81. Teaching Math: Grades 3-5: Representation to think about what the fractions, decimals, percents, and grid mean. In this situation, percents are easier to work with than lengthy decimal http://www.learner.org/channel/courses/teachingmath/grades3_5/session_05/section

Observing Student Representation Introduction Representing Data Problem Reflection #1 Is This Circle Graph Correct? Problem Reflection #2 Classroom Practice Observe a Classroom ... Your Journal Think about Martina's work and reflect on the following questions. After you've formulated an answer to each question, select "Show Answer" to see our response. Question: How does this problem provide an opportunity for students to build their understanding of numbers, including percents, which are often used when representing information in a graph? Show Answer Sample Answer: The writing assignment encourages students to think about what the fractions, decimals, percents, and grid mean. Martina has some understanding that the whole 100-grid represents the total, or the 60 students who were surveyed. She understands that 0.999999 in her table is a numerical representation of the number 1 (it is approximately equal to 1). She is beginning to understand that the fraction of the group that prefers basketball can also be represented as a decimal part, and as a percent, of the whole group. Her plan for her circle graph shows that she understands some link between the percents shown on the 100-grid representation and the circle graph that she plans to draw. Question: How is representation a critical part of analyzing data? Why is it helpful to use percents?

82. PART/WHOLE: The CORE Of MATH! It can be a KEY resource for you in teaching, a site you may want to put on yourown web page for Relationships among fractions, decimals and Percents http://members.tripod.com/~ozpk/0000mathcore

THE CORE of MATH: UNDERSTANDING PART/WHOLE RELATIONS Nearly all students can do decimal/fractions when counting money or making change. The relation of parts (Quarters) to wholes (Dollars) is a lot more concrete to them, and a field where their past experience helps. But fewer than 25% of students can consistently do Percents, Decimals and Fractions well. This site has over 40 valuable links centered on this core math area. It can be a KEY resource for you in teaching, a site you may want to put on your own web page for students and their families, and one you may want to use to brush up on this critical area of math. Understanding systems, being able to analyze situations, as well as more specific functions as doing taxes and shopping for bargains, are all based in this type of thinking. It really separates adults from children when it comes to both math and life! Give it the priority it is due! NUMBER SENSE and OPERATIONS Page 7: Strand Review Pages 19-20: Grades 5-6 Learning Standards Page 43: Grades 7-8 Learning Standards Page #'s Refer to Mass. Curriculum Math Frameworks

83. Teaching Arithmetic Lessons for decimals and Percents, Grades 5–6 • Complete Teaching ArithmeticSeries (11 books). Lessons for fractions Part of the acclaimed Teaching http://www.mathsolutions.com/mb/content/publications/p_pub_02.html

Math Solutions Publications Alphabetical List by Title Index of Classroom Lessons Book Reviews ... Sign Up for Online Newsletter Teaching Arithmetic Lessons That Work for Teaching the Basics Lessons for First Grade Lessons for Introducing Place Value, Grade 2 NEW Lessons for Extending Place Value, Grade 3 Lessons for Introducing Multiplication, Grade 3 Lessons for Introducing Division, Grade Complete Teaching Arithmetic Series (12 books) Lessons for Fractions Part of the acclaimed Teaching Arithmetic Lessons for Extending Fractions, Grade 5 Complete Set of 3 Fraction Books The Marilyn Burns Fraction Kit Lessons for First Grade by Stephanie Sheffield Read a Lesson from This Book #1 ISBN 0-941355-34-9 Lessons for Introducing Place Value, Grade 2 by Maryann Wickett and Marilyn Burns The investigations in this book help second graders build their understanding of the tens and ones structure of our number system. Lessons engage children in comparing and explaining the relative size of numbers, counting larger numbers in two or more ways, and recognizing that the number of objects always remains the same despite different ways of grouping.

84. References On The Teaching/Learning Of Decimals And Fractions References on the Teaching/Learning of decimals and fractions An annotatedbibliography on functions, decimals, and percents (rational number concepts). http://www.maa.org/pmet/resources/abiblio.html

References on the Teaching/Learning of Decimals and Fractions An annotated bibliography on functions, decimals, and percents (rational number concepts). Compiled March 7, 2004, by Dr. Annie Selden , New Mexico State University, Department of Mathematical Sciences and PMET Advisory National Advisory Committee Member. Annotations were taken from the abstracts of the articles, the ERIC database, or the texts of the articles, except as otherwise noted. Rational number, ratio, and proportion. In D. A. Grouws (Ed.), NCTM Handbook of Research on Mathematics Teaching and Learning (pp. 296-333), New York: Macmillan Publishing Company. This handbook is somewhat dated, but for folks who have never heard of any research in math ed on the teaching/learning of rational numbers, this provides a good start. Conceptual units analysis of preservice elementary teachers' strategies on a rational-number-as operator task. Journal for Research in Mathematics Education, 28(1), 48-69. Rational number leaning aids: Transfer from continuous models to discrete models.

85. Time To Teach Free Interactive Primary Maths Lessons Time to teach provides maths resources and maths lessons to teachers and Percentage 1Introduction to percents, percent equivalents in fractions and http://www.timetoteach.co.uk/index2.html

Subject Links School Worksheets Latest Teaching Articles Maths Science ... Free Educational CDs you only pay for the postage! Click here for all the mathematics teaching resources. I used it last year with my Year 4 class as homework. At the end of the year, out of 16 children who spoke English as a second language, 14 were above the UK national average in maths. Click here for Year 1 - Year 6 MAths scheme. (It is the most challenging, yet well supported maths scheme I have seen. It is also FREE which is great news! Click here for a Maths test generator - suit KS3 (Some good for Year 6). Anysubject Ltd Personal tutors, tuition, online tutoring, home schooling - all academic subjects and musical instruments - lessons from £12.50/hour. www.anysubject.com Click here if you are a teacher who would like to earn extra money from one of the best tutoring services. You can even work online from anywhere in the world! Vote for our site! Click here for Free Maths Scheme for Reception to Year 6. I use it in my Year 4 class with great effect. It is greatly appreciated by the parents who have been stunned at how their children have come on in leaps and bounds on it!

86. Percents & Decimals TeachersParadise.com Teacher Supplies School Supplies School Teacher Supplies School Supplies Teaching Materials TeachersParadise.com, Saveon school fractions, decimals Percents, Grades 7 to 8 Homework Booklet http://www.teachersparadise.com/c/index.php/cPath/21_36_207

My Account Help Free Teacher Resources Associates Program $$$ ... Teaching Aides Sort: All Manufacturers Carson Dellosa Didax Educational Insights Edupress Frank Schaffer Publications Great Wave Software Ideal School Supply Instructional Fair Judy Instructo LeapFrog Learning Resources McDonald Publishing Company Scholastic Professional Books Steck-Vaughn School Supply Teacher Created Materials TREND enterprises WORLD CLASS Learning Materials Displaying to (of products) Result Pages: FS-2476 Decimals Chart FS-36127 Cheap Charts: Operations With Decimals W-MM9333 CD-2007 IF-0283 Turbo Twist Math Fraction Tower Cubes Equivalency 51/Pk Overhead Decimal Cubes 51/Pk Fraction Tower IF-0281 Fraction Tower Cubes Percent 51/Pk IF-0282 IF-8771 Math Practice, Grades 7 to 8 How to Work with Fractions, Decimals, and Percents, Grades 4-6 DD-25029 The Fraction Book IF-87124 Mixed Skills in Math, Grades 7 to 8 SV-13013 Fraction Tower Cards Set Gr. 6-8 (1 Ea. 2514 2516-2518) MC-P133 Poster Set Fraction Fundamentals Displaying to (of products) Result Pages: Quick Site Directory Teacher Resources Language Arts Math Room Decorations ... more Shop by Brand Carson Dellosa Center Enterprises Creative Teaching Associates Creative Teaching Press ... Trend more EDUCATIONAL BRANDS United States Canada New Zealand / Australia / Pacific Oceania Region India ... TeachersParadise.com HOME

87. Adult Numeracy Themes: Number And Number Sense; Part I fractions, decimals, percents and ratios and their relationships with each otherare basic The choice of teaching complicated fraction computation, http://literacy.kent.edu/Oasis/Resc/Educ/numnum.html

You are here - OLRC Home Site Index Contact Us Go to.... - OLRC Home - About Us - ABLE - Projects - Publications Number and Number Sense Number sense is a content skill that encompasses many areas in our adult education classroom. Number sense needs to be explored using whole numbers, fractions, decimals, percents, ratio, money, and estimation. Being able to handle numbers comfortably and competently is important to adults as parents, workers, and community members. This competence relies upon having developed a kind of "number sense" about whole numbers, money, fractions, decimals, and percents. Number sense includes calculation skills with numbers as well as a sense of number and operation and an ability to appropriately use estimation, mental math, computation, calculators and other tools. Computation skills are necessary but not sufficient. Adults must have strongly developed computational understanding of arithmetic numbers as well as some procedural knowledge of computation and number facts. They must be able to perceive the idea of place value and be able to read, write, and represent whole numbers and numerical relationships in a wide variety of way. Simple paper and pencil computations are not enough. Adults must be able to make decisions regarding the best method of computation to use in a particular situation; mental math, paper-and-pencil, calculator/computer. To demand individual paper and pencil computation from all students at all times does a disservice to our students and society. Problem solving skills are often best developed using a calculator and group work. Calculator work, mental math, and pencil-and-paper skills are important skills to develop in all students during all class time.

88. Lakeside Middle School Mathematics Department In teaching mathematics, we try to pose questions and problems that encourage a topics operations on positive numbers; fractions, decimals, percents; http://www.lakesideschool.org/middleschool/departments/math/default.html

Lakeside Middle School Mathematics Department Department Overview and Course Syllabi Contents Goal of the Program Content Overview Features Tom Rona's Page Goal of the Program The main goal of our program is to provide a strong foundation in mathematics via challenging courses that are appropriate to the age, abilities, and needs of our students. We hope that, in addition to being well prepared for the mathematics they may encounter in future schooling or careers, our students will emerge from the program impressed with the elegance and scope of the subject, and excited by its vast potential for fun and creativity. We also aim to equip students with the mathematical skills of a competent citizen in today's world. These skills include the ability to model situations mathematically, to estimate and compare magnitudes, to interpret graphs and statistics, to calculate probabilities, to evaluate numerical and spatial conclusions, to solve problems mentally as well as with paper, calculator, and computer, and to communicate effectively in these areas. Finally, while much of the above is exercised in the context of individual work, we have the further goal of fostering the skills and value of doing mathematics cooperatively with others. Course Content Overview We define mathematics very broadly as a systematic approach to studying and representing quantities, forms, patterns, and logic. Thus the content of our courses encompasses the wide range of arithmetic, number theory, measurement, geometry, probability, statistics, graphing, pattern recognition, logic, and problem solving strategy.

89. Teaching And Learning About Decimals Confusion between fractions and decimals/percents even happens in high places . Care needs to be taken in teaching decimals with money. http://extranet.edfac.unimelb.edu.au/DSME/decimals/SLIMversion/tests/miscon.shtm

You are using the online sample of the Teaching and Learning about Decimals CDROM. Not all linked pages are accessible in this version. For further information about the complete CDROM please click here Summary of Misconceptions about Decimal Numbers Misconceptions can be diagnosed by listening and watching carefully when a child answers strategically designed tasks. One of the simplest and best tasks for this topic is to select the larger from pairs of decimals. Because this is such a good task, the misconceptions have been organized in three groups according to how the child orders decimals. Other tasks useful for revealing students' thinking are presented in teaching. Contents of this page Longer-is-larger misconceptions These students generally think a longer decimal is a larger number than a shorter decimal Whole number thinking Column overflow thinking Zero makes small thinking Reverse thinking ... Shorter-is-larger misconceptions These students generally think a shorter decimal is a larger number than a longer decimal. Denominator focussed thinking Reciprocal thinking Negative thinking Apparent-expert behavior These students can generally decide which of two decimals is larger but sometimes not for the right reasons.

90. Standard 6 to develop a strong sense of what numbers are (whole, fractions, decimals,percents, compute with whole numbers, fractions, decimals, and integers, http://www2.wgbh.org/MBCWEIS/LTC/CLC/stnd6numsense.html

Standard 6: Numbers, Operations, and Computation Rationale To be efficient workers or consumers in today's world, adults must have a strongly developed conceptual understanding of arithmetic operations as well as the procedural knowledge of computation and number facts. They must be able to perceive the idea of place value and be able to read, write and represent numbers and numerical relationships in a wide variety of ways. Simple paper-and-pencil computation skills are not enough. Adults must be able to make decisions regarding the best method of computation (mental math, paper-and-pencil, calculator/computer) to use for a particular situation. Knowledge of numbers, operations and computation must include both a well-developed number sense and the ability to use basic mathematics-related technologies. Application Adults in all the adult basic education learning environments bring a range of abilities, skill levels, and gaps in their learning and dealings with numbers as a result of their varied educational and cultural backgrounds. Some ABE-level adults demonstrate a limited understanding of place value and how big or small numbers are. ESL students from countries using metric measurement may demonstrate stronger skills in decimal concepts and computation while learners from the North American tradition may demonstrate greater facility with fractions. Still, to many other adults, fractions present a constant puzzle and irrelevancy to their daily life. While almost all adult learners have an understanding of the U.S. money system and a working knowledge of the underlying decimal notation, this knowledge may not translate to a deeper understanding of decimal skills and operations which are essential workplace skills.

91. Teaching Models: Grade 6 A percent can be written as a fraction or a decimal. At this grade level, Teaching Model 17.3 Compare and Order Ratios, decimals, and Percents http://www.eduplace.com/math/mw/models/overview/6_17_3.html

@import url(../includes/styles.css); /*IE and NN6x styles*/ Understand Percent Percent A percent is a ratio of a number to 100. Percent means "per hundred." Thus, 20 percent or 20% means . A percent can be written as a fraction or a decimal. At this grade level, students are introduced to fractional percents, such as 2.5%, as well as percents greater than 100%, such as 250%. To change a percent to a decimal, write the percent amount and move the decimal point 2 places to the left. To change a decimal to a percent, write the decimal, move the decimal point 2 places to the right, and add the percent sign. To change a percent to a fraction, use the given percent as the numerator of a fraction with 100 as the denominator, and then reduce the fraction to simplest form. One way to change a fraction to a percent is to write an equivalent fraction with a denominator of 100 and then change it to a percent. Examples: Comparisons of fractions, decimals, and percents can be completed in several ways, including locating each on a number line, rewriting each as a fraction with a common denominator, or rewriting each as a decimal. Teaching Model 17.3:

92. NCTM's Standards On Teaching Decimals Statements from NCTM s 1989 Standards on Teaching decimals By studyingfractions, decimals, and percents simultaneously, students can learn to move http://www.decimalsquares.com/NCTMstands.html

Say About Teaching Decimals Statements from NCTM's 1989 Standards on Teaching Decimals The approach to decimals should be similar to work with fractions, namely, placing a strong and continued emphasis on models and oral language and then connecting this work with symbols. This is necessary if students are to make sense of decimals and use them insightfully. Exploring ideas of tenths and hundredths with models can include preliminary work with equivalent decimals (fig. 12.5), counting sequences, the comparing and ordering of decimals, and addition and subtraction. Decimal instruction should include informal experiences that relate fractions to decimals so that students begin to establish connections between the two systems. For example, if students recognize that 1/2 is the same amount as 0.5, they can use this relationship to determine that 0.4 and 0.45 are a little less than 1/2 and that 0.6 and 0.57 are a little more than 1/2. Such activities help children develop number sense for decimals. To provide students with a lasting sense of number and number relationships, learning should be grounded in experience related to aspects of everyday life or to the use of concrete materials designed to reflect underlying mathematical ideas. Students should encounter number lines, area models, and graphs as well as representations of numbers that appear on calculators and computers (e.g., forms of scientific notation). Students should learn to identify equivalent forms of a number and understand why a particular representation is useful in a given setting.

93. Candy Fractions Lesson Plan, Teaching Worksheet CANDY fractions LESSON PLAN MATH ACTIVITY ELEMENTARY TEACHING AND LEARNING LANGUAGEARTS Show students how to show ¼ as a decimal and as a percentage. http://www.instructorweb.com/lesson/candyfractions.asp

CANDY FRACTIONS LESSON PLAN MATH ACTIVITY ELEMENTARY TEACHING AND LEARNING LANGUAGE ARTS WORKSHEET STUDENTS PRIMARY EDUCATION CURRICULUM KIDS THEME UNIT RESOURCES ACTIVITY A fun elementary fractions lesson for your class. CANDY FRACTIONS Content Area Elementary Math - Fractions Content Targets Identifying parts of a whole, percentages, working with fractions as discrete models, graphing data using bar graphs, recording data in a table, classifying and sorting objects, number sense Learning Objective After learning about the different types of fraction models, students will be able to analyze a discrete model in order to identify fractions (as fractions, decimals and percentages) by working with a candy sample to fill out a table and draw a bar graph. Grades 3rd Grade - 4th Grade -5th grade CANDY FRACTIONS LESSON PLAN Academic Language Focus • How to distinguish between an area model, discrete model and number line

94. OPS Math Curriculum Manipulatives should be the preliminary teaching material. the meaning offractions, including decimals, percents and ratios. that the various http://okemos.k12.mi.us/users/admin/curriculum/math/08number.htm

CORE CURRICULUM NUMBER (SENSE, SYSTEMS, RELATIONSHIPS AND THEORY) Children must understand numbers if they are to make sense of the ways numbers are used in their everyday world. We use numbers to interpret information, make decisions, and solve problems. The acquisition of this number sense should be developed by providing exploratory experiences which relate numbers to a child's real world and make use of the child's own language. Manipulatives should be the preliminary teaching material. These concrete experiences should be linked meaningfully to oral and written number symbols to solidify conceptual understanding. The student with good number sense has an understanding of the meaning of numbers, relationships between numbers and the effects of operations on numbers. Students who have developed number sense will be able to recognize the reasonableness of their solutions to numerical problems. It is essential to emphasize relationships between quantities and to avoid making false distinctions. Whole numbers can be expressed as fractions, fractions as percentages, etc. Decimals are fractions. They are simply expressed in a unique way. As they develop, students extend their understanding of number and facility with different notations in response to different situations encountered. Students should see the necessity of working with new number systems (fractions, decimals, integers, rationals, irrationals) required by new problem situations.

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