{"id":947,"date":"2020-06-04T15:07:36","date_gmt":"2020-06-04T22:07:36","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=947"},"modified":"2021-01-26T11:25:15","modified_gmt":"2021-01-26T19:25:15","slug":"parabolas-lesson-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-2-teachers\/","title":{"rendered":"Parabolas Lesson 2 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Connecting Geometry with Algebra<\/h3>\n\n\n\n<p class=\"has-normal-font-size\">Keoni and Sasha work with a parabola on the coordinate grid. They use the properties of the grid and the Pythagorean theorem to determine if the coordinates of a point are on a given parabola. They apply these methods to find the missing x-value of a point on the parabola for a given y-value.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-2-teachers\/parabolas-lesson-2-episode-1-teachers\/\">Episode 1: Making Sense<\/a><\/h5>\n\n\n\n<p class=\"has-normal-font-size\">Keoni  notices that the grid allows them to measure the distance between some  points and lines.&nbsp; Sasha and Keoni use the grid and the definition of a  parabola to validate that three points are on the parabola.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-2-teachers\/parabolas-lesson-2-episode-2-teachers\/\">Episode 2: Exploring<\/a><\/h5>\n\n\n\n<p class=\"has-normal-font-size\">Sasha and Keoni use the Pythagorean theorem to justify why (4,4) is a point on the parabola.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-2-teachers\/parabolas-lesson-2-episode-3-teachers\/\">Episode 3: Exploring<\/a><\/h5>\n\n\n\n<p class=\"has-normal-font-size\">Sasha  and Keoni justify how their three methods for finding points on a  parabola satisfy the criteria in the definition of a parabola.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-2-teachers\/parabolas-lesson-2-episode-4-teachers\/\">Episode 4: Repeating Your Reasoning<\/a><\/h5>\n\n\n\n<p class=\"has-normal-font-size\">Keoni  and Sasha extend their use of the Pythagorean theorem. They determine  the x-value for a point on the parabola that has a y-value of 5.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-2-teachers\/parabolas-lesson-2-episode-5-teachers\/\">Episode 5: Repeating Your Reasoning<\/a><\/h5>\n\n\n\n<p class=\"has-normal-font-size\">Sasha and Keoni find the x-value of a point on the parabola with a y-value of 10.<\/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\/parabolas-teacher-docs\/parabolas-l2-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\">Targeted Understandings <input type='hidden' bg_collapse_expand='69e27f2e53f599045562590' value='69e27f2e53f599045562590'><input type='hidden' id='bg-show-more-text-69e27f2e53f599045562590' value=' '><input type='hidden' id='bg-show-less-text-69e27f2e53f599045562590' value=' '><button id='bg-showmore-action-69e27f2e53f599045562590' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e27f2e53f599045562590' ><\/p>\n\n\n\n<p>This lesson can help students: <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Identify and apply key elements of the geometric definition of a parabola in the context of the Cartesian coordinate grid.<\/li><li>Conceive of a point on a Cartesian coordinate grid, not only as a location, but also as representing distances in 2-dimensional space.<\/li><li>Apply the Pythagorean Theorem in a new setting to measure distance. <\/div><\/li><\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Standards <input type='hidden' bg_collapse_expand='69e27f2e540358098603204' value='69e27f2e540358098603204'><input type='hidden' id='bg-show-more-text-69e27f2e540358098603204' value=' '><input type='hidden' id='bg-show-less-text-69e27f2e540358098603204' value=' '><button id='bg-showmore-action-69e27f2e540358098603204' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e27f2e540358098603204' ><\/p>\n\n\n\n<p><a rel=\"noreferrer noopener\" href=\"http:\/\/www.corestandards.org\/Math\/Content\/HSG\/GPE\/A\/2\/\" target=\"_blank\"><strong>CCSS.M.HSG.GPE.A.2<\/strong><\/a>: <em>Derive the equation of a parabola given a focus and directrix.<\/em><\/p>\n\n\n\n<p>Lesson 2 connects the geometric definition of a parabola from Lesson 1 with an algebraic coordinate grid, which makes the derivation of an equation of a parabola possible.&nbsp; Sasha and Keoni then derive the equation of:<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; o particular parabolas in Lessons 3 and 4;<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; o any parabola with vertex (0,0) in Lesson 5; and<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; o any parabola with vertex (h,k) in Lesson 9.<\/p>\n\n\n\n<p><strong><a rel=\"noreferrer noopener\" href=\"http:\/\/www.corestandards.org\/Math\/Content\/HSG\/GPE\/B\/4\/\" target=\"_blank\">CCSS.M.HSG.GPE.B.4<\/a>.<\/strong> <em>Use coordinates to prove simple geometric theorems algebraically.<\/em><\/p>\n\n\n\n<p>Sasha and Keoni use the coordinates on an algebraic Cartesian grid, along with the definition of a parabola, to validate that three points are on the parabola.<\/p>\n\n\n\n<p><strong><a rel=\"noreferrer noopener\" href=\"http:\/\/www.corestandards.org\/Math\/Content\/8\/G\/B\/8\/\" target=\"_blank\">CCSS.M.8.G.B.8<\/a>.<\/strong> <em>Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. <\/em>Keoni and Sasha use the Pythagorean theorem, along with the coordinate system and the definition of a parabola, to determine the x-value for a point on the parabola given its y-value. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Practices <input type='hidden' bg_collapse_expand='69e27f2e540d63035586477' value='69e27f2e540d63035586477'><input type='hidden' id='bg-show-more-text-69e27f2e540d63035586477' value=' '><input type='hidden' id='bg-show-less-text-69e27f2e540d63035586477' value=' '><button id='bg-showmore-action-69e27f2e540d63035586477' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e27f2e540d63035586477' ><\/p>\n\n\n\n<p><a rel=\"noreferrer noopener\" href=\"http:\/\/www.corestandards.org\/Math\/Practice\/MP5\" target=\"_blank\"><strong>CCSS.Math.Practice.MP5<\/strong><\/a> <em>Use appropriate tools strategically.<\/em><\/p>\n\n\n\n<p>In this lesson, Sasha and Keoni use an important mathematical tool\u2014 the Pythagorean theorem.&nbsp; A discussion in the lesson models an important habit of mind related to tool use. Specifically, when Keoni and Sasha are stumped about how to measure the length of a diagonal line segment from a point on the parabola to the focus <strong>[1:46, Episode 2]<\/strong>, their teacher encourages them to write down everything they know <strong>[1:56, Episode 2]<\/strong> and articulate what they are trying to find <strong>[2:53, Episode 2]<\/strong>. In the process, a right triangle emerges on the grid, with two sides of known length and one of unknown length.&nbsp; This practice of analyzing the situation prepares Sasha and Keoni to strategically apply the Pythagorean theorem once the teacher suggests its use <strong>[3:56, Episode 2]<\/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\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/parabolas-unit-teachers\/\" style=\"background-color:#2d4059\">Parabolas<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Connecting Geometry with Algebra Keoni and Sasha work with a parabola on the coordinate grid. They use the properties of the grid and the Pythagorean theorem to determine if the coordinates of a point are on a given parabola. They apply these methods to find the missing x-value of a point on the parabola for [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":543,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-947","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/947","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=947"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/947\/revisions"}],"predecessor-version":[{"id":2252,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/947\/revisions\/2252"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/543"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=947"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}