In the early childhood years of schooling, children also discover new worlds of literature. Immersed in stories, sounds, and letters, they make connections between what they hear and what they read. Starting in pre-kindergarten, children listen daily to a wide variety of literary and informational texts: stories, poems, songs, fables, myths, legends, biographies, and books on historical and scientific subjects. They engage with and respond to what the text says explicitly through oral and/or written language – including illustrations. By the end of second grade, students should be able to fluently read and demonstrate understanding of grade appropriate text.
By engaging in a writing process, they use writing to convey ideas, develop real or imagined experiences, and write opinion pieces on familiar topics. They revise and edit writing to attend to focus, content, organization, style, and conventions of language.
In the initial years of elementary school, children work with numbers and quantities using concrete materials and explore with and describe shapes. They represent quantities, compare amounts, and classify objects. Student’s model putting quantities together and taking them apart, which develops an understanding of addition and subtraction. Measuring skills will also be explored.
By the end of second grade, students use place value to understand number relationships, can quickly recall facts and use them to solve problems, and apply models for addition and subtraction as well as building arrays as a foundation for multiplication. Students measure using standard units, work with beginning ideas of time and money, describe shapes by examining their sides and angles, and partition shapes into equal-sized pieces.
Students will be engaged in these foundational concepts through the Standards of Mathematical Practice: by making sense of problems, reasoning and explaining, modeling and using tools, and recognizing and extending patterns with concrete materials and numbers. Through engaging in these practices, students will build confidence in themselves as productive mathematical thinkers.
To build a foundation for college and career readiness, students must read widely and deeply from a range of high-quality, increasingly challenging literary and informational texts. Students build literary and culture knowledge as they engage in extensive reading of stories, dramas, poems, and myths. Students read a broad range of informational texts that contribute to their understanding of specific content while providing them with a background to become better readers in all content areas.
Students are expected to read grade-appropriate complex text independently within their grade span. The cognitive demands of students increases throughout these grade levels, moving from describing text elements towards critically examining and analyzing literary and informational content within and among multiple texts.
Students need to learn to use writing as a way of offering and supporting opinions, demonstrating understanding of the subjects they are studying, and conveying real and imagined experiences and events. They understand that writing is way to communicate to multiple audiences and adapt the form and content of their writing to accomplish a specific purpose. Students must devote a significant time and effort to writing, producing numerous pieces over short and extended timeframes throughout the year.
During this grade span, students learn strategies for establishing credibility such as supporting opinions with evidence and citing textual evidence to support their answers and ideas. Students write in all content areas and move beyond participating in research to conducting research. They increasingly use technology and multi-media sources to research, produce and publish their writing.
In grades 3-5, students develop an understanding of and fluency with all four operations and extend their knowledge to 2-digit divisors and decimals to the hundredths. An understanding of fractions ranges from unit fractions to fraction equivalency, culminating with developing fluency with addition and subtraction of fractions, as well as an understanding of multiplication and division of fractions.
Geometry involves analyzing, comparing, and classifying geometric figures by their attributes, including sides and angles. The concept of geometric measurement develops as students move from an understanding of the structure of rectangular arrays, area, and perimeter to the conceptual understanding of volume.
In addition, students explore the concepts of measurement, including conversion of units, elapsed time, money, data, and patterns, metric and standard units.
Students use structures to convey ideas in the format most appropriate for the purpose and audience, using stylistic aspects of composition including complex sentences, voice, and formal academic style. They write logical arguments without personal opinions and judgments while citing credible sources and acknowledging counterclaims. Crucial in this grade band is the integration of information from different media sources including, quotes/paraphrasing, and citing accurate bibliographic information while avoiding plagiarism.
Students analyze and evaluate the central idea, to make generalizations, and to recognize the importance of author’s choice in point of view and structure. Analysis is to be done across genres, texts, and authors. Students must generate original questions in order to fully understand how plot and theme unfold, to recognize and manipulate shifts in time and place, and to explain how literary elements work together in narrative text.
Students will build on their understanding of whole number multiplication and division connecting ratio and rate to solve problems. They will develop an understanding of and apply proportional relationships. Students will relate this understanding of ratios and proportions to extend the notion of numbers to the system of rational numbers, which includes negative numbers, and irrational numbers.
Students will formulate and reason about expressions and equations by modeling data with linear equations and systems of linear equations. This will progress to a concept of functions and develop an understanding of functions to describe quantitative relationships. They will work with two- and three- dimensional shapes to solve problems involving area, surface area, and volume. Students will develop an understanding of statistical thinking and draw inferences about populations based on samples.
At this level, it is expected that students will be critical consumers of text and other media and demonstrate independence as readers and writers and engage in collaborative discussions while expressing themselves clearly.
Text shifts to a larger proportion of informational text including - moving from seminal U.S. documents of historical and literary significance to foundational U.S. and world documents of historical, political, and literary significance. Students have an awareness of author’s effectiveness, explicit and implicit assumptions and beliefs, purpose, style and the progression of over the course of a text.
As writers, students exhibit a sharp distinct focus identifying topic, task, and audience. Writing addresses specific tasks, purposes, perspectives, and intended audience. Both informational and argumentative writing reflect research and evidence to create a clear and coherent message.
Upon graduation, students possess the knowledge and skills needed for success in college and careers.
Numerical skill and quantitative reasoning remain crucial even as students move forward with algebra. Algebra, Functions, and Geometry are important not only as mathematical subjects in themselves but also because they are the language of technical subjects and the sciences. In a data-rich world, statistics and probability offer powerful ways of drawing conclusions from data and dealing with uncertainty.
The high school standards are organized into six major content areas: Number and Quantity; Algebra; Functions; Modeling; Geometry; and Statistics and Probability. These standards emphasize making connections, representations, and interpretations. Modeling is used to analyze real-world situations and links classroom mathematics and statistics to everyday life, work, and decision-making. Technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.
Upon graduation, students will have developed a depth of understanding and ability to apply mathematics to novel situations such as: quantities and their relationships in physical, economic, public policy. Social and everyday situations can be modeled using mathematical and statistical methods.