replace integers with variables

hacking around some wordpress default theme.

what i am trying to do is create a custom page template that when applied shows posts in that category using post meta. this is working well.

however, i’d also like the menu to display only the parent category and children of that the category.

i’m trying to replace child_of=3 to child_of=$categori_id

here is the code

<div id="sidebar" class="internet_bar">
			<ul>	<?php
				if (is_page() ) {
			$categorize = get_post_meta($posts[0]->ID, 'category', true);
			}
		if ($categorize) {
			$categori = get_the_category();
			$categori_id = get_cat_ID($categorize);

				echo "<li>" . $categorize ."</li>";
				$categlories=  get_categories('child_of=3');
		  foreach ($categlories as $categlory) {
		  	$option = '<li>'.$categlory->category_nicename.'</li>';

			echo $option;
		  }

		}
		?> 

			</ul>
			</div>

example page of this code here – http://bedepressed.org/criticalgeography/online

online only is parent, other two categories are children