TimeKeeper/questionGenerators/math/math_word_problems.php

<?php

/**
 * Worded maths problems ("word_problems").
 *
 * Rewritten. What was wrong with the old version:
 *  - it didn't work like the other generators: no form, no stored answer, no
 *    constructor taking the user, and TK2 never called it (the worded_*
 *    subjects were mapped to the spelling generator)
 *  - answers came from eval() of a text expression and were cut to an integer
 *    with (int), so most were wrong: ((7/2)*5) is 17.5, not 17
 *  - the sponge problem ignored the sponge's starting mass
 *  - difficulty() returned null for a new student, and the "diff" token in the
 *    templates broke when it did
 *  - `e107.e107_tkReport` hard-coded, user not escaped
 *
 * Now every problem is built backwards from its answer, so the answer is
 * always a whole number, there is no eval(), and the number ranges grow with
 * the student's accuracy over the last month (and with how many they have
 * answered, so one lucky answer doesn't jump to the hardest numbers).
 */
class math_word_problems {

    const SUBJECT = 'word_problems';

    private $user;
    private $level = 0; // 0-100: how hard to make the numbers
    private $names = ['Anna', 'George', 'Marie', 'Elliot', 'Paul', 'Stacey', 'Maureen', 'Priya', 'Sam', 'Mia'];

    /**
     * @param string $user User to supply the question for.
     */
    public function __construct($user) {
        $this->user = $user;
    }

    /**
     * Make a problem, show it, and remember it as the student's open question.
     */
    public function getWordProblem() {
        $problem = $this->getProblem();
        $questionHtml = $this->htmlify($problem);

        $db = e107::getDb();
        $db->delete('tkLastQuestion', "user = '" . $db->escape($this->user) . "'");
        $db->insert('tkLastQuestion', ['user' => $this->user, 'LastQuestionHtml' => base64_encode($questionHtml)]);

        e107::getRender()->tablerender('Word problems', $questionHtml);
    }

    /**
     * Make a problem without showing it.
     *
     * @return array ['answer1' => int, 'question' => string, 'type' => 'word_problems']
     */
    public function getProblem() {
        $this->level = $this->difficulty();

        $makers = ['pillowCases', 'sponges', 'elephant', 'sandwiches', 'marbles', 'beach', 'cupcakes', 'sugarBags'];
        $maker = $makers[array_rand($makers)];
        list($question, $answer) = $this->$maker();

        return ['answer1' => (int) $answer, 'question' => $question, 'type' => self::SUBJECT];
    }

    /**
     * How hard to make the numbers, 0-100: last month's accuracy, scaled up
     * over the first 30 answers.
     *
     * @return float
     */
    private function difficulty() {
        $db = e107::getDb();
        $stats = $db->retrieve(
            "SELECT (SUM(correct)/COUNT(correct)*100) AS percent, COUNT(correct) AS count
             FROM `" . MPREFIX . "tkReport`
             WHERE answereddatestamp >= UNIX_TIMESTAMP(NOW() - INTERVAL 1 MONTH)
             AND username = '" . $db->escape($this->user) . "' AND subject = '" . self::SUBJECT . "'"
        );

        if (!is_array($stats) || (int) $stats['count'] === 0) {
            return 0.0;
        }

        $sample = min(1.0, ((int) $stats['count']) / 30);
        return max(0.0, min(100.0, (float) $stats['percent'])) * $sample;
    }

    /**
     * A random whole number from $min up to $maxAtFull. At level 0 the top of
     * the range is a quarter of the way there; at level 100 it is all of it.
     */
    private function num($min, $maxAtFull) {
        $span = max(0, $maxAtFull - $min);
        $max = $min + (int) ceil($span * (0.25 + 0.75 * $this->level / 100));
        return mt_rand($min, max($min, $max));
    }

    private function name() {
        return $this->names[array_rand($this->names)];
    }

    // ---- the problems: each returns [question text, whole number answer]

    private function pillowCases() {
        $perCase = $this->num(2, 12);
        $made = $this->num(2, 10);
        $wanted = $this->num(2, 20);
        if ($wanted === $made) {
            $wanted++;
        }

        return [
            $this->name() . ' used ' . ($perCase * $made) . ' metres of cloth to sew ' . $made . ' pillow cases. How much cloth would be used to sew ' . $wanted . ' pillow cases?',
            $perCase * $wanted,
        ];
    }

    private function sponges() {
        $mass = $this->num(10, 60);
        $gain = $this->num(2, 30);
        $count = $this->num(2, 12);

        return [
            '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?',
            $gain * $count,
        ];
    }

    private function elephant() {
        $kg = $this->num(10, 150);
        $years = $this->num(2, 10);

        return [
            'An elephant eats ' . $kg . ' kg of food a week. How many kg will it eat in ' . $years . ' years? (Use 52 weeks in a year.)',
            $kg * 52 * $years,
        ];
    }

    private function sandwiches() {
        $each = $this->num(2, 5);
        $children = $this->num(3, 30);

        return [
            'A mother makes ' . ($each * $children) . ' sandwiches for a party. Each child receives ' . $each . ' sandwiches. How many children were at the party?',
            $children,
        ];
    }

    private function marbles() {
        $quarter = $this->num(5, 60);

        return [
            '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?',
            $quarter,
        ];
    }

    private function beach() {
        $fifth = $this->num(10, 200);

        return [
            'At the beach there were ' . ($fifth * 5) . ' people. One fifth were children and the rest were adults. How many adults were at the beach?',
            $fifth * 4,
        ];
    }

    private function cupcakes() {
        $fifth = $this->num(10, 100);

        return [
            $this->name() . ' baked ' . ($fifth * 5) . ' cupcakes and sold 2 fifths of them at the market. How many cupcakes were left?',
            $fifth * 3,
        ];
    }

    private function sugarBags() {
        $perBag = $this->num(2, 20);
        $bags = $this->num(2, 10);

        return [
            $this->name() . ' has to pack ' . ($perBag * $bags) . ' kg of sugar equally into ' . $bags . ' bags. How many kg of sugar will each bag contain?',
            $perBag,
        ];
    }

    private function htmlify($problem) {
        // Expected answer stays on the server; the form only carries a token.
        $token = TkAnswerStore::issue($this->user, $problem);

        $frm = e107::getForm();

        $fString = $frm->open('questionForm', 'post', '', ['autocomplete' => 'off', 'class' => 'formclass']);
        $fString .= $frm->label('<h4>Word problems</h4>') . "</br>\n";
        $fString .= $frm->label('Read the problem and write just the number as your answer.') . "\n";
        $fString .= '</br>';
        $fString .= '<p style="font-size:120%;">' . htmlspecialchars($problem['question']) . '</p>';
        $fString .= '</br>';
        $fString .= $frm->text('a1', '', 80, ['placeholder' => 'Write answer here!', 'autocomplete' => "off", 'spellcheck' => "false"]) . "\n";
        $fString .= $frm->hidden('checkerData', $token, ['id' => 'checkerData']);
        $fString .= $frm->hidden('subject', self::SUBJECT, ['id' => 'subject']);
        $fString .= '</br>' . "\n";
        $fString .= $frm->button('Answer', 'Check answer') . "\n";
        $fString .= $frm->close();
        $fString .= '</br></br>';

        return $fString;
    }
}