{"id":6860,"date":"2024-07-11T15:28:56","date_gmt":"2024-07-11T22:28:56","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=6860"},"modified":"2024-07-15T15:18:00","modified_gmt":"2024-07-15T22:18:00","slug":"binomials-lesson-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/","title":{"rendered":"Binomials Lesson 2 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading has-text-align-left\"><strong>Effect of Increasing Length and Width on <\/strong>Area<\/h3>\n\n\n\n<p>Emily and Mauricio compare the areas of two home offices. One office was formed by increasing both the length and width of the other office. The students create a visual representation of the area of the new office that breaks the room into four parts. They write arithmetic equations that express different ways to find the area of the new office.&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-1-teachers\/\" data-type=\"page\" data-id=\"6926\">Episode 1: Making Sense<\/a>&nbsp;<\/strong><\/h5>\n\n\n\n<p>Mauricio and Emily make sense of&nbsp;floor plans that architects use to represent rooms in a house.&nbsp;&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-2-teachers\/\" data-type=\"page\" data-id=\"6931\">Episode 2: Exploring&nbsp;<\/a><\/strong><\/h5>\n\n\n\n<p>The students make a drawing to find the area of a home office and explain its meaning.&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-3-teachers\/\" data-type=\"page\" data-id=\"6935\">Episode 3: Reflecting<\/a><\/strong><\/h5>\n\n\n\n<p>Emily and Mauricio reflect on the meaning of multiplication when finding the area of a rectangular room. They show multiplication as \u201cgroups of\u201d in their drawing.&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-4-teachers\/\" data-type=\"page\" data-id=\"6939\">Episode 4: Making Sense<\/a><\/strong><\/h5>\n\n\n\n<p>Mauricio and Emily make sense of a situation in which both the length and width of a rectangular office are increased by 3 feet. They make a prediction about how these increases will affect the area of the new room.&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-5-teachers\/\" data-type=\"page\" data-id=\"6943\">Episode 5: Exploring&nbsp;<\/a><\/strong><\/h5>\n\n\n\n<p>The students create a drawing to explain why increasing the length and width of a room increases the area so much more than they predicted in Episode 4.&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-6-teachers\/\" data-type=\"page\" data-id=\"6949\">Episode 6: Exploring<\/a>&nbsp;<\/strong><\/h5>\n\n\n\n<p>Emily and Mauricio create a drawing that splits the area of the new room (from Episodes 4 and 5) into four parts. They determine the area of each part.&nbsp;<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-7-teachers\/\" data-type=\"page\" data-id=\"6953\">Episode 7: Reflecting&nbsp;<\/a><\/strong><\/h5>\n\n\n\n<p>Mauricio and Emily reflect on their drawing from Episode 6 and write equations&nbsp;to express different ways to find the area of the new room.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-8-teachers\/\" data-type=\"page\" data-id=\"6957\">Episode 8: Repeating Your Reasoning<\/a><\/strong><\/h5>\n\n\n\n<p>The students apply what they learned in the previous episodes to explore a new situation in which the length of a media room is increased by 3 meters and the width is increased by 2 meters. They make a drawing and write equations to find the area of the new media room in different ways.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-vivid-cyan-blue-color has-css-opacity has-vivid-cyan-blue-background-color has-background\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Mathematics in this Lesson<\/h3>\n\n\n\n<p class=\"has-medium-font-size\">Targeted Understandings <input type='hidden' bg_collapse_expand='69db68a25a31a8004391270' value='69db68a25a31a8004391270'><input type='hidden' id='bg-show-more-text-69db68a25a31a8004391270' value=' '><input type='hidden' id='bg-show-less-text-69db68a25a31a8004391270' value=' '><button id='bg-showmore-action-69db68a25a31a8004391270' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69db68a25a31a8004391270' ><\/p>\n\n\n\n<p>This lesson can help students:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Understand that when you increase the length and width of a rectangle (e.g., when you increase both the length and width of a 10 ft by 8 ft rectangular office by 3 ft to create a new office), then the area is increased by the sum of the following areas: 10 ft\u00a0\u00d7\u00a03 ft = 30 ft<sup>2<\/sup>; 8 ft\u00a0\u00d7\u00a03 ft = 24 ft<sup>2<\/sup>; and 3 ft\u00a0\u00d7 3 ft = 9 ft<sup>2<\/sup>.\u00a0\u00a0\u00a0<\/li>\n\n\n\n<li>Create a drawing that shows what happens to the area of rectangle when both its length and width are increased.\u00a0<\/li>\n\n\n\n<li>Represent the area of the new rectangle through a 2-dimensional drawing that decomposes the new area into four parts, one of which is the area of the original rectangle.\u00a0<\/li>\n<\/ul>\n\n\n\n<p><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Standards <input type='hidden' bg_collapse_expand='69db68a25a4007089952650' value='69db68a25a4007089952650'><input type='hidden' id='bg-show-more-text-69db68a25a4007089952650' value=' '><input type='hidden' id='bg-show-less-text-69db68a25a4007089952650' value=' '><button id='bg-showmore-action-69db68a25a4007089952650' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69db68a25a4007089952650' ><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.thecorestandards.org\/Math\/Content\/HSN\/Q\/A\/2\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>CCSS.MATH.CONTENT.HSN.Q.A.2<\/strong><\/a><strong>.\u00a0<\/strong><em>Define appropriate quantities for the purpose of descriptive modeling.<\/em><br><br>Emily and Mauricio define many quantities in the modeling tasks in this lesson, which are set in the context of determining the area of rooms in a home using an architectural blueprint. These quantities include: the length and width of a given home office, the amount of increase in the length, the amount of increase in the width, the area of the original office, the area of the new office, and the length, width and area of three rectangular spaces that are created when the length and width of the original office are increased.\u00a0<br>  <\/li>\n\n\n\n<li><a href=\"https:\/\/www.thecorestandards.org\/Math\/Content\/3\/MD\/C\/7\/d\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>CCSS.MATH.CONTENT.3.MD.C.7.D<\/strong><\/a><strong>.\u00a0<\/strong><em>Recognize area as additive.<\/em><strong>\u00a0<\/strong><em>Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.<\/em><br><br>In this lesson, Mauricio and Emily consider the effect of increasing\u00a0both the length and width of a 10 ft by 8 ft rectangular office by 3 ft to create a new office. They predict that the area of the original office will be increase by 9 ft<sup>2<\/sup>\u00a0(3 ft \u00d7 3ft), when, in fact, that increase should be 63 ft<sup>2<\/sup>. The students create a drawing to explain why increasing the length and width of a room increases the area so much more than they predicted. Their drawing decomposes the area of the new office into four parts: the original office with an area of 80 ft<sup>2<\/sup>, the increase of 9ft<sup>2<\/sup>\u00a0that they predicted, and two other rectangles of area 30 ft<sup>2<\/sup>\u00a0and 24 ft<sup>2<\/sup>.\u00a0<\/li>\n<\/ul>\n\n\n\n<p><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Practices <input type='hidden' bg_collapse_expand='69db68a25a4bf9016764786' value='69db68a25a4bf9016764786'><input type='hidden' id='bg-show-more-text-69db68a25a4bf9016764786' value=' '><input type='hidden' id='bg-show-less-text-69db68a25a4bf9016764786' value=' '><button id='bg-showmore-action-69db68a25a4bf9016764786' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69db68a25a4bf9016764786' ><\/p>\n\n\n\n<p><a href=\"https:\/\/www.thecorestandards.org\/Math\/Practice\/MP4\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>CCSS.MATH.PRACTICE.MP4<\/strong><\/a><strong>.\u00a0<\/strong><em>Model with mathematics<\/em><strong>.<\/strong><\/p>\n\n\n\n<p>According to the CCSSM, mathematically proficient students \u201ccan apply the mathematics they know to solve problems arising in everyday life\u2026. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams\u2026They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.\u201d&nbsp;Throughout this lesson, Emily and Mauricio model with mathematics in the practical situation of finding the area of rooms in a house from architectural blueprints, and of determining the effect of changing the length and width on the area of the rooms. In&nbsp;<strong>Episode 1<\/strong>, they start by making sense of the floor plans that architects use to represent rooms in a house. Later, they tackle the challenge of creating a single drawing that shows both an original home office and a new office, which is formed by increasing the length and width of the original office&nbsp;<strong>[e.g., Episode 5, 3:11]<\/strong>. In&nbsp;<strong>Episode 6<\/strong>, they refine their drawing from&nbsp;<strong>Episode 5<\/strong>&nbsp;to better analyze how the changes in length and width affect the area&nbsp;<strong>[1:30]<\/strong>.<strong>&nbsp;<\/strong>Finally, in&nbsp;<strong>Episode 7<\/strong>, Emily and Mauricio write equations to express different ways to find the area of the new office and carefully interpret each number and term in their equations in the context of architectural floor plans.<\/p>\n\n\n\n<p><\/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 wp-element-button\" 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 wp-element-button\" 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 wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/\" style=\"background-color:#2d4059\">BinoMials<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Effect of Increasing Length and Width on Area Emily and Mauricio compare the areas of two home offices. One office was formed by increasing both the length and width of the other office. The students create a visual representation of the area of the new office that breaks the room into four parts. They write [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":553,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6860","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6860","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=6860"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6860\/revisions"}],"predecessor-version":[{"id":7191,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6860\/revisions\/7191"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/553"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=6860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}