{"id":1761,"date":"2020-07-08T10:29:27","date_gmt":"2020-07-08T17:29:27","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1761"},"modified":"2020-08-04T13:58:09","modified_gmt":"2020-08-04T20:58:09","slug":"proportions-lesson-5-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/proportional-reasoning-unit-teachers\/proportions-lesson-5-teachers\/","title":{"rendered":"Proportions Lesson 5 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Forming a Unit Ratio<\/h3>\n\n\n\n<p>Kate and Christopher extend their use of diagrams to form a unit ratio in a speed context.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/proportional-reasoning-unit-teachers\/proportions-lesson-5-teachers\/proportions-lesson-5-episode-1-teachers\/\">Episode 1: Making Sense<\/a><\/h5>\n\n\n\n<p>Kate and Christopher compare two different ways of reasoning \u2013 multiplicative reasoning and additive reasoning.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/proportional-reasoning-unit-teachers\/proportions-lesson-5-teachers\/proportions-lesson-5-episode-2-teachers\/\">Episode 2: Exploring<\/a><\/h5>\n\n\n\n<p>Christopher and Kate figure out how many miles a car should travel in one minute so it goes the same speed as a car traveling 10 miles in 4 minutes. This results in a unit ratio.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/proportional-reasoning-unit-teachers\/proportions-lesson-5-teachers\/proportions-lesson-5-episode-3-teachers\/\">Episode 3: Reflecting<\/a><\/h5>\n\n\n\n<p>Kate and Christopher use diagrams to demonstrate why additive reasoning does not work to find a unit ratio.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-background has-vivid-cyan-blue-background-color has-vivid-cyan-blue-color\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Mathematics in this Lesson <a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/proportions-teacher-docs\/proportions-l5-mathematics-in-this-lesson.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"34\" height=\"34\" class=\"wp-image-2214\" style=\"width: 34px; vertical-align: middle;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/07\/pdf.jpg\" alt=\"\"><\/a><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Standards <input type='hidden' bg_collapse_expand='69e20cd66652b4007623723' value='69e20cd66652b4007623723'><input type='hidden' id='bg-show-more-text-69e20cd66652b4007623723' value=' '><input type='hidden' id='bg-show-less-text-69e20cd66652b4007623723' value=' '><button id='bg-showmore-action-69e20cd66652b4007623723' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e20cd66652b4007623723' ><\/p>\n\n\n\n<p><a rel=\"noreferrer noopener\" href=\"http:\/\/www.corestandards.org\/Math\/Content\/7\/RP\/A\/2\/b\/\" target=\"_blank\"><strong>CCSS.M.7.RP.A.2.b<\/strong><\/a>. <em>Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.<\/em><\/p>\n\n\n\n<p>In this lesson, the students use two strategies to identify a unit rate for a car that is traveling 10 miles in 4 minutes.&nbsp; First, they find the unit rate by a numerical operation. They divide both the number of miles and minutes by 4. They state that this car is going at a speed of 2.5 miles in 1 minute. Secondly, the students also create a diagram to determine the unit rate of this car. They partition the diagram representing a car going 10 miles in 4 minutes into four identical little trips of 2.5 miles in 1 minutes. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Practices <input type='hidden' bg_collapse_expand='69e20cd6666be0064886178' value='69e20cd6666be0064886178'><input type='hidden' id='bg-show-more-text-69e20cd6666be0064886178' value=' '><input type='hidden' id='bg-show-less-text-69e20cd6666be0064886178' value=' '><button id='bg-showmore-action-69e20cd6666be0064886178' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e20cd6666be0064886178' ><\/p>\n\n\n\n<p><strong><a href=\"http:\/\/www.corestandards.org\/Math\/Practice\/MP4\/\" target=\"_blank\" rel=\"noreferrer noopener\">CCSS.MATH.PRACTICE.MP4<\/a><\/strong>:&nbsp;<em>Model with mathematics<\/em>.<\/p>\n\n\n\n<p>According to the Common Core\u2019s description of Math Practice 4, mathematically proficient students \u201cidentify important quantities in a practical situation and map their relationships using such tools as diagrams.\u201d In this lesson, Kate and Christopher, use diagrams in two productive ways. First, they use a diagram to show why traveling 2.5 miles in 1 minute is the same speed as traveling 10 miles in 4 minutes by iterating identical small journeys of 2.5 miles in 1 minute to make up the larger journey of 10 miles in 4 minutes <strong>[2:39 in Episode 2]<\/strong>. Later, they identify that a journey of 10 miles in 4 minutes can be partitioned into four identical trips of 2.5 miles in 1 minute <strong>[6:02 in Episode 3]<\/strong>. <\/div><\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/\" style=\"background-color:#2d4059\">Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/\" style=\"background-color:#2d4059\">Teachers Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" style=\"background-color:#2d4059\">Proportions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Forming a Unit Ratio Kate and Christopher extend their use of diagrams to form a unit ratio in a speed context. Episode 1: Making Sense Kate and Christopher compare two different ways of reasoning \u2013 multiplicative reasoning and additive reasoning. Episode 2: Exploring Christopher and Kate figure out how many miles a car should travel [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":547,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1761","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1761","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=1761"}],"version-history":[{"count":6,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1761\/revisions"}],"predecessor-version":[{"id":2489,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1761\/revisions\/2489"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/547"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}