Teaching Mathematics with Foldables!

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author dinah zike m ed educational consultant san antonio texas

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glencoe/mcgraw-hill copyright © by the mcgraw-hill companies inc all rights reserved printed in the united states of america except as permitted under the united states copyright act no part of this publication may be reproduced or distributed in any form or by any means or stored in a database or retrieval system without the prior written permission of the publisher send all inquiries to glencoe/mcgraw-hill 8787 orion place columbus oh 43240 part of isbn 0-07-830413-x 1 2 3 4 5 6 7 8 9 10 045 11 10 09 08 07 06 05 04 03 02 teaching mathematics with foldables

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table of contents letter from dinah zike .v introduction to foldables why use foldables in mathematics .vi correlation of foldables to glencoe mathematics .vii foldable basics .1 selecting the appropriate foldable .3 folding instructions basic foldable shapes .5 1-part folds half book .6 folded book .7 bound book .8 two-tab book .9 2-part folds matchbook .10 pocket book .11 shutter fold .12 3-part folds trifold book .13 three-tab book .14 three-tab book variations .15 pyramid fold or mobile .16 4-part folds layered-look book .17 four-tab book .18 envelope fold .19 standing cube .20 four-door book .21 top-tab book .22 accordion book .24 any number of parts pop-up book .25 folding into fifths .26 folded table chart or graph .27 folding a circle into tenths .28 circle graph .29 concept-map book .30 vocabulary book .31 projects using folds billboard project .32 sentence-strip holder .33 sentence strips .34 math activities using foldables number systems whole numbers .35 integers .36 integers adding and subtracting .37 integers multiplying and dividing .38 rational numbers .39 rational numbers fractions .40 rational numbers decimals .41 percents .42 ratios .43 proportions .43 irrational numbers .44 real number system .44 algebraic patterns and functions sets and variables .45 expressions .46 properties .47 equations .48 inequalities .49 relations and functions .50 factors .51 multiples .52 monomials and polynomials .53 powers and exponents .54 sequences .55 matrices .56 geometry points .57 lines and line segments .57 rays .57 angles .58 angle relationships .58 planes .59 polygons .60 triangles .61 right triangles .62 right triangle trigonometry .63 ©glencoe/mcgraw-hill iii teaching mathematics with foldables

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quadrilaterals .64 squares rectangles and rhombi .65 parallelograms .66 trapezoids .67 circles .68 three-dimensional figures .69 prisms and cylinders .70 pyramids and cones .71 coordinate geometry .72 slope .73 graphing equations and inequalities .74 measurement metric measurement .75 length width and height .75 distance .76 weight .76 volume .77 temperature .77 data analysis and probability statistics .78 stem-and-leaf plots .79 box-and-whisker plots .79 fundamental counting principle .80 frequency tables .80 pascal s triangle .80 permutations .81 combinations .81 probability .82 scatter plots .83 problem solving problem-solving plan .84 problem-solving strategies .84 communication vocabulary and writing definitions 85 journals .85 outline list and sequence .86 concept maps .86 writing instructions .86 main ideas and note taking .87 annotations .87 questioning .87 representation tables and charts .88 circle graphs .88 bar graphs and histograms .89 line graphs .89 pictographs .90 venn diagrams .90 index .91 ©glencoe/mcgraw-hill iv teaching mathematics with foldables

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from dinah zike dear teacher in this book you will find instructions for making foldables as well as ideas on how to use them they are an excellent communication tool for students and teachers national math standards and communication skills the principles and standards for school mathematics published by the national council of teachers of mathematics nctm in 2000 stress the importance of communication skills in a strong mathematics program not all students will become mathematicians engineers or statisticians but all students need to be able to think analyze and problem solve using skills acquired through the study of mathematics throughout their lives students will be called upon to be literate in mathematics personally and professionally they will need to have a basic understanding of numbers operations and quantitative reasoning patterns relationships and algebraic thinking geometry measurement and probability and statistics to solve real-life problems involving finances chance design science fine arts and more furthermore students must be able to share the results of their use of mathematics using various forms of oral and written communication foldables are one of many techniques that can be used to integrate reading writing thinking organizing data researching and other communication skills into an interdisciplinary mathematics curriculum who what when why you probably have seen at least one of the foldables featured in this book used in supplemental programs or staff-deveopment workshops today my foldables are used internationally i present workshops and keynotes to over fifty thousand teachers and parents a year sharing the foldables that i began inventing designing and adapting over thirty years ago around the world students of all ages are using them for daily work note-taking activities student-directed projects forms of alternative assessment math journals graphs charts tables and more add and amend after workshop presentations participants would ask me for lists of activities to be used with the foldables they had just learned to make they needed help visualizing how to convert math data into foldables so over fifteen years ago i began collecting and sharing the ideas listed in this book the ideas are organized by topic the table for each topic shows the math content being addressed and an appropriate foldable i hope you enjoy making foldables a part of your math classroom ©glencoe/mcgraw-hill v teaching mathematics with foldables

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introduction to foldables why use foldables in mathematics when teachers ask me why they should take time to use the foldables featured in this book i explain that they quickly organize display and arrange information making it easier for students to grasp math 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 and effect and finding similarities and differences into daily work and long-term projects for example these foldables can be used to compare and contrast student explanations and procedures for solving problems to the explanations presented by other students and teachers continue to immerse students in previously learned vocabulary and concepts providing them 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-solving strategies examples questions that arise during classwork and personal experiences that occur during learning can be used as alternative assessment tools by teachers to evaluate student progress or by students 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 ©glencoe/mcgraw-hill vi teaching mathematics with foldables

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introduction to foldables correlation of foldablestm to glencoe mathematics foldabletm topic mathematics mathematics mathematics applications and applications and applications and pre-algebra algebra 1 geometry algebra 2 connections connections connections course 1 course 2 course 3 number systems whole numbers integers integers adding and subtracting integers multiplying and dividing rational numbers rational numbers fractions rational numbers decimals percents ratios proportions irrational numbers real number system patterns and functions sets and variables expressions properties equations inequalities relations and functions factors multiples monomials and polynomials powers and exponents sequences matrices geometry points lines and line segments rays angles angle relationships planes polygons triangles right triangles ©glencoe/mcgraw-hill vii teaching mathematics with foldables

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introduction to foldables correlation of foldablestm to glencoe mathematics foldabletm topic mathematics mathematics mathematics applications and applications and applications and pre-algebra algebra 1 geometry algebra 2 connections connections connections course 1 course 2 course 3 algebra and right triangles quadrilaterals squares rectangles and rhombi parallelograms trapezoids circles three-dimensional figures prisms and cylinders pyramids and cones coordinate geometry slope graphing equations and inequalities measurement metric measurement length width and height distance weight volume temperature data analysis and probability statistics stem-and-leaf plots box-and-whisker plots fundamental counting principle frequency tables pascal s triangle permutations combinations probability scatter plots problem solving problem solving plan problem solving strategies communication vocabulary and writing definitions ©glencoe/mcgraw-hill viii teaching mathematics with foldables

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introduction to foldables correlation of foldablestm to glencoe mathematics foldabletm topic mathematics mathematics mathematics applications and applications and applications and pre-algebra algebra 1 geometry algebra 2 connections connections connections course 1 course 2 course 3 journals outline list and sequence concept map writing instructions main ideas and note taking annotations questioning representation tables and charts circle graphs bar graphs and histograms line graphs pictographs venn diagrams ©glencoe/mcgraw-hill ix teaching mathematics with foldables

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introduction to foldables foldable basics what to write and where teach students to write general information titles vocabulary words concepts questions main ideas and properties or theorems on the front tabs of their foldables general information is viewed every time a student looks at a foldable foldables help students focus on and remember key points without being distracted by other print ask students to write specific information supporting ideas student thoughts answers to questions research information computation steps class notes observations and definitions under the tabs as you teach demonstrate different ways in which foldables can be used soon you will find that students make their own foldables and use them independently for study guides and projects with or without tabs foldables with flaps or tabs create study guides that students can use to self check what they know about the general information on the front of the tabs use foldables without tabs for assessment purposes or projects where information is presented for others to view quickly venn diagram used as a study guide venn diagram used for assessment ©glencoe/mcgraw-hill 1 teaching mathematics with foldables

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introduction to foldables what to do with scissors and glue i don t expect secondary students to bring glue and scissors to math class instead i set up a small table in the classroom and provide several containers of glue numerous pairs of scissors sometimes tied to the table containers of markers and colored pencils a stapler clear tape and anything else i think students might need to make their foldables don t be surprised if students donate unusual markers decorative-edged scissors gel pens stencils and other art items to your publishing table the more they make and use graphic organizers the faster students become at producing them storing graphic organizers in student portfolios turn one-gallon freezer bags into student portfolios which can be collected and stored in the classroom students can also carry their portfolios in their notebooks if they place strips of two-inch clear tape along one side and punch three holes through the taped edge have each student write his or her name along the top of the plastic portfolio with a permanent 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 so student work was always available when needed and not left at home or in the car giant laundry-soap boxes make good storage containers for portfolios let students use this book as an idea reference make this book available to students to use as an idea reference for projects discussions extra credit work cooperative learning group presentations and more ©glencoe/mcgraw-hill 2 teaching mathematics with foldables

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introduction to foldables selecting the appropriate foldable dividing math concepts into parts foldables 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 which foldable best illustrates or fits those parts foldables that are three-dimensional also make the student interact with the information kinesthetically for example if you are studying the properties of equality you could choose a foldable that has five tabs or sections on the front tabs write the properties under the tabs explain the properties in words on one side and in symbols on the other side math concepts already divided into parts parts 5 3 2 2 2 7 2 3 2 algebra concept properties of equality parentheses brackets and braces parts 2 2 2 3 6 4 2 6 2 equations and inequalities numeric and algebraic expressions domain and range properties of addition and multiplication lcm and lcd monomials binomials and trinomials geometry concept collinear and noncollinear complementary and supplementary angles parallel and perpendicular translation rotation reflection types of triangles sss sas asa aas two types of special right triangles types of quadrilaterals statistics and probability parts concept 3 mean median mode 1 fundamental counting principle 4 who what when where blaise pascal 2 permutations and combinations 2 upper quartile and lower quartile 2 dependent and independent events 2 probability and odds 2 2 odds in favor and odds against mutually inclusive and exclusive events powers and exponents x-axis and y-axis math concepts that can be divided into parts algebra write algebraic expressions evaluate expressions sequence steps list algebraic rules solve equations find values for variables geometry draw angles with a protractor classify polygons illustrate quadrilaterals list examples of prisms name ordered pairs graph points statistics and probability determine ranges of sets interpret scatter plots display data collected in plots draw models of combinations ©glencoe/mcgraw-hill 3 teaching mathematics with foldables

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introduction to foldables dividing skills and foldables into parts reading writing and thinking skills can easily be used with foldables the following lists show examples of skills and activities and a selection of foldables divided into parts you may want to refer to this page as you select activities from the lists of math topics in this book see pages 35­90 skills and activities divided into parts 1 part find the main idea predict an outcome narrative writing descriptive writing expository writing persuasive writing 3 parts venn diagrams know like to know learned beginning middle end questioning flow charts vocabulary words timelines concept webs or maps 2 parts compare and contrast cause and effect similarities and differences opposite operations 4 parts who what when where what where when why/how any number of parts making and using tables making and using graphs making and using charts sequencing data or events foldables divided into parts 1 part half book folded book matchbook bound book 3 parts trifold book three-tab book pyramid book layered-look book concept map with three tabs accordion book layered-look book sentence-strip holder folded table chart or graph pyramid mobile top-tab book three or more sheets of paper ©glencoe/mcgraw-hill 4 2 parts two-tab book pocket book shutter fold matchbook cut in half concept-map book with two tabs 4 parts four-tab book standing cube top-tab book four-door book any number of parts circle graph concept-map book vocabulary book bound book pocket books teaching mathematics with foldables

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folding instructions basic foldable shapes the following figures illustrate the basic folds that are referred to throughout the following section of this book taco fold hamburger fold hot dog fold burrito fold valley fold shutter fold mountain fold ©glencoe/mcgraw-hill 5 teaching mathematics with foldables

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