{"id":2214,"date":"2014-01-26T00:15:28","date_gmt":"2014-01-26T07:15:28","guid":{"rendered":"http:\/\/qpr.ca\/blogs\/?page_id=2214"},"modified":"2014-01-26T23:40:55","modified_gmt":"2014-01-27T06:40:55","slug":"w1","status":"publish","type":"page","link":"https:\/\/qpr.ca\/blogs\/pages\/mathstuff5\/resources\/precalculus\/real-numbers\/pmmd\/geometric\/areas\/w1\/","title":{"rendered":"Worksheet #1 &#8211; The Area Model for Whole Numbers"},"content":{"rendered":"<p>Example 1.<\/p>\n<p>Draw a picture that shows why 3 copies of the rectangle with sides 1 and b make the rectangle with sides 3 and b.<\/p>\n<p>\u000f\u000f<a href=\"https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0008.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-2281\" title=\"IMG_0008\" src=\"https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0008-300x112.jpg\" alt=\"\" width=\"300\" height=\"112\" srcset=\"https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0008-300x112.jpg 300w, https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0008-1024x383.jpg 1024w, https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0008.jpg 1991w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><br \/>\n\u000f<br \/>\nExercise 1.<\/p>\n<p>Draw a picture that shows why 5 copies of the rectangle with sides 1\u00a0and b make the rectangle with sides 5 and b.<\/p>\n<p>Let n be a whole number. Note that n copies of the rectangle with sides 1 and b\u00a0make the rectangle with sides n and b. It follows the rectangle with sides n and\u00a0b has n times as much area as the rectangle with sides 1 and b. Hence, we must\u00a0assign nb to the measure of the area of the rectangle with sides n and b (why?).<\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p>Example 2.<\/p>\n<p>Let&#8217;s use the area model definition of multiplication to show that 3(4) = 12. First we construct a rectangle with sides 3 and 4 as shown below.<br \/>\nNext partition the rectangle into unit squares.<br \/>\nAnd finally place the top two rows alongside the bottom one.<\/p>\n<p>\u000f<a href=\"https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0009.jpg\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-2282\" title=\"IMG_0009\" src=\"https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0009-300x122.jpg\" alt=\"\" width=\"300\" height=\"122\" srcset=\"https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0009-300x122.jpg 300w, https:\/\/qpr.ca\/blogs\/wp-content\/uploads\/2014\/01\/IMG_0009-1024x416.jpg 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><br \/>\n\u000f\u000fWe note that the squares on the bottom row extend to a length of 12 units.<\/p>\n<p>&nbsp;<\/p>\n<p>Exercise 2.<\/p>\n<p>Go through the same process for the cases of 2(3) and 3(2)<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Example 1. Draw a picture that shows why 3 copies of the rectangle with sides 1 and b make the rectangle with sides 3 and b. \u000f\u000f \u000f Exercise 1. Draw a picture that shows why 5 copies of the &hellip; <a href=\"https:\/\/qpr.ca\/blogs\/pages\/mathstuff5\/resources\/precalculus\/real-numbers\/pmmd\/geometric\/areas\/w1\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":2198,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-2214","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/pages\/2214","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/comments?post=2214"}],"version-history":[{"count":5,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/pages\/2214\/revisions"}],"predecessor-version":[{"id":2283,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/pages\/2214\/revisions\/2283"}],"up":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/pages\/2198"}],"wp:attachment":[{"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/media?parent=2214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/categories?post=2214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/wp-json\/wp\/v2\/tags?post=2214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}