In this 12-day Grade 2 module, students engage in activities designed to deepen their conceptual understanding of measurement and to relate addition and subtraction to length.  Their work in Module 2 is exclusively with metric units in order to support place value concepts.  Customary units will be introduced in Module 7.

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

This workbook was created by mathematics instructors at Scottsdale Community College in Scottsdale, Arizona. It is designed to lead students through Intermediate Algebra, and to help them develop a deep understanding of the concepts. The included curriculum is broken into twelve lessons.

Developed by the NYCDOE CS education team, the Introduction to Physical Computing course is a 54-hour long introductory computer science course that guides students to explore fundamental CS concepts through tinkering with the micro:bit, a simple programmable computer device. Each unit of the course guides students through the learning process with three practices: analyzing computer applications around them based on a given issue; prototyping a project that reflects the result of the analysis plus their interest; and communicating about their projects, including the functionality of a project, a project development process, influence from other projects and their contribution to a project when working in a group. The curriculum and support sessions assist educators in discovering the most effective way of facilitating this course for their own classroom, while helping them to become comfortable with the main tool, the micro:bit.

Comprehensive coverage of core concepts grounded in both classic studies and current and emerging research, including coverage of the DSM-5 in discussions of psychological disorders. Incorporates discussions that reflect the diversity within the discipline, as well as the diversity of cultures and communities across the globe.

Introduction to Sociology adheres to the scope and sequence of a typical introductory sociology course. In addition to comprehensive coverage of core concepts, foundational scholars, and emerging theories, we have incorporated section reviews with engaging questions, discussions that help students apply the sociological imagination, and features that draw learners into the discipline in meaningful ways. Although this text can be modified and reorganized to suit your needs, the standard version is organized so that topics are introduced conceptually, with relevant, everyday experiences.

Introductory Statistics is intended for the one-semester introduction to statistics course for students who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermediate algebra. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a Try It problem that is designed as extra practice for students. This book also includes collaborative exercises and statistics labs designed to give students the opportunity to work together and explore key concepts. While the book has been built so that each chapter builds on the previous, it can be rearranged to accommodate any instructor’s particular needs.

Macroeconomics provides an introduction to economic principles and market forces including supply and demand, unemployment, inflation, international trade and capital flows, monetary policy and banking, fiscal policy and globalization.

Expressions

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Write and evaluate simple expressions that record calculations with numbers.
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.
Interpret numerical expressions without evaluating them.

Lesson Flow

Students learn to write and evaluate numerical expressions involving the four basic arithmetic operations and whole-number exponents. In specific contexts, they create and interpret numerical expressions and evaluate them. Then students move on to algebraic expressions, in which letters stand for numbers. In specific contexts, students simplify algebraic expressions and evaluate them for given values of the variables. Students learn about and use the vocabulary of algebraic expressions. Then they identify equivalent expressions and apply properties of operations, such as the distributive property, to generate equivalent expressions. Finally, students use geometric models to explore greatest common factors and least common multiples.

Students critique the work of other students and revise their own work based on feedback from the teacher and peers.Key ConceptsConcepts from previous lessons are integrated into this unit task: rewriting expressions, using parentheses, and using the distributive property. Students apply their knowledge, review their work, and make revisions based on feedback from you and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply knowledge of expressions to correct the work of other students.Track and review the choice of strategy when problem solving.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

Students explore the effects of wind on a plane's time and distance and represent these situations using algebraic expressions and equations. They use terms with positive, negative, and zero coefficients.Key ConceptsIn this lesson, students show what they remember from Grade 6 about writing expressions and solving one-step equations. They use what they learned earlier in Grade 7 about adding and subtracting integers. They extend these concepts to write and interpret an expression with a negative coefficient.Goals and Learning ObjectivesReview addition and subtraction of integers.Review the relationship between distance, time, and speed.Write an algebraic expression for distance in terms of time, t.Write a term with a negative coefficient.Review solving a one-step equation using the multiplication property of equality.

Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Students will complete the first part of their project, deciding on two right prisms for their models of buildings with polygon bases. They will draw two polygon bases on grid paper and find the areas of the bases.Key ConceptsProjects engage students in the application of mathematics. It is important for students to apply mathematical ways of thinking to solve rich problems. Students are more motivated to understand mathematical concepts if they are engaged in solving a problem of their own choosing.In this lesson, students are challenged to identify an interesting mathematical problem and choose a partner or a group to work collaboratively on solving that problem. Students gain valuable skills in problem solving, reasoning, and communicating mathematical ideas with others.GoalsSelect a project shape.Identify a project idea.Identify a partner or group to work collaboratively with on a math project.SWD: Consider how to group students skills-wise for the project. You may decide to group students heterogeneously to promote peer modeling for struggling students. Or you can group students by similar skill levels to allow for additional support and/or guided practice with the teacher. Or you may decide to create intentional partnerships between strong students and struggling students to promote leadership and peer instruction within the classroom.ELL: In forming groups, be aware of your ELLs and ensure that they have a learning environment where they can be productive. Sometimes, this means pairing them up with English speakers, so they can learn from others’ language skills. Other times, it means pairing them up with students who are at the same level of language skill, so they can take a more active role and work things out together. Other times, it means pairing them up with students whose proficiency level is lower, so they play the role of the supporter. They can also be paired based on their math proficiency, not just their language proficiency.

Gallery 2Allow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need to review the unit’s concepts or have fallen behind on work.Gallery OverviewOne World Trade CenterThis task gives students an opportunity to further explore figures that have been intersected by a plane. The task also allows students to revisit scale and think about the net of a sliced prism.Sketch ThreeThis task extends students’ knowledge of nets as they think about surfaces that are triangular and won’t line up parallel. Students may need to use a protractor to keep the angles of the sides consistent.Partial Cube NetThis task provides students with further experience in thinking about the revealed surface in a sliced prism, constructing a more complex net, and estimating area based on area formulas and measuring.Round PrismsThis task extends students’ knowledge of prism measurement to cylinders, which are really no different. Students will see that the only difference is that the base is circular, and they know how to find the circumference (perimeter) and area.Project Work TimeStudents may use a Gallery day to work on their projects and get help if needed.Cube Volume and NetsUsing the 2-D/3-D tool or the parallelogram cubes, students create a solid made of cubes. Using the 2-D views as a guide, they make a net for the figure and find its surface area. Students are challenged to make the net with one piece of paper.Same Surface Area, Different VolumeStudents create two solids with the same surface area but very different volumes. They that surface areas are the same by drawing the 2-D views.Tree House 2This task gives students further practice making a scale drawing and thinking about the net of a solid. Students should also realize that the plans for a building are the 2-D views of the building and are similar to a net.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

En este módulo de grado 2 de 12 días, los estudiantes participan en actividades diseñadas para profundizar su comprensión conceptual de la medición y para relacionar la suma y la rest sometida a la longitud. Su trabajo en el Módulo 2 está exclusivamente con unidades métricas para respaldar conceptos de valor de lugar. Las unidades habituales se introducirán en el Módulo 7.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
In this 12-day Grade 2 module, students engage in activities designed to deepen their conceptual understanding of measurement and to relate addition and subtraction to length.  Their work in Module 2 is exclusively with metric units in order to support place value concepts.  Customary units will be introduced in Module 7.

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

Newtonian Mechanics whereby fundamental concepts (momentum, energy, force, motion) are introduced on the first day and developed in parallel. Access entire curriculum: comprehensive lecture videos with questions, textbook (calculus based, algebra based, and conceptual), exams, syllabus, past student evaluations.

Full Curriculum, Newtonian Mechanics whereby fundamental concepts (momentum, energy, force, motion) are introduced on the first day and developed in parallel. Access entire curriculum: comprehensive lecture videos with questions, textbook (calculus based, algebra based, and conceptual), exams, syllabus, past student evaluations.

Newtonian Mechanics whereby fundamental concepts (momentum, energy, force, motion) are introduced on the first day and developed in parallel. Access entire curriculum: comprehensive lecture videos with questions, textbook (calculus based, algebra based, and conceptual), exams, syllabus, past student evaluations.