Students need many concrete experiences with fractions to develop a deep understanding of the three models of fractions: area, linear and set models. Teachers need to address all three models in well-designed instructional activities so that students develop a rich concept of fractions that they can use to make sense of numbers, operations, measurement and probability. The Math Tours include: activities, problem solving, games, writing to learn, templates, math-literature connections, and web links. Each page has a left navigation bar to easily take you through the tour and back to the homepage or the math topics page.

This website will help you understand and apply the Understanding by Design (UbD) or Backward Design planning process to develop equitable units of math instruction. The UbD content will draw from the work done by Grant Wiggins and Jay McTighe, digitalcommons@trinity.edu., OER Commons, other resources and from Granite State College math and methods instructors.

We will examine each of the 3 main stages of unit planning and apply these concepts to planning math instruction for K-12 students.

Word Count: 28360

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In this activity, a six-foot length of nylon rope is suspended at both ends to model a mathematical curve known as the hyperbolic cosine. In a write-pair-share activity, students are asked to make a conjecture concerning the nature of the curve and then embark on a guided discovery in which they attempt to determine a precise mathematical description of the curve using function notation.

This article explores how statistics can be interpreted in different ways to yield different conclusions. It describes the outcome and discussion of two class activities. In the first, the results are interpreted to "show" that taking a group rather than an individual perspective is ultimately beneficial to the individual. In the second, a variation is added "showing" that telling the truth is better that lying. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

This textbook attempts to provide you with an overview of the commonly used basic mathematical models, as well as a wide range of applications. It offers a perspective that brings you back to the modeling process and the assumptions that go into it.

Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. Version 3 of this book is almost identical to Version 2.1. The main change is that the preview activities in Version 2.1 have been renamed to beginning activities in Version 3. This was done to emphasize that these activities are meant to be completed before starting the rest of the section and are not just a short preview of what is to come in the rest of the section.

Short Description:
Mathematical Reasoning and Investigation is designed to help you develop the ability to use mathematics to solve the kinds of problems that don't come with answers in the back of the book. We like to think of it as a mathematics book for people who think they're not good at mathematics. The work will be useful for anyone wanting to develop their own skills in reasoning and problem solving using mathematics, and for teachers and preservice teachers hoping to help their students to develop these same skills.

Word Count: 36868

ISBN: 978-0-7300-0410-3

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This is a module framework. It can be viewed online or downloaded as a zip file.

It is as taught in 2009-2010.

This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration.

A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the associated theory, with a strong emphasis on rigorous proof.

This module is suitable for study at undergraduate level 2.

Dr Joel Feinstein, School of Mathematical Sciences

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.

A good way to learn to do math in English is to do math in English. The topics and materials should be accessible but engaging. This gives us incentive to make tangents into gambling, game theory, computers, art, and any other fields where we see connections. Interdisciplinary applied mathematics can be found within these pages.

This book was written for high school students in Japan studying English for Applied Purposes, so that they could potentially take math classes when studying abroad in the future. However, nothing in the book depends on the country.

Mathematics for Biomedical Physics is an open textbook, published by the Wayne State University Library System, geared to introduce several mathematical topics at the rudimentary level so that students can appreciate the applications of mathematics to the interdisciplinary field of biomedical physics. Most of the topics are presented in their simplest but rigorous form so that students can easily understand the advanced form of these topics when the need arises. Several end-of-chapter problems and chapter examples relate the applications of mathematics to biomedical physics. After mastering the topics of this book, students would be ready to embark on quantitative thinking in various topics of biology and medicine.

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.

The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:

• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.

• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).

• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.

Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.

Word Count: 49535

Included H5P activities: 1

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Word Count: 176231

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We will explore the mathematical strategies behind popular games, toys, and puzzles. Topics covered will combine basic fundamentals of game theory, probability, group theory, and elementary programming concepts. Each week will consist of a lecture and discussion followed by game play to implement the concepts learned in class.

The Mathematics of Nutrition Science is a workbook designed to integrate and contextualize developmental mathematics into an introductory college level Nutrition class. Definitions and skills from Community College Level Elementary Algebra and Quantitative Literacy courses are explained through examples analyzing the nutritional content of different foods. The book contains exercises for students to practice these skills, and also to reflect on the concepts through short writing assignments aligned with developmental English. These materials could be used by Nutrition course instructor in many different ways, and are designed to be self-contained and require minimal mathematical instruction.

Music & Math Using Supercollider

Word Count: 1861

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This paper makes recommendations for developing mathematics instruction for English Language Learners (ELLs) aligned with the Common Core State Standards. The recommendations can guide teachers, curriculum developers, and teacher educators as they develop their own ways of supporting mathematical reasoning and sense-making for ELLs.Some instructional recommendations discussed in the paper include: Focus on ELL students' mathematical reasoning, not the correctness of their mathematical language use. Shift to a focus on mathematical discourse practices; move away from simplified views of language. Support ELL students as they engage in complex mathematical language. Use ELL students' language and experiences as resources. Provide professional development to enhance teachers' awareness of ways to support ELs as they develop both language and mathematical knowledge.

Short Description:
The Math for Trades: Volume 2 textbook continues where the first volume left off. Volume 2 increases the challenge with topics such as converting units and working with equations, perimeter, area, and volume. Once again the material is presented from a trades perspective with easy-to-understand examples and videos explanations accompanying questions. The goal of this volume is to take the material you learned in Math for Trades: Volume 1 and apply it to more advanced topics that you may encounter during your trades training.

Long Description:
The Math for Trades: Volume 2 textbook continues where the first volume left off. Volume 2 increases the challenge with topics such as converting units, working with equations, perimeter, area and volume. Once again the material is presented from a trades perspective with easy-to-understand examples and videos explanations accompanying questions. The goal of this volume is to take the material you learned in Math for Trades: Volume 1 and apply it to more advanced topics that you may encounter during your trades training.

Word Count: 26548

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Short Description:
The Math for Trades: Volume 1 textbook represents the building blocks for math training. The book includes whole numbers, fractions, decimals, and percents. The material is presented from a trades perspective with easy-to-understand examples and video explanations accompanying questions. The goal of this volume is to get students prepared for the more advanced topics that they will encounter during their trades math education.

Word Count: 23344

ISBN: 978-1-77420-061-2

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