how to build a js calculator on a drupal 7 page/node?

I am trying to build a simple calculator module or I should say I am trying to learn the principals required to make a Drupal 7 math/calculator module that simply takes users inputs (form(numbers)) and dose some math on them and then displays the results on the same page with out a page refresh. dont need forme validation because not going to db; just calculating and displaying results.

I have been able to get hook_menu to work and build a path to js script function to work in my .module file:

<?php

/**
 * Implements hook_menu().
 */
function calculator_jquery_menu() {
  $items['calculator_jquery'] = array(
    'title' => "Craig's jquery calculator module",
    'description' => 'Demonstration of various JavaScript utilities',
    'page callback' => 'calculator_jquery_p',
    'access callback' => TRUE,
  );
  return $items;
}

function calculator_jquery_p(){
	 // Set the path to our script.
  $script = drupal_get_path('module', 'calculator_jquery') . '/calculator_jquery.js';

  // Include a JavaScript file.
  $js = drupal_add_js($script);

 $build = array(
 //  '#type' => 'markup',
 //  '#markup' => '<p>This is an examples page.</p>',
  );

  return $build;
}

My .js file is working:

jQuery(document).ready(function () {
//var text = jQuery('h1').text();
alert(1);
//<input type="checkbox" class="option" value="200" /> Name<br />;
//<input type="CHECKBOX" name="check1" value="yes" checked>;
//document.write('eee');
});

Sense I don't need a form validation I would like to use js forms not the Drupal form api. I have tried the following code in the js file with no luck as a simple test case using checkbox:
<input type="checkbox" class="option" value="200" /> Name<br />;
the check box is not recognized by Drupal.
Dose any body have a suggestion how I can get this to work? or a good code resource/strategy to making this type of module? I am confused with how to write js code in drupal that is self running; all info for js in Drupal that I have found is hooking into the csm content/frame work. I would think that there is value to making some modules that just perform simple stuff(calculators, ect) with out hooking in to something else.

Thank you for any suggestions.