Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.

Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

In this module, students synthesize and generalize what they have learned about a variety of function families.  They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4).  They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions.  They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3).  Students identify appropriate types of functions to model a situation.  They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit.  The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module.  In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.

Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and techonolgy to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.

This exemplar has been developed to guide high school students and instructors in a close reading of Lincoln's Gettysburg Address. The activities and actions described below follow a carefully developed set of steps that assist students in increasing their familiarity and understanding of Lincoln's speech through a series of text dependent tasks and questions that ultimately develop college and career ready skills identified in the Common Core State Standards. This unit can be broken down into three sections of instruction and reflection on the part of students and their teachers, which is followed by additional activities, some designed for history/social studies and some for ELA classrooms.his close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students.

By reading and rereading the passage closely and focusing their reading through a series of questions and discussion about the text, students will be equipped to unpack Dillard's essay. When combined with writing about the passage, students will learn to appreciate how Dillard's writing contains a deeper message and derive satisfaction from the struggle to master complex text. This close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students. Additional teacher background material: http://teachers.sduhsd.k12.ca.us/lcaston/documents/WeaselsEssayAnal.pdf

This close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. This exemplar features the following: readings tasks in which students are asked to read and reread passages and respond to a series of text dependent questions; vocabulary and syntax tasks which linger over noteworthy or challenging words and phrases; discussion tasks in which students are prompted to use text evidence and refine their thinking; and writing tasks that assess student understanding of the text. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students.

The goal of this exemplar is to reinforce the skills students have acquired regarding how to extend their understanding and interaction with multiple texts when investigating a set of focused historical themes. This close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students.

By reading and rereading the passage closely combined with classroom discussion about it, students will explore the historical truths related to poverty, city construction, and city services that led to the disaster. In this reading, students learn about historical disasters, but they may not fully comprehend causes or how human actions, nature, or even luck contributed to them, rendering history a flat subject to be memorized rather than explored. When combined with writing about the passage and teacher feedback, students will better understand the dangers inherent in cities and the government role in mitigating that danger. This close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students.

By reading and re-reading the text passage, closely combining classroom discussion about it, and writing about it, students come to an appreciation of the need to (a) re-read, paraphrase, and discuss ideas, (b) come to an accurate basic understanding level of a text, (c) come to an accurate interpretive understanding of a text, and (d) build a coherent piece of writing that both constructs and communicates solid understanding of text. This close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students.

The goal of this two to three day exemplar is to give students the opportunity to use the reading and writing habits theyve been practicing on a regular basis to absorb deep lessons from Richard Feynmans recollections of interactions with his father. By reading and rereading the passage closely, and focusing their reading through a series of questions and discussion about the text, students will identify how and why Feynman started to look at the world through the eyes of a scientist. When combined with writing about the passage, students will discover how much they can learn from a memoir. This close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students.

By reading and re-reading the Constitutional passages closely combined with classroom discussion about it, students will explore the questions Monk raises and perhaps even pursue additional avenues of inquiry. When combined with writing about the passage and teacher feedback, students will form a deeper appreciation not only of MonkŐs argument and the value of struggling with complex text, but of the Preamble of the Constitution itself. This close reading exemplar is intended to model how teachers can support their students as they undergo the kind of careful reading the Common Core State Standards require. Teachers are encouraged to take these exemplars and modify them to suit the needs of their students.

Making Evidence-Based Claims ELA/Literacy Units empower students with a critical reading and writing skill at the heart of the Common Core: making evidence-based claims about complex texts. These units are part of the Developing Core Proficiencies Program. This unit develops students' abilities to make evidence-based claims through activities based on a close reading of the Nobel Peace Prize Speeches of Rev. Dr. Martin Luther King, Jr. and President Barack Obama.

Making Evidence-Based Claims ELA/Literacy Units empower students with a critical reading and writing skill at the heart of the Common Core: making evidence-based claims about complex texts. These units are part of the Developing Core Proficiencies Program. This unit develops students€' abilities to make evidence-based claims through activities based on a close reading of President Ronald Reagan€'s First Inaugural Address and Secretary Hillary Clinton€'s 2011 APEC Address.

The goal of the Listening and Learning Strand is for students to acquire language competence through listening, specifically building a rich vocabulary, and broad knowledge in history and science by being exposed to carefully selected, sequenced, and coherent read-alouds. The 9 units (or domains) provide lessons (including images and texts), as well as instructional objectives, core vocabulary, and assessment materials. The domain topics include: Different Lands, Similar Stories; Fables and Stories; The Human Body; Early World Civilizations; Early American Civilizations; Astronomy; Animals & Habitats; Fairy Tales; and History of the Earth.

The Skills Strand teaches the mechanics of reading_Ŕstudents are taught systematic and explicit phonics instruction as their primary tool for decoding written English. By the end of grade 2, students have learned all of the sound_spelling correspondences in the English language and are able to decode written material they encounter. In addition to phonics, students also are taught spelling, grammar, and writing during the Skills Strand. A downloadable story "Jump!" with illustrations is provided for instruction.

This module ensures that students read, write, listen and speak to learn the history and contributions of Native Americans in New York State, particularly the Iroquois Confederacy. It focuses on reading and listening to primary and secondary sources to gather specific details and determine central ideas, and to reinforce reading fluency and paragraph writing. Students will read literature to develop an understanding of setting, characterization and theme, and informational writing.