[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-411724-105":59,"doc-detail-411724-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","standards-for-mathematical-practice-overview","Standards for Mathematical Practice - Overview","","Standards for Mathematical Practice outlines key expertise that mathematics educators should develop in students across grade levels. It describes eight interrelated practices, including understanding and persisting with problems, using abstract and quantitative reasoning, constructing arguments and analyzing reasoning, and modeling real situations. The framework also emphasizes communication, representation, strategic use of tools, and connecting ideas across equations, descriptions, graphs, tables, and contexts. Students learn to check solutions, compare approaches, and refine models for coherence.",{"@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/standards-for-mathematical-practice-overview/411724/",{"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/standards-for-mathematical-practice-overview/411724.png","ImageObject",300,407,{"name":92,"@type":93},"cksankcs","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-28",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do mathematically proficient students approach solving problems?","Question",{"text":112,"@type":113},"They explain the problem’s meaning, analyze givens and constraints, consider solution pathways, and use analogous problems or special cases to gain insight. They monitor progress, change course when needed, and check answers using different methods.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does it mean to reason abstractly and quantitatively?",{"text":117,"@type":113},"Students create coherent representations of quantities and relationships, attend to units and meanings, and flexibly use properties of operations. They also decontextualize by representing situations symbolically and contextualize by probing symbols’ referents.",{"name":119,"@type":110,"acceptedAnswer":120},"How are mathematical models used in real-life contexts?",{"text":121,"@type":113},"Students apply known mathematics to everyday life, society, and the workplace. They make assumptions to simplify situations, identify important quantities, map relationships using diagrams or tables, interpret results in context, and improve the model if necessary.","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},411724,1790837466,{"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":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":31,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},3985747882755,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","# Standards for Mathematical Practice\n\nThe Standads for Mathematical Practice describe varieties of expertise tha mathematics educators at all levels should seek to  \ndevelop in their students.These practices est on important “processes and prophecies with longstanding importance in mathematics education.The first of these are the NCTM process standards of problem solving,reasoning and proof,communication,representation,and connections.The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up:adaptive reasoning,strategic competence,conceptual understanding(comprehension of mathematical concepts,operations and relations),procedural fluency (skilin carrying out procedures flexibly,accurately,efficiently and appropriately),and productive disposition (habitual inclination to seemathematics as sensible,useful,and worthwhile,coupled with a belief in diligence and one's own efficacy).  \n## 1.Make sense of problems and persevere in solving them.\n\nMathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.They analyze givens,constraints,relationships,and goals.They make conjectures about the form and meaning of the solution and plan asolution pathway rather than simply jumping into a solution attempt.They consider analogous problems,and try special cases and simplerforms of the original problem in order to gain insight into its solution.They monitor and evaluate their progress and change course ifnecessary.Older students might,depending on the context of the problem,transform algebraic expressions or change the viewing window on theirgraphing calculator to get the information they need.Mathematically proficient students can explain correspondences between equations,verbal descriptions,tables,and graphs or draw diagrams ofimportant features and relationships,graph data,and search for regularity or trends.Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.Mathematically proficientstudents check their answers to problems using a diferent method,and they continually ask themselves,“Does this make sense?\"”They canunderstand the approaches of others to solving complex problems and identify correspondences between different approaches.  \n## 2.Reason abstractly and quantitatively.\n\nMathematically proficient students make sense of quantities and their relationships in problem situations.They bring two complementaryabilities to bear on problems involving quantitative relationships:the ability to decontextualize—to abstract a given situation and represent itsymbolically and manipulate the representing symbols as if they have a life of their own,without necessarily attending to their referents andthe ability to contextualize,to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.Quantitative reasoning entails habits of creating a coherent representation of the problem at hand;considering the units involved;attending tothe meaning of quantities,not just how to compute them;and knowing and flexibly using different properties of operations and objects.  \nMathemat._ly proficient students understand and use stated assumptio definitions,and previously established results in constructarguments.They make conjectures and build a logical progression of statements to explore the truth of their conjectures.They are able toanalyze situations by breaking them into cases,and can recognize and use counterexamples.Theyjustify their conclusions,communicate themto others,and respond to the arguments of others.They reason inductively about data,making plausible arguments that take into account thecontext from which the data arose.Mathematically proficient students are also able to compare the effectiveness oftwo plausible arguments,distinguish corect logic or reasoning from that which is flawed,and—if there is a fl","cbCaibI75KQ328u8","https://ap.wps.com/l/cbCaibI75KQ328u8","pdf",2106459,"English","# Standards for Mathematical Practice\n## 1. Make sense of problems and persevere in solving them.\n## 2. Reason abstractly and quantitatively.\n## 4. Model with mathematics.\n## 5. Use appropriate tools strategically.","[{\"question\":\"How do mathematically proficient students approach solving problems?\",\"answer\":\"They explain the problem’s meaning, analyze givens and constraints, consider solution pathways, and use analogous problems or special cases to gain insight. They monitor progress, change course when needed, and check answers using different methods.\"},{\"question\":\"What does it mean to reason abstractly and quantitatively?\",\"answer\":\"Students create coherent representations of quantities and relationships, attend to units and meanings, and flexibly use properties of operations. They also decontextualize by representing situations symbolically and contextualize by probing symbols’ referents.\"},{\"question\":\"How are mathematical models used in real-life contexts?\",\"answer\":\"Students apply known mathematics to everyday life, society, and the workplace. They make assumptions to simplify situations, identify important quantities, map relationships using diagrams or tables, interpret results in context, and improve the model if necessary.\"}]","Standards for Mathematical Practice - Overview | PDF",1790589459,126]