{"id":739,"date":"2017-12-20T22:42:00","date_gmt":"2017-12-21T03:42:00","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=739"},"modified":"2018-05-21T06:49:25","modified_gmt":"2018-05-21T11:49:25","slug":"integer-subtraction-2","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/integer-subtraction-2\/","title":{"rendered":"Subtracting Positive and Negative Integers &#8211; Part 2"},"content":{"rendered":"<p><iframe loading=\"lazy\" width=\"1104\" height=\"621\" src=\"https:\/\/www.youtube.com\/embed\/xj2zkIHKb0Y?wmode=transparent&amp;rel=0&amp;feature=oembed\" frameborder=\"0\" allow=\"autoplay; encrypted-media\" allowfullscreen><\/iframe><\/p>\n<p>In this post, we continue our work around integers from a visual perspective. You should definitely use the other <a href=\"https:\/\/mathisvisual.com\/tag\/integers\/\">integer posts<\/a> first prior to attempting this task as students intuitively build an understanding progressively through each activity.<\/p>\n<p>Here, we continue working with subtracting negative integers.<\/p>\n<p>Math is visual. Let&#8217;s teach it that way!<\/p>\n<h2>Math Is Visual Prompts<\/h2>\n<p>Are you finding the visual prompts useful? Leave a comment to let me know and I&#8217;ll keep them coming!<\/p>\n<p>Here are a few you might consider using for your classroom.<\/p>\n<p>In the Math Is Visual video, students are challenged to determine the result of:<\/p>\n<blockquote><p>10 black squares &#8211; 4 red squares<\/p><\/blockquote>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-907\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-1024x576.jpeg\" alt=\"Subtracting Positive and Negative Integers - Part 2 - 01 - 10 black squares minus 4 black squares intro v2\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>Using their understanding of the <strong>zero principle<\/strong> as demonstrated in previous integer videos <a href=\"https:\/\/mathisvisual.com\/integer-subtraction\/\">here<\/a> and <a href=\"https:\/\/mathisvisual.com\/integer-subtraction-2\/\">here<\/a>, the hope is that students are developing an intuitive understanding and will add 4 red squares and 4 black squares in order to have enough red to subtract as the problem asks.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-908\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-1024x576.jpeg\" alt=\"Subtracting Positive and Negative Integers - Part 2 - 02 - 10 black squares minus 4 black squares using zero principle v2\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-02-10-black-squares-minus-4-black-squares-using-zero-principle-v2.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>After removing the 4 red squares, students should be able to see that the result is actually 10 black squares plus an additional 4 black squares, which might help point them in the direction of building a conjecture.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-909\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-1024x576.jpeg\" alt=\"Subtracting Positive and Negative Integers - Part 2 - 03 - 10 black squares minus 4 black squares with 4 red removed v2\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-03-10-black-squares-minus-4-black-squares-with-4-red-removed-v2.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>After rearranging the concrete squares on their desks, students might have something look more like a 10 frame and 4 additional black squares.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-910\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-1024x576.jpeg\" alt=\"Subtracting Positive and Negative Integers - Part 2 - 014- 10 black squares minus 4 black squares simplified result v2\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-014-10-black-squares-minus-4-black-squares-simplified-result-v2.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>If you&#8217;re wondering whether it is worth creating some more situations on the fly like this to help your students out, the answer is: &#8220;YES!&#8221;<\/p>\n<p>Give your students tons of experience with concrete and visual representations before rushing to the symbolic!<\/p>\n<p>Remember: Math is visual. Let&#8217;s teach it that way!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this post, we continue our work around integers from a visual perspective. You should definitely use the other integer posts first prior to attempting this task as students intuitively build an understanding progressively through each activity. Here, we continue working with subtracting negative integers. Math is visual. Let&#8217;s teach it that way! Math Is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":907,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"video","meta":{"footnotes":""},"categories":[23],"tags":[32,33,34,30,31],"series":[43,35,42],"class_list":["post-739","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-integer-subtraction","series-integers","series-subtraction"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Subtracting Positive and Negative Integers - Part 2 - Math Is Visual<\/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:\/\/mathisvisual.com\/integer-subtraction-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Subtracting Positive and Negative Integers - Part 2 - Math Is Visual\" \/>\n<meta property=\"og:description\" content=\"In this post, we continue our work around integers from a visual perspective. You should definitely use the other integer posts first prior to attempting this task as students intuitively build an understanding progressively through each activity. Here, we continue working with subtracting negative integers. Math is visual. Let&#8217;s teach it that way! Math Is [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathisvisual.com\/integer-subtraction-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Math Is Visual\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/mathisvisual\" \/>\n<meta property=\"article:published_time\" content=\"2017-12-21T03:42:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-05-21T11:49:25+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2017\/12\/Subtracting-Positive-and-Negative-Integers-Part-2-01-10-black-squares-minus-4-black-squares-intro-v2.jpeg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1080\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"kylepearce3\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@mathisvisual\" \/>\n<meta name=\"twitter:site\" content=\"@mathisvisual\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kylepearce3\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathisvisual.com\/integer-subtraction-2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathisvisual.com\/integer-subtraction-2\/\"},\"author\":{\"name\":\"kylepearce3\",\"@id\":\"https:\/\/mathisvisual.com\/#\/schema\/person\/b47a49936e6a402ef530c1d283550a6e\"},\"headline\":\"Subtracting Positive and Negative Integers &#8211; 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You should definitely use the other integer posts first prior to attempting this task as students intuitively build an understanding progressively through each activity. Here, we continue working with subtracting negative integers. Math is visual. Let&#8217;s teach it that way! 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