{"id":1648,"date":"2012-02-12T07:48:30","date_gmt":"2012-02-12T15:48:30","guid":{"rendered":"http:\/\/kidnexions.com\/blog\/?p=1648"},"modified":"2012-08-06T06:57:48","modified_gmt":"2012-08-06T14:57:48","slug":"the-artistic-side-of-math-area","status":"publish","type":"post","link":"https:\/\/www.familymathnight.com\/blog\/?p=1648","title":{"rendered":"The Artistic Side of Math &#8211; Area"},"content":{"rendered":"<p><a href=\"http:\/\/kidnexions.com\/blog\/?attachment_id=1651\" rel=\"attachment wp-att-1651\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/kidnexions.com\/blog\/wp-content\/uploads\/2012\/02\/area1-300x225.jpg\" alt=\"\" title=\"area1\" width=\"300\" height=\"225\" class=\"alignnone size-medium wp-image-1651\" srcset=\"https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area1-300x225.jpg 300w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area1-450x337.jpg 450w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area1.jpg 720w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><a href=\"http:\/\/kidnexions.com\/blog\/?attachment_id=1650\" rel=\"attachment wp-att-1650\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/kidnexions.com\/blog\/wp-content\/uploads\/2012\/02\/area-225x300.jpg\" alt=\"\" title=\"area\" width=\"225\" height=\"300\" class=\"alignleft  size-medium wp-image-1650\" srcset=\"https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area-225x300.jpg 225w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area-450x600.jpg 450w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area.jpg 540w\" sizes=\"auto, (max-width: 225px) 100vw, 225px\" \/><\/a><\/p>\n<p>This is one of my favorite math and art activities.  That&#8217;s because it involves a mathematical pattern.<\/p>\n<p>Using centimeter graph paper, we start with the basic unit which, in this case, is simply one square.  I then ask students what they think the area would be if we doubled the size of the square.  The first thing they blurt out before thinking is &#8220;two&#8221;.<\/p>\n<p>I then use the graph paper to show them that if I double the square (double the length then the width) I end up with a square with the area of 4 square centimeters.  <\/p>\n<p>Then we triple the original square.  It&#8217;s important that they understand we&#8217;re tripling the ORIGINAL square, not the doubled square.  We discover that the area of the tripled square is 9 sq cm.  We transfer this data onto a table and continue looking for patterns.  I&#8217;m including the transparency of the last time I taught this lesson.  There&#8217;s a lot on it so you can see that one thing led to another and pretty soon we were doing algebra. <\/p>\n<p><a href=\"http:\/\/kidnexions.com\/blog\/?attachment_id=1686\" rel=\"attachment wp-att-1686\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/kidnexions.com\/blog\/wp-content\/uploads\/2012\/02\/2012-02-09-16.30.423-225x300.jpg\" alt=\"\" title=\"area transparency\" width=\"225\" height=\"300\" class=\"alignleft size-medium wp-image-1686\" srcset=\"https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/2012-02-09-16.30.423-225x300.jpg 225w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/2012-02-09-16.30.423-450x600.jpg 450w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/2012-02-09-16.30.423.jpg 1920w\" sizes=\"auto, (max-width: 225px) 100vw, 225px\" \/><\/a><\/p>\n<p>But the main objective was to get them to see that to double the size (area) of a shape, simply multiply it by 4.  To triple it, multiply it by 9.  Turns out, these numbers, 1, 4, 9, etc. are square numbers.  SUPER COOL!<\/p>\n<p>Next, I show them how to design a shape other than a square using the graph paper and then doubling it.  You can see on the transparency that I used a house.  We had already done work using geoboards to determine the area of rectangles and triangles, so this wasn&#8217;t an issue for them.<\/p>\n<p>Once they had the hang of it, I turn them loose.  <\/p>\n<p>This activity is filled with lots of math:  spatial geometry, measurement, patterns, algebra (if you turn the pattern in the table into an equation), arithmetic.  Too FUN!<\/p>\n<p><a href=\"http:\/\/kidnexions.com\/blog\/?attachment_id=1701\" rel=\"attachment wp-att-1701\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/kidnexions.com\/blog\/wp-content\/uploads\/2012\/02\/2012-02-09-16.31.57-300x225.jpg\" alt=\"\" title=\"enlarge area\" width=\"300\" height=\"225\" class=\"alignleft size-medium wp-image-1701\" srcset=\"https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/2012-02-09-16.31.57-300x225.jpg 300w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/2012-02-09-16.31.57-450x337.jpg 450w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><a href=\"http:\/\/kidnexions.com\/blog\/?attachment_id=1652\" rel=\"attachment wp-att-1652\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/kidnexions.com\/blog\/wp-content\/uploads\/2012\/02\/area2-300x225.jpg\" alt=\"\" title=\"area2\" width=\"300\" height=\"225\" class=\"alignnone size-medium wp-image-1652\" srcset=\"https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area2-300x225.jpg 300w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area2-450x337.jpg 450w, https:\/\/www.familymathnight.com\/blog\/wp-content\/uploads\/2012\/02\/area2.jpg 720w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is one of my favorite math and art activities. That&#8217;s because it involves a mathematical pattern. Using centimeter graph paper, we start with the basic unit which, in this case, is simply one square. I then ask students what they think the area would be if we doubled the size of the square. The first thing they blurt out before thinking is &#8220;two&#8221;. I then use the graph paper to show them that if I double the square (double&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.familymathnight.com\/blog\/?p=1648\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[123,76,54,53,52,57],"tags":[69,88,64,67,21,22,89,87],"class_list":["post-1648","post","type-post","status-publish","format-standard","hentry","category-activities","category-family-math-night-2","category-geometry-kids-and-math-3-5","category-measurement-kids-and-math-3-5","category-number-and-operations","category-problem-solving","tag-family-math-night","tag-hands-on-math","tag-k-5-geometry","tag-k-5-math","tag-karyn-hodgens","tag-kidnexions","tag-math-and-art","tag-measurement-2"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Artistic Side of Math - Area - Karyn&#039;s Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.familymathnight.com\/blog\/?p=1648\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Artistic Side of Math - Area - Karyn&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"This is one of my favorite math and art activities. That&#8217;s because it involves a mathematical pattern. Using centimeter graph paper, we start with the basic unit which, in this case, is simply one square. I then ask students what they think the area would be if we doubled the size of the square. The first thing they blurt out before thinking is &#8220;two&#8221;. I then use the graph paper to show them that if I double the square (double... 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