{"id":2412,"date":"2022-10-26T07:00:59","date_gmt":"2022-10-26T12:00:59","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=2412"},"modified":"2022-10-19T12:05:29","modified_gmt":"2022-10-19T17:05:29","slug":"real-world-integer-multiplication","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/real-world-integer-multiplication\/","title":{"rendered":"Real World Integer Multiplication"},"content":{"rendered":"\r\n<p><a href=\"https:\/\/youtu.be\/zyCoyIcTPrU\">https:\/\/youtu.be\/zyCoyIcTPrU<\/a><\/p>\r\n<p><\/p>\r\n<h2><b>In This Set of Visual Number Talk Prompts\u2026<\/b><\/h2>\r\n<p><span style=\"font-weight: 400;\">Through this <\/span><b>visual math talk<\/b><span style=\"font-weight: 400;\"> and <\/span><b>purposeful practice<\/b><span style=\"font-weight: 400;\">, students are encouraged to use the number line to model the behaviour of multiplying and dividing positive and negative integers. All division scenarios today will be quotative.<\/span><\/p>\r\n<h2>Intentionality\u2026<\/h2>\r\n<p><span style=\"font-weight: 400;\">The purpose of the Day 2 activities is to reinforce key concepts from Day 1. Students will also be introduced to a new multiplication scenario where a negative integer is multiplied by a negative integer. Students will engage in a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.\u00a0<\/span><\/p>\r\n<ul>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiplication can be understood as repeated equal groups;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The first factor can be understood as the number of groups and the second factor as the size of the groups;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A positive integer multiplied by a negative integer has a product that is negative;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A negative integer multiplied by a negative integer has a product that is positive;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Quotative division is when the total quota is known (the dividend), and the number per group or the rate (the divisor) is known;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Quotative division reveals the number of copies or iterations of a rate that can be derived from the overall quota (the dividend);<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A negative number divided by a negative number has a quotient that is positive.<\/span><\/li>\r\n<\/ul>\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;\"><b><i>At midnight, the temperature was 0 degrees.<\/i><\/b><\/p>\r\n<p style=\"padding-left: 40px;\"><b><i>The temperature continued to change by -3 degrees every hour.<\/i><\/b><\/p>\r\n<p style=\"padding-left: 40px;\"><b><i>What was the temperature 4 hours later?<\/i><\/b><\/p>\r\n<p style=\"padding-left: 40px;\"><b><i>Write an equation to represent this scenario.<\/i><\/b><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2413 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-1024x576.jpeg\" alt=\"Integer multiplication\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-02-Math-is-Visual-Image.001.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">From the animation, students will see that with every passing hour, the temperature drops by 3 degrees (or the change in temperature is -3 degrees per hour).\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">With this, students might create a table to track the number of hours and the current temperature beginning at 0 hours (12:00 am) and 0 degrees, then 1 hour (1:00 am) and -3 degrees, and so on.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Some students may recognize that they can simply multiply the rate of -3 degrees per hour by 4 hours giving a result of -12 degrees Celsius after the 4th hour.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2414 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-1024x576.jpeg\" alt=\"Integer multiplication\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/10\/Just-Keep-Digging-Day-2-Purposeful-Practice-03-Math-is-Visual-Image.002.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><b>Facilitator note:\u00a0<\/b><\/p>\r\n<p><span style=\"font-weight: 400;\">The purpose of this first scenario is to solidify the following big ideas.\u00a0<\/span><\/p>\r\n<ul>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiplication can be understood as repeated equal groups;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The first factor can be understood as the number of groups and the second factor as the size of the groups;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A positive integer multiplied by a negative integer has a product that is negative.<\/span><\/li>\r\n<\/ul>\r\n<h2>Want to Explore These Concepts &amp; Skills Further?<\/h2>\r\n<p><b><i>Two (2) additional number talk prompts are available<\/i><\/b><span style=\"font-weight: 400;\"> in <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/just-keep-digging-day2\"><span style=\"font-weight: 400;\">Day 2<\/span><\/a><span style=\"font-weight: 400;\"> of the <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/just-keep-digging\"><span style=\"font-weight: 400;\">Just Keep Digging 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 5-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>Explore a real world integer multiplication context involving temperature where the rate is negative (decreasing hourly temperature) over time.<\/p>\n","protected":false},"author":1,"featured_media":2419,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[92],"tags":[52,53,32,33,34],"series":[35,94],"class_list":["post-2412","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-patterning","tag-grade-5","tag-grade-6","tag-grade-7","tag-grade-8","tag-grade-9","series-integers","series-patterning"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Real World Integer Multiplication Through Patterning Visual Number Talk<\/title>\n<meta name=\"description\" content=\"Explore a real world integer 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