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 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.

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.

In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The full year of Algebra I curriculum is available below.

In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The Geometry curriculum is available below.

The following chart displays the array of inquiries being developed for each grade level. By viewing the topics for each inquiry, curriculum teams can begin planning their work to develop additional inquiries for the remaining grade-level topics.

The following chart displays the array of inquiries being developed for each grade level. By viewing the topics for each inquiry, curriculum teams can begin planning their work to develop additional inquiries for the remaining grade-level topics.

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 Pascal’s 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.