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Using a four-pan apparatus with a main balance plus chips and canisters as variables, the book helps students build understanding from concrete to semiconcrete to abstract reasoning. It emphasizes equilibrium and the Zero State, where equal amounts on the same side balance the scale, and supports whole-class, group, and learning-center activities. 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\nDigitized by the Internet Archivein 2022 with funding fromKahle/Austin Foundation  \nhttps://archive.org/details/isbn_1569110549  \nFOUR-PAN  \nALGEBRA BALANCEMODELING INTEGERSANDEQUATIONS  \n8  \nGary T.Nelson,Ph.D.  \nThis book is dedicated to the millions of students and teachers who willhopefully enjoy the activities.The book is also dedicated to my wife,Cathy,myconstant source of support and inspiration.Finally,the book is dedicated tothe memory of my mother,who instilled in me the love of learning  \nExecutive Editor:Doris Hirschhorn  \nEditorial Manager:Patsy Norvell  \nDevelopmental Editor:Sharon Schwartz  \nProduction/Manufacturing Director:Janet Yearian  \nProduction/Manufacturing Manager:Karen Edmonds  \nProduction/Manufacturing Coordinator:Karen Mancinelli  \nArt Director:Jim O'Shea  \nCover Design:Jim O'Shea  \nInterior Design:Don Taka  \nLine Art:Fiona Santoianni  \nCopyright ◎2001 by Cuisenaire Company of America,Inc.  \nAll rights reserved.  \nThis book is published by Cuisenaire,an imprint of Pearson Education.  \nCuisenaire Company of America,Inc.299 Jefferson RoadParsippany,NJ 07054-0480  \nLimited reproduction permission:The publisher grants permission to individual teachers who havepurchased this book to reproduce pages as needed for use with their own students.Reproductionfor an entire school or school district or for commercial use is prohibited.  \nThe word Cuisenaire and the color sequence of the rods,cubes,and squares are trademarks ofCuisenaire Company of America,Inc.,registered in the United States and other countries.  \nCode 020279ISBN 1-57452-338-4Printed in China.  \nINTRODUCTIONivIntroducing the Four-Pan Algebra Balance1Unit 1Comparing Integers2Unit 2Finding Additive Inverses5Unit 3Adding Integers8Unit 4Subtracting Integers13Unit 5Multiplying Integers17Unit 6Finding Equivalent Expressionsand Equations20Unit 7Solving Equations in One Variable27Unit 8Solving More Equations inOne Variable32Unit 9Solving Linear Equations inTwo Variables37Unit 10Solving Systems of Linear Equations42Blackline Masters47Unit Practice49Unit Practice Cards54  \nFour-Pan Algebra Balance Work Mat  \n57  \nn the early grades,it is generally recognized that learning begins atthe concrete level,then proceeds to the semiconcrete (pictorial)level,and ends at the abstract level.As students move to higher-grade levels,the use of concrete models,or manipulatives,to introduce new mathe-matical concepts and skills tends to decrease.It is frequently assumedthat older children do not need to work at the concrete level.Researchand experience,however,have shown that most,if not all,conceptsand skills are understood better when first introduced at the concretelevel no matter what the grade level or age of the learner.  \nThe Four-Pan Algebra Balance provides a unique way to model andexplore,at the concrete level,the concepts and procedures related towhole numbers,integers,equations,and inequalities.The apparatusconsists of four pans and a main balance.Weights,consisting of chipsand canisters,are used with the balance.Each chip represents onewhole.Chips placed in a canister,which with its lid has the sameweight as one chip,create the variables or unknowns.  \nOn each side of the balance there are a yellow pan and a red pan.Chipsplaced in either yellow pan represent positive numbers and chips placedin either red pan represent negative numbers.Equal amounts in boththe yellow pans balance the scale,as will equal amounts in both redpans.  \n-3=-3  \n4=4  \nThe unique property of this balance is that equal amounts in both panson the same side of the beam will also balance the scale.When the scaleis balanced,it is said to be in equilibrium or at the Zero State.  \n-2+2=0  \n-5≠-3  \n-5\u003C-3  \n0=0  \nMany textbooks use yellow to represent positive integers and red torepresent negative integers.Similarly,the yellow pans of the Four-PanA","cbCaijQcjmKWCGED","https://ap.wps.com/l/cbCaijQcjmKWCGED","pdf",4105201,68,"English","# Introduction\n## Four-Pan Algebra Balance model and equilibrium\n## Using the balance across concrete, semiconcrete, and abstract stages\n# Units\n## Unit 1: Comparing Integers\n## Unit 2: Finding Additive Inverses\n## Unit 3: Adding Integers\n## Unit 4: Subtracting Integers\n## Unit 5: Multiplying Integers\n## Unit 6: Finding Equivalent Expressions and Equations\n## Unit 7: Solving Equations in One Variable\n## Unit 8: Solving More Equations in One Variable\n## Unit 9: Solving Linear Equations in Two Variables\n## Unit 10: Solving Systems of Linear Equations\n# Blackline Masters and Practice","[{\"question\":\"What is the Four-Pan Algebra Balance used to teach?\",\"answer\":\"It models and explores concepts and procedures related to whole numbers, integers, equations, and inequalities across concrete, semiconcrete, and abstract stages.\"},{\"question\":\"How do chips and canisters represent mathematical values?\",\"answer\":\"Each chip represents one whole, and chips placed in a canister with its lid create variables or unknowns.\"},{\"question\":\"What does equilibrium (the Zero State) mean on the balance?\",\"answer\":\"When the scale is balanced, it is in equilibrium or at the Zero State, indicating equal amounts that balance the scale.\"}]","Four-Pan Algebra Balance - Modeling Integers, Equations, Inverses, and Equivalencies | PDF",1791877785,171]