[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-619186-105":59,"doc-detail-619186-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","drawing-a-regular-35-sided-polygon-encouraging-thinking-skills-ks3-ks4","Drawing a regular 3.5-sided polygon - Encouraging thinking skills (KS3 & KS4)","","Training material for MathsConf 32 (Summer 2023) by Greg Thomas, focused on encouraging thinking skills in KS3 and KS4 through challenging geometry tasks. The sessions aim to push students beyond comfort zones and prompt careful use of mathematical definitions and language. Activities include exploring prime numbers, building reasoning with sums of integers, finding maxima, interpreting multiple representations, and creatively constructing regular 3.5-sided and other fractional-sided polygons to generate conjectures and investigate rotational and angle patterns.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/drawing-a-regular-35-sided-polygon-encouraging-thinking-skills-ks3-ks4/619186/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/drawing-a-regular-35-sided-polygon-encouraging-thinking-skills-ks3-ks4/619186.png","ImageObject",300,407,{"name":92,"@type":93},"Lucas Martin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/vnd.openxmlformats-officedocument.presentationml.presentation","2026-10-29","2026-10-20",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What learning aims does the session state for encouraging thinking skills?","Question",{"text":112,"@type":113},"It aims to move students outside their comfort zone, encourage thinking skills, and make students consider mathematical definitions and language.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the activity use the idea of drawing regular fractional-sided polygons?",{"text":117,"@type":113},"Students are instructed to use a protractor, pencil, and ruler to draw a regular 3.5-sided polygon, then extend the work to other regular n-gons and related constructions.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of questions are suggested when investigating regular n-gons and the 3.5 case?",{"text":121,"@type":113},"The slide prompts conjectures about regular n-gons, explores angles for a 3.2-gon, compares 3-gon/3.5-gon/3.2-gon, considers rotations for sides to meet, and asks how angle measures change as n increases.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},619186,1792462636,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Drawing a regular 3.5-sided polygon: Encouraging thinking skills (KS3 & KS4)\nGreg Thomas\nMathsConf 32\n1\nSummer 2023\nCopyright © AQA and its licensors. All rights reserved.\nWelcome\n2\nAims:\nTo move students outside of their comfort zone\nTo encourage thinking skills\nTo make you consider mathematical definitions and language\n3\nThinking skills (and you thought you knew maths)\nCopyright © AQA and its licensors. All rights reserved.\nPrime numbers\nWhat’s your definition of a prime number?\n4\nCopyright © AQA and its licensors. All rights reserved.\nWhere a + b + c = 10\n(and a, b and c are integers)\n5\nFind the highest value you can:\nCopyright © AQA and its licensors. All rights reserved.\n6\nWhat are these multiple representations of?\nCopyright © AQA and its licensors. All rights reserved.\nUse a protractor, pencil and ruler to draw a regular 5-sided polygon.\nCopyright © AQA and its licensors. All rights reserved.\n7\nLet’s get creative\nUse a protractor, pencil and ruler to draw a regular 3.5-sided polygon.\nCopyright © AQA and its licensors. All rights reserved.\n8\nLet’s get creative\nUse a protractor, pencil and ruler to draw a regular 4.5-sided polygon.\nCopyright © AQA and its licensors. All rights reserved.\n9\nLet’s get creative\nCopyright © AQA and its licensors. All rights reserved.\n10\nWhere does the 3.5 fit in?\nWhat conjectures could students make about regular n-gons?\nIf given a regular 3.2-gon, what would the angles be?\nHow many sides would it have?\nHow many rotations would it take for the last side to meet the first side?\nHow are a 3-gon, a 3.5-gon and a 3.2-gon the same/different?\nAdd a 4.7-gon to the picture.\nWhy do some have lots of rotations and others only have one or two?\nWhat type of regular n-gon will have many rotations before the last side meets with the first side?\nWhat type will have few rotations?\nHow do the angle measures change as n-increases? Why?\nCan we build a regular ∏-gon? If so, what would it look like? If not, why not?\nCopyright © AQA and its licensors. All rights reserved.\n11\nQuestions to consider\nCopyright © AQA and its licensors. All rights reserved.\n12\nPolygons\nCopyright © AQA and its licensors. All rights reserved.\n13\nHow did you feel when you were given this task?\nCredit: © iStock.com/picture\nCopyright © AQA and its licensors. All rights reserved.\n14\nDiscussion points\nWho might you use this with in the classroom?\nHow might you adapt it?\nHow might you differentiate it?\nWhat are the key questions?\n(Patterns within the ball of string)\nCopyright © AQA and its licensors. All rights reserved.\n15\nHuman stars with a ball of string\nCredit: © iStock.com/malerapaso\nCopyright © AQA and its licensors. All rights reserved.\n16\nLevel 2 Certificate in Further Mathematics\nL2FM is intended to be taught alongside or after GCSE Maths Higher tier (not as a replacement).\nIt is designed to prepare students for the rigour of A-level Maths and Further Maths but doesn’t infringe upon the content of AS.\nIt features demanding topics including matrices and differentiation.\nIt doesn’t discount against GCSE Maths and does not get any performance points.\nCopyright © AQA and its licensors. All rights reserved.\n17\nWhy choose Level 2 Further Maths? (L2FM)\nIt’s for more able maths students, with a focus on higher-level thinking and reasoning.\nIt is designed to stretch students, supporting what they learn in GCSE Maths.\nIt gives students the chance to encounter more challenging maths, useful for those likely to study maths after GCSE.\nWith over 25,000 entries each year, we help students realise their potential.\nCopyright © AQA and its licensors. All rights reserved.\n18\nWho is it for?\nWe designed the L2FM qualification to:\nfill the gap for high-achieving students needing more stretch and challenge than GCSE Maths provides\nfocus on higher-order technical proficiency, rigorous argument and problem-solving skills and to help prepare students for further study of maths\nexpose students to a wider range of maths problems\nencourage more students to continu","cbCaihlBt2Q6x1xo","https://ap.wps.com/l/cbCaihlBt2Q6x1xo","pptx",9165054,25,"English","# Welcome\n## Aims\n# Thinking skills (and you thought you knew maths)\n## Prime numbers\n## Where a + b + c = 10\n## Find the highest value you can\n## Multiple representations\n# Let’s get creative\n## Draw a regular 3.5-sided polygon\n## Draw regular 4.5- and other fractional-sided polygons\n# Where does the 3.5 fit in?\n## Conjectures about regular n-gons\n# Discussion points\n## Who to use it with\n## How to adapt and differentiate\n# Level 2 Certificate in Further Mathematics (L2FM)\n## Why choose L2FM\n## Who is it for\n## Qualification aims\n# Resources\n## Planning, Teaching and Assessment tabs\n## MathsConf past presentations\n## All About Maths pages\n# Get in touch","[{\"question\":\"What learning aims does the session state for encouraging thinking skills?\",\"answer\":\"It aims to move students outside their comfort zone, encourage thinking skills, and make students consider mathematical definitions and language.\"},{\"question\":\"How does the activity use the idea of drawing regular fractional-sided polygons?\",\"answer\":\"Students are instructed to use a protractor, pencil, and ruler to draw a regular 3.5-sided polygon, then extend the work to other regular n-gons and related constructions.\"},{\"question\":\"What kinds of questions are suggested when investigating regular n-gons and the 3.5 case?\",\"answer\":\"The slide prompts conjectures about regular n-gons, explores angles for a 3.2-gon, compares 3-gon/3.5-gon/3.2-gon, considers rotations for sides to meet, and asks how angle measures change as n increases.\"}]","Drawing a regular 3.5-sided polygon - Encouraging thinking skills (KS3 & KS4) | PPTX",63]