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@@ -1,179 +1,209 @@
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<?php
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-/*
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- * To change this license header, choose License Headers in Project Properties.
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- * To change this template file, choose Tools | Templates
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- * and open the template in the editor.
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- */
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-
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/**
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- * Description of Math_word_Problems
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+ * Worded maths problems ("word_problems").
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+ *
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+ * Rewritten. What was wrong with the old version:
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+ * - it didn't work like the other generators: no form, no stored answer, no
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+ * constructor taking the user, and TK2 never called it (the worded_*
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+ * subjects were mapped to the spelling generator)
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+ * - answers came from eval() of a text expression and were cut to an integer
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+ * with (int), so most were wrong: ((7/2)*5) is 17.5, not 17
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+ * - the sponge problem ignored the sponge's starting mass
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+ * - difficulty() returned null for a new student, and the "diff" token in the
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+ * templates broke when it did
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+ * - `e107.e107_tkReport` hard-coded, user not escaped
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*
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- * @author gregory
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+ * Now every problem is built backwards from its answer, so the answer is
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+ * always a whole number, there is no eval(), and the number ranges grow with
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+ * the student's accuracy over the last month (and with how many they have
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+ * answered, so one lucky answer doesn't jump to the hardest numbers).
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*/
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class math_word_problems {
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-
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- public $state = "error";
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- private $debug = false;
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- private $sql;
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+
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+ const SUBJECT = 'word_problems';
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+
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private $user;
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- private $difficultyValue;
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- private $returnData;
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+ private $level = 0; // 0-100: how hard to make the numbers
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+ private $names = ['Anna', 'George', 'Marie', 'Elliot', 'Paul', 'Stacey', 'Maureen', 'Priya', 'Sam', 'Mia'];
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/**
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- * Setup new numbers engine
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- *
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- * @param bool $test Enable debug mode.
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+ * @param string $user User to supply the question for.
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*/
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- public function __construct($test = false) {
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-
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- if ($test) {
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- $this->debug = true;
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- }
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- $this->sql = e107::getDB();
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- $this->user = e107::getUser()->getLoginName();
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- $this->state = "ready";
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+ public function __construct($user) {
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+ $this->user = $user;
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}
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- public function getProblem() {
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+ /**
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+ * Make a problem, show it, and remember it as the student's open question.
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+ */
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+ public function getWordProblem() {
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+ $problem = $this->getProblem();
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+ $questionHtml = $this->htmlify($problem);
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- $this->difficultyValue = $this->difficulty();
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-
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- if($this->debug) {
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- $this->returnData['difficulty'] = $this->difficultyValue;
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- }
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-
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- $this->questionAssembler();
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-
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- return $this->returnData;
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- }
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-
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- private function questionAssembler() { //return [ 'answer1'=>$solution['/'], 'question'=>$TempQuestion, 'type'=>__CLASS__];
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-
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- $questionIndexSelected = array_rand($this->questionData());
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- $question = $this->questionData()[$questionIndexSelected];
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- $this->returnData['question'] = $this->substitutor($question);
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- //print_a([__CLASS__.' '.__FUNCTION__=>['rawQuestion'=>$question,'processedQuestion'=>$this->returnData['question']]]);
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+ $db = e107::getDb();
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+ $db->delete('tkLastQuestion', "user = '" . $db->escape($this->user) . "'");
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+ $db->insert('tkLastQuestion', ['user' => $this->user, 'LastQuestionHtml' => base64_encode($questionHtml)]);
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+
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+ e107::getRender()->tablerender('Word problems', $questionHtml);
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}
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-
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- private function questionData() {
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- $wordedMath = [
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- ['{name1} used {int,1,1,diff} meters of cloth to sew {int,2,1,diff} pillow cases. How much cloth would be used to sew {int,3,2,diff} pillow cases?','(({int,1,1,diff}/{int,2,1,diff})*{int,3,2,diff})'],
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- //['A mother makes {int,1,1,diff} sandwiches for a party. Each child received {int,2,1,diff} sandwiches. How many children were at the party?','({int,1,1,diff}/{int,2,1,diff})'],
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- ['The mass of a sponge is {int,1,1,diff} g. When put in water it expanded and gained a mass of {int,2,1,diff} g. Find the mass difference if {int,3,1,diff} similar sponges were used in the experiment?','({int,2,1,diff}*{int,3,1,diff})'],
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- //['{name1} is {int,1,1,diff} years old. His brother is {int,2,1,diff} months older than him. How old is {name1}’s brother?','({int,1,1,diff}+({int,1,1,diff}/12))'],
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- ['An elephant eats {int,1,1,diff} kg of food a week. How much will it eat in {int,2,1,10} years?','(({int,1,1,diff}*52)*{int,2,1,10})'],
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-// ['A cake recipe uses 60 g of flour. How many cakes can I bake with 4.2 kg of flour?'],
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-// ['On a scale there is 88 grams on side A and 1.3 kg on side B. How much more weight do I need to put on side A to balance the scale?','()'],
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-// ['{name1} baked 400 cupcakes and she sold 2 fifths at the market. How many cupcakes does she have left?'],
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-// ['A baker baked 720 slices of pizza. He sold 5 nineths of the pizzas and threw away 45 slices. How many slices were left?'],
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-// ['A cake recipe uses 1 quarter kilogram of sugar. How many cakes can I bake with 750 grams of sugar?'],
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-// ['There were 280 marbles in a jar. {name1} dropped the jar and lost 3 quarters of the marbles. How many marbles were left?'],
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-// ['At the beach there were 675 people. One fifth were children and the rest were adults. How many adults were at the beach?'],
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-// ['{name1} is 56 years old and has a brother who is 84 months younger. How old is his brother?'],
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-// ['{name1} has to pack 28.35 kg of sugar into 10 bags equally. How much sugar would each bag contain?'],
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-// ['There was 310.4 kg of sand. It has to be divided into 100 tubs equally. How much sand would each tub contain?'],
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-// ['A packet contains 2.39 kg of flour. {name1} bought 1000 packets for her cake shop. How much flour does she have in total?'],
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- ];
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- return $wordedMath;
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+
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+ /**
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+ * Make a problem without showing it.
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+ *
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+ * @return array ['answer1' => int, 'question' => string, 'type' => 'word_problems']
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+ */
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+ public function getProblem() {
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+ $this->level = $this->difficulty();
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+
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+ $makers = ['pillowCases', 'sponges', 'elephant', 'sandwiches', 'marbles', 'beach', 'cupcakes', 'sugarBags'];
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+ $maker = $makers[array_rand($makers)];
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+ list($question, $answer) = $this->$maker();
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+
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+ return ['answer1' => (int) $answer, 'question' => $question, 'type' => self::SUBJECT];
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}
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/**
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- * Return the difficulty based on previously answered questions.
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+ * How hard to make the numbers, 0-100: last month's accuracy, scaled up
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+ * over the first 30 answers.
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*
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- * @return int Difficulty as percent.
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+ * @return float
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*/
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private function difficulty() {
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+ $db = e107::getDb();
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+ $stats = $db->retrieve(
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+ "SELECT (SUM(correct)/COUNT(correct)*100) AS percent, COUNT(correct) AS count
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+ FROM `" . MPREFIX . "tkReport`
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+ WHERE answereddatestamp >= UNIX_TIMESTAMP(NOW() - INTERVAL 1 MONTH)
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+ AND username = '" . $db->escape($this->user) . "' AND subject = '" . self::SUBJECT . "'"
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+ );
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- $query = "SELECT (SUM(correct)/COUNT(correct)*100) as percent
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- FROM e107.`e107_tkReport` WHERE
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- answereddatestamp >= unix_timestamp((NOW()) - INTERVAL 1 MONTH)
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- AND username = '$this->user' AND subject = '".__CLASS__."';";
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-
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- if($this->debug) {
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- $this->returnData['difficultySQL'] = $query;
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+ if (!is_array($stats) || (int) $stats['count'] === 0) {
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+ return 0.0;
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}
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-
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- $this->sql->gen($query);
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- while ($row = $this->sql->fetch()) {
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- if (is_numeric($row["percent"])) {
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- return (int)$row["percent"];
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- } else {
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- return 1;
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- }
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- }
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-
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+
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+ $sample = min(1.0, ((int) $stats['count']) / 30);
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+ return max(0.0, min(100.0, (float) $stats['percent'])) * $sample;
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}
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-
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- private function substitutor($question) {
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-
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- $questionStr = $this->names($question[0]);
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- $solutionStr = $this->names($question[1]);
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-
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- $questionArray = preg_split("/{|}/",$questionStr);
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-
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- foreach ($questionArray as $questionPart) {
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- if($this->contains('int', $questionPart)) {
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- $substituteString = $this->ints(explode(',',$questionPart));
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- $questionStr = str_replace('{'.$questionPart.'}', $substituteString, $questionStr);
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- $solutionStr = str_replace('{'.$questionPart.'}', $substituteString, $solutionStr);
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- }
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-
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- }
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- // eval needed
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- return [ 'answer1'=>(int)eval("return ".$solutionStr.";"), 'question'=>$questionStr, 'type'=>__CLASS__];
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+
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+ /**
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+ * A random whole number from $min up to $maxAtFull. At level 0 the top of
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+ * the range is a quarter of the way there; at level 100 it is all of it.
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+ */
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+ private function num($min, $maxAtFull) {
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+ $span = max(0, $maxAtFull - $min);
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+ $max = $min + (int) ceil($span * (0.25 + 0.75 * $this->level / 100));
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+ return mt_rand($min, max($min, $max));
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}
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-
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- private function names($questionString) {
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-
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- $freeNames = ['Anna','George','Marie','Elliot','Paul','Stacey','Maureen'];
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-
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- for ($int = 1; $int <= 10; $int++) {
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- $randomName = array_rand($freeNames);
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-
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- if($this->contains('{name'.$int.'}', $questionString)) {
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- $name = $freeNames[$randomName];
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-
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- $questionString = str_replace('{name'.$int.'}', $name, $questionString);
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- unset($freeNames[$randomName]);
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- }else{
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- break;
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- }
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- }
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- return $questionString;
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+
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+ private function name() {
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+ return $this->names[array_rand($this->names)];
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}
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-
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- private function ints($dataBlock) {
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- foreach ($dataBlock as $key=>&$data) {
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- if($this->contains('diff', $data)) {
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- $data = (int)$this->difficultyValue;
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- if($data<$dataBlock[($key-1)]) {
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- $data = $dataBlock[($key-1)];
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- }
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- }
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-
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+ // ---- the problems: each returns [question text, whole number answer]
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+
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+ private function pillowCases() {
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+ $perCase = $this->num(2, 12);
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+ $made = $this->num(2, 10);
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+ $wanted = $this->num(2, 20);
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+ if ($wanted === $made) {
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+ $wanted++;
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}
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-
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- return mt_rand($dataBlock[2],$dataBlock[3]);
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+
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+ return [
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+ $this->name() . ' used ' . ($perCase * $made) . ' metres of cloth to sew ' . $made . ' pillow cases. How much cloth would be used to sew ' . $wanted . ' pillow cases?',
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+ $perCase * $wanted,
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+ ];
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}
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-
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- /**
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- * contains($needle, $haystack)
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- *
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- * <code>
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- * Example;<br/>
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- * $haystack = 'Hello how are you';<br/>
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- * $needle = 'are';<br/>
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- * contains($needle, $haystack); // == true<br/>
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- * </code>
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- * @param string $needle
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- * @param string $haystack
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- * @return bool
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- */
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- function contains($needle, $haystack)
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- {
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- return strpos($haystack, $needle) !== false;
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+
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+ private function sponges() {
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+ $mass = $this->num(10, 60);
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+ $gain = $this->num(2, 30);
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+ $count = $this->num(2, 12);
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+
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+ return [
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+ 'The mass of a sponge is ' . $mass . ' g. When put in water it expanded and its mass became ' . ($mass + $gain) . ' g. How much extra mass would ' . $count . ' similar sponges gain altogether?',
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+ $gain * $count,
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+ ];
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+ }
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+
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+ private function elephant() {
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+ $kg = $this->num(10, 150);
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+ $years = $this->num(2, 10);
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+
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+ return [
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+ 'An elephant eats ' . $kg . ' kg of food a week. How many kg will it eat in ' . $years . ' years? (Use 52 weeks in a year.)',
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+ $kg * 52 * $years,
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+ ];
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+ }
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+
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+ private function sandwiches() {
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+ $each = $this->num(2, 5);
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+ $children = $this->num(3, 30);
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+
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+ return [
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+ 'A mother makes ' . ($each * $children) . ' sandwiches for a party. Each child receives ' . $each . ' sandwiches. How many children were at the party?',
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+ $children,
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+ ];
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+ }
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+
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+ private function marbles() {
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+ $quarter = $this->num(5, 60);
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+
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+ return [
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+ 'There were ' . ($quarter * 4) . ' marbles in a jar. ' . $this->name() . ' dropped the jar and lost 3 quarters of the marbles. How many marbles were left?',
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+ $quarter,
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+ ];
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+ }
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+
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+ private function beach() {
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+ $fifth = $this->num(10, 200);
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+
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+ return [
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+ 'At the beach there were ' . ($fifth * 5) . ' people. One fifth were children and the rest were adults. How many adults were at the beach?',
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+ $fifth * 4,
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+ ];
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+ }
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+
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+ private function cupcakes() {
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+ $fifth = $this->num(10, 100);
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+
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+ return [
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+ $this->name() . ' baked ' . ($fifth * 5) . ' cupcakes and sold 2 fifths of them at the market. How many cupcakes were left?',
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+ $fifth * 3,
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+ ];
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+ }
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+
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+ private function sugarBags() {
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+ $perBag = $this->num(2, 20);
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+ $bags = $this->num(2, 10);
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+
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+ return [
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+ $this->name() . ' has to pack ' . ($perBag * $bags) . ' kg of sugar equally into ' . $bags . ' bags. How many kg of sugar will each bag contain?',
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+ $perBag,
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+ ];
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+ }
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+
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+ private function htmlify($problem) {
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+ // Expected answer stays on the server; the form only carries a token.
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+ $token = TkAnswerStore::issue($this->user, $problem);
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+
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+ $frm = e107::getForm();
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+
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+ $fString = $frm->open('questionForm', 'post', '', ['autocomplete' => 'off', 'class' => 'formclass']);
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+ $fString .= $frm->label('<h4>Word problems</h4>') . "</br>\n";
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+ $fString .= $frm->label('Read the problem and write just the number as your answer.') . "\n";
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+ $fString .= '</br>';
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+ $fString .= '<p style="font-size:120%;">' . htmlspecialchars($problem['question']) . '</p>';
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+ $fString .= '</br>';
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+ $fString .= $frm->text('a1', '', 80, ['placeholder' => 'Write answer here!', 'autocomplete' => "off", 'spellcheck' => "false"]) . "\n";
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+ $fString .= $frm->hidden('checkerData', $token, ['id' => 'checkerData']);
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+ $fString .= $frm->hidden('subject', self::SUBJECT, ['id' => 'subject']);
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+ $fString .= '</br>' . "\n";
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+ $fString .= $frm->button('Answer', 'Check answer') . "\n";
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+ $fString .= $frm->close();
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+ $fString .= '</br></br>';
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+
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+ return $fString;
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}
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-
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-}
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+}
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Gregory Huxley
