I am trying to convert one of my older scripts into OOP with a class but I have a question: how do I reference a variable between methods within the same class? I tried using $this->variable with no luck.

Here's the code:

Code:
<?php

class DisplayCat {

  // Insures that the value of $cat is valid

  public function CheckCatValue($cat)
    {
       if (($cat == "") || ($cat == "0")) 
         {
           echo "category was left blank";
         }
       elseif (is_numeric($cat) == false) 
         {
           echo "category must be a numeric value";
         }
        else 
         {
           $this->DisplayProducts($cat);	  
         }
    }

    // Loops through the category and displays produts

	public function DisplayProducts($cat)
	  {
            $getProducts = mysql_query("SELECT * FROM products WHERE prod_cat = $cat LIMIT $this->offset,$this->rowsperpage") or die(mysql_error());
            $num_rows = mysql_num_rows($getProducts);

            while($row = mysql_fetch_array( $getProducts )) 
		  {
		  $prod_id = $row["prod_id"];
		  $prod_title = $row["prod_title"];
		  $prod_pprice = $row["prod_pprice"];
		  $prod_gprice = $row["prod_gprice"];
		  $prod_thumb = $row["prod_thumb"];

		  for ($n = 1; $n <=4; $n++) 
		    {
		    }

            echo "
		<div class=\"catbody_block\">
	          <div class=\"catbody_img\">
		    <a href=\"product.php?product=$prod_id\"><img src=\"$prod_thumb\" border=\"0\" alt=\"$prod_id\" /></a>
		  </div>
		  <div class=\"catbody_data\">
		    &nbsp;$prod_id | $prod_pprice <br /> &nbsp;$prod_title
		    <br />&nbsp;<a href=\"product.php?product=$prod_id\"><img src=\"images/_info.gif\" border=\"0\" alt=\"info\"/></a><a href=\"addtocart.php?product=$prod_id\"><img src=\"images/_buy.gif\" border=\"0\" /></a>
		  </div>
		</div>";
	    }
	  }

  // Creates pagination values

  public function CreatePagination($cat,$sql,$conn) 
    {
      $sql = "SELECT COUNT(*) FROM products WHERE prod_cat = $cat";  
      $result = mysql_query($sql, $conn) or trigger_error("SQL", E_USER_ERROR);  
      $r = mysql_fetch_row($result);  
      $numrows = $r[0];  

		if ($numrows == 0) 
		  {
		    echo "Numrows = 0";
		  } 
        else 
		  {
		    $rowsperpage = 12;  
			$totalpages = ceil($numrows / $rowsperpage); 

        if (isset($_GET['currentpage']) && is_numeric($_GET['currentpage'])) 
	  {  
             $currentpage = (int) $_GET['currentpage'];  
          } 
        else 
	  {  
	    $currentpage = 1;  
	  } 
			
        if ($currentpage > $totalpages) 
	  {  
	    $currentpage = $totalpages;  
	  }  
				 
	if ($currentpage < 1) 
	  {  
	    $currentpage = 1;  
	  }  
				 
        $offset = ($currentpage - 1) * $rowsperpage;  
     }
  }

   // Displays pagination footer

    public function DisplayPagination($cat)
	{
          echo "<div class=\"catbody_pagination\">More:&nbsp;";
		
	  if ($this->currentpage > 1) 
	    {  
              echo "<a href='{$_SERVER['PHP_SELF']}?$this->currentpage=1&cat=$cat'><<&nbsp;</a> ";  

	      $prevpage = $this->currentpage - 1;  
        
	    } 

	  $range = 12;  
      
	  for ($x = ($this->currentpage - $range); $x < (($this->currentpage + $range)  + 1); $x++) 
	    {  
		  if (($x > 0) && ($x <= $this->totalpages)) 
		    {  
			  if ($x == $this->currentpage) 
			    {  
			      echo "$x";  
				} 
				else
				{  
                  echo " <a href='{$_SERVER['PHP_SELF']}?$this->currentpage=$x&cat=$cat'>$x</a> ";  
				}
			} 
		}
   
	  if ($this->currentpage != $this->totalpages) 
	    {  
		  $nextpage = $this->currentpage + 1;   
		  //  echo " <a href='{$_SERVER['PHP_SELF']}?currentpage=$nextpage&cat=$cat'>></a> ";  
		  echo " <a href='{$_SERVER['PHP_SELF']}?$this->currentpage=$this->totalpages&cat=$cat'>&nbsp;>></a>";  
		}

	  echo "&nbsp;&nbsp&nbsp;&nbsp&nbsp;&nbsp;</div>";
	}
}


?>

Code:
<?php
  include ("classes/displaycat.php");
  $cat = mysql_real_escape_string($_GET['cat']);

  $DisplayCat = new DisplayCat;

    $CheckCatValue = $DisplayCat->CheckCatValue($cat);
    $CreatePagination = $DisplayCat->CreatePagination($cat);
    $DisplayPagination = $DisplayCat->DisplayPagination($cat);
		
?>

I get this error:

You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '' at line 1

and assume it has to do with not properly passing the values of LIMIT $offset,$rowsperpage - how do I do that?