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- 1. AuthorDinah Zike, M. Ed.Educational ConsultantSan Antonio, Texas
- 2. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United Statesof America. Except as permitted under the United States Copyright Act, no part of this publicationmay be reproduced or distributed in any form or by any means, or stored in a database or retrievalsystem, without the prior written permission of the publisher.Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240Part of ISBN 0-07-830413-X Teaching Mathematics with Foldables1 2 3 4 5 6 7 8 9 10 045 11 10 09 08 07 06 05 04 03 02Glencoe/McGraw-Hill
- 3. Letter from Dinah Zike . . . . . . . . . . . . . . . . . . . . .vIntroduction to FoldablesWhy Use Foldables in Mathematics? . . . . . .viCorrelation of Foldables toGlencoe Mathematics . . . . . . . . . . . . . . . .viiFoldable Basics . . . . . . . . . . . . . . . . . . . . . . .1Selecting the Appropriate Foldable . . . . . . . .3Folding InstructionsBasic Foldable Shapes . . . . . . . . . . . . . . . . . . . . . .51-Part FoldsHalf Book . . . . . . . . . . . . . . . . . . . . . . . . . . .6Folded Book . . . . . . . . . . . . . . . . . . . . . . . . .7Bound Book . . . . . . . . . . . . . . . . . . . . . . . . .8Two-Tab Book . . . . . . . . . . . . . . . . . . . . . . . .92-Part FoldsMatchbook . . . . . . . . . . . . . . . . . . . . . . . . .10Pocket Book . . . . . . . . . . . . . . . . . . . . . . . .11Shutter Fold . . . . . . . . . . . . . . . . . . . . . . . . .123-Part FoldsTrifold Book . . . . . . . . . . . . . . . . . . . . . . . .13Three-Tab Book . . . . . . . . . . . . . . . . . . . . . .14Three-Tab Book Variations . . . . . . . . . . . . .15Pyramid Fold or Mobile . . . . . . . . . . . . . . . .164-Part FoldsLayered-Look Book . . . . . . . . . . . . . . . . . . .17Four-Tab Book . . . . . . . . . . . . . . . . . . . . . .18Envelope Fold . . . . . . . . . . . . . . . . . . . . . . .19Standing Cube . . . . . . . . . . . . . . . . . . . . . . .20Four-Door Book . . . . . . . . . . . . . . . . . . . . .21Top-Tab Book . . . . . . . . . . . . . . . . . . . . . . .22Accordion Book . . . . . . . . . . . . . . . . . . . . .24Any Number of PartsPop-Up Book . . . . . . . . . . . . . . . . . . . . . . . .25Folding into Fifths . . . . . . . . . . . . . . . . . . . .26Folded Table, Chart, or Graph . . . . . . . . . . .27Folding a Circle into Tenths . . . . . . . . . . . . .28Circle Graph . . . . . . . . . . . . . . . . . . . . . . . .29Concept-Map Book . . . . . . . . . . . . . . . . . . .30Vocabulary Book . . . . . . . . . . . . . . . . . . . . .31Projects Using FoldsBillboard Project . . . . . . . . . . . . . . . . . . . . .32Sentence-Strip Holder . . . . . . . . . . . . . . . . .33Sentence Strips . . . . . . . . . . . . . . . . . . . . . .34Math Activities using FoldablesNumber SystemsWhole Numbers . . . . . . . . . . . . . . . . . . . . . .35Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . .36Integers: Adding and Subtracting . . . . . . . . .37Integers: Multiplying and Dividing . . . . . . .38Rational Numbers . . . . . . . . . . . . . . . . . . . .39Rational Numbers: Fractions . . . . . . . . . . . .40Rational Numbers: Decimals . . . . . . . . . . . .41Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43Proportions . . . . . . . . . . . . . . . . . . . . . . . . .43Irrational Numbers . . . . . . . . . . . . . . . . . . . .44Real Number System . . . . . . . . . . . . . . . . . .44Algebraic Patterns and FunctionsSets and Variables . . . . . . . . . . . . . . . . . . . .45Expressions . . . . . . . . . . . . . . . . . . . . . . . . .46Properties . . . . . . . . . . . . . . . . . . . . . . . . . .47Equations . . . . . . . . . . . . . . . . . . . . . . . . . . .48Inequalities . . . . . . . . . . . . . . . . . . . . . . . . .49Relations and Functions . . . . . . . . . . . . . . . .50Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . .52Monomials and Polynomials . . . . . . . . . . . .53Powers and Exponents . . . . . . . . . . . . . . . . .54Sequences . . . . . . . . . . . . . . . . . . . . . . . . . .55Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . .56GeometryPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57Lines and Line Segments . . . . . . . . . . . . . . .57Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58Angle Relationships . . . . . . . . . . . . . . . . . . .58Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . .60Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . .61Right Triangles . . . . . . . . . . . . . . . . . . . . . .62Right Triangle Trigonometry . . . . . . . . . . . .63©Glencoe/McGraw-Hill iii Teaching Mathematics with FoldablesTable of Contents
- 4. Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . .64Squares, Rectangles, and Rhombi . . . . . . . .65Parallelograms . . . . . . . . . . . . . . . . . . . . . . .66Trapezoids . . . . . . . . . . . . . . . . . . . . . . . . . .67Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68Three-Dimensional Figures . . . . . . . . . . . . .69Prisms and Cylinders . . . . . . . . . . . . . . . . . .70Pyramids and Cones . . . . . . . . . . . . . . . . . .71Coordinate Geometry . . . . . . . . . . . . . . . . . .72Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73Graphing Equations and Inequalities . . . . . .74MeasurementMetric Measurement . . . . . . . . . . . . . . . . . .75Length, Width, and Height . . . . . . . . . . . . . .75Distance . . . . . . . . . . . . . . . . . . . . . . . . . . .76Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . .77Temperature . . . . . . . . . . . . . . . . . . . . . . . . .77Data Analysis and ProbabilityStatistics . . . . . . . . . . . . . . . . . . . . . . . . . . .78Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . .79Box-and-Whisker Plots . . . . . . . . . . . . . . . .79Fundamental Counting Principle . . . . . . . . .80Frequency Tables . . . . . . . . . . . . . . . . . . . . .80Pascal’s Triangle . . . . . . . . . . . . . . . . . . . . .80Permutations . . . . . . . . . . . . . . . . . . . . . . . .81Combinations . . . . . . . . . . . . . . . . . . . . . . .81Probability . . . . . . . . . . . . . . . . . . . . . . . . . .82Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . .83Problem SolvingProblem-Solving Plan . . . . . . . . . . . . . . . . .84Problem-Solving Strategies . . . . . . . . . . . . .84CommunicationVocabulary and Writing Definitions . . . . . . 85Journals . . . . . . . . . . . . . . . . . . . . . . . . . . . .85Outline, List, and Sequence . . . . . . . . . . . . .86Concept Maps . . . . . . . . . . . . . . . . . . . . . . .86Writing Instructions . . . . . . . . . . . . . . . . . . .86Main Ideas and Note Taking . . . . . . . . . . . .87Annotations . . . . . . . . . . . . . . . . . . . . . . . . .87Questioning . . . . . . . . . . . . . . . . . . . . . . . . .87RepresentationTables and Charts . . . . . . . . . . . . . . . . . . . .88Circle Graphs . . . . . . . . . . . . . . . . . . . . . . .88Bar Graphs and Histograms . . . . . . . . . . . . .89Line Graphs . . . . . . . . . . . . . . . . . . . . . . . . .89Pictographs . . . . . . . . . . . . . . . . . . . . . . . . .90Venn Diagrams . . . . . . . . . . . . . . . . . . . . . .90Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91©Glencoe/McGraw-Hill iv Teaching Mathematics with Foldables
- 5. ©Glencoe/McGraw-Hill v Teaching Mathematics with FoldablesFROM DINAH ZIKEDear Teacher,In this book, you will find instructions for making Foldables as well as ideas on how to usethem. They are an excellent communication tool for students and teachers.National Math Standardsand Communication SkillsThe Principles and Standards for School Mathematics, published by the NationalCouncil of Teachers of Mathematics (NCTM) in 2000, stress the importance ofcommunication skills in a strong mathematics program. Not all students willbecome mathematicians, engineers, or statisticians, but all students need to be ableto think, analyze, and problem solve using skills acquired through the study ofmathematics.Throughout their lives, students will be called upon to be literate in mathematics—personally and professionally. They will need to have a basic understanding ofnumbers, operations, and quantitative reasoning; patterns, relationships, andalgebraic thinking; geometry; measurement; and probability and statistics to solvereal-life problems involving finances, chance, design, science, fine arts, and more.Furthermore, students must be able to share the results of their use of mathematicsusing various forms of oral and written communication. Foldables are one of manytechniques that can be used to integrate reading, writing, thinking, organizing data,researching, and other communication skills into an interdisciplinary mathematicscurriculum.Who, What, When, WhyYou probably have seen at least one of the Foldables featured in this book used insupplemental programs or staff-deveopment workshops. Today, my Foldables areused internationally. I present workshops and keynotes to over fifty thousandteachers and parents a year, sharing the Foldables that I began inventing, design-ing, and adapting over thirty years ago. Around the world, students of all ages areusing them for daily work, note-taking activities, student-directed projects, formsof alternative assessment, math journals, graphs, charts, tables, and more.Add and AmendAfter workshop presentations, participants would ask me for lists of activities to beused with the Foldables they had just learned to make. They needed help visualizinghow to convert math data into Foldables. So, over fifteen years ago, I began collect-ing and sharing the ideas listed in this book. The ideas are organized by topic. Thetable for each topic shows the math content being addressed and an appropriateFoldable. I hope you enjoy making Foldables a part of your math classroom!©Glencoe/McGraw-Hill v Teaching Mathematics with Foldables
- 6. ©Glencoe/McGraw-Hill vi Teaching Mathematics with FoldablesINTRODUCTION TO FOLDABLESWhy Use Foldables in Mathematics?When teachers ask me why they should take time to use the Foldables featured in this book, Iexplain that they. . . quickly organize, display, and arrange information, making it easier for students to graspmath concepts and master skills.. . . result in student-made study guides that are compiled as students listen for main ideas,read for main ideas, and work their way through new concepts and procedures.. . . provide a multitude of creative formats in which students can present projects, research,and computations instead of typical poster board or math fair formats.. . . replace teacher-generated writing or photocopied sheets with student-generated print.. . . incorporate the use of such skills as comparing and contrasting, recognizing cause andeffect, and finding similarities and differences into daily work and long-term projects. Forexample, these Foldables can be used to compare and contrast student explanations andprocedures for solving problems to the explanations presented by other students andteachers.. . . continue to “immerse” students in previously learned vocabulary and concepts, providingthem with a strong foundation that they can build upon with new observations,experiences, and knowledge.. . . can be used by students or teachers to easily communicate data through graphs, tables,charts, models, and diagrams, including Venn diagrams.. . . allow students to make their own math journals for recording main ideas, problem-solvingstrategies, examples, questions that arise during classwork, and personal experiences thatoccur during learning.. . . can be used as alternative assessment tools by teachers to evaluate student progress or bystudents to evaluate their own progress.. . . integrate language arts, the sciences, and social sciences into the study of mathematics.. . . provide a sense of student ownership in the mathematics curriculum.
- 7. ©Glencoe/McGraw-Hill vii Teaching Mathematics with FoldablesNumber SystemsWhole Numbers ✓ ✓ ✓ ✓Integers ✓ ✓ ✓ ✓ ✓Integers: Adding ✓ ✓ ✓ ✓and SubtractingIntegers: Multiplying✓ ✓ ✓ ✓and DividingRational Numbers ✓ ✓ ✓ ✓ ✓Rational Numbers:✓ ✓ ✓ ✓FractionsRational Numbers:✓ ✓ ✓ ✓DecimalsPercents ✓ ✓ ✓ ✓ ✓Ratios ✓ ✓ ✓ ✓Proportions ✓ ✓ ✓ ✓ ✓Irrational Numbers ✓ ✓ ✓Real Number System ✓ ✓ ✓Patterns and FunctionsSets and Variables ✓ ✓ ✓ ✓ ✓ ✓Expressions ✓ ✓ ✓ ✓ ✓ ✓Properties ✓ ✓ ✓ ✓ ✓ ✓Equations ✓ ✓ ✓ ✓ ✓ ✓Inequalities ✓ ✓ ✓ ✓ ✓ ✓Relations and✓ ✓ ✓ ✓ ✓ ✓FunctionsFactors ✓ ✓ ✓ ✓Multiples ✓ ✓ ✓ ✓Monomials and✓ ✓ ✓ ✓PolynomialsPowers and Exponents ✓ ✓ ✓ ✓ ✓ ✓Sequences ✓ ✓ ✓ ✓Matrices ✓ ✓ ✓ ✓GeometryPoints ✓ ✓ ✓ ✓ ✓ ✓ ✓Lines and Line✓ ✓ ✓SegmentsRays ✓Angles ✓ ✓ ✓ ✓ ✓ ✓Angle Relationships ✓Planes ✓Polygons ✓ ✓ ✓ ✓ ✓Triangles ✓ ✓ ✓ ✓ ✓Right Triangles ✓ ✓ ✓ ✓ ✓ ✓ ✓Mathematics: Mathematics: Mathematics:FoldableTMTopicApplications and Applications and Applications andPre-Algebra Algebra 1 Geometry Algebra 2Connections, Connections, Connections,Course 1 Course 2 Course 3Correlation of FoldablesTMto Glencoe MathematicsINTRODUCTION TO FOLDABLES
- 8. ©Glencoe/McGraw-Hill viii Teaching Mathematics with FoldablesINTRODUCTION TO FOLDABLESAlgebra and Right✓ ✓ ✓ ✓TrianglesQuadrilaterals ✓ ✓ ✓ ✓Squares, Rectangles,✓ ✓ ✓ ✓ ✓and RhombiParallelograms ✓ ✓ ✓ ✓Trapezoids ✓ ✓ ✓ ✓Circles ✓ ✓ ✓ ✓ ✓Three-Dimensional✓ ✓ ✓ ✓ ✓FiguresPrisms and Cylinders ✓ ✓ ✓ ✓ ✓Pyramids and Cones ✓ ✓ ✓Coordinate Geometry ✓ ✓ ✓ ✓ ✓ ✓ ✓Slope ✓ ✓ ✓ ✓ ✓ ✓Graphing Equations✓ ✓ ✓ ✓ ✓ ✓and InequalitiesMeasurementMetric Measurement ✓Length, Width, and✓HeightDistance ✓Weight ✓Volume ✓Temperature ✓ ✓ ✓ ✓ ✓Data Analysis and ProbabilityStatisticsStem-and-Leaf Plots ✓Box-and-Whisker Plots ✓ ✓ ✓Fundamental Counting✓ ✓ ✓ ✓ ✓PrincipleFrequency Tables ✓ ✓ ✓ ✓Pascal’s Triangle ✓ ✓ ✓ ✓ ✓Permutations ✓ ✓ ✓ ✓ ✓Combinations ✓ ✓ ✓ ✓ ✓Probability ✓ ✓ ✓ ✓ ✓ ✓ ✓Scatter Plots ✓ ✓ ✓ ✓ ✓ ✓Problem SolvingProblem Solving Plan ✓ ✓ ✓ ✓ ✓ ✓ ✓Problem Solving✓ ✓ ✓ ✓ ✓StrategiesCommunicationVocabulary and Writing✓ ✓ ✓ ✓ ✓ ✓ ✓DefinitionsMathematics: Mathematics: Mathematics:FoldableTMTopicApplications and Applications and Applications andPre-Algebra Algebra 1 Geometry Algebra 2Connections, Connections, Connections,Course 1 Course 2 Course 3Correlation of FoldablesTMto Glencoe Mathematics
- 9. ©Glencoe/McGraw-Hill ix Teaching Mathematics with FoldablesINTRODUCTION TO FOLDABLESJournals ✓ ✓ ✓ ✓ ✓ ✓ ✓Outline, List, and✓ ✓ ✓ ✓ ✓ ✓ ✓SequenceConcept Map ✓ ✓ ✓ ✓ ✓ ✓ ✓Writing Instructions ✓ ✓ ✓ ✓ ✓ ✓ ✓Main Ideas and Note✓ ✓ ✓ ✓ ✓ ✓ ✓TakingAnnotations ✓ ✓ ✓ ✓ ✓ ✓ ✓Questioning ✓ ✓ ✓ ✓ ✓ ✓ ✓RepresentationTables and Charts ✓ ✓ ✓ ✓ ✓ ✓ ✓Circle Graphs ✓ ✓ ✓ ✓ ✓Bar Graphs and✓ ✓ ✓ ✓ ✓HistogramsLine Graphs ✓ ✓Pictographs ✓Venn diagrams ✓ ✓ ✓ ✓ ✓ ✓ ✓Mathematics: Mathematics: Mathematics:FoldableTMTopicApplications and Applications and Applications andPre-Algebra Algebra 1 Geometry Algebra 2Connections, Connections, Connections,Course 1 Course 2 Course 3Correlation of FoldablesTMto Glencoe Mathematics
- 10. ©Glencoe/McGraw-Hill 1 Teaching Mathematics with FoldablesFoldable BasicsWhat to Write and WhereTeach students to write general information—titles, vocabulary words, concepts, questions, mainideas, and properties or theorems—on the front tabs of their Foldables. General information isviewed every time a student looks at a Foldable. Foldables help students focus on and rememberkey points without being distracted by other print.Ask students to write specific information—supporting ideas, student thoughts, answers toquestions, research information, computation steps, class notes, observations, and definitions—under the tabs.As you teach, demonstrate different ways inwhich Foldables can be used. Soon you will findthat students make their own Foldables and usethem independently for study guides and projects.With or Without TabsFoldables with flaps or tabs create study guides that students can use to self check what theyknow about the general information on the front of the tabs. Use Foldables without tabs forassessment purposes or projects where information is presented for others to view quickly.INTRODUCTION TO FOLDABLESVenn Diagram used for assessmentVenn Diagram used as a study guide
- 11. ©Glencoe/McGraw-Hill 2 Teaching Mathematics with FoldablesWhat to Do withScissors and GlueI don’t expect secondary students to bringglue and scissors to math class. Instead, Iset up a small table in the classroom andprovide several containers of glue,numerous pairs of scissors (sometimes tiedto the table), containers of markers andcolored pencils, a stapler, clear tape, andanything else I think students might needto make their Foldables. Don’t besurprised if students donate unusualmarkers, decorative-edged scissors, gelpens, stencils, and other art items to your publishing table.The more they make and use graphic organizers, the faster students become atproducing them.Storing GraphicOrganizers inStudent PortfoliosTurn one-gallon freezer bags into studentportfolios which can be collected andstored in the classroom. Students can alsocarry their portfolios in their notebooks ifthey place strips of two-inch clear tapealong one side and punch three holesthrough the taped edge.Have each student write his or her namealong the top of the plastic portfolio with apermanent marker and cover the writing with two-inch clear tape to keep it from wearing off.Cut the bottom corners off the bag so it won’t hold air and will stack and store easily.HINT: I found it more convenient to keep student portfolios in my classroom sostudent work was always available when needed and not “left at home” or “inthe car.” Giant laundry-soap boxes make good storage containers for portfolios.Let Students Use This Book As an Idea ReferenceMake this book available to students to use as an idea reference for projects, discussions, extracredit work, cooperative learning group presentations, and more.INTRODUCTION TO FOLDABLES
- 12. INTRODUCTION TO FOLDABLESSelecting the Appropriate FoldableDividing Math Concepts into PartsFoldables divide information and make it visual. In order to select the appropriate Foldable,decide how many parts you want to divide the information into and then determine whichFoldable best illustrates or fits those parts. Foldables that are three-dimensional also make thestudent interact with the information kinesthetically.For example, if you are studying the Properties of Equality you could choose a Foldable thathas five tabs (or sections). On the front tabs write the properties. Under the tabs, explain theproperties in words on one side and in symbols on the other side.Math Concepts That Can Be Divided into PartsAlgebra Geometry Statistics and Probabilitywrite algebraic expressions draw angles with a protractor determine ranges of setsevaluate expressions classify polygons interpret scatter plotssequence steps illustrate quadrilaterals display data collected in plotslist algebraic rules list examples of prisms draw models of combinationssolve equations name ordered pairsfind values for variables graph pointsMath Concepts Already Divided into PartsAlgebra Geometry Statistics and ProbabilityParts Concept Parts Concept Parts Concept5 Properties of Equality 2 collinear and noncollinear 3 mean, median, mode3 parentheses, brackets, 2 complementary and 1 Fundamental Countingand braces supplementary angles Principle2 equations and inequalities 2 parallel and perpendicular 4 Who, What, When,Where: Blaise Pascal2 numeric and algebraic 3 translation, rotation, 2 permutations andexpressions reflection combinations2 domain and range 6 types of triangles 2 upper quartile and lowerquartile7 properties of addition and 4 SSS, SAS, ASA, AAS 2 dependent andmultiplication independent events2 LCM and LCD 2 two types of special right 2 probability and oddstriangles3 monomials, binomials, 6 types of quadrilaterals 2 odds in favor and oddsand trinomials against2 powers and exponents 2 x-axis and y-axis 2 mutually inclusive andexclusive events©Glencoe/McGraw-Hill 3 Teaching Mathematics with Foldables
- 13. ©Glencoe/McGraw-Hill 4 Teaching Mathematics with FoldablesDividing Skills and Foldables into PartsReading, writing, and thinking skills can easily be used with Foldables. The following listsshow examples of skills and activities and a selection of Foldables divided into parts. You maywant to refer to this page as you select activities from the lists of math topics in this book.(See pages 35–90.)INTRODUCTION TO FOLDABLESFoldables Divided into Parts1 Part 2 PartsHalf Book Two-Tab BookFolded Book Pocket BookMatchbook Shutter FoldBound Book Matchbook Cut in HalfConcept-Map Book with Two Tabs3 Parts 4 PartsTrifold Book Four-Tab BookThree-Tab Book Standing CubePyramid Book Top-Tab BookLayered-Look Book Four-Door BookConcept Map with Three TabsAny Number of PartsAccordion Book Circle GraphLayered-Look Book Concept-Map BookSentence-Strip Holder Vocabulary BookFolded Table, Chart, or Graph Bound BookPyramid Mobile Pocket BooksTop-Tab Book(three or more sheets of paper)Skills and Activities Divided into Parts1 Part 2 PartsFind the Main Idea Compare and ContrastPredict an Outcome Cause and EffectNarrative Writing Similarities and DifferencesDescriptive Writing Opposite OperationsExpository WritingPersuasive Writing3 Parts 4 PartsVenn Diagrams Who, What, When, WhereKnow?-Like to Know?-Learned? What, Where, When, Why/HowBeginning, Middle, EndAny Number of PartsQuestioning Making and Using TablesFlow Charts Making and Using GraphsVocabulary Words Making and Using ChartsTimelines Sequencing Data or EventsConcept Webs or Maps
- 14. ©Glencoe/McGraw-Hill 5 Teaching Mathematics with FoldablesBasic Foldable ShapesThe following figures illustrate the basic folds that are referred to throughout the followingsection of this book.Taco Fold Hamburger FoldHot Dog FoldShutter FoldBurrito FoldValley FoldMountain FoldFOLDING INSTRUCTIONS
- 15. ©Glencoe/McGraw-Hill 6 Teaching Mathematics with FoldablesHalf BookFold a sheet of 8ᎏ12ᎏ" ϫ 11" paper in half.1. This book can be folded vertically like ahot dog or . . .2. . . . it can be folded horizontally like ahamburger.Use this book for descriptive, expository,persuasive, or narrative math writing, as well asgraphs, diagrams, or charts.FOLDING INSTRUCTIONS: 1-PART FOLDS21
- 16. ©Glencoe/McGraw-Hill 7 Teaching Mathematics with FoldablesFolded Book1. Make a half book.2. Fold it in half again like a hamburger. Thismakes a ready-made cover, and two smallpages for information on the inside.Use photocopied worksheets, Internet print outs,and student-drawn diagrams or maps to make thisbook. One sheet of paper can be used for twoactivities and two grades.FOLDING INSTRUCTIONS: 1-PART FOLDS12When folded, the photocopied sheet becomes a bookfor recording notes and questions.
- 17. Bound Book1. Take two sheets of 8ᎏ12ᎏ" ϫ 11" paperand fold each one like a hamburger. Placethe papers on top of each other, leavingone sixteenth of an inch between themountain tops.2. Mark both folds one inch from the outeredges.3. On one of the folded sheets, cut from thetop and bottom edge to the marked spoton both sides.4. On the second folded sheet, start at one ofthe marked spots and cut the fold betweenthe two marks.5. Take the cut sheet from step 3 and fold itlike a burrito. Place the burrito throughthe other sheet and then open the burrito.Fold the bound pages in half to form aneight-page book.©Glencoe/McGraw-Hill 8 Teaching Mathematics with FoldablesUse for math journals. Make large math project books using 11" ϫ 17" paper.12453FOLDING INSTRUCTIONS: 1-PART FOLDS
- 18. ©Glencoe/McGraw-Hill 9 Teaching Mathematics with FoldablesTwo-Tab Book1. Take a folded book and cut up the valleyof the inside fold toward the mountain top.This cut forms two large tabs that can beused front and back for writing andillustrations.2. The book can be expanded by makingseveral of these folds and gluing themside-by-side.Use this book for data that occurs in twos, forexample opposite operations.12FOLDING INSTRUCTIONS: 1-PART FOLDS
- 19. 3©Glencoe/McGraw-Hill 10 Teaching Mathematics with FoldablesMatchbook1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paper likea hamburger, but fold it so that one sideis one inch longer than the other side.2. Fold the one-inch tab over the short sideforming an envelope-like fold.3. Cut the front flap in half toward themountain top to create two flaps.Use this book to report on one or two vocabularywords, questions, or concepts. Collect matchbooksand use them to make great student-made bulletinboards.12FOLDING INSTRUCTIONS: 2-PART FOLDS
- 20. ©Glencoe/McGraw-Hill 11 Teaching Mathematics with FoldablesPocket Book1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paperin half like a hamburger.2. Open the folded paper and fold one ofthe long sides up two inches to form apocket. Refold along the hamburgerfold so that the newly formed pocketsare on the inside.3. Glue the outer edges of the two-inchfold with a small amount of glue.4. Optional: Glue a cover around thepocket book.Variation: Make a multi-pagedbooklet by gluing several pocketsside-by-side. Glue a cover aroundthe multi-paged pocket book.Use 3" ϫ 5" index cards inside the pockets.Store student-made books, such as two-tabbooks and folded books in the pockets.Example of several pocket books glued side-by-side.123 4FOLDING INSTRUCTIONS: 2-PART FOLDS
- 21. ©Glencoe/McGraw-Hill 12 Teaching Mathematics with FoldablesShutter Fold1. Begin as if you were going to make ahamburger but instead of creasing the paper,pinch it to show the midpoint.2. Fold the outer edges of the paper to meet atthe pinch, or mid-point, forming a shutterfold.Use this book for data occurring in twos. Or, makethis fold using 11" ϫ 17" paper and smallerbooks—such as the half book, journal, and two-tab book—that can be glued inside to create alarge project full of student work.12FOLDING INSTRUCTIONS: 2-PART FOLDS
- 22. ©Glencoe/McGraw-Hill 13 Teaching Mathematics with FoldablesTrifold Book1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paper into thirds.2. Use this book as is, or cut into shapes. If thetrifold is cut, leave plenty of fold on bothsides of the designed shape, so the book willopen and close in three sections.Use this book to make charts with three columnsor rows, large Venn diagrams, or reports on dataoccurring in threes.12FOLDING INSTRUCTIONS: 3-PART FOLDS
- 23. ©Glencoe/McGraw-Hill 14 Teaching Mathematics with FoldablesThree-Tab Book1. Fold a sheet of paper like a hot dog.2. With the paper horizontal, and the fold of thehot dog up, fold the right side toward thecenter, trying to cover one half of the paper.NOTE: If you fold the right edge over first,the final graphic organizer will open andclose like a book.3. Fold the left side over the right side to makea book with three folds.4. Open the folded book. Place your handsbetween the two thicknesses of paper and cutup the two valleys on one side only. This willform three tabs.Use this book for data occurring in threes.1234FOLDING INSTRUCTIONS: 3-PART FOLDS
- 24. Three-Tab Book VariationsVariation ADraw overlapping circles on the three tabsto make a Venn Diagram.Variation BCut each of the three tabs in half to makea six-tab book.©Glencoe/McGraw-Hill 15 Teaching Mathematics with FoldablesFOLDING INSTRUCTIONS: 3-PART FOLDS
- 25. Pyramid Foldor Mobile1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paper intoa taco, forming a square. Cut off theexcess rectangular tab formed by thefold.2. Open the folded taco and refold it theopposite way forming another tacoand an X-fold pattern.3. Cut one of the folds to the center ofthe X, or the midpoint, and stop. Thisforms two triangular-shaped flaps.4. Glue one of the flaps under the other,forming a pyramid.5. Label front sections and writeinformation, notes, thoughts, andquestions inside the pyramid on theback of the appropriate tab.Use to make mobiles and dioramas.Use with data occurring in threes.©Glencoe/McGraw-Hill 16 Teaching Mathematics with Foldables1234Record data inside the pyramid.FOLDING INSTRUCTIONS: 3-PART FOLDS
- 26. ©Glencoe/McGraw-Hill 17 Teaching Mathematics with FoldablesLayered-Look Book1. Stack two sheets of 8ᎏ12ᎏ" ϫ 11" paper so thatthe back sheet is one inch higher than thefront sheet.2. Bring the bottom of both sheets upwardand align the edges so that all of the layers ortabs are the same distance apart.3. When all tabs are an equal distance apart,fold the papers and crease well.4. Open the papers and glue them togetheralong the valley or inner center fold or,staple them along the mountain.When using more than two sheetsof paper, make the tabs smaller than an inch.1234FOLDING INSTRUCTIONS: 4-PART FOLDS
- 27. Four-Tab Book1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paper in halflike a hot dog.2. Fold this long rectangle in half like ahamburger.3. Fold both ends back to touch the mountaintop or fold it like an accordion.4. On the side with two valleys and onemountain top, make vertical cuts through onethickness of paper, forming four tabs.Use this book for data occurring in fours. Forexample: the four steps in the order of operations.©Glencoe/McGraw-Hill 18 Teaching Mathematics with Foldables123 4FOLDING INSTRUCTIONS: 4-PART FOLDS
- 28. ©Glencoe/McGraw-Hill 19 Teaching Mathematics with FoldablesEnvelope Fold1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paper into a tacoforming a square. Cut off the excess paperstrip formed by the square.2. Open the folded taco and refold it theopposite way forming another taco and anX fold pattern.3. Open the taco fold and fold the cornerstoward the center point of the X forming asmall square.4. Trace this square on another sheet of paper.Cut and glue it to the inside of the envelope.Pictures can be placed under or on top of thetabs, or can be used to teach fractional parts.Use this book for data occurring in fours. Forexample, four operations.2341FOLDING INSTRUCTIONS: 4-PART FOLDS
- 29. ©Glencoe/McGraw-Hill 20 Teaching Mathematics with FoldablesStanding Cube1. Use two sheets of the same size paper. Foldeach like a hamburger. However, fold oneside one half inch shorter than the other side.This will make a tab that extends out one halfinch on one side.2. Fold the long side over the short side of bothsheets of paper, making tabs.3. On one of the folded papers, place a smallamount of glue along the the small foldedtab, next to the valley but not in it.4. Place the non-folded edge of the secondsheet of paper square into the valley andfold the glue-covered tab over this sheetof paper. Press flat until the glue holds.Repeat with the other side.5. Allow the glue to dry completely beforecontinuing. After the glue has dried, the cubecan be collapsed flat to allow students towork at their desks. The cube can also befolded into fourths for easier storage, or formoving it to a display area.Use with data occurring in fours or make itinto a project. Make a small display cube using8ᎏ12ᎏ" ϫ 11" paper. Use 11" ϫ 17" paper to makelarge project cubes that you can glue other booksonto for display. Notebook paper, photocopiedsheets, magazine pictures, and current events alsocan be displayed on the large cube.12345This large cube project can be storedin plastic bag portfolios.FOLDING INSTRUCTIONS: 4-PART FOLDS
- 30. ©Glencoe/McGraw-Hill 21 Teaching Mathematics with FoldablesFour-Door Book1. Make a shutter fold using 11" ϫ 17" or12" ϫ 18" paper.2. Fold the shutter fold in half like ahamburger. Crease well.3. Open the project and cut along the twoinside valley folds.4. These cuts will form four doors on theinside of the project.Use this fold for data occurring in fours.When folded in half like a hamburger, afinished four-door book can be glued insidea large (11" ϫ 17") shutter fold as part of alarger project.1234FOLDING INSTRUCTIONS: 4-PART FOLDS
- 31. ©Glencoe/McGraw-Hill 22 Teaching Mathematics with FoldablesTop-Tab Book1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paper inhalf like a hamburger. Cut the centerfold, forming two half sheets.2. Fold one of the half sheets fourtimes. Begin by folding in halflike a hamburger, fold again likea hamburger, and finally again like ahamburger. This folding has formedyour pattern of four rows and fourcolumns, or 16 small squares.3. Fold two sheets of 8ᎏ12ᎏ" ϫ 11" paperin half like a hamburger. Cut thecenter folds, forming four halfsheets.4. Hold the pattern vertically and placeon a half sheet of paper under thepattern. Cut the bottom right handsquare out of both sheets. Set thisfirst page aside.5. Take a second half sheet of paperand place it under the pattern. Cutthe first and second right handsquares out of both sheets. Place thesecond page on top of the first page.12453FOLDING INSTRUCTIONS: 4-PART FOLDS
- 32. ©Glencoe/McGraw-Hill 23 Teaching Mathematics with Foldables6. Take a third half sheet of paper andplace it under the pattern. Cut the first,second, and third right hand squaresout of both sheets. Place this thirdpage on top of the second page.7. Place the fourth, uncut half sheet ofpaper behind the three cut out sheets,leaving four aligned tabs across the topof the book. Staple several times onthe left side. You can also place gluealong the left paper edges, and stackthem together. The glued spine isvery strong.8. Cut a final half sheet of paper withno tabs and staple along the left sideto form a cover.678FOLDING INSTRUCTIONS: 4-PART FOLDS
- 33. ©Glencoe/McGraw-Hill 24 Teaching Mathematics with FoldablesAccordion BookNOTE: Steps 1 and 2 should be done only ifpaper is too large to begin with.1. Fold the selected paper into hamburgers.2. Cut the paper in half along the fold lines.3. Fold each section of paper into hamburgers.However, fold one side one half inch shorterthan the other side. This will form a tab thatis one half inch long.4. Fold this tab forward over the shorter side,and then fold it back away from the shorterpiece of paper. In other words, fold it theopposite way.5. Glue together to form an accordion by gluinga straight edge of one section into the valleyof another section.NOTE: Stand the sections on end to form anaccordion to help students visualize how to gluethem together. (See illustration.)Always place the extra tab at the back of the bookso you can add more pages later.Use this book for number lines, timelines, studentprojects that grow, sequencing events or data, andmore.When folded, this project is used like a book, and it can be stored in student portfolios. When open,it makes a nice project display. Accordion books can be stored in file cabinets for future use, too.12453FOLDING INSTRUCTIONS: 4-PART FOLDS
- 34. ©Glencoe/McGraw-Hill 25 Teaching Mathematics with FoldablesPop-Up Book1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paperin half like a hamburger.2. Beginning at the fold, or mountain top,cut one or more tabs.3. Fold the tabs back and forth several timesuntil there is a good fold line formed.4. Partially open the hamburger fold andpush the tabs through to the inside.5. With one small dot of glue, glue figuresfor the pop-up book to the front of eachtab. Allow the glue to dry before goingon to the next step.6. Make a cover for the book by foldinganother sheet of paper in half like ahamburger. Place glue around the outsideedges of the pop-up book and firmly pressinside the hamburger cover.1 234 56FOLDING INSTRUCTIONS: ANY NUMBER OF PARTS
- 35. ©Glencoe/McGraw-Hill 26 Teaching Mathematics with FoldablesFolding into Fifths1. Fold a sheet of paper in half like a hotdog orhamburger for a five-tab book, or leave openfor a folded table or chart.2. Fold the paper so that one third is exposedand two thirds are covered.3. Fold the two thirds section in half.4. Fold the one third section backward to formfifths. The paper will be divided into fifthswhen opened.1234FOLDING INSTRUCTIONS: ANY NUMBER OF PARTS
- 36. ©Glencoe/McGraw-Hill 27 Teaching Mathematics with FoldablesFolded Table, Chart, or Graph1. Fold the number of vertical columns neededto make the table or chart.2. Fold the horizontal rows needed to make thetable or chart.3. Label the rows and columns.Remember: Tables are organized along verticaland horizontal axes, while charts are organizedalong one axis, either horizontal or vertical.TableChartFOLDING INSTRUCTIONS: ANY NUMBER OF PARTS
- 37. ©Glencoe/McGraw-Hill 28 Teaching Mathematics with FoldablesFolding a Circle into Tenths1. Fold a paper circle in half.2. Fold the half circle so that one third isexposed and two thirds are covered.3. Fold the one third (single thickness)backward to form a fold line.4. Fold the two thirds section in half.5. The half circle will be divided into fifths.When opened, the circle will be dividedinto tenths.NOTE: Paper squares andrectangles are folded into tenthsthe same way. Fold them so thatone third is exposed and twothirds is covered. Continue withsteps 3 and 4.ᎏ23ᎏᎏ31ᎏ123 45FOLDING INSTRUCTIONS: ANY NUMBER OF PARTS
- 38. Circle Graph1. Cut out two circles using a pattern.2. Fold one of the circles in half on eachaxis, forming fourths. Cut along oneof the fold lines (the radius) to themiddle of each circle. Flatten the circle.3. Slip the two circles together along thecuts until they overlap completely.4. Spin one of the circles while holding theother stationary. Estimate how much ofeach of the two (or you can add more)circles should be exposed to illustrategiven percents or fractional parts of data.Add circles to represent more thantwo percents.©Glencoe/McGraw-Hill 29 Teaching Mathematics with FoldablesUse small circle graphs in student projectsor on the front of tab books.Use large circle graphs on bulletin boards.123 4FOLDING INSTRUCTIONS: ANY NUMBER OF PARTS
- 39. ©Glencoe/McGraw-Hill 30 Teaching Mathematics with FoldablesConcept-Map Book1. Fold a sheet of paper along the long or shortaxis, leaving a two-inch tab uncovered alongthe top.2. Fold in half or in thirds.3. Unfold and cut along the two or three insidefold lines.FOLDING INSTRUCTIONS: ANY NUMBER OF PARTS
- 40. Vocabulary Book1. Fold a sheet of notebook paper in half like ahotdog.2. On one side, cut every third line. This usuallyresults in ten tabs.3. Label the tabs.©Glencoe/McGraw-Hill 31 Teaching Mathematics with FoldablesUse for vocabulary books.Use to take notes andrecord data.Leave the notebook holesuncovered and theFoldable can be stored ina notebook.Use for recording student questionsand answers.FOLDING INSTRUCTIONS: ANY NUMBER OF PARTS
- 41. Billboard Project1. Fold all pieces of the same size of paper inhalf like hamburgers.2. Place a line of glue at the top and bottom ofone side of each folded billboard section andglue them edge-to-edge on a backgroundpaper or project board. If glued correctly, alldoors will open from right to left.3. Pictures, dates, words, etc., go on the front ofeach billboard section. When opened, writingor drawings can be seen on the inside left ofeach section. The base, or the part glued tothe background, is perfect for more in-depthinformation or definitions.Use for timelines or sequencing data and numberlines.©Glencoe/McGraw-Hill 32 Teaching Mathematics with Foldables123FOLDING INSTRUCTIONS: PROJECTS USING FOLDS
- 42. ©Glencoe/McGraw-Hill 33 Teaching Mathematics with FoldablesSentence-Strip Holder1. Fold a sheet of 8ᎏ12ᎏ" ϫ 11" paper inhalf like a hamburger.2. Open the hamburger and fold the twoouter edges toward the valley. This formsa shutter fold.3. Fold one of the inside edges of the shutterback to the outside fold. This fold forms afloppy “L”.4. Glue the floppy L-tab down to the base sothat it forms a strong, straight L-tab.5. Glue the other shutter side to the front ofthis L-tab. This forms a tent that is thebackboard for the flashcards or studentwork to be displayed.Fold the edge of the L-tab up one quarterto one half to form a lip that will keep thestudent work from slipping off the holder.Glue downUse these holders to display studentwork on a table, or glue them onto abulletin board to make it interactive.1345FOLDING INSTRUCTIONS: PROJECTS USING FOLDS2
- 43. ©Glencoe/McGraw-Hill 34 Teaching Mathematics with FoldablesSentence Strips1. Take two sheets of 8ᎏ12ᎏ" ϫ 11" paper andfold into hamburgers. Cut along the foldlines making four half sheets. (Use as manyhalf sheets as necessary for additional pagesto your book.)2. Fold each sheet in half like a hotdog.3. Place the folds side-by-side and staple themtogether on the left side.4. One inch from the stapled edge, cut the frontpage of each folded section up to themountain top. These cuts form flaps that canbe raised or lowered.To make a half-cover, use a sheet of constructionpaper one inch longer than the book. Glue theback of the last sheet to the contruction paper stripleaving one inch, on the left side, to fold over andcover the original staples. Staple this half-cover inplace.1234FOLDING INSTRUCTIONS: PROJECTS USING FOLDS
- 44. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 35 Teaching Mathematics with FoldablesWhole NumbersFoldableSkill Activity SuggestionPartsAssociativeLaw+CommutativeLawXAssociativeLawXCommutativeProperty+Four-Door BookSumDifferenceProductQuotientFour-Tab bookCommutativePropertyXAssociativePropertyXAssociativeProperty+Prime Both CompositeThree-Tab Venn diagramPrimeNumbersCompositeNumbersShutter Folddefine whole numbers as the counting numbers( 0, 1, 2, 3. …) and list examples 2explain why fractions such as ᎏ33ᎏ, ᎏ44ᎏ, and ᎏ88ᎏ are wholenumbers 1find 10 examples of equivalent whole numbers:3, ᎏ93ᎏ 10describe the two basic operations that can be performedon whole numbers:addition (combines individual numbers) andmultiplication (combines groups of numbers)subtraction and division as the inverse operationsof addition and multiplication 2explain the Commutative Property of Addition and theand use Commutative Property of Multiplication.the Associative Property of Addition and theAssociative Property of Multiplication 4outline the Distributive Property, also called the DistributiveProperty of Multiplication over Addition 1differentiate the Commutative Property, Associative Property, andbetween the Distributive Property 3define sum, difference, product, and quotient as theyrelate to whole numbers 4determine if subtraction and division are associative(neither are) and explain your answer 2list and the order in which operations should bedescribe performed: multiply and/or divide then addand/or subtract 2compare and two types of whole numbers: primes andcontrast composites 2note and every whole number is either prime or compositeexplain except for 0 and 1 which are neither 1give examples of prime factors for six whole numbers 6reduce given fractions to see what whole number theyrepresent: ᎏ142ᎏ, ᎏ198ᎏ any numberdetermine whole numbers are greater than, less than, orequal to other whole numbers 3round whether five whole numbers to the nearest ten,nearest hundred, nearest thousand 5demonstrate three ways whole numbers can be written 3use whole numbers to solve real-world problems any numberVenn diagram characteristics of prime numbers, composite numbers, 3and both
- 45. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 36 Teaching Mathematics with FoldablesFoldableSkill Activity SuggestionPartsdefine integers as the set of whole numbers and theiropposites, or negative numbers(…Ϫ3, Ϫ2, Ϫ1, 0, 1, 2, 3…) 1differentiate positive and negative numbersbetween 2list examples of positive and negative integers 2explain in your own words why you think zero is neitherpositive nor negative, but part of the set ofintegers 1show how the set of integers might be written{… Ϫ3, Ϫ2, Ϫ1, 0, 1, 2, 3, …} and explain the useof ellipses 2describe four examples of the use of negative numbers inthe real world: temperature, balancing accountbooks, reporting weight loss, distance lost in agame or sport 4define absolute value as the number of units a numberis from 0 on a number line 1write the definition of absolute value in words andsymbols 2find the absolute value of given expressions any numberexplain why absolute value can never be less than 0 1describe absolute value in terms of distance and giveexamples 2graph given integers on a number line any numbertwo points on a number line so that thecoordinates of both have an absolute value ofa given number any numberwrite inequalities using integers any numbersequence given integers from greatest to least, or fromleast to greatest any numberstate which integers have the greater absolute value any numberdescribe how to determine if one integer is less thanor greater than another integer 2design a concept map that shows integers as the union ofwhole numbers and their opposites 2make a number line for whole numbers and integers 1IntegersTemperatureAccountingWeight LossSportsFour-TabBookNumber LineNegativeNumbersPositiveNumbersIntegersWholeNumbersNegativeNumbersTwo-Tab Concept MapTwo-Tab BookFolded ChartNumberAbsolutevalue
- 46. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 37 Teaching Mathematics with FoldablesFoldableSkill Activity SuggestionPartsdescribe how to add integers with the same sign 1use a number line and show how to add integerswith the same sign 2explain how to add integers with different signs 1use a number line and show how to add integerswith different signs any numbercompare and adding integers with the same and different signscontrast 2draw a model that shows how to find the sum of twointegers on a number line and describe yourmodel 2explain how adding and subtracting are inverseoperations that “undo” each other 2use a number line to show what happens when youadd opposites like Ϫ9 and 9 any numberdefine an integer and its opposite as additive inversesof each other 1describe additive inverse in words, numerically, andalgebraically 3explain how to subtract integers using what you knowabout additive inverses 1describe how to subtract an integer in words, numerically,and algebraically 3draw a model that shows how to find 7 Ϫ (Ϫ2) 1simplify expressions such as 15x Ϫ 18x any numberAddIntegerswithSameSignsAddIntegerswithDifferentSignsTwo-Tab BookHow to Subtract anInteger UsingWordsFind SumsUsing a Number Line... 3 2 1 0 1 2 3 ...Half BookNumbers AlgebraThree-Tab Concept MapNumericalWordsPyramid FoldAdditive InversesAdding IntegersSubtracting IntegersShutter FoldIntegers: Adding and Subtracting
- 47. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 38 Teaching Mathematics with FoldablesIntegers: Multiplying and DividingFoldableSkill Activity SuggestionPartsdescribe how to multiply integers with the same sign 1use a number line to show and explain how to multiplyintegers with the same sign any numberexplain how to multiply integers with different signs 1use a number line to show and explain how tomultiply integers with different signs 2compare and multiplying integers with the same and differentcontrast signs 2draw a model that shows how to find the product oftwo integers on a number line and write aboutthe process 2review how multiplying and dividing are inverseoperations that “undo” each other 2explain how to divide integers with the same sign 1demonstrate how to divide integers with different signs 1describe how to divide integers with the same anddifferent signs in words, numerically, andalgebraically 3find similarities and differences between multiplyingand dividing integers with the same signs andmultiplying and dividing integers with differentsigns 4Multiply Integers with theSame SignMultiply Integers withDifferent SignsInverse OperationsMultiply DivideShutter FoldTwo-Tab Concept MapFind SumsUsing a Number Line... Ϫ3 Ϫ2 Ϫ1 0 1 2 3 ...Half BookDividingSame sign DifferentsignsMatchbook
- 48. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 39 Teaching Mathematics with FoldablesRational NumbersFoldableSkill Activity SuggestionPartsdefine rational numbers as numbers that can be writtenas a ratio, or fraction where a and b are integersand b is not equal to 0 1explain why whole numbers, integers, fractions, mixednumbers, terminating decimals, and repeatingdecimals are rational numbers 6chart and list examples of whole numbers, integers,fractions, terminating decimals, and repeatingdecimals 5document five rational numbers encountered in a day 5rename 10 rational numbers 10write decimals as fractions and fractions as decimals 2solve equations using rational numbers any numberdesign a concept map for rational numbers. rationalnumbers: fractions, repeating and terminatingdecimals, integers, and whole numbers 5estimate sums of rational numbers any numberfind sums of rational numbers any numbersolve equations involving rational numbers any numberinequalities involving rational numbers any numberexplain how adding and subtracting rational numbersfollow the same principles as adding andsubtracting integers 2use rational numbers to write three examples of theCommutative Property 3rational numbers to write three examples of theAssociative Property 3rational numbers to write three examples of theIdentity Property 3rational numbers to write three examples of theInverse Property 3DecimalsasFractionsFractionsasDecimalsCommutativePropertyAssociativePropertyIdentityPropertyInversePropertyFour-Tab BookVocabularyBookTwo-Tab BookConcept MapRational NumbersF D I W0.6250.40.3333...5 2/3Ϫ2 5/8Ϫ12.121...6/3Ϫ50.0915.8
- 49. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 40 Teaching Mathematics with FoldablesRational Numbers: FractionsFoldableSkill Activity SuggestionPartsdefine fractions three ways:as part of a wholeas multiplication (ᎏ35ᎏ means 3 times ᎏ15ᎏ)as division (ᎏ35ᎏ means 3 divided by 5) 3differentiate proper and improper fractionsbetween 2rename whole numbers as improper fractions with a givendenominator 2order ten fractions from least to greatest 10graph five fractions on a number line 5use a number line to determine if fractions areequivalent any numberexpress six ratios as fractions in simplest form 6determine if five fractions are in their simplest form bychecking to see if the GCF of the numerator andthe denominator is 1 5list examples of fractions in simplest form andfractions that are not in simplest form any numberexplain why it is easier to compare fractions with thesame denominator 1describe how the least common denominator of fractionscould be used to compare them 1define a mixed number as the sum of a whole number and afraction 1write mixed numbers as improper fractions and improperfractions as mixed numbers 2compare fractions and decimals 2chart equivalent fractions and decimals 2Venn diagram given specific examples, compare characteristics oflike fractions, unlike fractions, and both 3explain how to add like and unlike fractions in wordsand symbols 4add fractions with like and unlike denominators 2subtract fractions with like and unlike denominators 2explain how to subtract fractions with like and unlikedenominators 2compare and adding and subtracting unlike fractionscontrast 2multiply fractions with like and unlike denominators 2explain how to multiply fractions with like and unlikedenominators in words and symbols 4divide fractions with like and unlike denominators 2prove that dividing by 2 is the same as multiplyingby ᎏ12ᎏ, its multiplicative inverse 2write word problems that contain fractions any numberexpress given fractions as percents 2tell how you know if a fraction is greater than 100%or less than 1% 1compare and a fraction and an algebraic fractioncontrast 2write six algebraic fractions in simplest form 6Fraction asDivisionFrac-tionas awholePyramid FoldProperFractionsImproperFractionsTwo-Tab BookFractions in Simplest FormFractions not in SimplestFormShutter FoldFraction PercentFolded Chart
- 50. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 41 Teaching Mathematics with FoldablesFoldableSkill Activity SuggestionPartsorder ten decimals from least to greatest 10rename five decimals as fractions 5explain why decimals can be written as fractions withdenominators that are powers of ten 1find equivalent decimals and fractions 2differentiate between terminating decimals, repeatingdecimals, and decimals that do not terminatenor repeat 3compare and terminating and repeating decimalscontrast 2find examples of decimals that do not terminate orrepeat any numberwrite four fractions as terminating or repeating decimals 4define terminating decimals 1describe repeating decimals 1Venn diagram characteristics of terminating decimals, repeatingdecimals, both 3estimate sums of six decimals using rounding and describeeach 6find six sums of decimals and describe the process 6estimate six differences of decimals and write about theprocess 6find six differences of decimals and explain theprocess any numberstate additive inverses of five decimalsexample: 8.45 and Ϫ8.45 5illustrate the rule for placement of the decimal point whenmultiplying decimals 1explain in your own words how to divide by a decimal 1simplify four expressions with decimals and explain each step 4evaluate five expressions with decimals and explain each step 5Rational Numbers: DecimalsAssociativeLaw+CommutativeLawXAssociativeLawXCommutativePropertyFour-Door BookAssociativePropertyInversePropertyIdentityPropertyTerminating Both RepeatingThree-Tab Venn DiagramTerminatingDecimalsRepeatingDecimalsTwo-Tab BookThree-Tab Concept MapDecimalsTerminating Repeating Neither
- 51. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 42 Teaching Mathematics with FoldablesFoldableSkill Activity SuggestionPartsPercentsdefine percent as a ratio that compares a number to100 or tells how many out of 100 1explain why percent also means hundredths, or perhundred 1write five percents as fractions and explain 5use the percent symbol when writing percents any numberequations to solve problems with percents any numbermake a table that expresses decimals and fractions as percents 3that expresses percents as decimals and fractions 3describe times when it is more advantageous to usepercent and times when it is more advantageousto use fractions 2use the percent proportion to write five fractions aspercents 5solve six problems involving percents 6find the percent proportion of four numbers and explainExample: find 10% of 160 4estimate three percents and outline the process 3solve two percent problems with percent equationsand sequence the steps 2two real-world problems involving percent 2write expressions for percents any numberuse percents to estimate any numberexplain how to estimate x% of a number 1list five examples of percents used in everyday lifesuch as weather bureau’s rain prediction, interestrates, discounts, and commissions and explaintheir use 5describe percent of change as the ratio of the amount ofchange to the original amount 1differentiate between percent of increase and percent ofdecrease 2calculate percent of increase and percent of decrease 2FractionPercent%ofIncrease%ofDecreaseTwo-Tab BookDecimal Fraction PercentPercentIn daily lifeHalf BookFolded ChartThree-Tab BookBound BookPercentJournal
- 52. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 43 Teaching Mathematics with FoldablesRatiosProportionsFoldableSkill Activity SuggestionPartsFoldableSkill Activity SuggestionPartsdefine ratio as a comparison of two numbers by division 1write four ratios four different waysExample: 2 to 3, 2:3, ᎏ23ᎏ, and 2 Ϭ 3 4five ratios as fractions in simplest form 5expressions for five ratios 5describe rate as a ratio that is a comparison of twomeasurements with different units ofmeasurement 1Venn diagram characteristics of ratios, rates, and both 3make a table that shows five or more ratios and rates asfractions in simplest form 5ϩgive three examples of unit rate 3express given ratios as unit rates any numberresearch the history of the golden ratio and explain itspurpose 2investigate three examples of how the golden ratio has beenand discover used over the last 4000 years to create art andarchitectureExample: Pyramid of Khufu in Giza 3describe the golden ratio in your own words 1define a scale drawing as a drawing that is eithersmaller or larger than the actual object andgive examples of scale drawings 2explain scale as the ratio of the lengths on a drawingto the actual lengths of an object 1define proportion as two equal fractions, or anequivalent relationship between two ratios 1solve given proportions any numberdetermine if two ratios form a proportion by checking theircross productsExample: ratios, check, results 3state the property of proportions in your own words 1define extremes and means 2demonstrate how cross products can be used to tell whethertwo fractions form a proportion any numberuse proportions to solve real-world problems any numberproportions to estimate populations any numberVenn diagram ratios, proportions, both 3explain pi as a constant of proportionality and giveexamples 2RatioFractionSimplest FormRatios Both RatesExtremesMeansGolden RatioExample1Example3Terms andExamplesRatioRateUnit RateGolden RatioScaleProportionpi = Constant ProportionFolded ChartThree-tab Venn diagramTwo-Tab BookLayered Book(4 sheets of paper)Pyramid Fold
- 53. MATH ACTIVITIES USING FOLDABLES©Glencoe/McGraw-Hill 44 Teaching Mathematics with FoldablesReal Number SystemFoldableSkill Activity SuggestionPartsFoldableSkill Activity SuggestionPartsdesign a that shows the set of real numbers is composedconcept map of the set of rational numbers and the set ofirrational numbers 2identify numbers in the real number system any numberexplain in words and symbols the real number system 2Venn diagram the real number system 3chart numbers into the categories of whole number,integer, rational, irrational, and real squares andsquare roots 6define a square root as one of two equal factors of anumber 1describe a square root in words and symbols 2find the square root of 49, 25, 81, and 64 4estimate square roots any numbersolve equations by finding square roots any numbercompare and numbers that are and are not perfect squarescontrast 2Irrational Numbersdefine irrational numbers as numbers that cannot beexpressed as fractions ᎏabᎏ, where a and b areintegers and b does not equal 0 1explain irrational numbers in words and symbols 2determine whether three given numbers are rational orirrational and explain your reasoning 3compare and rational and irrational numberscontrast 2give examples of irrational numbers that are less than Ϫ15 any numberdescribe why pi and the square root of 3 are examples ofirrational numbers 2RationalNumbersIrrationalNumbersRationalNumbersIrrationalNumbersNumbersThatArePerfectSquaresNumbersThatAre NotPerfectSquaresSquareRoot of49SquareRoot of25SquareRoot of81SquareRoot of64WholeNumbersRealNumbersShutter FoldPocket BookTwo-Tab BookStanding CubeFour-Tab Book
- 54. ©Glencoe/McGraw-Hill 45 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESSets and VariablesFoldableSkill Activity SuggestionPartsdefine a variable as a placeholder used in algebra 1speculate as to why variables are usually letters 1explain how the use of a variable can help solve algebraproblems 1define like terms as terms with the same variable 1compare and a numeric expression and an algebraic expression,contrast or expressions with and without variables 2chart expressions in words and symbols, numerically,and algebraically 3 or 4state the Substitution Property of Equality (For allnumbers a and b, if a ϭ b, then a may bereplaced with b.) 1demonstrate the use of the Substitution Property of Equality 1show multiplication and division notations used withvariables 2write the meaning of several algebraic expressions any numberevaluate expressions containing variables any numbertranslate verbal phrases into algebraic expressions usingvariables 2write verbal phrases for given algebraic expressions 2chart words that can be used to denote addition,subtraction, multiplication, and division whenreading or writing algebraic expressions 4describe the use of the following symbols in algebra:parentheses, brackets, and braces 3compare an independent variable and a dependent variable 2research the “who, what, when, where” of: Georg Cantor(1845–1918) developer of the theory of sets 4AlgebraicExpressionBothNumericExpressionThree-TabVenn DiagramIndependentVariableDependentVariableTwo-Tab BookWrittenExpressionAlgebraicExpressionFolded ChartThree-Tab Book() {}[]
- 55. ©Glencoe/McGraw-Hill 46 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESExpressionsdefine a mathematical expression as any combinationof numbers and operations such as addition,subtraction, multiplication, and division 1describe what it means to evaluate an expression 1demonstrate how an expression can have several numericalvalues any numberexplain why it is important to have an order of operationswhen evaluating expressions 1sequence the steps used to find the value of an expression any numberevaluate expressions without grouping symbols using theorder of operations 2expressions with grouping symbols using theorder of operations 2demonstrate how the order of operations can be changedusing grouping symbols any numberillustrate the use of brackets [ ] and parentheses ( ) 2write ten expressions and find their values 10show different ways to indicate multiplication in anexpression 2different ways to indicate division in an expression any numberselect three numbers and use them to write as manyexpressions as you can 3compare and expressions with and without variables 2contrastexplain that an expression is in its simplest form whenit has no like terms and no parentheses 1chart expressions that are and are not in their simplestform 2describe radical expressions and give examples 2explain how to add, subtract, multiply and divideradical expressions 4FoldableSkill Activity SuggestionPartsDescribeExpressionsEvaluateExpressionsExpressionsWITHGroupingSymbolsExpressionsWITHOUTGroupingSymbolsShutter FoldTwo-Tab BookWriteExpressionsUsing4,8,6WriteExpressionsUsing5,9,12WriteExpressionsUsing3,8,15Three-Tab BookTwo-Tab Matchbook1st 2ndOrder of Operations
- 56. ©Glencoe/McGraw-Hill 47 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESFoldableSkill Activity SuggestionPartswrite the Commutative and Associative Properties ofAddition and Multiplication numerically andalgebraically 4use the Commutative Properties of Addition andMultiplication to evaluate expressions 2rewrite expressions using the Commutative Property 2use the Associative Properties of Addition andMultiplication to evaluate expressions 2rewrite expressions using the Associative Property any numbercompare and the Associative and Commutative Propertiescontrast 2describe the importance of the Identity Properties ofAddition and Subtraction 2describe and the Zero Product Propertyuse 2make a table to show seven properties of addition andmultiplication 7write the Distributive Property in words and numerically 2read the expression a(b ϩ c) as “a times the quantityb plus c” 1describe in your own words the purpose of the DistributiveProperty 1rewrite expressions different ways using the DistributiveProperty any numberrestate expressions using the Distributive Property any numbershow how the Distributive Property can be used tosimplify expressions with like terms 1make a table to describe and give examples of:Commutative Property of AdditionCommutative Property of MultiplicationAssociative Property of AdditionAssociative Property of MultiplicationIdentity Property of AdditionIdentity Property of MultiplicationZero Product Property any numberuse the Product Property of Radicals and theQuotient Property of Radicals to evaluateexpressions 2Seven properties of additionand multiplicationSimplestformExpressionNotsimplestformExpressionRewrittenexpressionLayered Book(4 sheets of paper)Folded ChartProductPropertyQuotientPropertyTwo-Tab BookPropertiesLayered Book(3 sheets of paper)2345671
- 57. ©Glencoe/McGraw-Hill 48 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESEquationsFoldableSkill Activity SuggestionPartsdifferentiate an expression and an equation 2betweencompare an equation to a balance 2Venn diagram characteristics of equations, open sentences, and both 3list examples of equations any numbertell about equations that have no solution, or have asolution set that is null or empty 2draw two symbols that represent the empty or null set 2compare and solution sets that are never true and solution setscontrast that are always true 2explain why equations that contain variables are calledopen sentences 1find values for variables that make equations true any numberexplain the solution of an equation 1solve equations with variables and write about how youfound the solution 2chart solutions and open sentences 2solve equations with variables on each side any numberequations using inverse operations any numberdescribe how inverse operations “undo” each other 1write inverse operations for addition equations 2inverse operations for subtraction equations 2solve equations using the Addition Property of Equality any numbersolve equations using the Subtraction Property ofEquality any numberwrite examples of equations that are and are notequivalent 2explain when to use the Addition Property of Equality tosolve an equation and give examples 2solve equations using the Division Property of Equality any numberequations using the Multiplication Property ofEquality any numbersix equations using rational numbers 6six equations with variables on each side 6six equations with grouping symbols 6ten equations that have an infinite number ofsolutions 10explain what is meant by the root, or roots, of threeequations 3use integers in equations any numbersolve equations containing rational numbers any numberequations with two or more operations any numberwrite five verbal problems for equations with two ormore operations 5Equations BothOpenSentenceThree-Tab Venn DiagramExpressionEquationTwo-Tab BookInverseEquationTwo-Tab BookFolded ChartMultiplication Property ofEqualityAddition Property ofEqualityShutter Fold
- 58. ©Glencoe/McGraw-Hill 49 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESInequalitiesFoldableSkill Activity SuggestionPartsdefine inequalities as mathematical sentences thatcontain greater than or less than symbols 1write inequalities that are true and inequalities that arefalse 2inequalities that are open, or contain a variablethat must be replaced with a number any numberchart inequalities that are true, false, and open 3explain inequality signs that are a combination of theequals sign and the inequality symbols 2chart common phrases that are heard in everyday lifethat correspond to inequalities any numberVenn diagram methods for solving equations, inequalities, and both 3solve ten inequalities 10write sentences for inequalities and translate sentencesinto inequalities 2five inequalities and graph the solutions 5solve inequalities mentally any numberstate in your own words the Addition Property ofInequality and give two examples 2explain the Subtraction Property of Inequality to someone 1solve inequalities by using the Addition and SubtractionProperties of Inequality 2describe the Addition and Subtraction Properties ofInequality in words and symbols 4write the Multiplication and Division Properties ofInequalities in words and symbols 4solve inequalities by multiplying or dividing by apositive number 2inequalities by multiplying by a negative number 2solve inequalities that involve more than one operation 2Venn diagram method for solving an inequality involvingmultiplication, and for solving an inequality involvingdivision, both 3use inequality symbols when comparing fractions any numbersolve inequalities containing rational numbers any numberVenn diagram solving an inequality with rational numbers,solving an inequality involving integers 3solve inequalities with multiple steps any numberwrite verbal problems with inequalities any numberdescribe a compound inequality as two inequalitiesconnected by “or” or “and” and give examples 2Sentence InequalityEquations Both InequalitiyThree-Tab Venn DiagramTrueInequalitiesFalseInequalitiesTwo-Tab BookAdditionProperty ofInequalitySubtractionProperty ofInequalityTwo-Tab BookFolded ChartTwo-Tab MatchbookSingle CompoundInequalities
- 59. ©Glencoe/McGraw-Hill 50 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESRelations and FunctionsFoldableSkill Activity SuggestionPartsdefine relations, functions, and graphing 3Venn diagram all functions are relations, but not all relations arefunctions 3make a concept map to show a relation as domain andrange 2write the domain and range of given relations 3define function as a relation in which each element ofthe domain is paired with exactly one element inthe range 1graph five relations to determine if they are functions 5determine whether four relations are functions by using thevertical line test 4use functions to describe relationships between twoquantities 2make function tables any numberuse function tables to find output values any numberdescribe the inverse of a relation 1DomainRelationRangeRelationFunctionGraphicsFactors MultiplesTwo-Tab BookFolded ChartThree-Tab BookBound BookRelationsandFunctionsJournalTwo-TabConcept Map BookDomain RangeRelation
- 60. ©Glencoe/McGraw-Hill 51 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESFactorsFoldableSkill Activity SuggestionPartsexplain that the factors of a whole number divide thatnumber with a remainder of 0 1use the phrase “divisible by” when describing thefactors of a given number 1determine whether one number is a factor of another any numbermake a chart of divisibility rules, examples, and descriptions 3differentiate even and odd numbers and explain how theybetween relate to factors 2describe multiplication facts as they relate to factors 1explain why 1 is a factor of every nonzero number 1mentally what five numbers are divisible bydetermine Example: 27, 64, 189, 370, 455 5chart numbers with exactly 2, 3, 4, 5, and 6 factors 5define the greatest common factor of two or morenumbers as the greatest factor these numbershave in common 1list the factors of three sets of numbers and find thegreatest factor each set has in common 3read GCF as the “greatest common factor” 1use prime factorization to find the GCF of a set ofnumbers any numberexplain how the product of the common prime factors oftwo or more monomials is their GCF 1Venn diagram find the GCF of two numbers by making a Venndiagram of their factors 3define relatively prime numbers as numbers with 1 astheir only common factor 1determine whether given pairs of numbers are relativelyprime any numberdefine a prime number as a whole number greater thanone that has exactly two factors, one and itself 1a composite number as a whole number greaterthan one that has more than two factors 1differentiate prime and composite numbers 2betweenprove that a composite number can always beexpressed as a product of two or more products any numberexplain why 0 and 1 are considered neither prime norcomposite 2list the factors of 1 and explain your list 1describe every whole number greater than 1 is eitherprime or composite 1Equations Both InequalityThree-Tab Venn DiagramPrimefactorsSet ofnumbersGCFEven numbersOdd numbersTwo-Tab BookFolded ChartNumber GCF NumberThree-Tab Venn Diagram27 64 189 370 455Five-Tab BookDivisible by ?
- 61. ©Glencoe/McGraw-Hill 52 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESMultiplesFoldableSkill Activity SuggestionPartsdefine a multiple of a number as a product of that numberand a whole number 1chart the multiples of 2, 3, 4, 5, 6, 7, 8, 9, and 10 9differentiate between factors and multiples 2find the common multiples of two numbers such as 2and 5 2determine the least common multiple of two numbers 2read LCM as Least Common Multiple 1use a Venn diagram to find the LCM of two numbersusing their prime factorization 3find the LCM of a set of numbers or algebraicexpressions any numberread LCD as Least Common Denominator 1find the LCD for given pairs of fractions any numberVenn diagram finding a LCM, finding a LCD, both 3explain why fractions need the same denominator to becompared 1find factors and multiples 2LCM Both LCDThree-Tab Venn DiagramMultiples of2345678910Layered Book(5 sheets of paper)Folded ChartFirstNumberLCMSecondNumber
- 62. ©Glencoe/McGraw-Hill 53 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESMonomials and PolynomialsFoldableSkill Activity SuggestionPartsdefine a monomial as an integer, a variable, or aproduct of integers and one or more variables 1a constant as a monomial that is a real number 1Venn diagram characteristics of monomials, constants, and both 3list ten examples of monomials and explain what theyhave in common 10determine whether an expression is or is not a monomial andexplain your reasoning 2multiply monomials any numberdescribe in words and symbols the Power of a Monomial 2Venn diagram Power of a Product Property, Power of a PowerProperty, both ϭ Power of a Monomial 3divide monomials any numberexplain the degree of a monomial as the sum of theexponents of its variables 1list four monomials and their degrees 4chart examples of polynomials, or algebraic expressions,with one, two, three, and many terms 4examples of monomials, binomials, and trinomials 3define polynomial as a monomial, or a sum of monomials,and give four examples 4find the degree of three polynomials using the following:1. find the degree of each term2. determine the greatest degree of the terms3. state the greatest degree of any term as thedegree of the polynomial 3add polynomials and write about the process any numbersubtract polynomials and write about the process any numberfind the additive inverses of five polynomials 5multiply a polynomial by a monomial and outline the steps 2simplify four expressions involving polynomials 4use the FOIL method to multiply two binomials andthe four steps 4BinomialsOtherPolynomialsMonomialsFolded ChartPower of aPowerPropertyPower of aMonomialPower of aProductPropertyThree-TabVenn DiagramAdditionpolynomialSubtractionpolynomialTwo-Tab BookTwo-Tab MatchbookWords SymbolsPower of aMonomialFOILHalf Book
- 63. ©Glencoe/McGraw-Hill 54 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESPowers and ExponentsFoldableSkill Activity SuggestionPartsPowers inExpressionsPowers inEquationsTwo-Tab BookPower of aPowerPower of aProductPower of aQuotientTwo-Tab MatchbookMultiply DividePowers that have the same baseThree-Tab BookVocabularyBook103(-9)3(-2)5b4c45a4b0-103(b-1)4a2+3a-172define powers as numbers that are expressed usingexponents 1read expressions containing powers any numberdescribe how the second and third powers have specialnames related to geometry 2write expressions containing powers any numberexpressions containing powers as multiplicationexpressions any numberwrite powers as multiplication expressions any numberexplain how to multiply powers that have the same base 1how to divide powers that have the same base 1compare and products of powers and quotients of powers 2contrastuse powers in expressions and equations 2define scientific notation as numbers written as theproduct of a factor and a power of 10 1write ten numbers using scientific notation 10read scientific notation any numberorder numbers written in scientific notation any numbercompare numbers in scientific notation with positive andnegative exponents 2use scientific notation to evaluate five equations 5outline Properties of Powers—Power of a Power, Power of aProduct, and Power of a Quotient 3explain how exponents are used to tell how many timesa number is used as a factor 1rational exponents in words and symbols 2define the term base as it relates to exponents 1write four expressions using exponents 4three expressions with rational exponents insimplest radical form 3evaluate five expressions using exponents 5show expressions in either exponential or radical form 2numbers in standard and expanded form 2use the order of operations to evaluate algebraicexpressions with powers any numberwrite expressions using positive and negative exponents 2compare the square of a difference and the square of a sum 2tell whether given expressions are in simplest form and why 2
- 64. SequencesFoldableSkill Activity SuggestionPartsdefine an arithmetic sequence 1explain how to describe even and odd numbers as arithmeticsequences 2differentiate numbers in a sequence and numbers in anbetween arithmetic sequence 2compare and sequences that are and are not arithmetic 2contrastdescribe the terms of a sequence 1find the next terms of five given sequences 5determine the common differences of three arithmeticsequences 3write an original arithmetic sequence 1outline the steps you took to write an arithmetic sequencewrite expressions that represent terms in a sequence any numberresearch the Fibonacci sequence and why the Fibonaccisequence is not arithmetic 2define a geometric sequence 1explain how each term in a geometric sequenceincreases or decreases by a common factor,called the common ratio 2determine if given sequences are geometric 2find the common ratio of a geometric sequence andlist the next five terms 3AssociativeLaw+CommutativeLawXAssociativeLawXLeonardoofPisaFour-Door BookWhereWhy/HowWhenNonarithmeticsequenceBoth ArithmeticsequenceThree-Tab Venn DiagramSequence CommonratioList next5 termsShutter FoldNumbers in SequenceNumbers in anArithmetic SequenceFolded Chart©Glencoe/McGraw-Hill 55 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLES
- 65. ©Glencoe/McGraw-Hill 56 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESFoldableSkill Activity SuggestionPartsdefine matrix, matrices, element, dimensions, matrix logic 5explain how matrices organize data and give an example 2give two examples of square matrices 2use the singular word “matrix” and its plural form“matrices” correctly 2compare and a matrix and a table 2contrastillustrate how a matrix can be used to add, subtract, andmultiply quantities 3describe how a matrix can be used to solve systems ofequations with one, two, and three variables 3research the “what, where, when, why/how” ofdiscrete mathematics 4Nine Chapters on the Mathematical Art, 250 B.C. 4list and explain algebraic rules for using matrices:scaler multiplication of a matrix, addition andsubtraction of matrices, and multiplying matrices any numbergive two examples of probability matrices 2write the identity matrices for three square matrices 3find the inverses of three 2 ϫ 2 matrices 3compare and the multiplicative inverse for real numbers to thecontrast inverse matrix 2MatricesAssociativeLaw+CommutativeLawXAssociativeLawXDiscreteMathFour-Door BookWhereHowWhenMatrix InverseMultiplicative Inversefor Real NumbersShutter FoldMatrixFive-Tab BookMatrix LogicDimensionsElementMatrices
- 66. PointsFoldableSkill Activity SuggestionPartsFoldableSkill Activity SuggestionPartsdefine a ray as a portion of a line that extends from onepoint infinitely in one direction 1describe how a ray is named 1Venn diagram characteristics of a line segment, a ray, and both 3illustrate how two rays form and define an angle 2compare and collinear and noncollinear rays 2contrastRaysFoldableSkill Activity SuggestionPartsdefine a line as a collection of points that extendsin two directions, shown by arrowheads 1list two ways a line can be named 2explain a line segment as part of a line containing twoendpoints and all of the points between 1describe how line segments are named 1draw and name five line segments 5identify and model lines that do and do not intersect 2differentiate between parallel lines and perpendicular lines 2between lines that intersect at a right angle andthose that do not 2illustrate and explain a line called a transversal 2find the slopes of lines and use slope to identifyparallel and perpendicular lines 2Lines and Line Segmentsdescribe a point as a specific location in space with nosize or shape that is represented by a dot andnamed with a capital letter 1identify and model points and coplanar points 2graph eight ordered pairs on a coordinate plane 8find the distance between two points on a numberline and two points in a coordinate plane 2identify how many end points a line, line segment, and aray have 3LineSegmentBoth RayThree-Tab Venn DiagramTwo-Tab Bookrc dPointsHalf Book.B.C.A©Glencoe/McGraw-Hill 57 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLES
- 67. ©Glencoe/McGraw-Hill 58 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESAngle RelationshipsFoldableSkill Activity SuggestionPartsjustify a straight line being called a “straight angle” 1use the term “transversal” when describing a line thatintersects two parallel lines 1draw two intersecting lines and measure the angles formed 2parallel lines and measure the angles formed 2perpendicular lines and a transversal and explain whyintersecting perpendicular lines form four right angles 2show rays and line segments can be perpendicular 2describe how the following are formed and give examples:vertical angles, adjacent angles, linear pair 3differentiate between complementary and supplementaryangles 2explain alternate interior angles, alternate exterior angles,and corresponding angles 3prove that corresponding angles are congruent,alternate interior angles are congruent, andalternate exterior angles are congruent 3compare and supplementary and complementary angles 2contrastAnglesFoldableSkill Activity SuggestionPartsdescribe an angle as two rays with the same endpoint 1draw and label the parts of an angle—vertex and sides 2make a concept map for “angles” any numbersummarize and demonstrate how angles are measured andnamed 2measure and ten angles using a protractor and report the measuresname in degrees 10demonstrate how a protractor can be used to draw an angleof a given measure any numberdifferentiate between acute, obtuse, and right angles 3Venn diagram characteristics of acute angles, obtuse angles, and both 3classify angles as acute, right, obtuse, or straight 4explain how an angle separates a plane into three parts:interior of the angle, exterior of the angle, andand the angle itself 3draw an angle that is congruent to a given angle 1construct the bisectors of four given angles 4AcuteRightObtuseStraightFour-TabBookSidesvertexAnglesAcuteObtusePyramid FoldCongruent AnglesWords Numbers AlgebraThree-Tab Concept MapAlternateInteriorAlternateExteriorPyramid FoldFolded Book
- 68. ©Glencoe/McGraw-Hill 59 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESFoldableSkill Activity SuggestionPartsPlanesdescribe a plane as a flat surface with no edges, orboundaries 1explain why lines in the same plane either intersect or areparallel 2define skew lines as two lines that do not intersect andare not in the same plane 1draw two examples of skew lines and explain why theyare skew lines 2find similarities between intersecting, parallel, and skew lines 2and differencesVenn diagram characteristics of parallel lines, skew lines, and both 3illustrate a rectangular prism and explain how it is formedby six planes 2find five examples of planes in your daily life 5model planes that do and do not intersect 2write five plane relationships and draw and label afigure for each 5describe and give four examples of coplanar points 5compare plane geometry and spherical geometry 2ParallelLinesBoth SkewLinesThree-Tab Venn DiagramIntersectingLineSkewPyramid FoldRaysLineSegmentsTwo-Tab BookLineLineSegmentRayThree-Tab Book
- 69. ©Glencoe/McGraw-Hill 60 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESPolygonsFoldableSkill Activity SuggestionPartsdefine polygons as simple closed figures in a planeformed by three or more line segments 1classify polygon as convex or concave 2determine the sum of the measures of the interior andexterior angles of a polygon 2how and why polygons are classified by theirsides 2explain the meaning of the following prefixes—tri-, quad-,penta-,hexa-, hepta-, octa-, nona-, deca-, dodeca-, n- 9draw and label a triangle, a quadrilateral, a pentagon, a hexagon,an octagon, and a decagon 6label the vertices of the polygons you draw any numberdefine a diagonal as a line segment that joins twononconsecutive vertices 1explain diagonals can not be drawn in a triangle, but canbe drawn in any polygons with more than threesides 2make a table to show the number of sides, diagonals, andtriangles formed in several different polygons—quadrilateral, pentagon, hexagon, heptagon,octagon 5make a that shows a regular polygon is equilateral andconcept map equiangular 2show examples of interior and exterior angles of apolygon 2differentiate polygons that are regular and polygons that arebetween not regular 2find the sum of the measures of the interior angles offour different polygonsheptagon ϭ 900°nonagon ϭ 1260°decagon ϭ 1440°dodecagon ϭ 1800° 4make a table to show the measures of the interior and exteriorangles of three regular polygons 3find the perimeters of different polygons any numbermake a collage of pictures of polygons 1draw a tessellation 1determine if three polygons will each tessellate 3observe tessellations in the form of quilts, fabric patterns,modern art, and more any numberidentify regular and semi-regular (uniform) tessellations 2define transformations as movements of geometricfigures 1make a to show three types of transformations:concept map translation, rotation, and reflection 3draw examples of translations, rotations, and reflections 3InteriorangleExteriorangleTwo-Tab BookTriangleQuadrilateralPentagonHexagonHeptagonOctagonTransformationsThree-Tab Concept MapT R RSix-Tab BookGeometricCollageHalf BookVocabulary BookTri-Quad-Penta-Hexa-Hepta-Octa-Nona-Deca-Dodeca-n-
- 70. ©Glencoe/McGraw-Hill 61 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESFoldableSkill Activity SuggestionPartsTrianglesdefine a triangle as a three-sided polygon formed bythree line segments that intersect only at theirendpoints 1similarity of triangles as reflexive, symmetric, andtransitive 3medians, altitudes, angle bisectors, andperpendicular bisectors 4draw and label a triangle and its vertices 2name triangles by their vertices any numberfind the areas of three triangles 3measure the angles of four triangles 4draw a about the sum of the measures of the angles of allconclusion triangles 1describe the six types of triangles—acute, right, obtuse,equilateral, isosceles, and scalene 6explain how triangles are classified and classify fourtriangles by their angles and sides 4draw and two congruent triangles and their correspondingdescribe parts 2make a concept map on congruent triangles thatexplains how their corresponding sides arecongruent and their corresponding angles arecongruent 2explain how to find the area of a triangle in words andsymbols 2make a table to define and give examples of the following:SSS, SAS, ASA, AAS 4write the Triangle Inequality Theorem and use it toshow that some sets of line segments cannotbe used to form triangles 2TriangleQuadrilateralPentagonHexagonHeptagonOctagonFour-Tab BookSix-Tab Book
- 71. ©Glencoe/McGraw-Hill 62 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESRight TrianglesFoldableSkill Activity SuggestionPartslabel the parts of a right triangle—right angle, legs,hypotenuse 3research the history of the Pythagorean Theorem 4explain the Pythagorean Theorem in words and symbols 2use the Pythagorean Theorem to find the length of aside of a right triangle 1determine whether a triangle is a right triangle and explainyour reasoning 2describe how to find the length of a leg of a right triangle if youknow the lengths of the hypotenuse and the other leg 1draw and label a diagram to show the three altitudes of a righttriangle 2construct right triangles from a square and form anequilateral triangle 2compare and 45°–45° right triangles, and 30°–60° right trianglescontrast 2tests for triangle congruence and tests forcongruence of right triangles 2illustrate LL, HA, and LA as tests for congruence of righttriangles 3AssociativeLaw+CommutativeLawXAssociativeLawXPythagoreanTheoremFour-Door BookWhereWhy/HowWhenTwo-Tab Book45456030Three-Tab BookLegs Vertex Hypotenuse
- 72. ©Glencoe/McGraw-Hill 63 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESRight Triangle TrigonometryFoldableSkill Activity SuggestionPartsdescribe trigonometry as the study of triangle propertiesand relationships 1explain the etymology of the word trigonometry 1define trigonometric ratios as the ratios of the measuresof the sides of a right triangle 1investigate the following trigonometric ratios—sine, cosine,tangent ratios 3report on the trigonometic ratios sine, cosine, and tangent inwords and symbols 3compare and the sine ratio with the cosine ratio 2contrasttell how to decide whether to use sine, cosine, ortangent when trying to measure an acute angle ina right triangle 3describe an angle of elevation and how it is formed by ahorizontal line and a line of sight above it 2show an angle of depression and how it is formed by ahorizontal line and a line of sight below it 2draw a diagram of an angle of elevation and an angleof depression 2Venn diagram characteristics of angle of elevation, an angle ofdepression, and both 3Angle ofdepressionBothAngle ofelevationThree-Tab Venn DiagramSine Cosine TangentAngle ofelevationAngle ofdepressionTwo-Tab BookThree-Tab Book3 x 4 Folded TableWords SymbolsSineCosineTangent
- 73. ©Glencoe/McGraw-Hill 64 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESFoldableSkill Activity SuggestionPartsdefine a quadrilateral as a closed figure formed by fourline segments that intersect only at theirendpoints 1draw and label a quadrilateral and its vertices 2compare and a quadrilateral and a non-example of acontrast quadrilateral 2measure the angles of several quadrilaterals any numberdraw a about the sum of the measures of the angles of aconclusion quadrilateral 1explain how quadrilaterals can be classified 1describe six types of quadrilaterals:1. quadrilaterals with no pairs of parallel lines2. parallelogram ϭ quadrilateral with two pairs ofparallel sides3. trapezoid ϭ quadrilateral with exactly one pair ofparallel sides4. rectangle ϭ parallelogram with four congruentangles5. square ϭ parallelogram with congruent sides andcongruent angles6. rhombus ϭ parallelogram withcongruent sides 6make that shows the six types of quadrilateralsa concept map 6illustrate different quadrilaterals and their diagonals any numberQuadrilateralsQuadrilateral Numberof verticesQuadrilateralsThree-Tab Concept MapRectangle Square RhombusParallelogramQuadrilateralTrapezoidRectangleSquareRhombusSix-Tab BookFolded Chart
- 74. ©Glencoe/McGraw-Hill 65 Teaching Mathematics with FoldablesMATH ACTIVITIES USING FOLDABLESFoldableSkill Activity SuggestionPartsSquares, Rectangles, and Rhombidescribe a square and a rectangle in words and symbols 2Venn diagram characteristics of a square, a rectangle, and both 3describe and illustrate two different quadrilaterals with fourright angles—a square and a rectangle 2find the perimeters of rectangles, squares, and rhombi 3the areas of rectangles, squares, and rhombi 3describe equilateral and equiangular figures 2draw a square and a rectangle with the same area ongrid paper 2illustrate the diagonals of squares and rectangles 2make a to compare and contrast the followingtable characteristics of squares and rectangles:• are diagonals congruent?• are pairs of opposite sides congruent?• are diagonals perpendicular?• is one pair of opposite sides parallel andcongruent? any numbersummarize and diagram the properties of a rectangle:• opposite sides are congruent and parallel• opposite angles are congruent• consecutive angles are supplementary• diagonals are congruent and bisect each other• all four angles are right angles 5compare and squares and rhombi 2contrastdiagram the diagonals of a rhombus and prove that they 2are perpendicularthe diagonals of a rhombus and show how theybisect opposite angles 2Venn diagram characteristics of rhombi, rectangles, and both 3QuadrilateralsThree-Tab Concept MapRectangle Square RhombusSquare RectanglePerimeterSquare RectangleTwo-Tab Concept MapTwo-Tab BookBothThree-Tab Venn DiagramEquilateralFigureEquiangularFigureTwo-Tab Book

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