Ratio and Proportion

Ratio and Proportion

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  • Author: David Ben-Chaim
  • Publisher: Springer Science & Business Media
  • ISBN: 9460917844
  • Category : Education
  • Languages : en
  • Pages : 264

Ratio and Proportion—Research and Teaching in Mathematics Teachers’ Education offers its readers an intellectual adventure where they can acquire invaluable tools to turn teaching ratio and proportion to professionals and school children into an enjoyable experience. Based on in-depth research, it presents a deep, comprehensive view of the topic, focusing on both the mathematical and psychological-didactical aspects of teaching it. The unique teaching model incorporates both theoretical and practical knowledge, allowing instructors to custom-design teacher courses according to their speci?c needs. The book reports on hands-on experience in the college classes plus teachers’ experience in the actual classroom setting. An important feature is the extensive variety of interesting, meaningful authentic activities. While these activities are on a level that will engage pre- and in-service mathematics teachers in training, most can also be utilized in upper elementary and middle school classes. Accompanying the majority of these activities are detailed remarks, explanations, and solutions, along with creative ideas on how to conduct and expand the learning adventure. While primarily written for educators of mathematics teachers, this book can be an invaluable source of information for mathematics teachers of elementary and middle school classes, pre-service teachers, and mathematics education researchers.


A Focus on Ratios and Proportions

A Focus on Ratios and Proportions

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  • Author: Marjorie M. Petit
  • Publisher: Routledge
  • ISBN: 1000071448
  • Category : Education
  • Languages : en
  • Pages : 264

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts. Special features include: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding. A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions. Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.


Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8

Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8

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  • Author: Joanne Elizabeth Lobato
  • Publisher: National Council of Teachers of English
  • ISBN: 9780873536226
  • Category : Curriculum planning
  • Languages : en
  • Pages : 0

"A series for teaching mathematics."--P. [1] of cover.


Prealgebra 2e

Prealgebra 2e

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  • Author: Lynn Marecek
  • Publisher:
  • ISBN: 9781680923261
  • Category :
  • Languages : en
  • Pages : 1148

The images in this book are in color. For a less-expensive grayscale paperback version, see ISBN 9781680923254. Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Students who are taking basic mathematics and prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi.


Ratios and Proportions Workbook

Ratios and Proportions Workbook

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  • Author: Maria Miller
  • Publisher:
  • ISBN: 9781533160799
  • Category :
  • Languages : en
  • Pages : 90

Ratios and Proportions Workbook covers the concept of the ratio of two quantities. From this concept, we develop the related concepts of a rate (so much of one thing per so much of another thing) and a proportion (an equation of ratios). We also study how tables of equivalent ratios can help to solve problems with rates, and how cross-multiplying can help to solve problems with proportions. The lesson Unit Rates defines the concept of the unit rate, shows how to calculate one, and gives practice at doing so, including practice with complex fractions. We also consider rates as two quantities that vary, graph the corresponding equation in the coordinate grid, and tie in the concept of unit rate with the concept of slope. The concept of direct variation is introduced in the lesson Proportional Relationships. Writing and graphing equations gives a visual understanding of proportionality. In two following lessons on proportions, students also practice solving rate problems in different ways, using the various methods they have learned throughout the workbook. The lessons Scaling Figures, Floor Plans, and Maps give useful applications and more practice to master the concepts of proportions. Before the Review there is also an optional lesson, Significant Digits, that deals with the concept of the accuracy of a measurement and how it limits the accuracy of the solution. It is optional because significant digits is not a standard topic for seventh grade, yet the concept in it is quite important, especially in science.


Developing Deep Knowledge in Middle School Mathematics

Developing Deep Knowledge in Middle School Mathematics

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  • Author: Sergei Abramovich
  • Publisher: Springer Nature
  • ISBN: 3030685640
  • Category : Education
  • Languages : en
  • Pages : 451

This textbook is for prospective teachers of middle school mathematics. It reflects on the authors’ experience in offering various mathematics education courses to prospective teachers in the US and Canada. In particular, the content can support one or more of 24-semester-hour courses recommended by the Conference Board of the Mathematical Sciences (2012) for the mathematical preparation of middle school teachers. The textbook integrates grade-appropriate content on all major topics in the middle school mathematics curriculum with international recommendations for teaching the content, making it relevant for a global readership. The textbook emphasizes the inherent connections between mathematics and real life, since many mathematical concepts and procedures stem from common sense, something that schoolchildren intuitively possess. This focus on teaching formal mathematics with reference to real life and common sense is essential to its pedagogical approach. In addition, the textbook stresses the importance of being able to use technology as an exploratory tool, and being familiar with its strengths and weaknesses. In keeping with this emphasis on the use of technology, both physical (manipulatives) and digital (commonly available educational software), it also explores e.g. the use of computer graphing software for digital fabrication. In closing, the textbook addresses the issue of creativity as a crucial aspect of education in the digital age in general, and in mathematics education in particular.


Glencoe Math, Course 1, Student Edition

Glencoe Math, Course 1, Student Edition

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  • Author: McGraw-Hill Education
  • Publisher: McGraw-Hill Education
  • ISBN: 9780076691005
  • Category : Mathematics
  • Languages : en
  • Pages : 528

The Glencoe Math Student Edition is an interactive text that engages students and assist with learning and organization. It personalizes the learning experience for every student. The write-in text, 3-hole punched, perfed pages allow students to organize while they are learning.


The Art and Science of Drawing

The Art and Science of Drawing

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  • Author: Brent Eviston
  • Publisher: Rocky Nook, Inc.
  • ISBN: 1681987775
  • Category : Art
  • Languages : en
  • Pages : 479

Drawing is not a talent, it's a skill anyone can learn. This is the philosophy of drawing instructor Brent Eviston based on his more than twenty years of teaching. He has tested numerous types of drawing instruction from centuries old classical techniques to contemporary practices and designed an approach that combines tried and true techniques with innovative methods of his own. Now, he shares his secrets with this book that provides the most accessible, streamlined, and effective methods for learning to draw.

Taking the reader through the entire process, beginning with the most basic skills to more advanced such as volumetric drawing, shading, and figure sketching, this book contains numerous projects and guidance on what and how to practice. It also features instructional images and diagrams as well as finished drawings. With this book and a dedication to practice, anyone can learn to draw!


Putting Essential Understanding of Ratios and Proportions Into Practice in Grades 6-8

Putting Essential Understanding of Ratios and Proportions Into Practice in Grades 6-8

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  • Author: Travis Olson
  • Publisher: National Council of Teachers of English
  • ISBN: 9780873537179
  • Category : Ratio and proportion
  • Languages : en
  • Pages : 0

Focuses on the specialized pedagogical content knowledge that you need to teach ratios and proportions effectively in grades 6-8. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with ratios and proportions.


Ratio

Ratio

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  • Author: Michael Ruhlman
  • Publisher: Simon and Schuster
  • ISBN: 1416566120
  • Category : Cooking
  • Languages : en
  • Pages : 307

Michael Ruhlman’s groundbreaking New York Times bestseller takes us to the very “truth” of cooking: it is not about recipes but rather about basic ratios and fundamental techniques that makes all food come together, simply. When you know a culinary ratio, it’s not like knowing a single recipe, it’s instantly knowing a thousand. Why spend time sorting through the millions of cookie recipes available in books, magazines, and on the Internet? Isn’t it easier just to remember 1-2-3? That’s the ratio of ingredients that always make a basic, delicious cookie dough: 1 part sugar, 2 parts fat, and 3 parts flour. From there, add anything you want—chocolate, lemon and orange zest, nuts, poppy seeds, cinnamon, cloves, nutmeg, almond extract, or peanut butter, to name a few favorite additions. Replace white sugar with brown for a darker, chewier cookie. Add baking powder and/or eggs for a lighter, airier texture. Ratios are the starting point from which a thousand variations begin. Ratios are the simple proportions of one ingredient to another. Biscuit dough is 3:1:2—or 3 parts flour, 1 part fat, and 2 parts liquid. This ratio is the beginning of many variations, and because the biscuit takes sweet and savory flavors with equal grace, you can top it with whipped cream and strawberries or sausage gravy. Vinaigrette is 3:1, or 3 parts oil to 1 part vinegar, and is one of the most useful sauces imaginable, giving everything from grilled meats and fish to steamed vegetables or lettuces intense flavor. Cooking with ratios will unchain you from recipes and set you free. With thirty-three ratios and suggestions for enticing variations, Ratio is the truth of cooking: basic preparations that teach us how the fundamental ingredients of the kitchen—water, flour, butter and oils, milk and cream, and eggs—work. Change the ratio and bread dough becomes pasta dough, cakes become muffins become popovers become crepes. As the culinary world fills up with overly complicated recipes and never-ending ingredient lists, Michael Ruhlman blasts through the surplus of information and delivers this innovative, straightforward book that cuts to the core of cooking. Ratio provides one of the greatest kitchen lessons there is—and it makes the cooking easier and more satisfying than ever.