Dynamically Creating Mathematical Expressions

Question

I have a site that requires random mathematical problems to be generated based on 3 parameters: operator (addition, subtraction, multiplication, division), regrouping (to carry or not to carry), and columns (one or two). I've been trying to wrap my head around how to go about doing this, but everything I come up with has a flaw in some way or other.

Here is what I am working with currently:

function create_problem($operator, $regrouping, $columns){
    $top = rand(1,9);
    $bottom = rand(1,9);

    if($operator == "+"){
        if($columns == 1 && $regrouping === false){
            $result = array(
                'top' => $top,
                'bottom' => $bottom,
                'formula' => "$top.$operator.$bottom"
            );
        }
        if($columns == 2){
            if($regrouping === false){
                if($top+$bottom > 9){
                    $diff = ($top+$bottom)-10;
                    $top = $diff+rand(1, 3);    
                }
                $result = array(
                    'top' => $top,
                    'bottom' => $bottom,
                    'formula' => "$top.$operator.$bottom"
                );
            }else{
                if($top+$bottom < 10){
                    $top = rand(1, $bottom+1);
                }
            }
        }
    }
    return $result;
}

If anyone has dealt with this, or if anyone has any pointers, I would be most appreciative!

Justin McDonald · Accepted Answer · 2012-12-09 08:36:27Z

2

this function first checks for regrouping, and produces random numbers so that the sum of common-column numbers are less than 10 (for no-carry) or greater or equal to 10 (for carry).

function create_problem($operator, $regrouping, $columns){
$x1 = '';
$x2 = '';
$y1 = '';
$y2 = '';
if ($regrouping){
    if ($columns == 2){
    $x1 = rand(1,9);
    $x2 = rand(0,9);
    $y1 = rand(9-$x1,9);
    $y2 = rand(10-$x2,9);
    } else {
    $x1 = rand(1,9);
    $y1 = rand(9-$x1,9);
    }
} else {
    if ($columns == 2){
    $x1 = rand(1,8);
    $x2 = rand(0,8);
    $y1 = rand(1,9-$x1);
    $y2 = rand(0,9-$x2);
    } else {
    $x1 = rand(1,8);
    $y1 = rand(1,9-$x1);
    }
}

return $x1.$x2.$operator.$y1.$y2;
}

ex..

31 +54

..where 3=$x1 1=$x2 5=$y1 4=$y2

edited Dec 9, 2012 at 8:36

answered Dec 9, 2012 at 6:37

Justin McDonald

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3 Comments

chaoskreator Over a year ago

A simple test run looks great with two minor issues. 1) create_problem("-", false, 2); returns an output of 68-3-5 instead of a two column expression. 2) create_problem("-", true, 2); returns 67-40 which doesn't require regrouping. Looks great otherwise!

Justin McDonald Over a year ago

try again now with edits.. first error was a typo, second error was logic problem.

Charles Over a year ago

-1, you seem to have forgotten to explain what this is and why it works how it does. Code dumps are not answers.

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