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.
This inquiry examines the 20th century history of migration from Mexico to the United States and recent efforts to limit the movement of people across the southern U.S. border. The inquiry takes its inspiration from a 2018 podcast episode by Malcom Gladwell titled, “General Chapman’s Last Stand.” The podcast is part of Gladwell’s Revisionist History series (http://revisionisthistory.com). In the podcast, Gladwell tells the story of General Leonard F. Chapman Jr., Commandant of the Marine Corps during the Vietnam War, who went on to serve as the Commissioner of the Immigration and Naturalization Service (INS) from 1972 to 1975. Chapman is credited with reforming the INS into a more efficient and effective agency, but Gladwell argues that Chapman’s efforts also led to an unintentional increase in unauthorized immigrants. In 1970, 760,000 Mexican immigrants, or 1.4% of Mexico’s population, lived in the U.S. By 2008, there were 12.7 million Mexican immigrants in the U.S. which amounted to 11% of all people born in Mexico; an increase of almost 800% in less than 30 years. The question of how and why this happened is the central focus of this inquiry.
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 StateŰŞs vision for a college- and career-ready education for all students.
This tenth grade annotated inquiry leads students through an investigation of the French Revolution. Adolescent students are quite concerned with challenging authority and establishing their independence within the world; the concept of revolution brings those two concerns to their most world-altering levels. This inquiry gives students an entry point into thinking like historians about the French Revolution. The question of success invites students into the intellectual space that historians occupy. By investigating the question of the French Revolution’s success, students will need to make decisions about what the problems of the Revolution were, how to give weight to the events of three different periods of the Revolution, and what distance, if any, was between intentions and effects.
Module 1A focuses on building community by making connections between visual imagery, oral accounts, poetry and written texts of various cultures with a focus on the Haudenosaunee (Iroquois) culture. Students will determine a central idea and demonstrate how gathering information from a variety of sources can help us understand a central idea more fully.| Module 1 also reinforces reading fluency, close text analysis, explanatory paragraph writing, and presenting to peers. The module reinforces the fact that Native Americans—specifically the Iroquois (Haudenosaunee, People of the Longhouse) —were early inhabitants of the New York region and state, and continue to contribute to the region’s history.
In this module, students explore the concept of personal identity formation and transformation in both historical and modern-day societies. The module begins with an overview of what “identity” means and how it can mean different things to different people. In Unit 1, students read first-person narratives that focus on various social identifiers—from race to gender to socioeconomic status—as they begin to frame their understanding of what identity means. Students read informational text, identifying central ideas, analyzing how an author develops his or her claims, and identifying how the sections of the text interact to form those ideas.
In this module, students analyze arguments and the evidence used to support arguments to determine whether sufficient evidence has been used and whether the evidence is relevant in support of the claim an author or speaker is making. They then research to gather evidence to make their own spoken and written arguments. Students will read Michael Pollan’s The Omnivore’s Dilemma (930L), a literary non-fiction text about where food comes from and about making decisions about what food to buy and eat. They build background knowledge about what happens to food before it gets to the consumer, and the different choices the consumer can make when buying food while analyzing Michael Pollan’s arguments and the evidence he uses to support his claims. In Unit 2, students engage in a robust research project in which they further investigate the consequences of each of the food chains and the stakeholders affected in those food chains. To help students grapple with this issue, they use a decision-making process called “Stakeholder Consequences Decision-Making” (see the end of this document for details). This process will help students understand the implications of various choices, and will scaffold their ability to determine, based on evidence and their own values, to take a position on which food chain they would choose if they were trying to feed everyone in the US. Students finish the module by writing a position paper explaining which of Michael Pollan’s food chain they would choose to feed the US and why, and creating a poster stating their position. This task addresses NYSP12 ELA Standards RI.8.1,W.8.1, W.8.1a, W.8.1b, W.8.1c, W.8.1d, W.8.1e and W.8.9.
In Grade 8 Module 1, students expand their basic knowledge of positive integer exponents and prove the Laws of Exponents for any integer exponent. Next, students work with numbers in the form of an integer multiplied by a power of 10 to express how many times as much one is than the other. This leads into an explanation of scientific notation and continued work performing operations on numbers written in this form.
In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.
In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles. The module begins with the definition of dilation, properties of dilations, and compositions of dilations. One overarching goal of this module is to replace the common idea of same shape, different sizes with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.
In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.
In the first topic of this 15 day module, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. Once a formal definition of a function is provided, students then consider functions of discrete and continuous rates and understand the difference between the two. Students apply their knowledge of linear equations and their graphs from Module 4 to graphs of linear functions. Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line. They learn to interpret the equation y=mx+b as defining a linear function whose graph is a line. Students compare linear functions and their graphs and gain experience with non-linear functions as well. In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve real-world and mathematical problems related to volume from simple solids to include problems that require the formulas for cones, cylinders, and spheres.
In Grades 6 and 7, students worked with data involving a single variable. Module 6 introduces students to bivariate data. Students are introduced to a function as a rule that assigns exactly one value to each input. In this module, students use their understanding of functions to model the possible relationships of bivariate data. This module is important in setting a foundation for students work in algebra in Grade 9.
Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons 13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle. In cases where the side length was an integer, students computed the length. When the side length was not an integer, students left the answer in the form of x2=c, where c was not a perfect square number. Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general.
In this module, students will read, discuss, and analyze contemporary and classic texts, focusing on how complex characters develop through interactions with one another and how authors structure text to accomplish that development. There will be a strong emphasis on reading closely and responding to text dependent questions, annotating text, and developing academic vocabulary in context.
In this module, students engage with literature and nonfiction texts that develop central ideas of guilt, obsession, and madness, among others. Building on work with evidence-based analysis and debate in Module 1, students will produce evidence-based claims to analyze the development of central ideas and text structure. Students will develop and strengthen their writing by revising and editing, and refine their speaking and listening skills through discussion-based assessments.
In Module 9.3, students engage in an inquiry-based, iterative process for research. Building on work with evidence-based analysis in Modules 9.1 and 9.2, students explore topics of interest, gather research, and generate an evidence-based perspective to ultimately write an informative/explanatory research paper that synthesizes and articulates their findings. Students use textual analysis to surface potential topics for research, and develop and strengthen their writing by revising and editing.
In this module, students read, analyze and evaluate informational and argument writing and build, through focused instruction, the skills required to craft strong and well-supported argument writing of their own. Through the study of a variety of texts, students learn to think of the products they use and consume everyday as part of a complex web of global production and trade that extends not only to distant lands but to the past as well.
Module 2 explores two-dimensional and three-dimensional shapes. Students learn about flat and solid shapes independently as well as how they are related to each other and to shapes in their environment. Students begin to use position words when referring to and moving shapes. Students learn to use their words to distinguish between examples and non-examples of flat and solid shapes.
After students observed, analyzed, and classified objects by shape into pre-determined categories in Module 2, they now compare and analyze length, weight, volume, and, finally, number in Module 3. The module supports students understanding of amounts and their developing number sense. The module culminates in a three-day exploration, one day devoted to each attribute: length, weight, and volume.
Module 4 marks the next exciting step in math for kindergartners, addition and subtraction! They begin to harness their practiced counting abilities, knowledge of the value of numbers, and work with embedded numbers to reason about and solve addition and subtraction expressions and equations. In Topics A and B, decomposition and composition are taught simultaneously using the number bond model so that students begin to understand the relationship between parts and wholes before moving into formal work with addition and subtraction in the rest of the module.
Kindergarten comes to a close with another opportunity for students to explore geometry in Module 6. Throughout the year, students have built an intuitive understanding of two- and three-dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area through composition of geometric figures.
Up to this point in Grade K, students have worked intensively within 10 and have often counted to 30 using the Rekenrek during fluency practice. This work sets the stage for this module where students clarify the meaning of the 10 ones and some ones within a teen number and extend that understanding to count to 100.
Module 1 of the Kindergarten curriculum in A Story of Units. In Topics A and B, classification activities allow students to analyze and observe their world and articulate their observations. Reasoning and dialogue begin immediately. In Topics C, D, E, and F, students order, count, and write up to ten objects to answer how many? questions from linear, to array, to circular, and finally to scattered configurations wherein they must devise a path through the objects as they count. In Topics G and H, students use their understanding of relationships between numbers and know that each successive number name refers to a quantity that is one greater and that the number before is one less.
This document provides opportunities for students to gain fluency in middle grades math. They are aligned to the Common Core Standards.
This annotated kindergarten inquiry focuses on the economics concept of scarcity by developing an understanding of needs and wants and goods and services through the compelling question, “Can we ever get everything we need and want?” The distinctions between these constructs serve as the necessary components of an examination of the choices people must make when faced with potential limitations.
Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the study of complex numbers and linear transformations in the complex plane. The teacher materials consist of the teacher pages including exit tickets, exit ticket solutions, and all student materials with solutions for each lesson in Module 1.
Module 2 extends the concept of matrices introduced in Module 1. Students look at incidence relationships in networks and encode information about them via high-dimensional matrices. Matrix properties are studied as well as the role of the zero and identity matrices. Students then use matrices to study and solve higher order systems of equations. Vectors are introduced, and students study the arithmetic of vectors and vector magnitude. The module ends as students program video games using matrices and vectors.
Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascals Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions.
This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced for solving geometric and modeling problems through the power of trigonometry. Students explore sine, cosine, and tangent functions and their periodicity, derive formulas for triangles that are not right, and study the graphs of trigonometric functions and their inverses.
In this module, students build on their understanding of probability developed in previous grades. In Topic A the multiplication rule for independent events introduced in Algebra II is generalized to a rule that can be used to calculate probability where two events are not independent. Students are also introduced to three techniques for counting outcomes. Topic B presents information related to random variables and discrete probability distributions. Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts.
In the first half of this module, students identify measurable attributes of objects in terms of length, weight, and capacity. Students learn words such as small, big, short, tall, empty, full, heavy, and light so that they will have the vocabulary needed to describe objects (PK.MD.1). The comparison of length, weight, and capacity naturally leads to discussions about quantity and number. In the second half, measurement is connected to quantity as students reason if there are enough, more than, less than, or the same number of objects in a set using matching and counting strategies (PK.CC.5). Comparing concrete sets leads to comparing quantities and abstract numbers. Children will also focus on identifying first and last in quantities up to 5 and 10 in different configurations (PK.CC.6).
Module 5 is the culmination of childrens work with number in the Pre-K year. Throughout Modules 1 and 3, they had extensive counting experiences with numbers 010. In Module 4, they examined the relationships between numbers 15 through comparison. In Module 5, children transition from the comparative concept of more (4 apples is more than 1 apple) to the concept of addition (3 apples and 1 more apple make 4 apples). They are ready to begin work with operations, focusing on addition and subtraction stories with numbers 1 to 5. Students will also learn to write numerals 0-5 and explore patterns in this final module.
Module 1 capitalizes on the energy and excitement young students have as they enter their first day of Pre-K by providing a playful and active yet carefully sequenced structure through which children progress. In this module, we set up a friendly learning environment in which children have sustained interaction with four core ideas, collectively referred to as the number core: rote counting (the number word list), one-to-one correspondence (one object paired with one number word), cardinality (how many in a set), and written numerals. Throughout the module, children have experiences that help them make critical connections between these four understandings.
In Module 2, in the context of classroom play, children learn to identify, describe, sort, compare, and create two-dimensional (2-D) and three-dimensional (3-D) shapes and objects. Children develop vocabulary to describe the relative position of objects (e.g., top, bottom, up, down, in front of, behind, over, under, and next to), building foundational spatial reasoning abilities. In Module 1, students developed an understanding of numbers to 5. In Module 2, students practice these counting skills in the context of geometry (counting sides, corners, a group of triangles, etc.).
Module 3 challenges students to build on their work with numbers through 5 to make sense of and count groups of 0, 6, 7, 8, 9, and 10 objects. Students also continue their work with the number core in the following ways (PK.CC.14): Rote counting (the number word list up to 15); one-to-one correspondence (one object paired with one number word from 0 to 10); cardinality (how many in a set of up to 10 objects); andnumber recognition (matching written numerals 0, 6, 7, 8, 9, and 10 to quantities). Throughout the module, children participate in engaging experiences that help them make critical connections between these four understandings.
This seventh grade annotated inquiry provides students with an opportunity to explore how words affect public opinion through an examination of Harriet Beecher Stowe’s novel Uncle Tom’s Cabin. Students will investigate historical sources related to the novel and reactions in the North and South in order to address the compelling question, “Can words lead to war?” This query takes advantage of the mixed messages students often receive about the power of words. Students’ understanding about how words can make a difference is often grounded in discussions of words used to bully, instead of the power of words to encourage reform. This is an ANNOTATED inquiry with additional information on the questions, tasks, and sources within.