Grade 4 Module 2:  Unit Conversions and Problem Solving with Metric Measurement

Module 2 uses length, mass and capacity in the metric system to convert between units using place value knowledge.  Students recognize patterns of converting units on the place value chart, just as 1000 grams is equal 1 kilogram, 1000 ones is equal to 1 thousand.  Conversions are recorded in two-column tables and number lines, and are applied in single- and multi-step word problems solved by the addition and subtraction algorithm or a special strategy.  Mixed unit practice prepares students for multi-digit operations and manipulating fractional units in future modules. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 4 Module 3: Multi-Digit Multiplication and Division

In this 43-day module, students use place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students’ ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 4 Module 4: Angle Measure and Plane Figures

This 20-day module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and define these geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role in their work throughout the module, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures. In these problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning through the solving of an equation. Through decomposition and composition activities as well as an exploration of symmetry, students recognize specific attributes present in two-dimensional figures. They further develop their understanding of these attributes as they classify two-dimensional figures based on them. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 4 Module 5: Fraction Equivalence, Ordering, and Operations

In this 40-day module, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers.  This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models.  Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes.  Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 4 Module 6: Decimal Fractions

This 20-day module gives students their first opportunity to explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms.  Utilizing the understanding of fractions developed throughout Module 5, students apply the same reasoning to decimal numbers, building a solid foundation for Grade 5 work with decimal operations. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 4 Module 7: Exploring Measurement with Multiplication

In this 20-day module, students build their competencies in measurement as they relate multiplication to the conversion of measurement units.  Throughout the module, students will explore multiple strategies for solving measurement problems involving unit conversion. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 5 ELA Module 2B

In this eight-week module, students learn about new or improved technologies that have been developed to meet societal needs and how those inventions have changed people’s lives. They conduct authentic research to build their own knowledge and teach others through writing. In Unit 1, students read the graphic novel Investigating the Scientific Method with Max Axiom, Super Scientist by Donald B. Lemke as well as several informational articles about inventions that have been developed to meet people’s needs. Students learn about and analyze structures and visual elements authors use to convey complex ideas. Then, they will write a short opinion paragraph about which of the inventions they learned about has been most important to people and why. In Unit 2, students will read The Boy Who Invented TV: The Story of Philo Farnsworth by Kathleen Krull, focusing on how the television was invented to meet societal needs. Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

Material Type: Module

Grade 5 ELA Module 3B

In this module, students explore how native Inuit and other people of Canada have used the natural resources available to meet their needs. In Unit 1, students read The Inuit Thought of It: Amazing Arctic Innovations, by Alootook Ipellie with David MacDonald, to learn about how the native Inuit people of Canada used natural resources in the Arctic to adapt and meet the needs of their community hundreds of years ago. In Unit 2, students read and view a variety of informational texts and media, including graphs, charts, and maps, to examine how the resources available in Canada today are used to develop products that meet the needs and wants of people in Canada and throughout the Western Hemisphere. Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

Material Type: Module

Grade 5 ELA Module 4

This module engages students in a high-interest topic—natural disasters—with a literacy focus on point of view in literature, research, opinion writing, and public speaking. The module integrates science content (about extreme natural events) with a Social Studies focus on the Western Hemisphere and the role of multinational organizations. Find the rest of the EngageNY ELA resources at https://archive.org/details/engageny-ela-archive .

Material Type: Module

Grade 5 Math Module 1

In Module 1, students’ understanding of the patterns in the base ten system are extended from Grade 4’s work with place value of multi-digit whole numbers and decimals to hundredths to the thousandths place. In Grade 5, students deepen their knowledge through a more generalized understanding of the relationships between and among adjacent places on the place value chart, e.g., 1 tenth times any digit on the place value chart moves it one place value to the right. Toward the module’s end students apply these new understandings as they reason about and perform decimal operations through the hundredths place. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Activity/Lab, Assessment, Lesson Plan

Grade 5 Module 2:  Multi-Digit Whole Number and Decimal Fraction Operations

In Module 2 students apply patterns of the base ten system  to mental strategies and a sequential study of multiplication via area diagrams and the distributive property leading to fluency with the standard algorithm.  Students move from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products. Multiplication is explored as a method for expressing equivalent measures in both whole number and decimal forms.  A similar sequence for division begins concretely with number disks as an introduction to division with multi-digit divisors and leads student to divide multi-digit whole number and decimal dividends by two-digit divisors using a vertical written method.  In addition, students evaluate and write expressions, recording their calculations using the associative property and parentheses.  Students apply the work of the module to solve multi-step word problems using multi-digit multiplication and division with unknowns representing either the group size or number of groups.  An emphasis on the reasonableness of both products and quotients, interpretation of remainders and reasoning about the placement of decimals draws on skills learned throughout the module, including refining knowledge of place value, rounding, and estimation. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 5 Module 3: Addition and Subtraction of Fractions

In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Grade 5 Module 4: Multiplication and Division of Fractions and Decimal Fractions

Grade 5’s Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions.  Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication.  The module proceeds to fraction by fraction multiplication in both fraction and decimal forms.  An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa.  Students are introduced to the work of division with fractions and decimal fractions.  Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers.  Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients.  Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Common Core Curriculum: Kindergarten ELA: Skills Strand

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 .

Material Type: Diagram/Illustration, Reading

Common Core Curriculum: Grade 1 ELA: Skills Strand

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 .

Material Type: Diagram/Illustration, Reading

Grade 3 ELA Module 3B

In this eight-week module, students explore the questions: “Who is the wolf in fiction?” and “Who is the wolf in fact?” They begin by analyzing how the wolf is characterized in traditional stories, folktales, and fables. Then they research real wolves by reading informational text. Finally, for their performance task, students combine their knowledge of narratives with their research on wolves to write a realistic narrative about wolves.

Abnormal Psychology

This course is designed to provide an engaging and personally relevant overview of the discipline of Abnormal Psychology. You will examine the cognitive and behavioral patterns which impair personal effectiveness and adjustment. Students will provide much of the substantive content and teaching presence in this course. Additional content has been curated from "The Noba Project (http://nobaproject.com/)" and "Abnormal Psychology: An e-text! (http://abnormalpsych.wikispaces.com/). Openly-licensed course materials developed for the Open Educational Resources (OER) Degree Initiative, led by Achieving the Dream. https://courses.lumenlearning.com/catalog/achievingthedream

Material Type: Full Course, Homework/Assignment, Syllabus, Textbook

Author: Bill Pelz

Adopting Open Educational Resources in the Classroom

VCCS's "Pathways" Course provides faculty with an introduction to the laws that influence the use, re-use, and distribution of content they may want to use in a course. Activities include finding openly licensed content for use in a class and publishing openly licensed works created by faculty. At the end of the course, students will have openly licensed content that will be ready for use in a course.

Material Type: Full Course, Textbook

Author: Linda Williams

Applied Calculus

Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

Material Type: Full Course, Textbook

Authors: Dale Hoffman, David Lippman, Shana Calaway

Arithmetic for College Students

This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers model—integers are only introduced at the end of the course.

Material Type: Full Course, Textbook

Author: David Lippman