php checkbox from mysql

Put checked="checked" just like you have put value="check":

<td><input type='checkbox' name='check[$row{['GradeID']}] value='check' checked="checked" /></td>

Edit:

Probably I misunderstood you. What do you expect to see?

First, you should make the form to perform POST request instead of GET (default):

print "<form method='POST' action='THE_FILE_YOU_PRINT_RESULTS.php'>"

Then in "THE_FILE_YOU_PRINT_RESULTS.php" do a print_r($_POST); to see what you get and how to display it.

A better way to do this would be to name your checkboxes check[]. Each checkbox value should then be the ID (rather than check).

Then on your results page, just loop through each instance of check[] and print the value out.

check[$row{['GradeID']}]

Seems incorrect to me, should it be:

check[{$row['GradeID']}]

Notice the moved opening curly bracket to before the $

Sorry if this is wrong haven't used PHP in long time but it stood out for me

The are a couple of error in the form print function. You have to put the action on the first form, not on the second, you have to change the way how you print the checkbox as well. Try to print the form in this way:

<?php 
    include('connect.php');
    $query = 'SELECT * FROM grades'; 

    if ($r = mysql_query($query)) {  
        print "

            <form action=\"check2.php\" method=\"POST\">

            <table>"; 

        while ($row = mysql_fetch_array($r)) { 
            print  
                "<tr> 
                     <td>{$row['InstitutionName']}</td> 
                     <td>{$row['InstitutionAddress']}</td> 
                     <td>{$row['SubjectArea']}</td> 
                     <td><input type='checkbox' name='check[".$row['GradeID']."]         value='".$row['GradeID']."' /></td>
                 </tr>"; 
        }

        print "</table>
               <input type='submit' name='Submit' value='Submit'>
               </form>"; 

        $checkbox[] = isset($_POST['checkbox']) ? true : false;
    } else {  
        print '<p style="color: blue">Error!</p>'; 
    }  
?>

And print the checked box reading the _REQUEST array:

<?php   
    if(isset($_REQUEST["check"])) 
    { 
        foreach($_REQUEST["check"] as $key=>$value) 
        { 
            echo $key."<br>"; //it will print the value of your checkbox that you checked 
        } 
    } 
?>

This should work.