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  • Alpha Omega Publications, Inc.Rock Rapids, IA

    bySareta A. Cummins

    Edited byDavid J. Korecki

    Illustrated byTye A. Rausch

    Editorial AssistantChristine A. Korecki

    Teachers Guide

    3Mathematics

  • Horizons Mathematics 3 Teachers Guide MCMXCIII Alpha Omega Publications, Inc.

    804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759

    All rights reserved. No part of this publication may be reproduced, stored in an electronicretrieval system, or transmitted, in any form or by any means, electronic, mechanical,photocopying, recording, or otherwise, without the prior written permission of the publisher.Brief quotations may be used in literary review.

    Printed in the United States of AmericaISBN 978-1-58095-971-1

  • Contents

    Section One PageIntroduction

    Before You Start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Readiness Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Preparing a Lesson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Scope & Sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Manipulatives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Where to Use Mathematics Worksheets . . . . . . . . . . . . . . . . . . 20Appearance of Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Development of Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    Section TwoTeachers Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    Section ThreeAnswer Key (Lessons 1160) . . . . . . . . . . . . . . . . . . . . . . . . . 353

    Section FourWorksheets (180) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

    Section FiveWorksheets Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 527

  • Introduction

    H o r i z o n s M a t h e m a t i c s 3

  • 1

    Before You Start THE CHALLENGETodays average high schoolgraduate knows and can do lessmath than their counterpart often, fifteen, or twenty yearsago. Basic math skills havedeteriorated to the point thatmany wonder if this countrycan continue to be a leader inshaping the technology of thefuture. Unfortunately, thegeneral trend of moderneducation of all types isdownward. Students in privateeducation, while they scorehigher overall than publicschool students, still do poorlyin math computation skills.

    THE GOALThe goal of this curriculum isto provide the parent andteacher with a tool that willhelp them effectively combatthis deterioration of math skillsby raising the level of studentperformance. Research of thecontent and methods of otherexisting curriculums, theconcepts evaluated byachievement tests, and typicalcourses of study resulted inselection of the Scope andSequence starting on page 14.This curriculum was notplanned around any particulargroup of students. Rather, itwas determined that thematerial in this curriculumconstituted a reasonable levelof performance for third gradestudents. The curriculum isdesigned so that the teachercan adapt its use to student(s)of widely varying ability. In

    other words, the curriculum isa tool that is capable ofperforming well over a broadrange of student ability to helpthem achieve a higherminimum level of proficiency.The two major components ofthe curriculum are the studenttext (in two volumes) and theTeachers Guide. These are theabsolute minimum componentsfor accomplishing the objectiveof teaching the concepts in theScope and Sequence. Since thisguide was designed as anintegral part of the curriculum,its use is absolutely necessary.The guide contains activitiesnot found in the student textsthat are essential to theaccomplishment of thecurriculum objectives. As youwill see in the followingsections, this Teachers Guidecontains a significant numberof suggestions and helps for theteacher. Unlike first grade, allmanipulatives are identifiedwith italics so that the teachermay easily see them at aglance.

    THE DESIGNTake a moment to look at thesample chart entitled,Development of Concepts, onpages 2829. Take note of howthe curriculum concepts aredeveloped. The firstpresentation is usually a brieffamiliarization. Then the basicteaching is accomplished aspart of three to five lessons.The thoroughness of apresentation depends on how

  • 2

    new and how important theconcept is to the studentsacademic development.

    THE DEVELOPMENTEach concept will be reviewedfor three to five lessons afterthe complete presentation. Forthe next two months theconcept will be presented everytwo weeks as a part of two orthree consecutive lessons.After a break in presentation offour weeks, the concept will bethoroughly reviewed as part ofthe lesson for three to fivedays. This will be followed by aperiod of two months where theconcept will be reviewed everytwo weeks as part of two orthree lessons. This progressioncontinues until the student(s)have had the opportunity tothoroughly master the concept.

    AN EXAMPLESome mathematics curriculumsmight teach graphs for twoweeks and not go back to itagain. In this curriculum itwill be introduced andpracticed for two weeks. Forthe next two months, graphswill be presented every twoweeks as a part of two or threelessons to give the student(s)continual practice to developmastery of the concept. Thethird month will be considereda break from presenting theconcept and graphs will not betaught. In the fourth month,graphs will first be thoroughlyreviewed and again practicedevery two weeks as a part oftwo or three lessons. By havinga series of practices every twoweeks, the student(s) willretain what they have learned

    to a greater degree. Shortperiods of exposure repeatedmany times is much moreeffective than long periods withfewer exposures. Since thereare three types of graphs tostudy at this level (bar, line,and pictograph), each type isintroduced at separateintervals. The bar graph istaught at the introduction tothe study. Line graphs areintroduced a month later(following the sameprogression), and pictographsanother month later. Aftereach type of graph has beencompletely introducedindividually, the three types arepresented together for theremainder of the year. Reviewthe chart on pages 2829 to seehow the concepts aredeveloped.

  • 9

    Preparing a LessonGENERAL INFORMATIONThere is some room on theteacher lessons for you towrite your own notes. Themore you personalize yourteachers guide in this way, themore useful it will be to you.

    You will notice that there are160 student lessons in thecurriculum. This allows forthe inevitable interruptions tothe school year like holidays,test days, inclement weatherdays, and those unexpectedinterruptions. It also allowsthe teacher the opportunity tospend more time teaching anyconcept that the student(s)may have difficulty with. Or,you might wish to spend a daydoing some of the funactivities mentioned in theTeaching Tips. If you find thatthe student(s) need extra drill,use the worksheets as extralessons. There are no newconcepts introduced afterlesson 142. The last eighteenlessons reinforce byapplication the conceptspresented throughout the year.

    STUDENTS LESSONSORGANIZATIONThe lessons are designed to becompleted in thirty to thirty-five minutes a day. If extramanipulatives or worksheetsare utilized, you will need toallow more time for teaching.Each lesson consists of amajor concept and practice ofpreviously taught concepts.

    If the student(s) find thepresence of four or fivedifferent activities in onelesson a little overwhelmingat the beginning, startguiding the student(s)through each activity. By theend of two weeks, they shouldbe able to work moreindependently as they adjustto the format. Mastery of anew concept is not necessarythe first time it is presented.Complete understanding of anew concept will come as theconcept is approached fromdifferent views using differentmethods at differentintervals. Because of the waythe curriculum is designed,the student(s) need to do allthe problems in every lessonevery day. Directions to thestudent(s) are given in blacktype and examples orexplanations are presented inblue type. If you expect tohave very many students, youwill find it extremely helpfulto remove all pages from theindividual student books andfile them (all of Lesson 1 inone file, all of Lesson 2 inanother file, etc.) before schoolstarts. This will keep thelessons from being damagedor lost in the students desks.

    TestsStarting with Lesson 10, testsare included in every tenthlesson. They should requireapproximately twentyminutes to administer. If

  • your daily schedule time is amajor factor, the studentlesson may be completed thefollowing day. This willrequire efficient scheduling ofthe lessons throughout theyear to complete the programby the end of the school year.The 16 tests and 160 lessonseach administered or taughton separate days would bringthe scheduled curriculumdays to a total of 176.

    Do not make the test a speciallesson. Allow the student(s) toperceive the test as a regularlesson with no unduepressure. The purpose oftesting is not just to measurestudent progress, althoughthat is an importantconsideration. A test is alsoan important teaching tool. Itshould be returned to thestudent and any missed itemsdiscussed so that it is a truelearning experience. For thisreason, it is important tograde and return the tests assoon as possible whilematerial is fresh in thestudents mind.

    The test structure is such thatthe student(s) will have hadsufficient practice with aconcept to have learned itbefore being tested.Therefore, no concept is testeduntil the initial presentationhas been completed. Forexample, test 2 in lesson 20covers concepts completed inlessons 615. Lessons 1619may include the introductionof some new material which

    will not be covered in test 2.Test 8 in lesson 80 will coverlessons 6675. The newmaterial from lessons 7679will not be covered in test 8.

    TEACHERS LESSONSORGANIZATIONEach lesson is organized intothe following sections:Concepts; Objectives; TeachingTips; Materials, Supplies, andEquipment; Activities;Worksheets; and occasionally amaxim or proverb. Each ofthe sections have a distinctsymbol to help you locatethem on the page of theteachers lesson. To be amaster teacher you will needto prepare each lesson well inadvance.

    ConceptsConcepts are listedat the beginning ofeach lesson in thefollowing order: 1.) Conceptstaught by the teacher from theactivities in the TeachersGuide that do not have acorresponding written activityin the student lesson 2.) Newconcepts 3.) Concepts that arepracticed from previouslessons (listed in the orderthey appear in the studentlesson). Third grade math hassixteen major concepts. Theseare developed in a progressionthat is designed to give thestudent(s) a solid foundationin the basic math skills whileproviding enough variety tohold the students interest.Definitions are given for newterms.

    10

  • ObjectivesThe Objectives listcriteria for thestudents perfor-mance. They state whatthe student should be able todo at the completion of thelesson. You will findobjectives helpful indetermining the studentsprogress, the need forremedial work, and readinessfor more advancedinformation. Objectives arestated in terms of measurablestudent performance so thatthe teacher has a fixed level ofperformance to be attainedbefore the student(s) are readyto progress to the next level.

    Teaching TipsEach tip is related toone of the Activities inthe lesson. SomeTeaching Tips requirethe teacher to make amanipulative needed tocomplete the activity.Teaching Tips are optionalactivities that the teacher cando to enhance the teachingprocess. You will find themuseful for helping the studentwho needs additional practiceto master the concepts or forthe student who needs to bechallenged by extra work.

    Materials,Supplies, andEquipmentMaterials, Supplies,and Equipment liststhe things youll need to findbefore you teach each lesson.Sometimes you will also find

    instructions on how to makeyour own materials, supplies,and equipment. WhenNumber Chart is listed, it isunderstood to refer to thechart for 099. The numberchart for 100199 will stateNumber Chart 100199. Acomplete list of allmanipulatives and where theyare used starts on page 16.

    ActivitiesThe teachersgreatestconcentration shouldbe on the Activitiessection. Here the teacher willfind step-by-step directionsfor teaching each lesson. Allactivities are designed to beteacher directed both in thestudent lesson and in theteachers guide. You will needto use your own judgementconcerning how much time isnecessary to carry out theactivities. Be sure, however,that the student(s) do everyproblem of every lesson.When the activity is part ofthe student lesson, you willfind it referred to as StudentActivity One, StudentActivity Two, etc.referring to the numberin the circle on the studentlesson. If the activity is notpart of the student lesson,there will be no bold faceitalic reference, and thestudent will receive theactivity from the teacher.Each activity is important tothe overall scope of the lessonand must be completed. Donot omit any portion of the

    11

    1

  • activities, particularly themultiplication and divisiondrill with flash cards, unlessthe student(s) havethoroughly mastered theconcept being presented.Please do not put off lookingat the activities in the lessonuntil you are actuallyteaching. Taking time topreview what you will beteaching is essential. Choosethe manipulatives that fityour program best.

    WorksheetsThere isapproximately oneworksheet for everytwo lessons. If worksheetsare suggested in a particularlesson, you will find themlisted in the Worksheetssection. Each worksheet hasa worksheet number and thenumber of the lesson withwhich it is associated. TheTeachers Guide identifieswhere these resourceworksheets are essential tothe lessons. All addition,subtraction, andmultiplication drill sheets areincluded in the worksheets. Ifthe Worksheet symbol is onthe page, there is a worksheetassociated with that lesson.The worksheets will be handyfor many purposes. You mightuse them for extra work forstudent(s) who demonstrateextra aptitude or ability or asremedial work for thestudent(s) who demonstrate alack of aptitude or ability.You may also make your own

    worksheets and note whereyou would use them in theworksheet section on theteachers lesson.

    MaximsIn some lessons you will finda short maxim or proverb atthe bottom of the right-handpage. These maxims providea collection of various wiseand pithy sayings that dealwith character. They areintended for the teacher toshare and discuss with thestudent(s). Ask the student(s)to suggest ways that theycould apply the maxim totheir day-to-day activities oflife. Have them think of atime when their friends mayhave put the maxim intopractice. Tell them to watchfor opportunities to practicethe maxim in the next weekand report the incident toyou. You may use or not usethem as you wish.

    Lesson SummaryThe curriculum will work bestwhen you prepare in thefollowing manner. First, notethat the teachers lesson hasitems that pertain to anoverview of the lesson on theleft-hand page. The detailsare on the right-hand page. Itis suggested that you firstlook at the Concepts involvedin the lesson. Then study theObjectives to get an idea ofthe tasks that the student(s)will need to perform tocomplete the lesson. Next,look at the Activities to get an

    12

  • idea of the presentation of thelesson. If you would like toview the student lessons, thecomplete student curriculumis included in reduced formatin the answer key section.This presentation will allowyou to see the whole studentlesson in one place as well asall the answers at the sametime. You will need morepreparation for some of theactivities that arent in thestudent lessons. Some of theactivities will refer to aworksheet which you will findlisted in the Worksheetsection below the Activitiessection. You might also wantto check the Teaching Tipssection for any additionalideas on presenting thelesson. Finally, check theMaterials, Supplies, andEquipment for any resourcesthat you may need before youbegin the lesson.

    ANSWER KEYSThe answer keys section ofthe Teachers Guide providesanswers to the studentlessons (reduced so that thereare four student pages oneach answer key page andprinted in black and white).It is suggested that you givethe student(s) a grade fortests only. Daily work is to bea learning experience for thestudent, so do not putunnecessary pressure onthem. You should correctevery paper, but you shouldnot grade every paper. Thismeans that each lesson

    should be marked for correctand incorrect answers, but itis not necessary to record aletter or percentage grade onevery lesson. The lessonsshould then be returned tothe student(s) so that theyhave the opportunity to learnfrom their mistakes.

    WORKSHEETSThe next section contains theworksheets. They arereproducible and may becopied freely. You will find acomplete listing of worksheetsand where they are used onpages 20 and 21. Separatepackets of all the necessaryworksheets for an individualstudent are also available.

    WORKSHEET ANSWERKEYSAnswer keys to theworksheets are provided inthe same manner as for thestudent lessons and reducedso that there are fourworksheets on each page ofthe answer key. The multipleuse worksheets do not haveanswer keys since theanswers will vary each timethe worksheets are used.

    13

  • 14

    1. NUMBER THEORY(Recognition, Read, and Write)

    Counting by 1s through 10sEven and odd numbersWord numbers 0999,999,999Roman numerals

    2. PLACE VALUE(Digit Value)

    Ones, tens, hundreds, andthousands place

    Ten thousands placeHundred thousands placeMillions, ten millions, and hundred

    millions place

    3. NUMBER ORDER(Recognition and Use)

    Ordinal numbers to 100EstimationGreater than and less thanEqual and not equalAssociative, commutative, anddistributive principles

    The number that comes before andafter a given number

    4. ADDITIONAddition termsRegroupingWord problemsWord sentencesEquations

    5. TIME(Read and Write)

    Hour, half hour, quarter hour, fiveminute, and one minute

    A.M. and P.M.Word problemsEquivalents

    6. SUBTRACTION

    Subtraction termsRegroupingEstimationWord problemsEquations

    7. MONEY(Recognition, Value, and Use)

    Counting coins and billsAdding, subtracting, and

    multiplying moneyWord problems

    8. MULTIPLICATIONMultiplication termsFacts for 010Word problemsRegroupingEquations

  • 15

    9. GEOMETRY(Recognition andCharacteristics)

    Shapes and solidsSymmetryCongruent and similar shapesGeometric terms

    10. FRACTIONS(Meaning, Recognition,and Use)

    Fractional part of whole and setFractional wordsComparison of fractionsComparison of fractions and

    decimalsEquivalent fractionsMixed numbersReducing fractionsAdd and subtract like fractions and

    mixed numbersWord problems

    11. DECIMALS(Meaning, Recognition,and Use)

    Tenths of a wholeComparison of decimals, fractions,

    and mixed numbersWord numbersAddition of decimals in tenths

    12. DIVISION

    Division termsFacts 010Single-digit divisorDouble-digit quotient with

    regrouping and remainderWord problems

    13. MEASUREMENT(Practice and Use)

    Inches in halves, fourths, and eighthsCentimeters in tenthsEnglish units of measureMetric units of measureMap readingTemperature in Fahrenheit and

    Celsius

    14. GRAPHS(Draw and Interpret)

    Bar graphs, line graphs, pictographs,and grids

    15. AREA, PERIMETER,ANDVOLUME(Calculate)

    Perimeter of shapesArea of rectangle and squareVolume of cube and rectangular

    prismWord problems

    16. RATIO(Write and Use)

    Comparison of two numbersWord problems

  • 16

    Manipulatives

    Bar graph 61, 62

    Beans pound 65

    Blocks 110, 111

    Bread 1 lb. loaf 64

    Butter pound 64

    Calendar 1, 147

    Checkbook and check 109

    Clock model large 3, 5, 14, 15, 17, 19, 20, 24, 25, 29, 31, 32, 33, 34, 38,43, 46, 47, 48, 53, 58, 63, 68, 70, 71, 72, 73, 78, 83,84, 85, 88, 93, 97, 98, 100, 103, 108, 113, 118, 123,128, 133, 134, 135, 138, 143, 147, 148, 153, 158

    Clock model small 4, 6, 18, 19, 20, 33, 34, 46, 47, 71, 73, 85, 86, 98, 99,112, 113, 124, 134

    Construction paper 92, 102,

    Counting chips 10, 122

    Crayons 65

    Flannel board 8, 9, 41, 60, 88, 89, 101, 104, 105, 112, 117, 131, 144,145

    Flannel board materials 8, 9, 60, 104, 105, 117, 144, 145

    Flash cards addition facts 6, 11, 15, 16, 21, 25, 26, 31, 35, 36, 41, 45, 46, 51, 55,56, 61, 65, 66, 71, 75, 76, 81, 85, 86, 91, 95, 96, 101,105, 106, 111, 115, 116, 121, 125, 126, 131, 135, 136,141, 145, 146, 151, 155, 156

    Flash cards addition terms 7, 8, 22, 26

    Flash cards cardinal and 32ordinal numbers

    Flash cards congruent 141figures

    Manipulative Name Description Used In Lesson

  • 17

    Flash cards division facts 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82,83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96,97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107,108, 109, 110, 111, 112, 113, 114, 115, 116, 117,118, 119, 120, 121, 122, 123, 124, 125, 126, 127,128, 129, 130, 131, 132, 133, 134, 135, 136, 137,138, 139, 140, 141, 142, 143, 144, 145, 146, 147,148, 149, 150, 151, 152, 153, 154, 155, 156, 157,158, 159, 160

    Flash cards division terms 62, 64, 75, 99, 100, 129, 145

    Flash cards English linear 38, 77, 86, 94, 96, 123, 136, 137, 148, 149, 150,equivalents 158, 159

    Flash cards English liquid 47, 48, 77, 86, 94, 96, 136, 137, 148, 149, 150, 158,equivalents 159

    Flash cards English weight 77, 86, 94, 96, 136, 137, 148, 149, 150, 158, 159equivalents

    Flash cards = and symbols 26

    Flash cards fraction terms 14, 43, 59, 73

    Flash cards geometric terms 128, 155, 156, 158, 159

    Flash cards < and > symbols 11, 19, 22, 27

    Flash cards metric linear 123, 131, 136, 137, 148, 149, 150, 158, 159equivalents

    Flash cards metric liquid 120, 123, 131, 136, 137, 148, 149, 150, 158, 159equivalents

    Flash cards metric weight 123, 131, 136, 137, 148, 149, 150, 158, 159equivalents

    Flash cards minus sign 16

    Flash cards multiplication facts 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65,66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93,94, 95, 96, 97, 98, 99, 101, 102, 104, 106, 107, 109,111, 112, 114, 116, 117, 119, 121, 122, 124, 126,127, 129, 131, 132, 134, 136, 137, 139, 141, 142,144, 146, 147, 149, 151, 152, 154, 156, 157, 159

    Manipulative Name Description Used In Lesson

  • 18

    Flash cards multiplication terms 21, 39, 40, 59, 87, 88, 103, 126, 152

    Flash cards Roman numerals 13, 14, 15, 16, 26, 27, 28, 29, 39, 40, 42, 54, 55, 56,78, 79, 80, 81, 91, 92, 105, 121, 122, 133, 134, 151,155

    Flash cards shapes and solids 11, 12, 13, 25, 26, 27, 28, 29, 30, 41, 42, 43, 55, 56,57, 58, 68, 69, 70, 93, 94, 106, 117, 118, 121, 139, 14

    Flash cards similar figures 143

    Flash cards subtraction facts 7, 10, 12, 17, 20, 22, 27, 30, 32, 37, 40, 42, 47,50,52, 57, 60, 62, 67, 70, 72, 77, 80, 82, 87, 90, 92,97, 100, 102, 107, 110, 112, 117, 120, 122, 127,130, 132, 137, 140, 142, 147, 150, 152, 157, 160

    Flash cards subtraction terms 13, 14, 29, 30, 49, 50, 76

    Flash cards word numbers 2, 3, 15, 16, 28, 39, 40, 72, 96, 97

    Fraction materials 14, 41, 43, 44, 56, 57, 60, 70, 88, 89, 101, 112, 116,117, 131

    Geoboard 117

    Graph paper 153, 154

    Grid 139, 147, 148, 149, 151, 152, 153, 157

    Ink 116

    Line graph 73, 74, 110

    Liquid measure containers English 46, 47, 48

    Map United States 85, 120

    Measuring cup two cup 65

    Medicine cup milliliter 119

    Meter stick 106

    Mirror 103

    Multiplication chart 13, 14, 15, 16, 22, 23, 24, 26, 27, 28, 34, 35, 43, 52,55, 61, 62, 63, 64, 65, 66, 67, 69, 74, 75, 76, 77, 80,87, 99, 109, 112, 113, 114, 122, 147

    Manipulative Name Description Used In Lesson

  • 19

    Manipulative Name Description Used In Lesson

    Number chart 099 1, 2, 3, 4, 5, 6, 10, 11, 15, 16, 20

    Number chart 100199 20, 21

    Number line 18, 31, 118, 125

    Pictograph 84, 85, 123, 124

    Place value materials 1, 2, 4, 5, 6, 13, 34, 36, 37, 53, 54, 68, 69, 90, 91,97, 98, 102, 113, 124, 126, 127

    Play money 1, 2, 3, 5, 6, 7, 8, 9, 10, 15, 23, 24, 25, 37, 38, 49,50, 51, 52, 53, 54, 65, 66, 92, 93, 103, 104, 105,117, 130, 131, 157

    Real money 6, 8

    Rice 65

    Rubber bands 117

    Ruler 12 inch 37, 39, 46, 56, 76, 78, 155

    Ruler 30 cm 106, 107, 108, 133, 134

    Scales English & metric 65, 122

    Shoe box 111, 143

    Solid models 27, 68, 152, 153

    Stamp or stickers smiley face 14

    String 8 inches 86

    Teaspoon 119

    Thermometer models Fahrenheit and 89, 90, 91, 92, 101, 102, 114, 115, 125, 126, 138,Celsius 149, 150

    Typing paper 102, 103, 116, 142

    Yardstick 37, 86, 106

  • 20

    Where To UseMathematicsWorksheets

    In this guide you will find eighty worksheets to be used as Duplication Masters.

    This chart shows where worksheets may be used. You will need to duplicate any worksheetused more than once.

    No. Master Worksheet Name Lessons Where Worksheets Are Used1 Addition facts drill sheet 1

    2 Subtraction facts drill sheet 2

    3 Time for hour, half hour, and quarter hour 5

    4 Addition and subtraction drill sheet 8

    5 Money 11

    6 Addition and subtraction drill sheet 13

    7 Multiplication chart 13

    8 Time for five minutes 17

    9 Addition and subtraction drill sheet 18

    10 Addition equations 21

    11 Addition and subtraction drill sheet 23

    12 Addition grouping 24

    13 Addition and subtraction drill sheet 28

    14 Roman numerals 29

    15 Time 32

    16 Addition and subtraction drill sheet 33

    17 Numbers in expanded form 36

    18 Addition and subtraction drill sheet 38

    19 Word problems 39

    20 Multiplication 42

    21 Addition and subtraction drill sheet 43

    22 Equations 47

    23 Addition and subtraction drill sheet 48

    24 Word problems 49

    25 Addition and subtraction drill sheet 53

    26 Rounding numbers 55

    27 Roman numerals 56

    28 Meaning of division visualized 57

    29 Addition and subtraction drill sheet 58

    30 Fractional word problems 61

    31 Addition and subtraction drill sheet 63

    32 Distributive principle 65

    33 Addition and subtraction drill sheet 68

    34 Rounding numbers 70

    35 Multiplication drill sheet 71

    36 Time 73

  • 21

    37 Addition and subtraction drill sheet 73

    38 Map reading 77

    39 Addition and subtraction drill sheet 78

    40 Multiplication 82

    41 Addition and subtraction drill sheet 83

    42 Equivalent fractions 84

    43 Addition and subtraction drill sheet 88

    44 Temperature 90

    45 Word problems 91

    46 Addition and subtraction drill sheet 93

    47 Bar graph information chart 93

    48 Addition, subtraction, and multiplication drill sheet 98

    49 Comparison of six-digit numbers 99

    50 Mixed numbers 102

    51 Addition, subtraction, and multiplication drill sheet 103

    52 Line graph chart 106

    53 Addition, subtraction, and multiplication drill sheet 108

    54 Division with remainder 109

    55 Subtraction 111

    56 Area and volume 112

    57 Addition, subtraction, and multiplication drill sheet 113

    58 Symmetry 116

    59 Geopaper 117

    60 Addition, subtraction, and multiplication drill sheet 118

    61 Pictograph chart 121

    62 Addition, subtraction, and multiplication drill sheet 123

    63 Grid 126

    64 Addition, subtraction, and multiplication drill sheet 128

    65 Division 132

    66 Addition, subtraction, and multiplication drill sheet 133

    67 Division 135

    68 Mixed numbers 137

    69 Addition, subtraction, and multiplication drill sheet 138

    70 Congruent figures 141

    71 Addition, subtraction, and multiplication drill sheet 143

    72 Subtraction equations 146

    73 Addition and subtraction of mixed numbers 147

    74 Addition, subtraction, and multiplication drill sheet 148

    75 Grid 152

    76 Addition, subtraction, and multiplication drill sheet 153

    77 Addition drill sheet 156

    78 Subtraction drill sheet 157

    79 Addition, subtraction, and multiplication drill sheet 158

    80 Multiplication drill sheet 159

    Where To Use Mathematics Worksheets, continued:No. Master Worksheet Name Lessons Where Worksheets Are Used

  • 22

    APPEARANCE OF CONCEPTSMATHEMATICS 3

    1. NUMBER THEORY Appears in Lesson

    Counting by 1s to 100 1, 2, 3, 4, 5Counting by 10s to 100 6, 7, 8, 9, 10Counting by 5s to 100 11, 12, 13, 14, 15Counting by 2s to 24 16, 17, 18, 19, 20Counting by 3s to 36 21, 22, 23, 24, 25Counting by 6s to 72 26, 27, 28, 29, 30Counting by 9s to 108 31, 32, 33, 34, 35Counting by 4s to 48 36, 37, 38, 39, 40Counting by 8s to 98 41, 42, 43, 44, 45, 46, 47, 48, 49, 50Counting by 7s to 84 51, 52, 53, 54, 55, 56, 57, 58, 59, 60Word numbers

    (0-9,999) 1, 2, 3, 4, 15, 16, 27, 28, 109, 110, 142, 159(10,000-99,999) 39, 40, 63, 64, 72, 75, 76(100,000-999,999) 96, 97, 111, 112, 123, 124, 136, 137(1,000,000-999,999,999) 146, 147, 160

    Even and odd 10, 11, 22, 23, 35, 36, 59, 60, 77, 79, 90Roman numerals 13, 14, 15, 16, 26, 27, 28, 29, 39, 40, 41, 42, 43, 54, 55, 56, 57,

    78, 79, 80, 81, 91, 92, 93, 94, 105, 106, 121, 122, 133, 134, 151,155

    Word problems 27, 82

    2. PLACE VALUEOnes, tens, hundreds, and

    thousands 1, 2, 3, 4, 5, 16, 17, 18, 19Ten thousands 30, 31, 32, 33, 36, 37, 44, 45, 46, 47, 48, 49, 58, 59, 60, 66, 67,

    68, 69, 71, 72, 73, 74Hundred thousands 95, 96, 97, 98, 101, 102, 111, 112, 113, 114, 123, 124, 125, 128,

    129, 136, 137, 138, 139Millions, ten millions, and

    hundred millions 145, 146, 147, 148, 149, 152, 153, 160

    3. NUMBER ORDEROrdinal numbers 1, 2Estimation 3, 4, 5, 6

    rounding to nearest 10 7, 8, 9, 10, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 51, 52, 53, 54,55, 136, 137, 138, 151, 152, 153, 154

    rounding to nearest 100 66, 67, 68, 69, 70, 71, 81, 82, 83, 84, 85, 86, 96, 97, 98, 99, 100,101, 111, 112, 113, 114, 115, 116, 139, 140, 144, 145, 146, 151,152, 153, 154, 158

    Greater than and less than 11, 12, 13, 21, 22, 23, 27, 34, 35, 44, 45, 52, 53, 63, 64, 71, 72,76, 81, 82, 86, 87, 88, 93, 96, 98, 102, 106, 110, 111, 125, 136,137, 138, 155, 156, 157, 158

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    Equal and not equal 19, 20, 26, 31, 33, 42, 45, 54, 74, 75, 76, 77, 82, 83, 84, 92, 93,94, 96, 98, 99, 105, 107, 120, 121, 142, 143, 146, 151, 152, 155

    Greater than, less than,and equal 55, 57, 101, 113

    Distributive principle 61, 62, 63, 64, 65, 76, 77, 79, 80, 86, 87, 96, 97, 107, 108

    4. ADDITIONCarrying

    two numbers doubledigit 1, 2, 3, 4, 5

    two numbers tripledigit 6, 7, 8, 9, 10, 11

    two numbers fourdigit 16, 17, 18, 121

    three numbers doubledigit 21, 22, 23

    three numbers tripledigit 26, 27, 28, 29

    three numbers fourdigit 31, 32, 33, 40

    four numbers doubledigit 51, 52, 53

    four numbers tripledigit 45, 58, 59, 60

    four numbers fourdigit 63, 64, 65

    five numbers doubledigit 70, 71, 72, 73, 83, 84, 85

    five numbers singledigit 78, 79, 80

    two numbers fivedigit 122, 123

    three numbers fivedigit 131, 132, 133

    five numbers fivedigit 158

    Word problems 4, 5, 14, 15, 16, 17, 20, 22, 28, 31, 38, 39, 43, 47, 52, 53, 59,60, 78, 79, 82, 83, 85, 87, 88, 92, 93, 95, 100, 114, 115, 127,136

    Addition terms 7, 9, 22, 33, 26, 27, 45, 59, 60, 70, 71, 122, 123Facts 12, 30, 52Add 10 15, 20, 44, 45, 50Equations 18, 19, 20, 21, 22, 24, 33, 34, 36, 37, 41, 42, 43, 46, 47, 48, 51,

    52, 53, 68, 67, 71, 72, 96, 97, 111, 112, 139, 141Addition grouping 21, 22, 23, 24, 35, 36, 37, 46, 47, 59, 88, 89, 90Write own word problems 23, 29, 32, 42, 57, 133Add 100 55, 60, 64, 65Horizontal to vertical 106, 107, 108, 116, 118, 141, 142, 143, 156, 157Like fractions 116, 117, 118, 119, 120, 159, 160Mixed numbers 136, 137, 146, 148

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    5. TIMEA.M. and P.M. 3, 4, 5, 6, 17, 18, 19, 70Hour 3Half hour 4Quarter hour 5Hour, half hour, quarter

    hour 6, 70Five minute 17, 18, 19, 20, 71One minute 31, 32, 33, 34, 35, 46, 47, 48, 49, 72, 73, 84, 85, 86, 97, 98,

    99, 100, 111, 112, 113, 124, 133, 134, 135, 146, 148Word problems 35, 69, 70, 83, 95, 99, 136, 147Calendar 63, 73, 84, 93Equivalents

    6. SUBTRACTIONWithout borrowing

    double digit 1, 2, 3, 5, 8, 9, 10Word problems 4, 5, 14, 15, 22, 27, 28, 31, 39, 41, 43, 47, 52, 53, 60, 66, 78,

    85, 91, 92, 93, 115, 128, 130, 132, 136Regrouping 4, 5, 6, 7Facts 7, 9With borrowing

    double digit 13, 14triple digit 15, 19, 20, 24, 25, 28, 29, 30, 34, 35, 36, 40, 43, 66, 79, 103,

    104, 105, 109, 110, 111, 144, 145, 146, 149, 150, 151four digit 48, 49, 50, 54, 55, 56, 61, 62, 63, 65, 67, 68, 69, 74, 75, 76,

    77, 80, 81, 82, 83, 89, 90, 91, 96, 97, 98, 119, 120, 121, 125, 126,127, 134, 135, 136, 139, 140, 154, 155, 156, 157, 158, 159, 160.

    Subtraction terms 13, 14, 29, 30, 49, 50, 76, 77, 97, 98, 119, 120, 135, 136Write own word problems 23, 29, 32, 42, 49, 62, 70, 113, 133Subtract 10 94, 95, 100, 104, 105, 110Equations 118, 119, 120, 122, 123, 124, 129, 131, 132, 135, 146, 147Subtract 100 125, 126, 127, 138, 139, 140, 152Like fractions 131, 132, 133, 134, 135, 159, 160Mixed numbers 147, 148

    7. MONEYCounting coins 6, 7, 23, 24, 49, 52, 53, 104, 105, 106, 117, 118, 119, 130, 131,

    132Counting bills 8, 9Counting coins and bills 10, 11, 12, 25, 38, 50, 51, 54, 65, 66, 79, 80, 156, 157, 158Subtraction 15, 36, 65, 66, 67, 69, 77, 79, 80, 104, 121, 136, 154, 156,

    157, 158, 160Word problems 22, 28, 37, 38, 52, 66, 78, 83, 85, 87, 91, 92, 100, 123, 130,

    132, 136, 144, 158Addition 16, 28, 32, 60, 65, 116, 133, 143, 157, 158Multiplication 64, 80, 90, 104

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    8. MULTIPLICATIONReadiness 8, 9, 10Facts 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28,

    29, 32, 33, 34, 35, 43, 44, 66, 67, 77By 10, 100, 1000 18, 19, 114, 115, 116Terms 21, 22, 23, 38, 39, 40, 59, 61, 87, 88, 103, 104, 126, 127, 152,

    153Word problems 25, 31, 41, 47, 59, 83, 91, 95, 99, 104, 109, 115, 126, 132, 143Without carrying

    double digit timessingle digit 38, 39, 40, 41, 42

    triple digit timessingle digit 45, 46, 61

    four digit times singledigit 50, 51

    Write own word problems 49, 57, 113With carrying

    double digit timessingle digit 53, 54, 55, 68, 69, 70, 71, 72, 73, 74, 75

    triple digit timessingle digit 62, 77, 79, 80, 81, 82, 126, 127, 128, 129, 130

    four digit times singledigit 63, 64, 87, 88, 89, 90, 92, 93, 94, 141, 142, 143, 152, 153, 154

    five digit times singledigit 99, 100, 101, 102, 103, 104

    Equations 83, 84, 86, 93, 94, 98, 106, 107, 152, 153, 154, 155, 156, 157Fractions 135, 136, 137, 145, 146, 147, 150, 155, 160

    9. GEOMETRYShapes and solids (14) 11, 12, 13, 14Shapes and solids (18) 25, 26, 27, 28, 29, 30, 41, 42, 43, 44, 55, 56, 57, 58, 68, 69,

    70, 81, 82, 93, 94, 95, 105, 106, 117, 118, 121, 139, 140Symmetry 102, 103, 104, 116, 117, 118, 128, 129, 130, 141, 142, 143,

    153, 154, 157Line, line segment, ray,

    endpoint, right angle 115, 116, 117, 128, 129, 130, 155, 156, 158, 159Congruent figures 141, 142, 148, 150, 154, 155Similar figures 143, 144, 149, 150, 154, 155

    10. FRACTIONSTerms 14, 15, 31, 43, 44, 45, 59, 60, 72, 73, 82, 83, 93, 94, 121, 139, 140Fractional part of whole 14, 15, 16, 17, 41, 42, 45, 48, 101, 103, 104, 116, 117, 118Word fractions 30, 31, 32, 33Fractions as decimals 41, 48, 49, 57, 77, 78, 80, 100, 111Comparison of fractions 43, 44Word problems 54, 61, 74, 75, 87, 114, 148, 151, 154, 155, 160Equivalent fractions 56, 57, 58, 59, 60, 61, 70, 71, 72, 73, 74, 75, 76, 77, 82, 83,

    84, 93, 101, 102, 103, 104, 105, 107, 112, 121, 142, 143, 151, 152Mixed numbers 88, 89, 90, 91, 92, 113, 124, 125, 155, 156Reduce 105, 106, 108, 115, 116, 127, 128, 139, 140, 153, 154Addition of like fractions 116, 117, 118, 119, 120, 159, 160

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    Subtraction of likefractions 131, 132, 133, 134, 135, 159, 160

    Multiplication 135, 136, 137, 145, 146, 147, 150, 155, 160Addition of mixed

    numbers 136, 137, 146, 148Subtraction of mixed

    numbers 147, 148

    11. DECIMALSFractions as decimals 41, 48, 49, 57, 77, 78, 80, 100, 111Decimal part of whole 42Word numbers 43, 49, 56, 77, 78, 80, 100Mixed numbers as

    decimals 91, 92, 102, 103, 113, 124, 125Addition 121, 122, 141, 142, 143, 156

    12. DIVISIONReadiness 57, 58, 59, 60, 61, 62, 63, 64, 65Terms 62, 63, 64, 75, 76, 99, 100, 128, 129, 144, 145Facts 66, 67, 69, 74, 75, 76, 87Single-digit divisor

    double-digit quotient 97, 98, 99, 100single-digit quotient

    with remainder 107, 108, 109, 112, 113, 114, 117, 119, 120, 122, 123, 124double-digit quotient 126, 127, 128, 129, 131double-digit quotient

    with remainder 132, 133, 134, 135, 138, 140, 144, 145, 149, 150, 160Word problems 79, 100, 104, 119, 120, 121, 122, 123, 124, 140, 145Write own word problems 159

    13. MEASUREMENTEnglish units of measure

    linear equivalents 37, 38, 76, 77, 78, 86, 94, 96, 123, 136, 137, 148, 149, 150, 158,159

    inches 39, 46, 56, 76, 78liquid equivalents 46, 47, 48, 76, 77, 79, 86, 94, 96, 123, 136, 137, 148, 149, 150,

    158, 159dry equivalents 56, 57, 58weight equivalents 64, 65, 66, 76, 77, 86, 94, 95, 96, 123, 136, 137, 148, 149, 150,

    158, 159Map reading 77, 78, 85, 120, 130, 135Temperature 89, 90, 91, 92, 101, 102, 103, 114, 115, 125, 126, 137, 138, 149,

    150Metric units of measure

    linear equivalents 106, 107, 108, 109, 123, 131, 132, 136, 137, 148, 149, 150, 158,159

    centimeters 106, 133, 134millimeters 107, 108, 109

    liquid equivalents 118, 119, 120, 123, 131,132, 136, 137, 148, 149, 150, 158, 159weight equivalents 122, 123, 131, 132, 136, 137, 148, 149, 150, 158, 159

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    14. GRAPHS AND GRIDSBar graph 34, 35, 46, 47, 61, 62, 93, 95Line graph 36, 37, 48, 49, 73, 74, 110Pictograph 38, 39, 50, 51, 84, 85, 121, 125Grid 126, 127, 128, 137, 138, 139, 147, 148, 149, 151, 152,

    153, 156, 157

    15. PERIMETER, AREA, AND VOLUMEPerimeter 86, 87, 88, 94, 107, 121, 140Word problems 88Area 95, 96, 98, 99, 108, 109, 122, 123, 141, 142, 150, 151Volume 110, 111, 112, 124, 125, 143, 144, 152, 153

    16. RATIOWrite three ways 103Comparison 104, 105, 117, 118, 119, 129, 144, 145, 157, 158, 159Word problems 108, 130, 131, 146, 147

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    Development

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    of Concepts

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  • Lessons

    H o r i z o n s M a t h e m a t i c s 3

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    Teaching Tips:1. The regrouping principle in activity 4 is called the associative

    principle. It is not necessary for the student(s) to learn the nameat this time but mention it as you introduce the activity.

    Objectives:1. The student shall be able to count out loud by threes to 36.

    2. The student shall be able to write the numbers necessary toillustrate the grouping principle for addition.

    3. The student shall be able to write the numbers (multiples of ten)between which a given number falls.

    4. The student shall be able to write the correct symbol (< or >)between two double- or triple-digit numbers.

    5. The student shall be able to write the sum of three double-digitnumbers when the ones column has a double-digit answer.

    6. The student shall be able to write the name of the terms in amultiplication problem.

    7. The student shall be able to write the product of the multiplicationfacts for five, two, and three.

    8. The student shall be able to write the value of a variable in anaddition equation.

    9. The student shall be able to write two addition and twosubtraction equations corresponding to three given numbers.

    Materials, Supplies, & Equipment:1. Flash cards for addition facts, multiplication facts, and

    multiplication terms

    2. Number chart 100199

    Concepts:Counting by threes, addition grouping, estimation, greater thanand less than, addition, multiplication, multiplication terms,and equations

    Lesson 21

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    Lesson 21

    Worksheets:1. Worksheet 10 Addition equations

    Activities:1. Count out loud with the student(s) by threes to 36.

    2. Drill all addition facts with flash cards.

    3. Using flash cards for multiplication facts, drill 0s, 1s, 10s, and 5sas pairs without the answers showing. Drill 2s and 3s as pairswith the answers showing.

    4. Write (4 + 3) + 6 = __ + 6 = ___ and 4 + (3 + 6) = 4 + __ = ___ onthe chalk board. Have the student(s) tell you what three numbersare being added together in each equation. Ask the student(s) whatnumbers are grouped together in the first and second equations.Write their sum on the blank and add. Discuss with them how thenumbers may be grouped differently without changing the sum.They must always add what is in the parenthesis first. Write severalsimilar equations on the chalk board for the student(s) to solve. Givehelp where needed as they complete Student Activity One.

    5. Point to several numbers on the number chart 100199 and havethe student(s) tell between what two numbers (multiples of ten) thegiven numbers fall (e.g. 148 falls between 140 and 150). Remindthem to find the digit in the tens place (4) and that it will fallbetween that ten (140) and the next ten (150). Then write severalnumbers over 200 on the chalk board. Have the student(s) tellbetween what two numbers (multiplies of ten) the given numbersfall. The student(s) should be able to complete Student ActivityTwo without further help.

    6. Once you have reviewed the symbols < and >, the student(s)should be able to complete Student Activity Three alone.

    7. Have the student(s) check their answers in Student ActivityFour by applying the grouping principle from Student ActivityOne. Find the answer by adding down and check by adding up.

    8. Discuss with the student(s) the meaning of the words product,multiplicand, and multiplier using the multiplication termsflash card. Have them write the words on the correct blanks inStudent Activity Five. The student(s) should be able to completethe activity independently.

    9. The student(s) should be able to complete Student Activity Sixon their own. Further practice can be found on Worksheet 10.

    10. Write 12, 5, and 7 on the chalk board. Have the student(s)write two addition and two subtraction facts using the threenumbers. The student(s) should be able to complete StudentActivity Seven without much help.

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    Teaching Tips:1. Some student(s) might still have a difficult time choosing the closer

    number in activity 4. Tell them the following: If the ones digit isgreater than 5, it is closer to the larger number and if it is less than5, it is closer to the smaller number. Remind the student(s) thatthey are learning to round a number to the nearest ten.

    Materials, Supplies, & Equipment:1. Flash cards for subtraction facts, multiplication facts, addition

    terms, and greater than and less than

    2. Multiplication chart

    Objectives:1. The student shall be able to count out loud by threes to 36.

    2. The student shall be able to write the numbers (multiples of ten)between which a given number falls and to which of the two it isthe closer.

    3. The student shall be able to write the sum of three double-digitnumbers when the tens column has a double-digit answer andwrite the names of the terms.

    4. The student shall be able to write the product to the multiplicationfacts for two and three and write the names of the terms.

    5. The student shall be able to write the correct symbol (< or >)between two triple-digit numbers.

    6. The student shall be able to write the numbers necessary toillustrate the grouping principle for addition.

    7. The student shall be able to write the value of a variable in anaddition equation.

    Concepts:Counting by threes, estimation, addition, even and odd, additionterms, multiplication, multiplication terms, greater than and lessthan, addition grouping, equations, and word problems

    Lesson 22

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    Lesson 22Activities:1. Count out loud with the student(s) by threes to 36.

    2. Drill all subtraction facts with flash cards.

    3. Using flash cards for multiplication facts, drill 0s, 1s, 10s, and 5sas pairs without the answers showing. Drill 2s and 3s as pairswith the answers showing.

    4. Write several three-digit numbers on the chalk board. Ask thestudent(s) to tell between what two numbers (multiplies of ten)the given numbers fall. Remind them to find the tens digit and itwill fall between that ten and the next ten. Then have themdetermine to which number it is closer. The student(s) should beable to complete Student Activity One with little help.

    5. Use the addition terms flash card to review addends and sum.Discuss what makes a number even or odd (if last digit is 2, 4, 6,8, 0 its even and 1, 3, 5, 7, 9 its odd). As the student(s) beginStudent Activity Two, discuss the directions.

    6. Ask the student(s) to tell what the terms multiplicand, multiplier,and product mean. Aid them in writing the words on the correctlines in Student Activity Three. Allow the student(s) to use themultiplication chart to be accurate when completing the activity.

    7. Have the student(s) read the greater than and less than signs fromthe flash cards. Discuss how to remember the names. Also askthem how to tell the correct way to write the symbols in StudentActivity Four (the point is always towards the smaller number).Once they have written the symbol, have them read the problem.Watch for the incorrect use of the word and.

    8. Write (8 + 3) + 2 = __ + __ = ___ and 8 + (3 + 2) = __ + __ = ___on the chalk board. Have the student(s) tell you what threenumbers are being added together in each equation. Discuss withthem how the numbers may be grouped differently withoutchanging the sum. They must always add what is in theparenthesis first. Write several similar equations on the chalkboard for the student(s) to solve. Give help where needed as theycomplete Student Activity Five.

    9. The student(s) should be able to complete Student Activity Sixwithout further help.

    10. Allow the student(s) to complete Student Activity Sevenindependently. Check to see that they labeled their answers. Thenhave a thorough discussion of why each step is completed as it is.

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    Teaching Tips:1. When doing activity 5, write (6 - 2) - 1 = 6 - (2 - 1) on the chalk

    board. Have the student(s) subtract the parenthesis on each side ofthe equation first. Then simplify both sides to find that 3 5.Therefore, the grouping principle does not hold true for subtraction.

    Objectives:1. The student shall be able to count out loud by threes to 36.

    2. The student shall be able to circle the coins necessary to equal onedollar.

    3. The student shall be able to write the numbers necessary toillustrate the grouping principle for addition.

    4. The student shall be able to write the product of the multiplicationfacts for five, two, and three.

    5. The student shall be able to write the correct symbol (< or >)between two four-digit numbers.

    6. The student shall be able to write the numbers (multiples of ten)between which a given number falls and to which of the two it isthe closer.

    7. The student shall be able to write the sum of three double-digitnumbers when the answers in the ones and tens columns aredouble digit and write the correct word (even or odd) below eachanswer.

    8. The student shall be able to write an addition and a subtractionword problem using money.

    Materials, Supplies, & Equipment:1. Flash cards for multiplication facts

    2. Play money

    3. Multiplication chart

    Concepts:Counting by threes, money, addition grouping, multiplication,multiplication terms, greater than and less than, estimation,addition, even and odd, and word problems

    Lesson 23

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    Lesson 23

    Worksheets:1. Worksheet 11 Addition and subtraction drill sheet

    Activities:1. Count out loud with the student(s) by threes to 36.

    2. Drill the addition facts using Drill #1, Worksheet 11.

    3. Using flash cards for multiplication facts, drill 0s, 1s, 10s, and 5sas pairs without the answers showing. Drill 2s and 3s as pairswith the answers showing.

    4. Give the student(s) enough coins in play money to equal more thana dollar. Ask them to find the coins they would need to equal$1.00. Suggest they start with the largest coins. Have themexchange coins and do it again. They should be able to completeStudent Activity One without further help.

    5. Write (2 + 4) + 6 = 2 + (4 + 6) on the chalk board. Underneath itwrite __ + 6 = 2 + __. Underneath that write ___ = ___. Remindthe student(s) to always add what is in the parenthesis first. Havethem tell you what to write in the first two blanks. Then havethem add both the right hand side and the left hand side to findwhat to write in the last two blanks. Discuss the groupingprinciple. Have the student(s) complete the first problem inStudent Activity Two together. They should be able to finish theremaining problems by themselves.

    6. The student(s) should be able to complete Student Activity Threeon their own. Have them use the multiplication chart if necessary.

    7. Write 2,569 __ 4,672 3,968 __ 3,451 and 6,253 __ 6,284 on thechalk board. Review the meaning of the greater than and less thansymbols. Ask the student(s) which symbol would go between eachset of numbers. If the first digits are different, they only comparethe first digits. If the first digits are the same, they need to comparethe second digits. If the first two digits are the same, they comparethe third digits. Give help where needed as the student(s) completeStudent Activity Four.

    8. Explain to the student(s) that they are rounding a number to thenearest ten when they are determining to which ten the numberis closer. Say several triple-digit numbers for them to round to thenearest ten. After completing the first problem in StudentActivity Five together, allow the student(s) to finish theremaining problems alone.

    9. The student(s) should be able to complete Student Activity Sixand Seven without assistance.

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    Materials, Supplies, & Equipment:1. Clock model

    2. Flash cards for multiplication facts

    3. Play money

    4. Multiplication chart

    Teaching Tips:1. Have the student(s) illustrate a subtraction problem similar to

    Student Activity Four by using play money pennies, dimes, andone dollar bills. When they need to borrow one hundred and changeit to ten tens, have them take one dollar bill and change it into tendimes. Add the ten dimes to the dimes they have and subtract.

    Objectives:1. The student shall be able to count out loud by threes to 36.

    2. The student shall be able to write the number to the nearest tenof a given number.

    3. The student shall be able to circle the coins necessary to equaleighty cents.

    4. The student shall be able to draw a line to match a symbol with itscorresponding word.

    5. The student shall be able to write the difference of two triple-digitnumbers when borrowing from the hundreds column.

    6. The student shall be able to write the value of a variable in anaddition equation.

    7. The student shall be able to write the numbers necessary toillustrate the grouping principle for addition.

    8. The student shall be able to write the product of the multiplicationfacts for one, five, two, and three.

    Concepts:Counting by threes, estimation, money, subtraction, equations,addition grouping, and multiplication

    Lesson 24

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    Lesson 24

    Worksheets:1. Worksheet 12 Addition grouping

    2. Worksheet 11 Addition and subtraction drill sheet

    Activities:1. Count out loud with the student(s) by threes to 36.

    2. Drill the subtraction facts using Drill #2, Worksheet 11.

    3. Use the clock model to drill the multiplication facts for 0s, 1s, 10s,and 5s as pairs. Using flash cards for the multiplication facts, drill2s and 3s as pairs with the answers showing.

    4. Point to several numbers on the clock model and multiply them by10, then 100, then 1,000.

    5. Write several three-digit numbers on the chalk board. Have thestudent(s) tell the ten to which the numbers are closest. Remindthem that they are rounding the number to the nearest ten.Continue until they can complete Student Activity Onesuccessfully alone.

    6. Using play money, have the student(s) select the different coinsneeded to equal 60. See how many different combinations theycan find. They should be able to complete Student Activity Twoon their own.

    7. Have the student(s) complete Student Activity Three alone.

    8. Write several sets of two triple-digit numbers on the chalk boardas a subtraction problem with borrowing in the hundreds column.Have the student(s) copy the problems on a sheet of paper and findthe answers. Work the problems on the chalk board to enablethem to check their answers. They should be able to completeStudent Activity Four independently.

    9. Give assistance where needed as the student(s) complete StudentActivity Five.

    10. Write 3 + (6 + 2) = (3 + 6) + 2, __ + __ = __ + __, and ___ = ___on the chalk board in three rows underneath each other. Have thestudent(s) tell the numbers to write in the blanks. Do severalsimilar problems until the student(s) can complete StudentActivity Six by themselves.

    11. The student(s) should be able to complete Student ActivitySeven without help except for the multiplication chart.

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    Materials, Supplies, & Equipment:1. Flash cards for addition facts, multiplication facts, shapes, and

    solids

    2. Play money

    3. Clock model

    Teaching Tips:1. When the student(s) are doing activity 4, they may question the

    difference between a diamond and a rhombus. This will bediscussed when the characteristics of the new shapes and solidsare discussed later. For now, tell them that the rhombus is thegeometric name for a diamond.

    Objectives:1. The student shall be able to count out loud by threes to 36.

    2. The student shall be able to draw a line to match an object to itscorresponding shape or solid.

    3. The student shall be able to write the number needed to round agiven number to its nearest ten.

    4. The student shall be able to write the difference of two triple-digitnumbers when borrowing from the hundreds column.

    5. The student shall be able to write the symbol that represents agiven word.

    6. The student shall be able to circle the coins and dollar billsnecessary to equal a given amount of money.

    7. The student shall be able to write the product of the multiplicationfacts for two, three, and five.

    Concepts:Counting by threes, shapes, solids, estimation, subtraction, money,multiplication, and word problems

    Lesson 25

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    Lesson 25

    Circumstances without are not as importantas determination within.

    Activities:1. Count out loud with the student(s) by threes to 36.

    2. Drill the addition facts by reading a series of ten facts from theaddition flash cards to the student(s). Have them write theanswers in a column on a sheet of paper. Check their answers andgive them another series of ten facts. Continue doing thisfor 5 minutes.

    3. Using flash cards for multiplication facts, drill 0s, 1s, 10s, and 5sas pairs without the answers showing. Drill 2s and 3s as pairswith the answers showing.

    4. Display the shape and solid flash cards for the trapezoid,rhombus, parallelogram, and rectangular prism. The goal for thislesson is to learn to identify these four shapes. Say and spell eachone as the picture is displayed. The student(s) should completeStudent Activity One together.

    5. Write several three-digit numbers on the chalk board that do nothave 5 as the ones digit. Ask the student(s) to round the numbersto the nearest ten. Relate this to the previous problem of findingthe number to which ten is closer. First they find the tens digitand decide if it is closer to that ten or the next ten. The ones digitwill always become zero. Give help where needed as the student(s)complete Student Activity Two.

    6. The student(s) should be able to complete Student ActivityThree and Four independently.

    7. Give the student(s) dollar bills and coins in play money. Ask themto count several amounts between one and two dollars. Theyshould be able to complete Student Activity Five alone.

    8. The student(s) should be able to complete Student Activity Sixby themselves.

    9. Point to several numbers on the clock model and multiply them by10, 100, and 1,000. When the student(s) write their answers forStudent Activity Seven, allow them to leave the answer as allcents or as dollar and cents. Discuss both answers for eachquestion.

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    Materials, Supplies, & Equipment:1. Flash cards for addition facts, multiplication facts, shapes, solids,

    equal and not equal, Roman numerals, and addition terms

    2. Multiplication chart

    Teaching Tips:1. Spend most of the drill time in activity 3 on 4 x 6, 6 x 6, 7 x 6, 8 x

    6, and 9 x 6 as pairs. The student(s) should know the other 6s ifthey have been drilling in pairs. Notice that the 0s, 1s, and 10shave been omitted from the drill time. The student(s) should havemastered the rules for these facts by this time.

    Objectives:1. The student shall be able to count out loud by sixes to 72.

    2. The student shall be able to circle the object that is a differentshape than the given shape.

    3. The student shall be able to write the correct symbol (= or )between a Roman numeral and an Arabic number.

    4. The student shall be able to write the name of the terms in anaddition problem.

    5. The student shall be able to write the sum of three triple-digitnumbers when the ones column has a double-digit answer.

    6. The student shall be able to write the correct symbol (+, -, or x)after the key word used in a word problem.

    7. The student shall be able to write the product of the multiplicationfacts for six.

    Concepts:Counting by sixes, shapes, solids, equal and not equal, Romannumerals, addition, addition terms, and multiplication

    Lesson 26

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    Lesson 26

    We must adapt to circumstancesbut should never allow them to control us.

    Activities:1. Count out loud with the student(s) by sixes to 72.

    2. Drill all addition facts with flash cards.

    3. Using flash cards for multiplication facts, drill 5s and 2s as pairswithout the answers showing. Drill 3s and 6s as pairs with theanswers showing. The drill of the multiplication facts with flashcards is very important to the students success in memorizing theirfacts. Do not omit this practice.

    4. Looking at the shape and solid flash cards, have the student(s)describe the three shapes and one solid used in Student ActivityOne. Accept any valid description. It does not have to becomplete. Allow the student(s) to do the activity together.

    5. Have the student(s) identify the equal and not equal flash cardsymbols. Using the Roman numeral flash cards, display severalnumerals up to XX on the chalk board rail. Have the student(s)identify the corresponding Arabic number. Write several Romannumerals and Arabic numbers on the chalk board side by side.Ask the student(s) to tell if they should put an equal or not equalsymbol between the two numbers. The student(s) should be ableto complete Student Activity Two with little help.

    6. Review the addition terms flash card. Remind the student(s) towrite the terms on the lines given in Student Activity Three. Besure they check their answers by adding up and then adding downor vise versa.

    7. Have the student(s) look at the words or word phrases given inStudent Activity Four. Make up a question using each key wordand see if the student(s) can tell if they should add or subtract (e.g.How many marbles are left? or How many marbles are therealtogether?). Complete the activity in this manner.

    8. The student(s) may need their multiplication chart to completeStudent Activity Five.

    9. The student(s) should be able to complete Student Activity Sixon their own.

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    Teaching Tips:1. When the student(s) are doing Student Activity Two, have them

    read to themselves the number they have written as a checkagainst the word number that is given. Remind them that the zerois a place holder to show that there are no ones, tens, or hundredsin the number.

    Objectives:1. The student shall be able to count out loud by sixes to 72.

    2. The student shall be able to draw a line to match a shape or solidwith its name.

    3. The student shall be able to write the number that corresponds toa given word number.

    4. The student shall be able to write the correct symbol (< or >)between two Roman numerals.

    5. The student shall be able to write the product of the multiplicationfacts for five, two, three, and six.

    6. The student shall be able to write the sum of three triple-digitnumbers when the tens column has a double-digit answer andwrite the names of the terms.

    7. The student shall be able to write the key words used in anaddition or subtraction word problem.

    Materials, Supplies, & Equipment:1. Flash cards for subtraction facts, multiplication facts, shapes,

    solids, greater than and less than, and Roman numerals

    2. Rectangular prism model

    3. Multiplication chart

    Concepts:Counting by sixes, shapes, solids, word numbers, greater than andless than, Roman numerals, multiplication, addition, additionterms, and word problems

    Lesson 27

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    Lesson 27

    Circumstances do not cause a person to be weak or strong;they only reveal whether he is weak or strong.

    Activities:1. Count out loud with the student(s) by sixes to 72.

    2. Drill all subtraction facts with flash cards.

    3. Using flash cards for multiplication facts, drill 5s and 2s as pairswithout the answers showing. Drill 3s and 6s as pairs with theanswers showing.

    4. Using the shape and solid flash cards, discuss the characteristicsof each shape (trapezoid: 4 straight sides, 2 sides parallel, 2 sidesnot parallel; rhombus: 4 straight equal sides, opposite sidesparallel; parallelogram: 4 straight sides, opposite sides parallel;rectangular prism: solid (3 dimensions), 6 rectangular sides, 12straight line edges, opposite sides parallel). Show the student(s)a model of a rectangular prism. They should be able to completeStudent Activity One independently.

    5. Say several four-digit numbers for the student(s) to write on asheet of paper. Use zero as one of the digits in each number. Besure they put a comma between the hundreds and thousandsplace. Allow them to complete Student Activity Two alone.

    6. Review the greater than and less than flash cards. Put twodifferent Roman numerals (120) on the chalk board rail using theRoman numeral flash cards. Have the student(s) determine whichsymbol (< or >) should be placed between the Roman numerals. Doseveral similar examples until the student(s) can completeStudent Activity Three by themselves. They may need to writeeach corresponding Arabic number under the Roman numeralbefore making the comparison.

    7. The student(s) should be able to complete Student Activity Fourand Five without assistance. The multiplication chart may beneeded for Student Activity Four.

    8. The student(s) may need to refer to lesson 26, Student ActivityFour, to refresh their minds when starting Student Activity Sixor you may write the words on the chalk board. Have the student(s)make up a question that could be used in a word problem usingeach of the key words. Complete the activity together.

    9. The student(s) should be able to complete Student ActivitySeven on their own.

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    Materials, Supplies, & Equipment:1. Flash cards for multiplication facts, Roman numerals, shapes,

    solids, and word numbers

    2. Multiplication chart

    Teaching Tips:1. Insist that the student(s) put the dollar sign and the period in

    their answers in Student Activity Three. This is as important aslabeling an answer in a word problem. It should be counted wrongif they do not do so.

    Objectives:1. The student shall be able to count out loud by sixes to 72.

    2. The student shall be able to write the Roman numeral thatcorresponds to the given Arabic number.

    3. The student shall be able to write the name of each given shape orsolid.

    4. The student shall be able to write the sum of three triple-digitnumbers when the answers in the ones and the hundredthscolumns are double digits.

    5. The student shall be able to write the number that corresponds toa given word number.

    6. The student shall be able to write the difference of two triple-digitnumbers when borrowing from the tens and hundreds columns.

    7. The student shall be able to write the letter in the box thatcorresponds to the product of the multiplication problem.

    Concepts:Counting by sixes, Roman numerals, shapes, solids, addition,money, word numbers, subtraction, multiplication, and wordproblems

    Lesson 28

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    Lesson 28

    Worksheets:1. Worksheet 13 Addition and subtraction drill sheet

    Activities:1. Count out loud with the student(s) by sixes to 72.

    2. Drill the addition facts using Drill #1, Worksheet 13.

    3. Using flash cards for multiplication facts, drill 5s and 2s as pairswithout the answers showing. Drill 3s and 6s as pairs with theanswers showing.

    4. Write several double-digit numbers on the chalk board and havethe student(s) choose the Roman numeral flash cards needed torepresent the numbers. Remind them to choose what is needed foreach place value digit (e.g. for 63 they need to choose what isneeded for 60 and then what is needed for 3). The student(s)should be able to complete Student Activity One alone.

    5. Place the three shapes and one solid flash cards on the chalk boardrail used in Student Activity Two. Ask the student(s) to spell andidentify each one by the picture. Turn the cards over and have themdescribe each one. Leave the names on the chalk board for spellingreference as the student(s) complete the activity.

    6. The student(s) should be able to complete Student ActivityThree independently. Be sure they are writing the number theycarry above the next column each time.

    7. Write several four-digit numbers on the chalk board. As you pointto each one, have the student(s) write the number on a sheet ofpaper. Then have them read their number back to you to see if itis the same as the one on the chalk board. Place the word numberflash cards on the chalk board rail for the student(s) to use forspelling reference as they complete Student Activity Four.

    8. On the chalk board, write several sets of two triple-digit numbersas subtraction problems with borrowing from the tens and thehundreds columns. Work the first problem with the student(s)step by step. Ask them to copy the second one on a sheet of paperand work it by themselves. Then work it on the chalk board withthe student(s). This will enable them to find any mistakes theyhave made. Continue the same procedure with the remainingproblems. Check the student(s) work carefully as they completeStudent Activity Five, helping those who need it.

    9. The student(s) should be able to complete Student Activity Sixon their own. They may need the help of the multiplication chart.

    10. Discuss with the student(s) how they answered each question inStudent Activity Seven.

  • 88

    Teaching Tips:1. Give the student(s) some parameters for the word problems in

    Student Activity Seven (e.g. use students selling tickets to a ballgame, have a reading contest, use a friends name, etc.).

    Objectives:1. The student shall be able to count out loud by sixes to 72.

    2. The student shall be able to draw a line to match a shape or solidto its name.

    3. The student shall be able to write the sum of three triple-digitnumbers when the answers in the tens and the hundredscolumns are double digits.

    4. The student shall be able to write the Arabic number thatcorresponds to a given Roman numeral.

    5. The student shall be able to write the correct symbol (+, -, x, or =)in a given equation.

    6. The student shall be able to write the difference of two triple-digitnumbers when borrowing in the tens and hundreds columns andwrite the names of the terms.

    7. The student shall be able to write the product of the multiplicationfacts for five, two, three, and six.

    8. The student shall be able to write an addition and a subtractionword problem using double-digit numbers.

    Materials, Supplies, & Equipment:1. Clock model

    2. Flash cards for multiplication facts, shapes, solids, Romannumerals, and subtraction terms

    Concepts:Counting by sixes, shapes, solids, addition, Roman numerals,subtraction, subtraction terms, multiplication, and word problems

    Lesson 29

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    Lesson 29

    Generosity is determined by the spirit in which you givenot the amount you give.

    Worksheets:1. Worksheet 14 Roman numerals

    2. Worksheet 13 Addition and subtraction drill sheet

    Activities:1. Count out loud with the students by sixes to 72.

    2. Drill the subtraction facts using Drill #2, Worksheet 13.

    3. Use the clock model to drill the multiplication facts for 5s and 2sas pairs. Using flash cards for the multiplication facts, drill 3s and6s as pairs with the answers showing.

    4. Have the student(s) identify all of the shape and solid flash cardsby picture. Repeat those which they have difficulty identifying. Thestudent(s) should be able to complete Student Activity One alone.

    5. The student(s) should need no assistance when doing StudentActivity Two.

    6. Use the Roman numeral flash cards to display several Romannumerals under 100 on the chalk board rail. The number that goesin the tens place will begin with either an X or L. The number thatgoes in the ones place will begin with either an I or V. Have thestudent(s) tell the corresponding Arabic number. They should beable to complete Student Activity Three on their own.

    7. Write 5 __ 4 = 9, 8 __ 3 = 24, 17 - 9 __ 8, 15 __ 8 = 7 on thechalk board. Ask the student(s) to tell what symbols (+, -, x, or =)should be placed on each blank. They should be able to completeStudent Activity Four independently.

    8. Review the subtraction terms flash card. Say and spell each word.Remind the student(s) to write the terms on the lines as they beginStudent Activity Five.

    9. In Student Activity Six, the student(s) are to multiply thenumbers in the squares and write the answers in the circlesbetween the two numbers they have multiplied.

    10. Have the student(s) complete Student Activity Seven withoutany help. Read several of the word problems and let the student(s)solve them together.

  • 90

    Materials, Supplies, & Equipment:1. Flash cards for subtraction facts, multiplication facts, shapes,

    solids, and subtraction terms

    Teaching Tips:1. Be sure the student(s) put the comma in their answers between

    the hundreds and the thousands in Student Activity One. Thispractice will be very important when they begin to read muchbigger numbers.

    2. If time permits, have the student(s) try a subtraction squaresimilar to the addition squares in Student Activity Six. See ifthe difference in the last row and the last column equal the samenumber. Determine if the numbers can always be subtracted.Find out if the grouping principle applies to subtraction.

    Objectives:1. The student shall be able to count out loud by sixes to 72.

    2. The student shall be able to write the value of a given number often thousands.

    3. The student shall be able to write the name of a given shape orsolid.

    4. The student shall be able to write the difference of two triple-digitnumbers when borrowing in the tens and hundreds columns andwrite the names of the terms.

    5. The student shall be able to draw a line to match a fraction andthe word name for the fraction.

    6. The student shall be able to write the correct symbol (+, -, x, or =)used in a given equation.

    Concepts:Counting by sixes, place value, shapes, solids, subtraction,subtraction terms, fractions, and addition

    Lesson 30

  • 91

    Lesson 30Activities:1. Administer Test 3.

    2. Count out loud with the student(s) by sixes to 72.

    3. Drill the subtraction facts by reading a series of ten facts from thesubtraction flash cards to the student(s). Have them write theanswers in a column on a sheet of paper. Check their answers andgive them another series of ten facts. Continue to do so for 5minutes.

    4. Using flash cards for multiplication facts, drill 5s and 2s as pairswithout the answers showing. Drill 3s and 6s as pairs with theanswers showing.

    5. Copy the chart at the top of Student Activity One on the chalkboard. Discuss with the student(s) how the value of the four is four10,000s = 4 x 10,000 = 40,000. Complete Student Activity Onetogether.

    6. Have the student(s) look around the room to identify as many of theshapes and solids as possible. See if they can think of some objectshaped like the ones that they cannot find in the room. Display theshape and solid flash cards on the chalk board rail with the namesshowing for the student(s) to use as a spelling reference whilecompleting Student Activity Two.

    7. Use the subtraction terms flash card to say and spell each term.Have the student(s) write the terms on the lines in StudentActivity Three. Give individual help to those student(s) who havedifficulty subtracting when borrowing from the tens and hundredscolumns in the activity.

    8. Ask the student(s) to read several fractions written on the chalkboard. Discuss the name of the fractions (numerator is a cardinalnumber and the denominator is an ordinal number). Have thestudent(s) say what the numerator and denominator tell them(numerator: number of parts being used; denominator: number ofparts into which the whole is divided). The student(s) should be ableto complete Student Activity Four on their own.

    9. Write 6 __ 5 = 11, 6 __ 5 = 30, 6 __ 5 = 1, and 3 + 7 __ 10 onthe chalk board. Ask the student(s) to determine the correct symbol(+, -, x, or =) to place in each blank. The student(s) should be able tocomplete Student Activity Five independently.

    10. In Student Activity Six, the 4 squares in the upper left handcorner are to be added across and down. The last column addeddown and the last row added across should equal the same number.Remind the student(s) that this is an example of the groupingprinciple (numbers may be grouped differently without changingthe sum) for addition.

  • 232

    Teaching Tips:1. When the student(s) are completing Student Activity Six, they

    may need to be reminded that any number times 0 is always equalto 0 and any number added to 0 is always the same number.

    Objectives:1. The student shall be able to write the mixed number and improper

    fraction represented by the shaded graphic.

    2. The student shall be able to write the number needed to round agiven amount of money to the nearest dollar.

    3. The student shall be able to write the fractional part of a whole thatis shaded.

    4. The student shall be able to write the correct symbol (, or =)between two fractions.

    5. The student shall be able to write the temperature in Celsius orFahrenheit degrees displayed on a given thermometer.

    6. The student shall be able to write the value of each digit for a givennumber in expanded and standard form.

    7. The student shall be able to write the product of a five-digit numberand a single-digit number.

    Materials, Supplies, & Equipment:1. Flash cards for addition, multiplication, and division facts

    2. Fraction materials

    3. Flannel board

    4. Thermometer model

    Concepts:Fractions, estimation, greater than and less than, equal to,temperature, place value, and multiplication

    Lesson 101

  • 233

    Lesson 101

    The good deeds we dodetermine part of the worth of our lives.

    Activities:1. Drill all addition facts with flash cards.

    2. Using flash cards for multiplication facts, drill 3s, 6s, 9s, 4s, 8s,and 7s as pairs without the answers showing.

    3. Use flash cards for division facts without the answers showing.Drill the facts that have a divisor of 1 or 10 or a dividend of 0. Besure to drill the facts as pairs. Drill the facts that have a divisor of2, 5, or 3 with the answers showing.

    4. Using fraction materials, demonstrate several mixed numbers onthe flannel board or chalk board. Discuss how many wholes andwhat fractional part of a whole are in each of the problems. Thendiscuss how many fractional parts there are altogether includingthe wholes (e.g. 4 pies cut into 2 pieces and 1 piece in the fifth pie 412 or 92). The student(s) may need your help when they completeStudent Activity One.

    5. To round dollars and cents to the nearest dollar, tell the student(s)to see if the cents is closer to zero or to one hundred. If closer to zero,the cents become zeros. If closer to one hundred, the dollar is raisedby 1 and the cents become zeros. Practice several examples with thestudent(s) before they attempt to complete Student Activity Two.

    6. Have the student(s) look at the first problem in Student ActivityThree. Determine the fractional part of the whole that is shadedand write it on the blank. Compare the two shaded areas anddetermine if the first is , or = to the second. Note that if thenumerators are the same, the fraction with the larger denominatoris smaller in size. Allow those who are capable to continue on theirown. Give individual help to those who need it.

    7. Using the thermometer model, set several temperatures for thestudent(s) to read. They should be able to complete StudentActivity Four with little help.

    8. Write several problems on the chalk board similar to those inStudent Activity Five. Have the student(s) tell what numbersshould be written in the blanks. They should be able to complete theactivity on their own.

    9. The student(s) should be able to complete Student Activity Six ontheir own.

  • 234

    Materials, Supplies, & Equipment:1. Flash cards for subtraction, multiplication, and division facts

    2. Symmetrical shape cut from construction paper

    3. 3 symmetrical shapes per student cut from typing paper

    4. Place value materials

    5. Thermometer model

    Teaching Tips:1. In activity 3, the drilling of 2s will be changed to drill without the

    answers showing in two more lessons. Check the student(s) on aone-to-one basis to see if they have mastered the division factswhen 2 is the divisor. Give individual attention to the student(s)who still need further drill with the answers showing.

    Objectives:1. The student shall be able to write the correct word (yes or no) after

    determining if a line is a line of symmetry.

    2. The student shall be able to write the product of a five-digitnumber and a single-digit number.

    3. The student shall be able to write the correct symbol (< or >)between two fractions.

    4. The student shall be able to write the mixed number and decimalequivalent represented by the given graphic.

    5. The student shall be able to color the liquid in a thermometer fora given temperature.

    6. The student shall be able to write the value of each digit for agiven number in expanded and standard form.

    Concepts:Symmetry, multiplication, greater than and less than, fractions,decimals, temperature, and place valueDefinition: A symmetrical shape is a shape that is folded so that

    the two halves match or lay exactly on top of eachother.

    Lesson 102

  • 235

    Lesson 102

    Worksheets:1. Worksheet 50 Mixed numbers

    Activities:1. Drill all subtraction facts with flash cards.

    2. Using flash cards for multiplication facts, drill 3s, 6s, 9s, 4s, 8s,and 7s as pairs without the answers showing.

    3. Use flash cards for division facts without the answers showing.Drill the facts that have a divisor of 1 or 10 or a dividend of 0. Besure to drill the facts as pairs. Drill the facts that have a divisor of2, 5, or 3 with the answers showing.

    4. Show the student(s) a large symmetrical shape cut fromconstruction paper. Explain that the shape is symmetrical if it canbe folded so that the two halves match or lay exactly on top of eachother. Fold the shape so that the two halves match or lay exactly ontop of each other. Explain that the fold line is called the line ofsymmetry. Then fold the shape so that part of one half overlaps theother half. Now the fold line is not a line of symmetry. Give thestudent(s) three different shapes cut from typing paper that have aline of symmetry drawn on them. Ask them to fold the shapes onthe line of symmetry to see how the two parts match. CompleteStudent Activity One as a group project.

    5. The student(s) should complete Student Activity Two alone.

    6. Write several sets of two fractions with like numerators on the chalkboard. Draw two congruent shapes by the first set of fractions.Shade the shapes to represent the fractions. Then have thestudent(s) determine if the first fraction is < or > to the secondfraction. Note when the numerators are the same, the fraction withthe larger denominator is the smaller in size. The more parts intowhich a whole is divided, the smaller each part will be. Using thisprinciple, ask the student(s) to determine the correct symbol theyshould place between the remaining sets of fractions. Thestudent(s) may need your assistance as they complete StudentActivity Three. Have them draw pictures if necessary.

    7. Use the tens and ones from the place value materials to displayseveral mixed numbers. Discuss how the student(s) would write amixed number and its decimal equivalent. They should be able tocomplete Student Activity Four by themselves.

    8. Allow the student(s) to set several given temperatures on thethermometer model. They should be able to complete StudentActivity Five independently.

    9. Before the student(s) begin Student Activity Six, point out thatthe terms are out of order.

  • 236

    Materials, Supplies, & Equipment:1. Clock model

    2. Flash cards for division facts and multiplication terms

    3. Typing paper 1 sheet per student

    4. Play money

    5. Mirror

    Teaching Tips:1. Have the student(s) take the symmetrical design they cut out in

    activity 7 and fold it on a line of symmetry. Then hold the foldeddesign perpendicular to a mirror. If the design is folded on the lineof symmetry, the folded design and the reflection in the mirror willform the same design as the unfolded paper. Fold a design not on aline of symmetry. Hold it to the mirror. The folded design and thereflection in the mirror should not be the same as the unfoldedpaper. This is a test for a line of symmetry.

    Objectives:1. The student shall be able to write the fractional part of a whole that

    is shaded.

    2. The student shall be able to write the product of a five-digit numberand a single-digit number and write the names of the terms.

    3. The student shall be able to write a ratio three ways.

    4. The student shall be able to write the correct word (yes or no)indicating that a line is a line of symmetry.

    5. The student shall be able to write the difference of any two triple-digit numbers.

    6. The student shall be able to color the liquid in a thermometer for agiven temperature.

    7. The student shall be able to write the mixed number, improperfraction, and decimal equivalent displayed with bills and coins.

    Concepts:Fractions, multiplication, multiplication terms, ratio, symmetry,subtraction, temperature, and decimals

    Lesson 103

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    Lesson 103

    Worksheets:1. Worksheet 51 Addition, subtraction, and multiplication drill sheet

    Activities:1. Drill the addition facts using Drill #1, Worksheet 51.

    2. Use the clock model to drill the multiplication facts for 3s, 6s, 9s,4s, 8s, and 7s as pairs.

    3. Use flash cards for division facts without the answers showing.Drill the facts that have a divisor of 2. Be sure to drill the facts aspairs. Drill the facts that have a divisor of 5, 3, or 6 with theanswers showing. The drill of the division facts with flash cards isvery important to the students success in memorizing their facts.Do not omit this practice.

    4. Draw two circles on the chalk board with the first one cut into 4equal parts and the second one cut into 2 equal parts. Shade onehalf of each. Have the student(s) tell the fractional part shaded foreach (24 and 12). Ask them if the two fractions are equivalentfractions. Then ask them by what number the numerator anddenominator of the first fraction are divided to equal the secondfraction (2). Do several problems following the same procedure. Thestudent(s) should be able to complete Student Activity One withlittle help.

    5. The student(s) should be able to complete Student Activity Two ontheir own after reviewing the multiplication terms flash card.

    6. Discuss with the student(s) the meaning of ratio (a relationship orcomparison of two numbers). Show them three ways a ratio can bewritten (3:4, 3 to 4, or 34). The student(s) should be able to completeStudent Activity Three independently.

    7. Give the student(s) a sheet of typing paper folded into fourths. Tellthem to cut a design from one folded edge to the other. Unfold thepaper. They have cut a symmetrical design. The folds on the designare the lines of symmetry. Discuss what makes a designsymmetrical. After the student(s) have completed StudentActivity Four, discuss why the diagonal of a rectangle is not a lineof symmetry.

    8. The student(s) should be able to complete Student Activity Fiveand Six by themselves.

    9. Using play money, display several mixed numbers. A dollar billrepresents a whole and the dimes represent 110 of a whole. Have thestudent(s) tell the mixed number, improper fraction, and decimalequivalent represented. They should be able to complete StudentActivity Seven with little assistance.

  • 238

    Materials, Supplies, & Equipment:1. Flash cards for multiplication and division facts

    2. Play money

    3. Flannel board and materials

    Teaching Tips:1. In activity 3, the 1s, 10s, and 0s have been dropped from the drill

    with flash cards. Notice that the 2s as pairs are now being drilledwithout the answers showing. The 6s as pairs are to be added tothe drill with the answers showing.

    Objectives:1. The student shall be able to write the number of coins needed to

    equal a given amount of money three ways.

    2. The student shall be able to write the correct word (yes or no)indicating that a line is a line of symmetry.

    3. The student shall be able to write the fractional part of a wholethat is shaded.

    4. The student shall be able to write the difference of a two-, three-,or four-digit number and 10.

    5. The student shall be able to write the difference of any two triple-digit numbers.

    6. The student shall be able to write the ratio of two given sets.

    7. The student shall be able to write the product of a five-digit numberand a single-digit number and write the names of the terms.

    Concepts:Money, symmetry, fractions, subtraction, ratio, multiplication, multi-plication terms, and word problems

    Lesson 104

  • 239

    Lesson 104

    Worksheets:1. Worksheet 51 Addition, subtraction, and multiplication drill sheet

    Activities:1. Drill the subtraction facts using Drill #2, Worksheet 51.

    2. Using flash cards for multiplication facts, drill 3s, 6s, 9s, 4s, 8s,and 7s without the answers showing. Have the student(s) write theanswers

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