{"id":7268,"date":"2024-07-18T10:21:16","date_gmt":"2024-07-18T17:21:16","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7268"},"modified":"2024-08-20T11:00:57","modified_gmt":"2024-08-20T18:00:57","slug":"trigonometry-lesson-8-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-8-teachers\/","title":{"rendered":"Trigonometry Lesson 8 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading has-text-align-left\">Modeling Climate Data with a Sinusoidal Function<\/h3>\n\n\n\n<p>In this lesson, Mary and Claire transform the sine function using sliders to model temperature data. They use their models to predict future patterns in temperature.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-8-teachers\/trigonometry-lesson-8-episode-1-teachers\/\" data-type=\"page\" data-id=\"7468\">Episode 1: Making Sense<\/a><\/strong><\/h5>\n\n\n\n<p>The students begin by exploring an applet to investigate how various transformations of the sine function affect the shape of its graph.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-8-teachers\/trigonometry-lesson-8-episode-2-teachers\/\" data-type=\"page\" data-id=\"7473\">Episode 2: Exploring<\/a><\/strong><\/h5>\n\n\n\n<p>Mary and Claire use the applet to create a model of the average maximum temperature in Houghton, using averages from 1961 to 1990.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-8-teachers\/trigonometry-lesson-8-episode-3-teachers\/\" data-type=\"page\" data-id=\"7477\">Episode 3: Repeating Your Reasoning<\/a><\/strong><\/h5>\n\n\n\n<p>Mary and Claire use the applet to create a model of the average maximum temperature in Houghton, using averages from 1981-2010.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-8-teachers\/trigonometry-lesson-8-episode-4-teachers\/\" data-type=\"page\" data-id=\"7481\">Episode 4: Reflecting<\/a><\/strong><\/h5>\n\n\n\n<p>Mary and Claire reflect on what the differences in these models might suggest for future temperatures.<\/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='69db860184be76090459842' value='69db860184be76090459842'><input type='hidden' id='bg-show-more-text-69db860184be76090459842' value=' '><input type='hidden' id='bg-show-less-text-69db860184be76090459842' value=' '><button id='bg-showmore-action-69db860184be76090459842' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69db860184be76090459842' ><\/p>\n\n\n\n<p>This lesson can help students:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Notice that in the function&nbsp;y =&nbsp;A&nbsp;\u2022&nbsp;sin(2\ud835\udf0b\/P(x &#8211; h)) + k,&nbsp;varying A stretches the graph vertically, varying P stretches the graph horizontally, varying h shifts the graph horizontally, and varying k shifts the graph vertically.<\/li>\n\n\n\n<li>Realize that sinusoidal functions can model phenomena beyond heights on a circle.<\/li>\n\n\n\n<li>Use mathematics to model data that describe an important phenomenon.<\/li>\n\n\n\n<li>Use models to interpret the world around them.&nbsp;<\/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='69db860184cb84020775348' value='69db860184cb84020775348'><input type='hidden' id='bg-show-more-text-69db860184cb84020775348' value=' '><input type='hidden' id='bg-show-less-text-69db860184cb84020775348' value=' '><button id='bg-showmore-action-69db860184cb84020775348' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69db860184cb84020775348' ><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.thecorestandards.org\/Math\/Content\/HSF\/TF\/B\/5\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>CCSS.MATH.CONTENT.HSF.TF.B.5<\/strong><\/a>.\u00a0<em>Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.<\/em><br><br>As they model temperature data, Mary and Claire try to determine which sinusoidal function will fit. They use an applet with sliders for each parameter, to make conjectures for how changing A, P, h, and k affect the graph and relate it to their previous understanding of circular motion. They formalize their ideas by creating functions to model temperature data.<br> <br><\/li>\n\n\n\n<li><a href=\"https:\/\/www.thecorestandards.org\/Math\/Content\/HSF\/IF\/C\/7\/e\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>CCSS.MATH.CONTENT.HSF.IF.C.7.E<\/strong><\/a><strong>.\u00a0<\/strong><em>Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.\u00a0<\/em><br><br>Claire and Mary explore parameters that influence the shape of the graph of the sine function, including amplitude, period, and the midline.<br> <br><\/li>\n\n\n\n<li><a href=\"https:\/\/www.thecorestandards.org\/Math\/Content\/HSF\/IF\/B\/4\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>CCSS.MATH.CONTENT.HSF.IF.B.4<\/strong><\/a>.&nbsp;<em>For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.&nbsp;Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.<\/em><br><br>Mary and Claire create functions for different data sets and compare their models for different time periods. They use what they\u2019ve learned to make predictions for what graphs might look like for new data.<\/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='69db860184d5f7070005277' value='69db860184d5f7070005277'><input type='hidden' id='bg-show-more-text-69db860184d5f7070005277' value=' '><input type='hidden' id='bg-show-less-text-69db860184d5f7070005277' value=' '><button id='bg-showmore-action-69db860184d5f7070005277' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69db860184d5f7070005277' ><\/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>.&nbsp;<\/strong><em>Model with mathematics.<\/em><\/p>\n\n\n\n<p>According to the CCSSM, \u201cmathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace\u2026They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions.\u201d Mary and Claire analyze climate data and use an applet to model that data with a sinusoidal function. They experiment with changing the height of the midline to match the average temperature [e.g.,&nbsp;<strong>Episode 2, 1:00<\/strong>]. They explore changing the amplitude to match the difference between the maximum and average temperatures [e.g.,&nbsp;<strong>Episode 3, 0:47<\/strong>]. They also use their model to predict the shape of graphs that would represent new data&nbsp;<strong>[Episode 4]<\/strong>.<\/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\/trigonometric-concepts-unit-teachers\/\" style=\"background-color:#2d4059\">Trigonometry<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Modeling Climate Data with a Sinusoidal Function In this lesson, Mary and Claire transform the sine function using sliders to model temperature data. They use their models to predict future patterns in temperature. Episode 1: Making Sense The students begin by exploring an applet to investigate how various transformations of the sine function affect the [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":555,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7268","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7268","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=7268"}],"version-history":[{"count":7,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7268\/revisions"}],"predecessor-version":[{"id":7833,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7268\/revisions\/7833"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/555"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=7268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}