{"id":531,"date":"2024-07-25T12:54:18","date_gmt":"2024-07-25T12:54:18","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=531"},"modified":"2024-09-30T15:03:37","modified_gmt":"2024-09-30T15:03:37","slug":"teaching-algebra-chapter-7-function-families","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/teaching-algebra-chapter-7-function-families\/","title":{"rendered":"Teaching Algebra Chapter 7-Function Families"},"content":{"rendered":"\n<p class=\"has-text-color has-link-color wp-elements-65f4ae917c54d3dce2aa425fbfe2040c\" style=\"color:#d14905\"><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/\" data-type=\"page\" data-id=\"71\">Teaching Algebra<\/a> &gt; Chapter 7<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group alignwide has-base-2-color has-text-color has-background has-link-color wp-elements-52d71fd627c1c31ef727d1f09893fb9d has-global-padding is-layout-constrained wp-container-core-group-is-layout-9daa8ca1 wp-block-group-is-layout-constrained\" style=\"background-color:#d14905;margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--10);padding-right:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10);padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-1be0671b wp-block-group-is-layout-constrained\" style=\"background-color:#d14905;padding-right:var(--wp--preset--spacing--10);padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-group alignwide is-vertical is-content-justification-center is-layout-flex wp-container-core-group-is-layout-ce155fab wp-block-group-is-layout-flex\">\n<div class=\"wp-block-columns has-base-2-color has-text-color has-background has-link-color wp-elements-5aade4b5c3938c0cdb5f5ba6bc0dbd7d is-layout-flex wp-container-core-columns-is-layout-28747e1f wp-block-columns-is-layout-flex\" style=\"background-color:#d14905;padding-top:0;padding-right:var(--wp--preset--spacing--10);padding-bottom:0;padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:15%\"><figure style=\"height:150px; padding-top:0;padding-bottom:0;padding-left:var(--wp--preset--spacing--10);padding-right:var(--wp--preset--spacing--10);\" class=\"alignleft wp-block-post-featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"1305\" height=\"1318\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/alg_page_logo.png\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" style=\"height:150px;object-fit:contain;\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:85%\"><h2 style=\"background-color:#d14905; font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);font-style:normal;font-weight:800;\" class=\"has-link-color wp-elements-fbed58c1dcfb124481494af6efad93d2 wp-block-post-title has-text-color has-base-2-color has-background\">Teaching Algebra Chapter 7-Function Families<\/h2><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">When examining a real situation that we want to model with mathematics, recognizing particular behaviors and knowing which function families they are consistent with can help determine which functions might be best to model that situation. In this chapter, teachers will examine multiple representations of function families including, geometric objects, DynaGraphs and Cartesian graphs. Teachers will explore function families through geometric transformations, and parameter explorations using sliders in dynamic mathematics software. Finally, teachers will consider the role of context in mathematical modeling tasks to build an understanding of the sine function family.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-base-2-color has-alpha-channel-opacity has-base-2-background-color has-background is-style-wide\" \/>\n\n\n\n<p style=\"padding-right:0;padding-left:0;font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><img loading=\"lazy\" decoding=\"async\" alt=\"ESP Logo\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXcjAd2LaOquLZl6f1QVpgTFIR0s-x34bYMeOj5KF22AC9imcETtmdweOx7T0KKEbvi6hPoKHHeOmirNbUmwGSZFMsa1rYA1i76c46HlNoe-0_QhuB83R-Btv18oQLTRuFQVQvdyy67SaTOI24g1orW2j8E_?key=_-Ah_2wP0wYww8pv4LkjOg\" width=\"56\" height=\"56\"> This chapter could be used alongside four Modules within the Examining Students&#8217; Practices (ESP) in Algebra and Function:<\/p>\n\n\n\n<p style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><strong><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-4-characteristics-of-function-families\/\" data-type=\"page\" data-id=\"771\">Module 4:<\/a><\/strong> Characteristics of Function Families<br><strong><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-6-key-features-of-quadratic-functions\/\" data-type=\"page\" data-id=\"778\">Module 6:<\/a> <\/strong>Key Features of Quadratic Functions<br><strong><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-7-key-features-of-the-sine-function\/\" data-type=\"page\" data-id=\"781\">Module 7:<\/a> <\/strong>Key Features of the Sine Functions<br><strong><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-8-using-dynagraphs-to-explore-functions\/\" data-type=\"page\" data-id=\"786\">Module 8:<\/a> <\/strong>Using Dynagraphs to Explore Functions<\/p>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading alignwide has-text-align-center has-contrast-color has-text-color has-link-color wp-elements-208aa9db7b270d678bf7783b0f206f18\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Class Materials<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"background-color:#d14905\">\n<div style=\"height:5px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-28b55a6e wp-block-columns-is-layout-flex\" style=\"padding-top:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-9673d066dd9581ed4fdbc0160c833a17\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/14gg6VzS0dxbpfP4qxjJ3KtjfWo6F644g\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Chapter Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1.png\" alt=\"\" class=\"wp-image-636 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-253ac132ab6a45dec3e3ffffa8d09692\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1IS5tYsgt8xBUDd7r8bIi2mUGN8S5B8p9\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Video Transcripts<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2.png\" alt=\"\" class=\"wp-image-638 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-2f31739b41d00e160650111edfe860b3\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1L8Kaim3eGCv0lJanHryJWCqLPq1rN5pM\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download Tech Files<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-contrast-color has-text-color has-link-color wp-elements-a86768f3e199c5930020ae75f971b4e8\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Instructor Materials<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"background-color:#d14905\">\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-28b55a6e wp-block-columns-is-layout-flex\" style=\"padding-top:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-805b8e1f463007ced8f30f7db31ef46f\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1WHgrVEdJdvKP-igW0S3AVO1k7Yx6FlQL\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Teaching Tips<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-08641cd39a60e59caa6363775ac7e25c\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1lEaPUCGn85ha73HlRdNWxv11RYBEvUyf\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Suggested Readings<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-bb5aa210d59245facc0e7dbf55d753a9\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1Xh0fuY4w2mZTnaq5b-tN1LbHwgY-vktS\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Sample Solutions<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Teaching Algebra &gt; Chapter 7 When examining a real situation that we want to model with mathematics, recognizing particular behaviors and knowing which function families they are consistent with can help determine which functions might be best to model that situation. In this chapter, teachers will examine multiple representations of function families including, geometric objects, [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":229,"parent":71,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"test-blank-page","meta":{"_acf_changed":false,"ncst_custom_author":"","ncst_show_custom_author":false,"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-531","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/comments?post=531"}],"version-history":[{"count":39,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/531\/revisions"}],"predecessor-version":[{"id":1873,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/531\/revisions\/1873"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/71"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/229"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}