"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.

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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.

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"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.

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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 technology 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.

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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.

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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.

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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.

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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 the first chapter of W.E.B. Du Bois€' The Souls of Black Folk.

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.

Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

The Skills Strand teaches the mechanics of reading. Students 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 "Kits Hats" with illustrations is provided for instruction.

Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

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.

Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

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 Commencement Address Steve Jobs delivered at Stanford University on June, 2005.

Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

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: Nursery Rhymes and Fables; Five Senses; Stories; Plants; Farms; Kings and Queens; Seasons and Weather; Colonial Towns; and Taking Care of the Earth.

Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

The Skills Strand teaches the mechanics of reading. Students 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 "Kits Hats" with illustrations is provided for instruction.

Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

EngageNY.org is developed and maintained by the New York State Education Department (NYSED) to support the implementation of key aspects of the New York State Board of Regents Reform Agenda. This is the official web site for current materials and resources related to the Regents Reform Agenda. The agenda includes the implementation of the New York State P-12 Common Core Learning Standards (CCLS), Teacher and Leader Effectiveness (TLE), and Data-Driven Instruction (DDI). EngageNY.org is dedicated to providing educators across New York State with real-time, professional learning tools and resources to support educators in reaching the State‰ŰŞs vision for a college- and career-ready education for all students.

Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2.  To be able to discuss similarity, students must first have a clear understanding of how dilations behave.  This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria.  An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry.

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Module 3, Extending to Three Dimensions, builds on students’ understanding of congruence in Module 1 and similarity in Module 2 to prove volume formulas for solids. The student materials consist of the student pages for each lesson in Module 3. The copy ready materials are a collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials.

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This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year.  It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story.  This module's focus is on the possible geometric relationships between a pair of intersecting lines and a circle drawn on the page.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.