{"id":2325,"date":"2022-08-17T07:30:16","date_gmt":"2022-08-17T12:30:16","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=2325"},"modified":"2022-09-18T13:01:03","modified_gmt":"2022-09-18T18:01:03","slug":"subtracting-negative-numbers","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/subtracting-negative-numbers\/","title":{"rendered":"Subtracting Negative Numbers"},"content":{"rendered":"\r\n<p><iframe loading=\"lazy\" title=\"Subtracting Negative Numbers Number Talk | Emerging Subtracting Negative Integers Through Difference\" width=\"1104\" height=\"621\" src=\"https:\/\/www.youtube.com\/embed\/svn5sTx56eI?wmode=transparent&amp;rel=0&amp;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\r\n<h2><b>In This Set of Visual Number Talk Prompts\u2026<\/b><\/h2>\r\n<p>Students will explore integer subtraction through a real world contextual situation involving rising and falling temperatures.<\/p>\r\n<h2>String of Related Problems<\/h2>\r\n<p><span style=\"font-weight: 400;\">Present the following subtraction sentences one at a time. Create a context that encourages students to leverage the subtraction structure of difference. For example, the temperature rose from 5 degrees to 12 degrees. How much warmer is it? The temperature rose from to -9 degrees to -2 degrees, how much warmer is it? Encourage students to use an open number line to defend their answer. Model student thinking on the open number line.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">In this set of visual number talk prompts, we will explore the first two (2) of the five (5) related problems from <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/rising-water-day5\"><span style=\"font-weight: 400;\">Day 5 of the Rising Water problem based unit<\/span><\/a><span style=\"font-weight: 400;\">:<\/span><\/p>\r\n<p style=\"text-align: center;\"><em><strong>12 &#8211; 5<\/strong><\/em><\/p>\r\n<p style=\"text-align: center;\"><em><strong>7 &#8211; 0\u00a0<\/strong><\/em><\/p>\r\n<p style=\"text-align: center;\"><em><strong>3 &#8211; (-4)<\/strong><\/em><\/p>\r\n<p style=\"text-align: center;\"><em><strong>-2 &#8211; (-9)<\/strong><\/em><\/p>\r\n<p style=\"text-align: center;\"><em><strong>-3 &#8211; (-10)\u00a0<\/strong><\/em><\/p>\r\n<p><b>Facilitator note<\/b><span style=\"font-weight: 400;\">: The first four expressions are part of a string. Students will quickly realize that all four expressions have the same difference, they are simply adjusted down the number line by subtracting the same amount from both the minuend and the subtrahend.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">The fifth equation is unique. Encourage students to adjust these values along the number line to defend their answer. For example, if I add 10 to both -3 and -10, my equation is 7 &#8211; 0.\u00a0<\/span><\/p>\r\n<h2><b>Visual Math Talk Prompt #1<\/b><\/h2>\r\n<p><span style=\"font-weight: 400;\">Students will be prompted with:<\/span><\/p>\r\n<p style=\"padding-left: 40px;\"><strong><em>Construct a subtraction sentence to represent and determine the difference in temperature. Use a number line to defend your answer.<\/em><\/strong><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2386 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-1024x576.jpeg\" alt=\"\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-02-Math-Talk-1-Image.001-1.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">In this set of visual number talks, we give students yet another opportunity to wrestle with integer subtraction using the linear context of temperature.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">As we did on <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/rising-water-day3\"><span style=\"font-weight: 400;\">Day 3 of this real world math unit<\/span><\/a><span style=\"font-weight: 400;\">, we begin with rising temperature from one positive temperature to another positive temperature resulting in a positive difference. Again, we want to model this using the number line despite most students firmly knowing and understanding the difference is 7 degrees Celsius in order to encourage the use of the tool for more challenging differences coming later in the string.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2387 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-1024x576.jpeg\" alt=\"Subtracting negative numbers\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-03-Math-Talk-1-Image.002-1.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<h2><b>Visual Math Talk Prompt #2<\/b><\/h2>\r\n<p><span style=\"font-weight: 400;\">Students will be prompted with:<\/span><\/p>\r\n<p style=\"padding-left: 40px;\"><em><strong>Construct a subtraction sentence to represent and determine the difference in temperature. Use a number line to defend your answer.<\/strong><\/em><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2388 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-1024x576.jpeg\" alt=\"Subtracting negative numbers\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-04-Math-Talk-2-Image.001-1.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">Again, students are given a very low floor opportunity to not only find the difference between a higher temperature and a lower temperature using the number line as a tool to represent their thinking.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">It is important to model student thinking with the number line so that they are later able to leverage the number line as a <\/span><b><i>tool for thinking <\/i><\/b><span style=\"font-weight: 400;\">when we begin working with negative temperatures.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">It is worth noting that the difference between 7 degrees and 0 degrees is the same difference between 12 degrees and 5 degrees.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2389 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-1024x576.jpeg\" alt=\"Subtracting negative numbers\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/08\/Rising-Water-Day-5-Purposeful-Practice-05-Math-Talk-2-Image.002-1.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">Offer additional subtraction sentences where the difference is 7 degrees such as:<\/span><\/p>\r\n<p style=\"text-align: center;\"><em><strong>3 &#8211; (-4)<\/strong><\/em><\/p>\r\n<p style=\"text-align: center;\"><em><strong>-2 &#8211; (-9)<\/strong><\/em><\/p>\r\n<p style=\"text-align: center;\"><em><strong>-3 &#8211; (-10)<\/strong><\/em><\/p>\r\n<p><span style=\"font-weight: 400;\">After this string, students should feel convinced that if the current temperature is greater than the initial temperature, the difference should be positive.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Can we generalize a rule for subtracting integers where the minuend is larger than the subtrahend?<\/span><\/p>\r\n<h2>Want to Explore These Concepts &amp; Skills Further?<\/h2>\r\n<p><b><i>Three (3) additional number talk prompts are available<\/i><\/b><span style=\"font-weight: 400;\"> in <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/rising-water-day5\"><span style=\"font-weight: 400;\">Day 5<\/span><\/a><span style=\"font-weight: 400;\"> of the <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/rising-water\"><span style=\"font-weight: 400;\">Rising Water problem based math unit<\/span><\/a><span style=\"font-weight: 400;\"> that you can dive into now.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Why not start from the beginning of this contextual 6-day unit of <\/span><a href=\"https:\/\/learn.makemathmoments.com\/tasks\"><span style=\"font-weight: 400;\">real world lessons<\/span><\/a><span style=\"font-weight: 400;\"> from the Make Math Moments Problem Based Units page.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Did you use this in your classroom or at home? How\u2019d it go? Post in the comments!<\/span><\/p>\r\n<p><b>Math IS Visual. Let\u2019s teach it that way.<\/b><\/p>","protected":false},"excerpt":{"rendered":"<p>Investigate subtracting negative numbers by finding the difference in temperature using the thermometer as a linear model number line.<\/p>\n","protected":false},"author":1,"featured_media":2333,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23,92],"tags":[52,53,32,33,34],"series":[35,42],"class_list":["post-2325","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-number","category-patterning","tag-grade-5","tag-grade-6","tag-grade-7","tag-grade-8","tag-grade-9","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 Negative Numbers Number Talk | Temperature Differences<\/title>\n<meta name=\"description\" content=\"Investigate subtracting 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