This site teaches Expressions and Equations to 8th graders through a series of 4712 questions and interactive activities aligned to 32 Common Core mathematics skills.
This site teaches Functions to 8th graders through a series of 1920 questions and interactive activities aligned to 17 Common Core mathematics skills.
This site teaches Geometry to 8th graders through a series of 2398 questions and interactive activities aligned to 19 Common Core mathematics skills.
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
This site teaches Statistics and Probability to 8th graders through a series of 303 questions and interactive activities aligned to 5 Common Core mathematics skills.
This site teaches The Number System to 8th graders through a series of 676 questions and interactive activities aligned to 6 Common Core mathematics skills.
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
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.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
Students construct a model roadway with congestion and apply their knowledge of level of service (LOS) to assign a grade to the road conditions. The roadway is simply a track outlined with cones or ropes with a few students walking around it to mimic congestion. The remaining students employ both techniques of density and flow to classify the LOS of the track.
Fundamental principles of biochemistry. Analysis of the mode of action and structure of regulatory, binding, and catalytic proteins. The tools and analytical methods that biochemists use to dissect biological problems. Analysis of the mode of action and structure of regulatory, binding, and catalytic proteins.
Pite Saami is a highly endangered Western Saami language in the Uralic language family currently spoken by a few individuals in Swedish Lapland. This grammar is the first extensive book-length treatment of a Saami language written in English. While focussing on the morphophonology of the main word classes nouns, adjectives and verbs, it also deals with other linguistic structures such as prosody, phonology, phrase types and clauses. Furthermore, it provides an introduction to the language and its speakers, and an outline of a preliminary Pite Saami orthography. An extensive annotated spoken-language corpus collected over the course of five years forms the empirical foundation for this description, and each example includes a specific reference to the corpus in order to facilitate verification of claims made on the data. Descriptions are presented for a general linguistics audience and without attempting to support a specific theoretical approach, but this book should be equally useful for scholars of Uralic linguistics, typologists, and even learners of Pite Saami.