "anything", "can_override": false}, "generator_dict": {"name": "generator_dict", "group": "Ungrouped variables", "definition": "dict(zip(generator_names,generators))", "description": "

A dictionary mapping generator names to the corresponding permutation of the leaves.

", "templateType": "anything", "can_override": false}, "permutation_to_produce": {"name": "permutation_to_produce", "group": "Ungrouped variables", "definition": "apply_word(word_to_produce)", "description": "

A permutation to be produced by a word given by the student.

", "templateType": "anything", "can_override": false}, "word_to_produce": {"name": "word_to_produce", "group": "Ungrouped variables", "definition": "shuffle(generator_names)[0..3]", "description": "

A word corresponding to the permutation that the student must produce.

Chosen so that the student's word is at least 3 letters long.

", "templateType": "anything", "can_override": false}, "generator_to_reproduce": {"name": "generator_to_reproduce", "group": "Ungrouped variables", "definition": "random(generator_names[1..len(generator_names)])", "description": "

A generator that the student must write in terms of the other generators. $a$ is excluded, since it can't be written in terms of the others.

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You can use this part to see how different words act on the graph.

Each time you submit this part, you will be shown the order of the leaves under the action of the word you typed.

", "settings": {"generators": "generator_dict", "correctWord": "a"}}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What are each of the leaves mapped to under the action of the word $\\var{latex(join(word_to_apply,' '))}$?

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Write a word which produces the following ordering of the leaves:

{join(list(permutation_to_produce),' ')}

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Write another word which produces that ordering of the leaves, of length at least 6.

", "settings": {"generators": "generator_dict", "correctWord": "{join(word_to_produce,\"\")}"}}, {"type": "m_n_x", "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": "

Which generators commute?

", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": false, "displayType": "checkbox", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": "generator_names", "matrix": "commutes", "layout": {"type": "lowertriangle", "expression": ""}, "answers": "generator_names"}, {"type": "write-a-word-producing-a-given-permutation", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "didnt_use_target:\n assert(not (settings[\"correctWord\"] in student_letters),\n incorrect(\"You must not use the letter $\"+settings[\"correctWord\"]+\"$ in your word.\")\n )\n\nmark:\n apply(base_mark);\n apply(didnt_use_target)", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Write a word equivalent to the generator $\\var{latex(generator_to_reproduce)}$, without using $\\var{latex(generator_to_reproduce)}$.

", "settings": {"generators": "generator_dict", "correctWord": "{generator_to_reproduce}"}}, {"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, "prompt": "

What is the order of each of the generators?

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What is the order of the group $\\Gamma(B_\\var{depth})$?

", "minValue": "2^(2^(depth)-1)", "maxValue": "2^(2^(depth)-1)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Give an expression for the order of $\\Gamma(B_n)$.

", "answer": "2^(2^n-1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "n", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Offer hints at different levels of detail", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question demonstrates how you can offer a selection of hints, with each giving a different level of detail and applying a different penalty.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "Write a number", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Vague hint", "rawLabel": "", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "", "penalty": "Hints revealed", "penaltyAmount": "1", "lockAfterLeaving": false}, {"label": "More specific hint", "rawLabel": "", "otherPart": 2, "variableReplacements": [], "availabilityCondition": "", "penalty": "Hints revealed", "penaltyAmount": "2", "lockAfterLeaving": false}, {"label": "Guided steps", "rawLabel": "", "otherPart": 3, "variableReplacements": [], "availabilityCondition": "", "penalty": "Hints revealed", "penaltyAmount": "3", "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Write the number 3435", "prompt": "

In this question, you need to write the number 3435.

If you need help, ask for a hint.

", "minValue": "3435", "maxValue": "3435", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Vague hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The thing you need to write is an integer.

"}, {"type": "information", "useCustomName": true, "customName": "More specific hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Use the digit keys on your keyboard to write the number.

"}, {"type": "gapfill", "useCustomName": true, "customName": "Guided steps", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Try writing the digits one at a time.

Write 3: [[0]]

Write 4: [[1]]

Write 3 again: [[2]]

Write 5: [[3]]

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Explore mode makes it possible to create open-ended questions, where the student is free to choose their own path.

In this question, the student is guided through the steps of designing a probability experiment, and then assessed based on the criteria they chose.

See this question in the public editor.

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In this exercise you will decide if a coin is biased by flipping it repeatedly and deciding if it lands heads more often than you'd expect.

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How many times will you flip your coin?

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How many heads would make you think the coin is biased?

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With an unbiased coin, how many flips would you expect to land heads up?

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Flip the coin {num_flips} times. Each time it lands heads, write an H in the box below. Each time it lands tails, write a T.

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Your flips were:

{cleaned_flips_string}

What percentage of the flips landed heads?

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Result	Heads	Tails
Frequency	{num_heads}	{num_tails}

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Do you think your coin is biased?

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You said that a coin is biased if it comes up heads at least {critical_number} times out of {num_flips}. What's that as a percentage?

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

Guides the student through the process of writing an integer in binary. They can pick any number they like, then choose from a selection of methods, or just do their own method and have the answer checked.

The largest power of 2 less than or equal to n.

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The description of the current state of the process of subtracting the largest possible power of 2.

", "templateType": "anything", "can_override": false}, "working_n": {"name": "working_n", "group": "Ungrouped variables", "definition": "n", "description": "

The value that the student is working with at the current step.

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Is the working value odd?

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Pick a positive integer. Any positive integer.

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You chose $n = \\var{n}$.

Your task is to write $n$ in binary.

How would you like to do that?

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$\\var{n} = \\var{subtracting_powers_description}$

What's the largest power of 2 less than or equal to $\\var{working_n}$?

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$\\var{n} = \\var{subtracting_powers_description}$.

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$\\var{n} = \\var{subtracting_powers_description}$.

Now write the binary representation of $\\var{n}$.

", "answer": "{binary_encoding}", "displayAnswer": "", "matchMode": "exact"}, {"type": "information", "useCustomName": true, "customName": "Binary encoding hint - subtracted powers", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": true, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

For each power of 2, from the largest one you wrote down to $2^0 = 1$, write a $1$ if that power is in your list, or a $0$ if it isn't.

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$\\var{working_n} = \\var{dividing_description}$

Is $\\var{working_n}$ odd?

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$\\var{working_n} = \\var{dividing_description}$

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$0 = \\var{dividing_description}$.

Now write the binary representation of $\\var{n}$.

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$0 = \\var{dividing_description}$

Adding a 0 to the end of the binary representation of $n$ gives you the binary representation of $2n$.

You can use this to build up the binary representation of $\\var{n}$ while unravelling the expression above.

So, starting with an empty string, read the expression from right to left, adding a $0$ when you see $/2$, or changing the rightmost $0$ to $1$ when you see $-1$.

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Write the binary representation of $\\var{n}$.

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This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

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The Venn diagram below represents the set of integers, with the positive and even numbers as subsets.

For each of the numbers {join(ns,', ')}, decide if it is positive and if it is even. Move the points representing the numbers to the appropriate positions on the diagram.

{venn_diagram_many_solo}

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The student must write a word on the given generators which is equivalent to the given word.

The generators are given as a dictionary mapping letters to permutations.

The letters in the student's word. Any non-letter characters are removed.

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Are all of the letters in the student's word in the generator dictionary? Fail if not.

The permutation produced by the student's word.

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.