{"id":702,"date":"2017-12-15T16:58:27","date_gmt":"2017-12-15T21:58:27","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=702"},"modified":"2018-05-21T06:49:47","modified_gmt":"2018-05-21T11:49:47","slug":"integer-addition-2","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/integer-addition-2\/","title":{"rendered":"Adding Positive and Negative Integers, Part 2"},"content":{"rendered":"<p><iframe loading=\"lazy\" width=\"1104\" height=\"621\" src=\"https:\/\/www.youtube.com\/embed\/n7SNrTLortQ?wmode=transparent&amp;rel=0&amp;feature=oembed\" frameborder=\"0\" allow=\"autoplay; encrypted-media\" allowfullscreen><\/iframe><\/p>\n<p>In my previous post, we looked at <strong>adding and subtracting integers<\/strong> by implicitly introducing the idea of the Zero Principle through the use of squares on the screen. While some might interpret the black squares to represent positive values and red to represent negative, the choice is really up to the viewer.<\/p>\n<p>This post introduces the red dots first. Under the assumption that many will believe the red to be negative, this post is intended to help students realize that order doesn&#8217;t matter; positive or negative.<\/p>\n<p>Math is visual. Let&#8217;s teach it that way!<\/p>\n<p>Use the following visual prompts to help students to conceptualize more difficult <strong>integer operation<\/strong> ideas like subtracting negative values (coming in the next couple posts).<\/p>\n<h2>Math Is Visual Prompts<\/h2>\n<p>Feel free to use the video and pause in-between ideas or alternatively, use the following visual prompts.<\/p>\n<h4>Visual #1 Prompts<\/h4>\n<p>Show the following image:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-703\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-1024x576.jpeg\" alt=\"Adding Positive and Negative Integers - Video 2 - Negative Plus a Positive - VIsual 1a\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-1a.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>You may consider working only with the visual prior to introducing the numerical symbols included in the visual below:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-871\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-1024x576.jpeg\" alt=\"Adding Positive and Negative Integers Part 2 Visual Prompts 1a - 5 red plus 3 black\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-1a-5-red-plus-3-black.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>After giving students some time to determine how many squares will remain and what colour they will be, you can show them the visual that matches this scenario.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-895\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-1024x576.jpeg\" alt=\"Adding Positive and Negative Integers Part 2.003 5 red plus 3 black equals 2 red\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.003-5-red-plus-3-black-equals-2-red.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<h4>Visual #2 Prompts<\/h4>\n<p>Show the following image:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-706\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-1024x576.jpeg\" alt=\"Adding Positive and Negative Integers - Video 2 - Negative Plus a Positive - VIsual 2b\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Video-2-Negative-Plus-a-Positive-VIsual-2b.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>After students use square tiles and come to their conclusion, have them write out their thinking using a numerical expression.<\/p>\n<p>Then, show them this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-869\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-1024x576.jpeg\" alt=\"Adding Positive and Negative Integers Part 2 Visual Prompts 2a - 9 red plus 5 black\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2-Visual-Prompts-2a-9-red-plus-5-black.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>And finally, a simplified version:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-896\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-1024x576.jpeg\" alt=\"Adding Positive and Negative Integers Part 2.006 9 red plus 5 black equals 4 red\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Adding-Positive-and-Negative-Integers-Part-2.006-9-red-plus-5-black-equals-4-red.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Last time, we added positive and negative integers using black and red squares. Now we will show the red squares first and students see that the rules are the same.<\/p>\n","protected":false},"author":1,"featured_media":698,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"video","meta":{"footnotes":""},"categories":[23],"tags":[32,33,34,30,31],"series":[44,45,35],"class_list":["post-702","post","type-post","status-publish","format-video","has-post-thumbnail","hentry","category-number","tag-grade-7","tag-grade-8","tag-grade-9","tag-integers","tag-intermediate","post_format-post-format-video","series-addition","series-integer-addition","series-integers"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Adding Positive and Negative Integers, Part 2 - Math Is Visual<\/title>\n<meta name=\"description\" content=\"Last time, we added positive and negative integers using black and red squares. 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