{"id":778,"date":"2024-08-15T01:59:24","date_gmt":"2024-08-15T01:59:24","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=778"},"modified":"2024-08-24T19:46:42","modified_gmt":"2024-08-24T19:46:42","slug":"esp-module-6-key-features-of-quadratic-functions","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-6-key-features-of-quadratic-functions\/","title":{"rendered":"ESP_AF Module 6-Key Features of Quadratic Functions"},"content":{"rendered":"\n<p class=\"has-text-color has-link-color wp-elements-a50e2df20d3ab8183b196e2b34ab0112\" style=\"color:#008473\"><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/\" data-type=\"page\" data-id=\"313\">Examining Students&#8217; Practices in Algebra and Function<\/a> &gt; Module 6<\/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-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-1be0671b wp-block-group-is-layout-constrained\" style=\"background-color:#008473;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-499ac0fdb0c73d9827c8838d1ea0e929 is-layout-flex wp-container-core-columns-is-layout-28747e1f wp-block-columns-is-layout-flex\" style=\"background-color:#008473;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=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/ESP-icon.png\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" style=\"height:150px;object-fit:contain;\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/ESP-icon.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/ESP-icon-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/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:#008473; 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-a2775ed33b1248ee5abebcb317563e14 wp-block-post-title has-text-color has-base-2-color has-background has-system-sans-serif-font-family\">ESP_AF Module 6-Key Features of Quadratic Functions<\/h2><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-media-text has-media-on-the-right is-stacked-on-mobile is-vertically-aligned-top\" style=\"margin-top:0;margin-right:0;margin-bottom:0;margin-left:0;padding-top:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10);grid-template-columns:auto 35%\"><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-24caa2f585cda38a865c7be19fc92fba\" style=\"margin-top:0;margin-bottom:0;padding-top:0;padding-bottom:0;font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">This module uses three Desmos tasks which focus on exploration of the effect of parameters on quadratic functions in vertex form. Video clips of student work provide the context for teachers to use noticing of student thinking and examine how particular design choices align with the learning and performance goals for each task.<\/p>\n<\/div><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/Mod_6_Image-1024x466.png\" alt=\"\" class=\"wp-image-779 size-medium\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/Mod_6_Image-1024x466.png 1024w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/Mod_6_Image-300x136.png 300w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/Mod_6_Image-768x349.png 768w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/Mod_6_Image.png 1438w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:15% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"250\" height=\"252\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252.png\" alt=\"\" class=\"wp-image-651 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252.png 250w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252-150x150.png 150w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-f0c7e7bfa54cd6009b1b7c0c097ed4dd\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">This module could be used alongside a Chapter from Teaching Algebra materials:<\/p>\n\n\n\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-c634d1eddbb3223c3a0117165e8fce3b\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra-chapter-7-function-families\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Chapter 7:<\/strong><\/a>&nbsp;Function Families.<\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Overview Documents<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-b13d32f8 wp-block-group-is-layout-constrained\" style=\"background-color:#008473;padding-right:var(--wp--preset--spacing--10);padding-left:var(--wp--preset--spacing--10)\">\n<div style=\"height:5px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide has-background is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" style=\"background-color:#008473\">\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-720c6f7ab173c659005e711d835ea3ac\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1otqIRvwPpjlv2iUJib4l-M2Jv9sWnxRW\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Read the Overview 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-f3de43452e150940eaec48cea8e3496e\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/www.youtube.com\/watch?v=pkKv-GoLzNk\"><strong>How to Read a Module Overview 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\/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-0472c4b1a29c63f7eb408cf6a5e666b2\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><strong><a href=\"https:\/\/drive.google.com\/file\/d\/1EHw5Fme_K1m64wAUS0mNzsRctTJcH5Og\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\">Download All Materials<\/a><\/strong><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Module Elements<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-base-2-color has-text-color has-link-color wp-elements-3693ae5163af8bea340c1f2dcf928635 has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">\n<figure class=\"wp-block-table alignfull is-style-stripes\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><table class=\"has-base-color has-text-color has-background has-link-color\" style=\"background-color:#008473\"><tbody><tr><td><\/td><td><\/td><\/tr><tr><td><strong>6.1 Comparing and Contrasting Function Parameter Explorations: Quadratic Functions in Vertex Form<\/strong><br><br>Teachers will engage in three Desmos tasks to examine the effect of parameters on the parent function of a quadratic function and identify appropriate performance goals for each task<\/td><td><img loading=\"lazy\" decoding=\"async\" width=\"59\" height=\"59\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfORx2qmz53AImpkUcJytPvEFCKCCEXoinBv0jqWAH5fRAP2qrFokOpzyI17_JtuWYIKlOr2QfWWnXLeDDstGfIrENodcZ_ppOxENxC67SChrBkKOLfG-N0m2dkra13PY0zo15rNM8aN-cjdr8f0skGQCc?key=_-Ah_2wP0wYww8pv4LkjOg\"><br><strong><a href=\"https:\/\/drive.google.com\/file\/d\/1hn2kOlWZMPlzYSxXb3kmS3DCFxP_bkOV\/view?usp=drive_link\">Class Materials<\/a><\/strong><br><img loading=\"lazy\" decoding=\"async\" width=\"59\" height=\"59\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfORx2qmz53AImpkUcJytPvEFCKCCEXoinBv0jqWAH5fRAP2qrFokOpzyI17_JtuWYIKlOr2QfWWnXLeDDstGfIrENodcZ_ppOxENxC67SChrBkKOLfG-N0m2dkra13PY0zo15rNM8aN-cjdr8f0skGQCc?key=_-Ah_2wP0wYww8pv4LkjOg\"><br><a href=\"https:\/\/drive.google.com\/file\/d\/1L28tEStMNpGxFybWZugnfFESDXDfBGEw\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Instructor Materials<\/strong><\/a><br><\/td><\/tr><tr><td><\/td><td><\/td><\/tr><tr><td><strong>6.2 Matching Learning Goals to Task Design: Quadratic Function Parameter Explorations<\/strong><br><br>Teachers will engage with noticing pairs of students engaging with each of the three Desmos tasks with a focus on the students\u2019 language, engagement with the technology, and identify performance goals for each task.<\/td><td><img loading=\"lazy\" decoding=\"async\" width=\"59\" height=\"59\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfORx2qmz53AImpkUcJytPvEFCKCCEXoinBv0jqWAH5fRAP2qrFokOpzyI17_JtuWYIKlOr2QfWWnXLeDDstGfIrENodcZ_ppOxENxC67SChrBkKOLfG-N0m2dkra13PY0zo15rNM8aN-cjdr8f0skGQCc?key=_-Ah_2wP0wYww8pv4LkjOg\"><br><a href=\"https:\/\/drive.google.com\/file\/d\/1-RGgB17-U4qjxuncU6LEki8wDZ82Ve7c\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Class Materials<\/strong><\/a><br><img loading=\"lazy\" decoding=\"async\" width=\"59\" height=\"59\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfORx2qmz53AImpkUcJytPvEFCKCCEXoinBv0jqWAH5fRAP2qrFokOpzyI17_JtuWYIKlOr2QfWWnXLeDDstGfIrENodcZ_ppOxENxC67SChrBkKOLfG-N0m2dkra13PY0zo15rNM8aN-cjdr8f0skGQCc?key=_-Ah_2wP0wYww8pv4LkjOg\"><br><a href=\"https:\/\/drive.google.com\/file\/d\/1Cu_iBPIhfKR9IenhxwEljAm9x0a3K0_5\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Instructor Materials<\/strong><\/a><\/td><\/tr><tr><td><\/td><td><\/td><\/tr><tr><td><strong>6.3 Adapting an Existing Desmos Quadratic Parameter Task<\/strong><br><br>Teachers will adapt an existing Desmos Activity so that it meets specific learning and performance goals and takes into consideration the design principles for effective technology-based tasks.<br><\/td><td><img loading=\"lazy\" decoding=\"async\" width=\"59\" height=\"59\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfORx2qmz53AImpkUcJytPvEFCKCCEXoinBv0jqWAH5fRAP2qrFokOpzyI17_JtuWYIKlOr2QfWWnXLeDDstGfIrENodcZ_ppOxENxC67SChrBkKOLfG-N0m2dkra13PY0zo15rNM8aN-cjdr8f0skGQCc?key=_-Ah_2wP0wYww8pv4LkjOg\"><br><a href=\"https:\/\/drive.google.com\/file\/d\/1gXlN_WQjPanS5N8Bdm231PonsXtlObJ-\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Class Materials<\/strong><\/a><br><img loading=\"lazy\" decoding=\"async\" width=\"59\" height=\"59\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfORx2qmz53AImpkUcJytPvEFCKCCEXoinBv0jqWAH5fRAP2qrFokOpzyI17_JtuWYIKlOr2QfWWnXLeDDstGfIrENodcZ_ppOxENxC67SChrBkKOLfG-N0m2dkra13PY0zo15rNM8aN-cjdr8f0skGQCc?key=_-Ah_2wP0wYww8pv4LkjOg\"><br><a href=\"https:\/\/drive.google.com\/file\/d\/1v3yEGkI-M_dLbAvvEl_OaFCHqU_n6pQF\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Instructor Materials<\/strong><\/a><\/td><\/tr><tr><td><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Examining Students&#8217; Practices in Algebra and Function &gt; Module 6 This module uses three Desmos tasks which focus on exploration of the effect of parameters on quadratic functions in vertex form. Video clips of student work provide the context for teachers to use noticing of student thinking and examine how particular design choices align with [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":230,"parent":313,"menu_order":6,"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-778","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/778","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=778"}],"version-history":[{"count":13,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/778\/revisions"}],"predecessor-version":[{"id":1695,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/778\/revisions\/1695"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/313"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/230"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}