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Performance level descriptors connect the state measure to classroom instruction and formative assessments, describing proficiency as an observable range. The framework links proficiency to text/task complexity and context, then outlines what learners can do from below proficient through above proficient, including exponent properties, rational and irrational numbers, and complex numbers in operations and equation solving.",{"@graph":69,"@context":126},[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/mathematics-high-school-numbers-quantity-proficiency-level-descriptors/538031/",{"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/mathematics-high-school-numbers-quantity-proficiency-level-descriptors/538031.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-10",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118,122],{"name":109,"@type":110,"acceptedAnswer":111},"What is the purpose of performance level descriptors in this framework?","Question",{"text":112,"@type":113},"They connect the state assessment to classroom instruction and local formative assessments, defining academic proficiency as an observable range of student performance.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does text and task complexity affect student proficiency?",{"text":117,"@type":113},"A student’s ability to demonstrate proficiency depends on the complexity of stimuli, the tasks required, and the contexts in which learning occurs; as performance improves, students handle more challenging materials more accurately and consistently.",{"name":119,"@type":110,"acceptedAnswer":120},"What skills are expected under Claim 1 across performance levels?",{"text":121,"@type":113},"Claim 1 covers applying and operating with exponent properties, working with rational exponents and roots, distinguishing rational and irrational numbers, and using properties to justify and solve related multi-step problems, progressing from computation to justification and application in contexts.",{"name":123,"@type":110,"acceptedAnswer":124},"How does Claim 2 address complex numbers and quadratic equations with complex solutions?",{"text":125,"@type":113},"Claim 2 ranges from identifying complex number components and basic complex operations to simplifying expressions, manipulating powers of i, and solving quadratic or higher-degree polynomial equations with complex solutions through increasingly multi-step approaches.","https://schema.org",{"og:url":83,"og:type":128,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":130,"canonical":83},"index,follow",{"doc_id":132,"site_id":62},538031,1791732116,{"code":4,"msg":5,"data":135},{"doc_id":132,"user_id":136,"nickname":92,"user_avatar":137,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":138,"file_id":139,"file_url":140,"file_type":141,"file_size":142,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":143,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":144,"faqs":145,"seo_title":146,"seo_description":67,"update_tm":147,"read_time":24,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","| \u003Cbr>\u003Cbr>MATHEMATICS HIGH SCHOOL NUMBERS & QUANTITY |  | Theory of Action: Academic standards represent a collective commitment around what students should learn each year. The state assessment asks students to demonstrate their knowledge, skills, and understanding related to these standards using a common measure. The resulting data allows us to see patterns in performance that should guide school and district improvement, helping identify areas of strength and opportunity.\u003Cbr>Role of Performance Level Descriptors in Defining Proficiency: Performance level descriptors bridge the state assessment to classroom instruction and the systems of formative assessments that guide local instruction and choices about individual students. Academic proficiency represents a range of observable student performance characteristics. There are multiple pathways to proficiency, and students rely upon their strengths differently within that range of performance.\u003Cbr>Proficiency and Difficulty: A student’s ability to demonstrate proficiency is influenced by the complexity of the texts or stimuli presented, tasks they’re asked to complete, and the contexts in which they are engaged. As student performance improves, students are typically able to handle more challenging texts/stimuli, tasks, and contexts, and are able to demonstrate their skills and knowledge more accurately and consistently. |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| Numbers & Quantity Student performance indicates the ability to… |  |  |  |  |  |\n| Claim 1 | Below Proficient |  | Approaching Proficient | Proficient | Above Proficient |\n| RN.1-2 | Apply integer exponent properties (e.g., simplify expressions involving integer exponents. Identify equivalent expressions with integer exponents) .\u003Cbr>Compute basic exponential expressions. |  | Write roots as rational exponents and rational exponents as roots. | Apply properties of rational exponents. For example, perform operations on expressions involving radicals and rational exponents using the properties of exponents.\u003Cbr>Compute exponential expressions with rational exponents and real number bases. Simplify exponential expressions with rational exponents with variable bases. | Recognize rational exponents in contexts. Apply properties of exponents to solve (multi-step) equations involving rational exponents. |\n| RN.3 | Classify numbers as rational or irrational. |  | Perform addition and multiplication operations with rational and irrational numbers.\u003Cbr>Approximate the placement of irrational numbers on the real number line/graph or compare relative to available rational numbers. | Justify how the sum and product of two rational, nonzero numbers are rational even if the answer is unknown.\u003Cbr>Demonstrate how the sum of two irrational numbers elicits an irrational value.\u003Cbr>Justify how the sum of a rational number and an irrational number is irrational. | Apply properties of rational and irrational numbers to contexts like area and volume to identify reasonable answers. |\n\n\n| Numbers & Quantity Student performance indicates the ability to… |  |  |  |  |\n| --- | --- | --- | --- | --- |\n| Claim 2 | Below Proficient\u003Cbr>| Approaching Proficient\u003Cbr>| Proficient\u003Cbr>| Above Proficient\u003Cbr>|\n| CN.1-2 | Identify real and imaginary\u003Cbr>components of a complex number. | Perform sums and differences of complex numbers. Rewrite negative radicands as a complex number. | Simplify algebraic expressions with complex numbers. Calculate the product and quotient of two complex numbers. Calculate powers of 􀝅 . Simplify algebraic expressions that require multiple steps and algebraic properties of equality. | Create and apply problems with complex numbers that involve higher order manipulation. |\n| CN.7 | Find solutions to quadratic equations with complex solutions by graphing. Identify the complex solutions in the factored form. | Recognize the conjugate pairs solutions for a polynomial with real coefficients. | Perform quadratic formula, completin","cbCairFZIrPDwhkF","https://ap.wps.com/l/cbCairFZIrPDwhkF","pdf",238997,"English","# Numbers & Quantity\n## Theory of Action and Role of Performance Level Descriptors\n## Proficiency, Difficulty, and Context\n## Claim 1: Exponents, Rational Exponents, and Number Types\n## Claim 2: Complex Numbers and Complex Solutions","[{\"question\":\"What is the purpose of performance level descriptors in this framework?\",\"answer\":\"They connect the state assessment to classroom instruction and local formative assessments, defining academic proficiency as an observable range of student performance.\"},{\"question\":\"How does text and task complexity affect student proficiency?\",\"answer\":\"A student’s ability to demonstrate proficiency depends on the complexity of stimuli, the tasks required, and the contexts in which learning occurs; as performance improves, students handle more challenging materials more accurately and consistently.\"},{\"question\":\"What skills are expected under Claim 1 across performance levels?\",\"answer\":\"Claim 1 covers applying and operating with exponent properties, working with rational exponents and roots, distinguishing rational and irrational numbers, and using properties to justify and solve related multi-step problems, progressing from computation to justification and application in contexts.\"},{\"question\":\"How does Claim 2 address complex numbers and quadratic equations with complex solutions?\",\"answer\":\"Claim 2 ranges from identifying complex number components and basic complex operations to simplifying expressions, manipulating powers of i, and solving quadratic or higher-degree polynomial equations with complex solutions through increasingly multi-step approaches.\"}]","MATHEMATICS HIGH SCHOOL NUMBERS & QUANTITY - Proficiency Level Descriptors | PDF",1791606025]