{"id":220,"date":"2014-06-13T15:10:57","date_gmt":"2014-06-13T15:10:57","guid":{"rendered":"http:\/\/newblog.primefactorisation.com\/2014\/06\/13\/new-things-thursday\/"},"modified":"2024-11-02T15:04:45","modified_gmt":"2024-11-02T20:04:45","slug":"new-things-thursday","status":"publish","type":"post","link":"https:\/\/www.primefactorisation.com\/blog\/2014\/06\/13\/new-things-thursday\/","title":{"rendered":"New Things Thursday!"},"content":{"rendered":"<p>So after my <a href=\"https:\/\/www.primefactorisation.com\/blog\/2014\/06\/09\/new-things\/\">last post<\/a> I started to have a crisis of confidence in what I was planning to do. I felt like I oversold my plans a bit too much. <em>What if this is a complete disaster? I&#8217;ve kind of committed to blogging about it now!<\/em><\/p>\n<p>Thankfully it seemed to go well, and the feedback I got from the students was really positive.<\/p>\n<p>So anyway, introducing&#8230; <br \/>\n(drum roll, drawing out the tension, not really a surprise since it&#8217;s in the title&#8230;)<\/p>\n<p><img decoding=\"async\" src=\"\/content\/images\/2014\/Jun\/ntt.PNG\" alt=\"New Things Thursday\" title=\"\" \/> Powerpoint slide I used to introduce &#8216;New Things Thursday&#8217;.<\/p>\n<p>So this is the idea &#8211; Thursdays are now all about &#8216;new things&#8217;. As I wrote last time, I want to capture the excitement of discovery that I see in maths but seems to go unnoticed by students. By putting the idea that <em>this is something<\/em> new front and center, I&#8217;m hoping I can sidestep that part of a kid&#8217;s brain that tells them each lesson is just the same old boring maths.<\/p>\n<p>So I&#8217;m putting these rules on myself for Thursdays. That said, I&#8217;m completely prepared to break these rules I feel the need to. And given that New Things Thursday is itself a new thing, it may need to change.<\/p>\n<h3 id=\"rulesfornewthingsthursday\">Rules for New Things Thursday<\/h3>\n<ul>\n<li>\n<p>Each lesson will be about on something new. A new rule, a new concept, a new perspective, whatever. We will still do some revision, and the new content will build on what the students already know, but the &#8216;new thing&#8217; will be the focus of the lesson.<\/p>\n<\/li>\n<li>\n<p>Rather than explicitly telling students the new thing, I will find a way to let them discover it themselves. This will be a challenge, as it will take a lot longer to introduce each idea, but hopefully it leads to more solid understanding from the start.<\/p>\n<\/li>\n<li>\n<p>For each &#8216;new thing&#8217;, students will create a &#8216;new thing page&#8217;: a page in their workbooks that summarises the new content. This page will be their main reference to the concept in future lessons.<\/p>\n<\/li>\n<\/ul>\n<p>To set the tone of New Things Thursday, I&#8217;m also allowing students a few minutes where they can share with me and the class any &#8216;new things&#8217; that they&#8217;re excited about, which can be whatever they&#8217;re interested in and doesn&#8217;t even need to relate to maths. (I realised afterwards that I may have subconciously ripped this idea off from Sarah Hagan&#8217;s <a href=\"https:\/\/mathequalslove.net\/weekly-schedule\/\">Good Things Mondays<\/a>, so thanks goes her. Actually, most of elements of New Things Thursday are probably stolen from other bloggers.)<\/p>\n<h3 id=\"thefirstnewthingpythagorastheorem\">The first New Thing: Pythagoras&#8217; Theorem<\/h3>\n<p>Introducing Pythagoras is always an interesting moment; it&#8217;s one of those key points where high school maths transitions from being &#8216;arithmetic&#8217; to &#8216;mathematics&#8217;, and might even be the first time students hear the word &#8216;theorem&#8217;.<\/p>\n<p>The statement of rule (a<sup>2<\/sup>&nbsp;+&nbsp;b<sup>2<\/sup>&nbsp;=&nbsp;c<sup>2<\/sup>) is so simple to students that they don&#8217;t always recognise the significance of it, and unfortunately it is often only treated as a tool for calculating lengths. I think our aim should be to helps students realise the surprising elegance of the theorem, the mathematical truth it reveals.<\/p>\n<p>We started the lesson talking about square numbers and I asked why they were called &#8216;square&#8217; numbers. It took a little prompting, but they realised that they relate to the area of squares. I had them list all of them from 1<sup>2<\/sup> to 20<sup>2<\/sup>, which didn&#8217;t take too long. Once they had their lists, I pointed out that 144&nbsp;+&nbsp;25&nbsp;=&nbsp;169, or 12<sup>2<\/sup>&nbsp;+&nbsp;5<sup>2<\/sup>&nbsp;=&nbsp;13<sup>2<\/sup>.<\/p>\n<p>I asked if they could find any more combinations like it, and gave them a few minutes in groups to see how many they could find. (I deliberately didn&#8217;t use 3<sup>2<\/sup>&nbsp;+&nbsp;4<sup>2<\/sup>&nbsp;=&nbsp;5<sup>2<\/sup> as my example so they would have an easier one to find.) A few students asked me whether the ones they&#8217;d found were correct. I told them they didn&#8217;t need to check with me &#8211; they could check themselves using their calculator.<\/p>\n<p>I then listed the combinations on the whiteboard. Some had found up to 8<sup>2<\/sup>&nbsp;+&nbsp;15<sup>2<\/sup>&nbsp;=&nbsp;17<sup>2<\/sup>. Some had realised that many were multiples of 3<sup>2<\/sup>&nbsp;+&nbsp;4<sup>2<\/sup>&nbsp;=&nbsp;5<sup>2<\/sup>. (YES!) I had each student choose one equation from the board, and asked them to cut out three squares representing the numbers in their equation from grid paper that I had handed out.<\/p>\n<p>Notice that so far I have not mentioned triangles or right-angles, or even the name Pythagoras. That was the secret truth that I wanted my students to discover.<\/p>\n<p>I asked them to create a triangle by using the edges of their squares. What sort of triangle was it? It turned out they all had right angle triangles!<\/p>\n<p>It was at this point that I finally put up some notes about Pythagoras&#8217; theorem, and had them create their new things page. I&#8217;d already prepared one myself in case any students didn&#8217;t know what to put on theirs:<\/p>\n<p><img decoding=\"async\" src=\"\/content\/images\/2014\/Jun\/nttpage.jpg\" alt=\"My new thing page! Sorry I'm not that artistic...\" \/><\/p>\n<p>Thankfully a lot of of the pages the class made looked a lot better than mine. Some students even decided to create a &#8216;new things&#8217; section in their book so it would be easier to look up in the future.<\/p>\n<p>I pointed out that though we&#8217;d discovered this pattern, it&#8217;s not really a theorem until we prove it &#8211; which hopefully will happen next lesson.<\/p>\n<p>Unfortunately, that was the last Thursday I&#8217;ll have them this term &#8211; they have an excursion next week and I have one the week after. But I think I&#8217;ve built some enthusiasm from the class for &#8216;new things&#8217;, and set a pattern we can start in earnest next term. And anyway, there&#8217;s no reason I can&#8217;t do this:<\/p>\n<p><img decoding=\"async\" src=\"\/content\/images\/2014\/Jun\/ntfriday.PNG\" alt=\"New things Friday!\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>So after my last post I started to have a crisis of confidence in what I was planning to do. I felt like I oversold my plans a bit too much. What if this is a complete disaster? I&#8217;ve kind of committed to blogging about it now! Thankfully it seemed to go well, and the &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.primefactorisation.com\/blog\/2014\/06\/13\/new-things-thursday\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;New Things Thursday!&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-220","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/comments?post=220"}],"version-history":[{"count":3,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/220\/revisions"}],"predecessor-version":[{"id":570,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/220\/revisions\/570"}],"wp:attachment":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/media?parent=220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/categories?post=220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/tags?post=220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}