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It breaks 5.3 into three knowledge, skills and understanding statements: exploring and analysing outcome frequencies, systematically recording outcomes to derive theoretical probabilities, and calculating and using probabilities of single and combined events. It also provides overview guidance on engaging students through experiments, developing language precision, distinguishing events vs outcomes and probability vs possibility, and checking prior learning for secure foundations.",{"@graph":69,"@context":123},[70,84,106],{"@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/mastery-professional-development-53-probability-key-stage-3/414415/",{"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/mastery-professional-development-53-probability-key-stage-3/414415.png","ImageObject",300,407,{"name":92,"@type":93},"Aria Callaghan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-28",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the three knowledge, skills and understanding statements for 5.3 Probability?","Question",{"text":113,"@type":114},"They are: explore, describe and analyse the frequency of outcomes; systematically record outcomes to find theoretical probabilities; and calculate and use probabilities of single and combined events.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How should students be introduced to probability before quantifying?",{"text":118,"@type":114},"Students should engage in experiments to develop an intuition for likely, unlikely, even, certain and impossible chances, including building understanding of equally likely outcomes.",{"name":120,"@type":111,"acceptedAnswer":121},"What misconceptions about “even” chance and “one in n” are highlighted?",{"text":122,"@type":114},"Students may think an event with two outcomes always has an even chance, or that the probability of an event with n possible outcomes is always “one in n”; the guidance recommends comparing cases where this is true and where it is not.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},414415,1791126090,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":56,"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":144,"read_time":145,"preview_page_count":4},962084926284,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Mastery Professional Development  \n5 Statistics and probability  \n5.3 Probability Guidance document | Key Stage 3  \nMaking connections  \nThe NCETM has identified a set of six ‘mathematical themes’ within Key Stage 3 mathematics that bring together a group of ‘core concepts’.  \nThe fifth of these themes is Statistics and probability, which covers the following interconnected core concepts:  \n5.1 Statistical representations and measures  \n5.2 Statistical analysis  \n5.3 Probability  \nThis guidance document breaks down core concept 5.3 Probability into three statements of knowledge, skills and understanding:  \n5.3.1 Explore, describe and analyse the frequency of outcomes in a range of situations  \n5.3.2 Systematically record outcomes to find theoretical probabilities  \n5.3.3 Calculate and use probabilities of single and combined events  \nThen, for each of these statements of knowledge, skills and understanding we offer a set of key ideas to help guide teacher planning.  \nPlease note that these materials are principally for professional development purposes. Unlike a textbook scheme they are not designed to be directly lifted and used as teaching materials. The materials can support teachers to develop their subject and pedagogical knowledge and so help to improve mathematics teaching in combination with other high-quality resources, such as textbooks.  \nOverview  \nStudents will encounter probability in many aspects of their daily lives, from sporting events to weather reports. However, probability is an area of mathematics that students can find perplexing. Students may feel that their lived experiences do not reflect calculated mathematical likelihoods. For example, rolling a six on a dice in order to win a board game often ‘feels’ far less likely than any of the other outcomes. The introduction of probability at Key Stage 3 will offer students a way to quantify, explore and explain likelihood and coincidence, and to reason about uncertainty.  \nStudents should have the opportunity to engage in experiments and develop a feel for likely, unlikely, even, certain and impossible chances, before starting to quantify probabilities and the likelihood of different outcomes. An understanding of equally likely outcomes is key to this. Often, students mistakenly believe that an event with only two possible outcomes has an ‘even’ chance of happening, or that the probability of one event occurring when there are n possible outcomes is ‘one in n’. Students should be exposed to examples of when this is true and when this is not true (for example, whether it will rain or not rain tomorrow, whether the school football team would beat Brazil if they were to play them, whether the teacher choosing a student from a class of 30 has a probability of 1 out of 30) and discuss what’s the same and what’s different about the situations.  \nFurthermore, students need to appreciate that predictions of likelihood do not predict individual events. Rather, experimental data will tend towards this theoretical value (for example, knowing that flipping ahead or a tail on a coin has an even chance of occurring does not mean these outcomes will occur an equal number of times) .  \nAs they start to quantify outcomes, students should be exposed to different ways to systematically organise and represent possible results, including lists, tables, grids and Venn diagrams.  \nSpecific and precise language is key to working with probability. For example, students should understand the distinctions between an event (for example, flipping a coin) and an outcome (for example, a coin landing on heads) or between probability and possibility (for example, it is possible that it will snow in summer, but not probable) .  \nPrior learning  \nBefore beginning to teach Probability at Key Stage 3, students should already have a secure understanding of the following from previous study:  \n\n| Key stage | Learning outcome |\n| --- | --- |\n| Key Stage 3 | • 3.1.3 Understand that fractions are an","cbCaivyZ2aeN8tRo","https://ap.wps.com/l/cbCaivyZ2aeN8tRo","pdf",521418,"English","# Overview\n# Core statements for 5.3 Probability\n## Explore outcomes and frequencies\n## Record outcomes and find theoretical probabilities\n## Calculate and use probabilities of single and combined events\n# Language and reasoning about uncertainty\n# Prior learning and checking prior learning\n## Key vocabulary","[{\"question\":\"What are the three knowledge, skills and understanding statements for 5.3 Probability?\",\"answer\":\"They are: explore, describe and analyse the frequency of outcomes; systematically record outcomes to find theoretical probabilities; and calculate and use probabilities of single and combined events.\"},{\"question\":\"How should students be introduced to probability before quantifying?\",\"answer\":\"Students should engage in experiments to develop an intuition for likely, unlikely, even, certain and impossible chances, including building understanding of equally likely outcomes.\"},{\"question\":\"What misconceptions about “even” chance and “one in n” are highlighted?\",\"answer\":\"Students may think an event with two outcomes always has an even chance, or that the probability of an event with n possible outcomes is always “one in n”; the guidance recommends comparing cases where this is true and where it is not.\"}]","Mastery Professional Development - 5.3 Probability - Key Stage 3 | PDF",1790597492,48]