{"id":68,"date":"2021-04-03T20:24:11","date_gmt":"2021-04-03T20:24:11","guid":{"rendered":"http:\/\/blogs.dickinson.edu\/playing-with-polygons\/?page_id=68"},"modified":"2025-01-22T16:59:35","modified_gmt":"2025-01-22T16:59:35","slug":"file-1","status":"publish","type":"page","link":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/file-1\/","title":{"rendered":"1. Polygons &amp; Stars"},"content":{"rendered":"<div class=\"su-row\">\n<div class=\"su-column su-column-size-4-5\"><div class=\"su-column-inner su-u-clearfix su-u-trim\">\n<p style=\"text-align: center\"><strong>Polygons and Stars<\/strong><\/p>\n<p>Polygon basics: Based on Erfle, Wensel, Erfle and Polinka \u201c<a href=\"https:\/\/sie.scholasticahq.com\/article\/21267-teaching-number-patterns-with-polygons-and-stars\" target=\"_blank\" rel=\"noopener\">Connecting Geometric Patterns to Numeric Patterns using the <em>Polygons and Stars<\/em> Excel File<\/a>,\u201d <em>Spreadsheets in Education<\/em>, 2021.<\/p>\n<p>The link above takes you to a paper and Excel file (click here for the <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/09\/1.PolygonsAndStars.xlsx\" target=\"_blank\" rel=\"noopener\">1.Polygons and Stars<\/a> Excel file). This paper is targeted to K-2 and hence can be covered very quickly for those who are beyond these grades. There are two main sheets there, <strong><em>Polygons<\/em><\/strong> and <strong><em>Stars<\/em><\/strong>, together with supplementary sheets that are of interest mainly to teachers. The first sheet (<strong><em>Polygons<\/em><\/strong>) introduces users to <strong><em>n<\/em><\/strong>,<em> the number of vertices<\/em> (and sides) in a regular polygon and the second sheet (<strong><em>Stars<\/em><\/strong>) introduces the notion of vertex jumps <strong><em>J<\/em><\/strong> which produce continuously drawn stars.<\/p>\n<p><strong>E1<\/strong>. How to read the string art portion of this book: <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/10\/Just-The-Basics-Chapter-1-v2.pdf\" target=\"_blank\" rel=\"noopener\">Just The Basics (Chapter 1)<\/a> . Note: In <strong>PwP<\/strong>, the identifier<strong> E#<\/strong> identifies this material as being in Chapter # of <a href=\"https:\/\/www.taylorfrancis.com\/books\/mono\/10.1201\/9781003402633\/electronic-string-art-stephen-erfle\" target=\"_blank\" rel=\"noopener\">ESA<\/a>.<\/p>\n<p><strong>E2. <\/strong>These <em>explainers<\/em> (short documents) supplement the article above. Those denoted <strong>MA<\/strong> (for <em><strong>M<\/strong>athematical <strong>A<\/strong>pproach<\/em>) dive more deeply into the material and may not be accessible to primary school audiences.<\/p>\n<ol>\n<li>On how polygons are drawn: <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.How-Polygons-Are-Drawn.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.1. How Polygons Are Drawn<\/a><\/li>\n<li>Continuously drawn stars: 1.2a. <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.Stars-that-Work-and-Stars-that-Dont.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Stars that Work and Stars that Don&#8217;t<\/a>\n<ul>\n<li>1.2b. <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/How-many-points-does-an-nJ-star-have.pdf\" target=\"_blank\" rel=\"noopener\">How many points does an <em><strong>n<\/strong><\/em>,<em><strong>J<\/strong><\/em>-star have?<\/a><\/li>\n<\/ul>\n<\/li>\n<li>Sharpest stars: Take 1, <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.Sharpest-Stars.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.3a. Sharpest Stars<\/a>\n<ul>\n<li>Take 2, <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.How-Sharpest-Stars-are-Drawn-1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.3b. How Sharpest Stars are Drawn<\/a><\/li>\n<li>1.3c. <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/Not-all-Even-Stars-are-Created-Equal.pdf\" target=\"_blank\" rel=\"noopener\">Not all Even Sharpest Stars are Created Equal<\/a><\/li>\n<\/ul>\n<\/li>\n<li>About angles: Take 1, <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.Angles-of-Polygons-and-Stars.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.4a. Angles of Polygons and Stars<\/a>\n<ul>\n<li><strong>MA.<\/strong> Take 2, <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.Two-Questions-about-Angles.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.4b. Two Questions about Angles<\/a><\/li>\n<li><strong>MA.<\/strong> <strong>Totally Optional<\/strong> Take 3, <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.Creating-the-Angles-Table-using-Excel.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.4c.i. Creating the Angles Table using Excel<\/a>\n<ul>\n<li>MA. <em>Excel<\/em> file for Take 3: <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.Angles-Table.xlsx\" target=\"_blank\" rel=\"noopener noreferrer\">1.4c.ii. Angles Table<\/a><\/li>\n<\/ul>\n<\/li>\n<li>1.4d. <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/Sharpest-Star-Angles.pdf\" target=\"_blank\" rel=\"noopener\">Sharpest Star Angles<\/a><\/li>\n<\/ul>\n<\/li>\n<li>Stars as rotating polygons and stars: <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/07\/1.Stars-as-Rotating-Polygons.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1.5a. Stars as Rotating Polygons<\/a>\n<ol>\n<li><strong>MA.<\/strong> <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/Angle-Analysis-of-Stars-as-Rotating-Polygons.pdf\" target=\"_blank\" rel=\"noopener\">1.5b. Angle Analysis of Stars as Rotating Polygons<\/a><\/li>\n<\/ol>\n<\/li>\n<li>Internal Stars: <a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/Stars-inside-a-Star.pdf\" target=\"_blank\" rel=\"noopener\">1.6a. Stars inside a Star<\/a>\n<ol>\n<li><strong>MA. <\/strong><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/Analyzing-Stars-inside-a-Star.pdf\" target=\"_blank\" rel=\"noopener\">1.6b. Analyzing Stars inside a Star<\/a><\/li>\n<li>\u00a0<a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/Calculating-Triangle-Angles-using-Vertices.pdf\" target=\"_blank\" rel=\"noopener\">1.6c. Calculating Triangle Angles using Vertices<\/a><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2025\/01\/Draw-a-Star2.pdf\" target=\"_blank\" rel=\"noopener\">Draw a Star<\/a>\u00a0is a link to a four slide PowerPoint file (presented as a pdf) that I have used in classes to see how people draw a star. I have used this for multiple classes and my classes include both international and domestic students from various parts of the country. Surprisingly, I have found strong uniformity regarding how most of us draw a star. More than 80% of students I have surveyed start at the same vertex and move around the vertices in the same direction (I won&#8217;t tell you which vertex and which direction, but if you try this in your class, my guess is that you will figure it out). See what happens in your class, it only takes a couple of minutes and even college students found it fun.<\/p>\n<\/div><\/div>\n<div class=\"su-column su-column-size-1-5\"><div class=\"su-column-inner su-u-clearfix su-u-trim\"><strong>EXTRA MATERIALS<\/strong><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/08\/1.-Glossary.pdf\" target=\"_blank\" rel=\"noopener\">1. Glossary<\/a><\/p>\n<p><strong><em>FOR USERS<\/em><\/strong><\/p>\n<p>Challenge Questions<\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/08\/1.-Polygon-Questions.pdf\" target=\"_blank\" rel=\"noopener\">a. Polygon Questions<\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/08\/1.-Stars-Challenge-Questions.pdf\" target=\"_blank\" rel=\"noopener\">b. Stars Questions<\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/1.5b-CQs.pdf\" target=\"_blank\" rel=\"noopener\">1.5b CQs<\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/123-124-stars-CQs.pdf\" target=\"_blank\" rel=\"noopener\">12,3 &amp; 12,4 stars CQs<\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2022\/09\/1.6c-CQs.pdf\" target=\"_blank\" rel=\"noopener\">1.6c CQs<\/a><\/p>\n<p><strong><em>FOR INSTRUCTORS<\/em><\/strong><\/p>\n<p>Instructor Excel File<\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/09\/1.P-and-S-for-Teachers-2-1-2-1.xlsx\" target=\"_blank\" rel=\"noopener\">1.P-and-S-for-Teachers<\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/09\/1.Quick-Start-Guide.pdf\" target=\"_blank\" rel=\"noopener\">&#8211; 1.Quick-Start Guide<\/a><\/p>\n<p>Videos<\/p>\n<p><a href=\"https:\/\/youtu.be\/-szW3GM5j_Y\" target=\"_blank\" rel=\"noopener\">Introductory Video<\/a><\/p>\n<p><a href=\"https:\/\/youtu.be\/DfsoSeVx2kY\" target=\"_blank\" rel=\"noopener\">Using the <em>Drawing Tool<\/em><\/a><\/p>\n<p><a href=\"https:\/\/youtu.be\/XvktiujIM-Y\" target=\"_blank\" rel=\"noopener\">Building Worksheets<\/a><\/p>\n<p>Documents<\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/08\/1.-Common-Core.pdf\" target=\"_blank\" rel=\"noopener\">1. Links to <em>Common Core<\/em><\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/08\/1.-15-Worksheet-Exercises.pdf\" target=\"_blank\" rel=\"noopener\">1. 15 Worksheet Exercises<\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/08\/1.-Lesson-Plans-K-2.pdf\" target=\"_blank\" rel=\"noopener\">1. Lesson Plans K-2<\/a><\/p>\n<p><a href=\"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/files\/2021\/08\/1.-Kindergarten-Test.pdf\" target=\"_blank\" rel=\"noopener\">1. A Kindergarten Test<\/a><\/p>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1719,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-fullwidth.php","meta":{"footnotes":""},"class_list":["post-68","page","type-page","status-publish","hentry","post-preview"],"_links":{"self":[{"href":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/wp-json\/wp\/v2\/pages\/68","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/wp-json\/wp\/v2\/users\/1719"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/wp-json\/wp\/v2\/comments?post=68"}],"version-history":[{"count":0,"href":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/wp-json\/wp\/v2\/pages\/68\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.dickinson.edu\/playing-with-polygons\/wp-json\/wp\/v2\/media?parent=68"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}