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Christopher Hammond, Professor of Mathematics at Connecticut College, published The Art of Analysis, an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.

The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply a special case of integrability, with particular properties that are worth noting. This point of view has implications for the treatment of other topics, particularly continuity and differentiability.

Subject:
Mathematics
Material Type:
Textbook
Provider:
Connecticut College
Author:
Christopher Hammond
08/19/2022
Unrestricted Use
CC BY
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0.0 stars

This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)

Subject:
Calculus
Functions
Mathematics
Material Type:
Assessment
Full Course
Syllabus
Textbook
Provider:
The Saylor Foundation
04/16/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

CK-12 Calculus Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Calculus Student Edition. The solution guide is available upon request.

Subject:
Calculus
Functions
Mathematics
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Dreyfuss, Andrew
Narasimhan, Ramesh
Prolo, Jared
06/24/2011
Conditional Remix & Share Permitted
CC BY-SA
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0.0 stars

Subject:
Applied Science
Environmental Science
Technology
Material Type:
Lesson Plan
Provider:
Ohio State University College of Education and Human Ecology
Provider Set:
Beyond Penguins and Polar Bears: An Online Magazine for K-5 Teachers
Author:
Clarissa Reeson
Tracey Allen
10/17/2014
Only Sharing Permitted
CC BY-ND
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This lesson using activities to help students enjoy studying math revising rules ,vocab and their learning Knowledge .

Subject:
Mathematics
Material Type:
Game
01/20/2014
Conditional Remix & Share Permitted
CC BY-NC
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0.0 stars

This site explains how teachers can tier activities in their World Language classrooms. It includes background information about tiering, steps for teachers to develop tiered activities, and examples of tiered activities.

Subject:
Arts and Humanities
Languages
Material Type:
Teaching/Learning Strategy
Author:
Heather Sherrow
07/18/2018
Unrestricted Use
CC BY
Rating
0.0 stars

Differentiation in the Online Classroom is an interactive synchronous training for teachers. It explains why providing content appropriate for every individual is vital to students' success. This module provides ideas and methods for how to meet each students' needs.

Subject:
Education
Educational Technology
Material Type:
Teaching/Learning Strategy
Author:
Stephanie Prosser
Washington OSPI OER Project
Barbara Soots
06/25/2021
Unrestricted Use
CC BY
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This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Scientists have uncovered new details about endothelial cell differentiation that could lead to better management of vascular disease. Endothelial cells are often damaged in conditions like coronary artery disease. This damage can be repaired through the transplantation of healthy endothelial cells. But acquiring these cells at the quantities and purity needed for therapeutic transplantation is no easy task. To help solve this problem, the researchers took a closer look at the molecular factors that direct stem cells to adopt an endothelial phenotype. The team started by isolating mononuclear cells from just 1 mL of blood. They later reprogrammed these cells into induced pluripotent stem cells. To accomplish this, they used an optimized, non-integrating protocol – with very good results. The stem cells were then differentiated into endothelial cells, and the researchers tracked gene expression throughout the process..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

Subject:
Biology
Life Science
Material Type:
Diagram/Illustration
Provider:
Research Square
Provider Set:
Video Bytes
09/20/2019
Only Sharing Permitted
CC BY-NC-ND
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0.0 stars

In a multi-grade class of fourth, fifth, and sixth graders, students learn to work and communicate in teams. Through projects and a class structure that supports differentiation, Ms. Ehrke is able to keep students challenged and engaged. Her strategies for differentiation and communication can be used in any classroom.

Subject:
Arts and Humanities
Material Type:
Lesson Plan
Teaching/Learning Strategy
Provider:
Teaching Channel
Provider Set:
Teaching Channel
11/01/2012
Unrestricted Use
CC BY
Rating
0.0 stars

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Mesenchymal stem cells (MSCs) are multifunctional cells with the ability to reduce inflammation and repair tissue when injected directly. But MSC use is controversial, especially in patients with cancer or in cancer remission, as MSCs can release growth factors that can promote tumor growth. Fortunately, new research is showing that certain MSC contents can exert targeted beneficial effects without these drawbacks, most notably, microRNAs packaged inside exosomes. These loaded exosomes can accumulate at sites of tissue damage, and many studies suggest that MSC exosomes can be applied to cancer therapy, gene therapy, drug delivery, regenerative medicine, and other biomedical applications. Further research could reveal new and more effective ways of packaging and transferring exosomes from MSCs to recipient cells, and thereby lead to new methods of treating and monitoring various diseases..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

Subject:
Biology
Life Science
Material Type:
Diagram/Illustration
Provider:
Research Square
Provider Set:
Video Bytes
11/12/2020
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 1: Module 1 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 1: Module 2 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 1: Module 3 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 1: Module 4 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 2: Module 1 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 2: Module 2 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 2: Module 3 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade 2: Module 4 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade K: Module 1 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education
12/16/2019
Unrestricted Use
CC BY
Rating
0.0 stars

Grade K: Module 2 of the EL Education K-2 Reading Foundations Skills Block, part of the EL Education K-8 Language Arts Curriculum. The Skills Block provides one hour of structured phonics instruction, to be taught alongside Module Lessons and Labs. For more information on getting started with the K-2 Reading Foundations Skills Block, visit https://curriculum.eleducation.org/about-skills-blocks.

Subject:
English Language Arts
Material Type:
Module
Provider:
EL Education
Provider Set:
EL Education Language Arts Curriculum
Author:
EL Education