horizons mathematics 3 teacher’s guide photocopying ... · horizons mathematics 3 teacher’s...

88

Upload: lamquynh

Post on 10-Jul-2018

229 views

Category:

Documents


4 download

TRANSCRIPT

Alpha Omega Publications, Inc.Rock Rapids, IA

bySareta A. Cummins

Edited byDavid J. Korecki

Illustrated byTye A. Rausch

Editorial AssistantChristine A. Korecki

Teacher’s Guide

3Mathematics

Horizons Mathematics 3 Teacher’s 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 Page

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

Section TwoTeacher’s Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Section ThreeAnswer Key (Lessons 1–160) . . . . . . . . . . . . . . . . . . . . . . . . . 353

Section FourWorksheets (1–80) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 CHALLENGEToday’s 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 theTeacher’s 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 Teacher’s 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 28–29. 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 student’sacademic 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 28–29 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 yourteacher’s 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.

STUDENT’S 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 thestudent’s 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 6–15. Lessons 16–19may include the introductionof some new material which

will not be covered in test 2.Test 8 in lesson 80 will coverlessons 66–75. The newmaterial from lessons 76–79will not be covered in test 8.

TEACHER’S 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 theteacher’s 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 Teacher’sGuide 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 student’s interest.Definitions are given for newterms.

10

ObjectivesThe Objectives listcriteria for thestudent’s perfor-mance. They state whatthe student should be able todo at the completion of thelesson. You will findobjectives helpful indetermining the student’sprogress, 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 you’ll need to findbefore you teach each lesson.Sometimes you will also find

instructions on how to makeyour own materials, supplies,and equipment. When“Number Chart” is listed, it isunderstood to refer to thechart for 0–99. The numberchart for 100–199 will state“Number Chart 100–199.” Acomplete list of allmanipulatives and where theyare used starts on page 16.

ActivitiesThe teacher’sgreatestconcentration 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 theteacher’s 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. TheTeacher’s 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 theteacher’s 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 teacher’s 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 aren’t 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 Teacher’s 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 1’s through 10’sEven and odd numbersWord numbers 0–999,999,999Roman 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. ADDITION

Addition 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. MULTIPLICATION

Multiplication termsFacts for 0–10Word 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 0–10Single-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 0–99 1, 2, 3, 4, 5, 6, 10, 11, 15, 16, 20

Number chart 100–199 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 1’s to 100 1, 2, 3, 4, 5Counting by 10’s to 100 6, 7, 8, 9, 10Counting by 5’s to 100 11, 12, 13, 14, 15Counting by 2’s to 24 16, 17, 18, 19, 20Counting by 3’s to 36 21, 22, 23, 24, 25Counting by 6’s to 72 26, 27, 28, 29, 30Counting by 9’s to 108 31, 32, 33, 34, 35Counting by 4’s to 48 36, 37, 38, 39, 40Counting by 8’s to 98 41, 42, 43, 44, 45, 46, 47, 48, 49, 50Counting by 7’s 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

23

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

24

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

25

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

26

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

27

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

28

Development

29

of Concepts

30

Lessons

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

72

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 100–199

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

Lesson 21

73

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 0’s, 1’s, 10’s, and 5’sas pairs without the answers showing. Drill 2’s and 3’s 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 100–199 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.

74

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

75

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 0’s, 1’s, 10’s, and 5’sas pairs without the answers showing. Drill 2’s and 3’s 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 it’s even and 1, 3, 5, 7, 9 it’s 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.

76

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

77

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 0’s, 1’s, 10’s, and 5’sas pairs without the answers showing. Drill 2’s and 3’s 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.

78

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

79

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 0’s, 1’s, 10’s,and 5’s as pairs. Using flash cards for the multiplication facts, drill2’s and 3’s 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.

80

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

81

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 0’s, 1’s, 10’s, and 5’sas pairs without the answers showing. Drill 2’s and 3’s 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.

82

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 6’s ifthey have been drilling in pairs. Notice that the 0’s, 1’s, and 10’shave 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

83

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 5’s and 2’s as pairswithout the answers showing. Drill 3’s and 6’s 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 there“altogether?”). 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.

84

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

85

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 5’s and 2’s as pairswithout the answers showing. Drill 3’s and 6’s 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 thousands’place. Allow them to complete Student Activity Two alone.

6. Review the greater than and less than flash cards. Put twodifferent Roman numerals (1–20) 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.

86

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 hundredths’columns 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

87

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 5’s and 2’s as pairswithout the answers showing. Drill 3’s and 6’s 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 friend’s 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 hundreds’columns 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

89

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 5’s and 2’sas pairs. Using flash cards for the multiplication facts, drill 3’s and6’s 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 5’s and 2’s as pairswithout the answers showing. Drill 3’s and 6’s 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 four10,000’s = 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 hundreds’columns 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 3’s, 6’s, 9’s, 4’s, 8’s,and 7’s 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 –41⁄2 or 9⁄2). 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 2’s 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 3’s, 6’s, 9’s, 4’s, 8’s,and 7’s 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

237

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 3’s, 6’s, 9’s,4’s, 8’s, and 7’s 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 (2⁄4 and 1⁄2). 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 3⁄4). 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 1⁄10 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 1’s, 10’s, and 0’s have been dropped from the drill

with flash cards. Notice that the 2’s as pairs are now being drilledwithout the answers showing. The 6’s 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 3’s, 6’s, 9’s, 4’s, 8’s,and 7’s without the answers showing. Have the student(s) write theanswers in a column on a sheet of paper. After 10 facts, check theiranswers and give them another series of ten facts.

3. Use flash cards for division facts without the answers showing.Drill the facts that have a divisor of 2. Be sure to drill all facts aspairs. Drill the facts that have a divisor of 5, 3, or 6 with theanswers showing.

4. Give the student(s) play money. Tell them several amounts ofmoney under a dollar and have them choose the coins they need toequal each amount. Then ask them to find two other sets of coinsthat will also equal each amount of money. The student(s) shouldbe able to complete Student Activity One alone.

5. Write several symmetrical capital letters on the chalk board thatcome after F (H, I, M, O, etc.). Allow the student(s) to come to thechalk board and draw a line of symmetry on them. Discuss if theirlines are correct and why or why not. The student(s) should be ableto complete Student Activity Two with little help.

6. Draw two squares on the chalk board with the first one cut into 9equal parts and the second one cut into 3 equal parts. Shade twothirds of each. Have the student(s) tell the fractional part shadedfor each (6⁄9 and 2⁄3). Ask them if the two fractions are equivalentfractions. Then ask them what the numerator and denominator ofthe first fraction are divided by to equal the second fraction. Doseveral problems following the same procedure. The student(s)should be able to complete Student Activity Three on their own.

7. Write two, three, and four-digit numbers on the chalk board.Discuss how to mentally subtract 10 from each number (find thetens’ digit and lower it by 1). The student(s) should be able tocomplete Student Activity Four, Five, and Seven by themselves.

8. Using flannel board materials, display two sets of objects. Have thestudent(s) tell the ratio of the first set to the second and the secondset to the first. Emphasize that whatever set is mentioned firstmust be written first. The student(s) should complete StudentActivity Six together.

9. Have the student(s) read the word problems in Student ActivityEight carefully. Let them each decide what they think is missing.Supply the part they suggest and see if they can then solve theproblem.

240

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

2. Flannel board and materials

3. Play money

Teaching Tips:1. For activity 7, see if the student(s) can remember another way in

which to tell if the two fractions are equivalent or not equivalent.The fractions are equivalent if there is a number by which thenumerator and denominator of the first fraction can be multipliedor divided to make it equal the second fraction. This is a goodmethod only if the number being divided into the numerator anddenominator of the first fraction is a whole number and not amixed number or fraction.

Objectives:1. The student shall be able to write a fraction resulting from

reducing a given fraction.

2. The student shall be able to write the ratio of part of a given set tothe whole set.

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

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

5. The student shall be able to write the correct name for a givenshape or solid.

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

7. The student shall be able to write the number of coins needed toequal a given amount of money three ways.

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

Concepts:Fractions, ratio, Roman numerals, equal and not equal, shapes,solids, subtraction, and money

Lesson 105

241

Lesson 105

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

Activities:1. Drill the addition facts by reading a series of ten facts from the

addition flash cards to the student(s). Have them write the answersin a column on a sheet of paper. Check their answers and give themanother series of ten facts. Continue doing this for 5 minutes.

2. Drill the multiplication facts using Drill #3, Worksheet 51. Allow 3minutes for the drill.

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.

4. Draw two rectangles on the chalk board. Divide one into eight equalparts and shade four of them; divide the other into two equal partsand shade one of them. Ask the student(s) what fraction each of theshaded rectangles represent and write it under the rectangle. Havethe student(s) determine if the fractions are equivalent. Next havethem decide by what number the numerator and denominator of thefirst fraction is divided to equal the second fraction. Write “4⁄8 = 4÷4⁄8÷4

= 1⁄2.” Write “6⁄9 = 6÷3⁄9÷3 = ___” on the chalk board. Tell the student(s)they are going to reduce the fraction 6⁄9 by dividing 3 into thenumerator and denominator to equal 2⁄3. Ask what number they candivide into the numerator and denominator of several reduciblefractions (e.g. 12⁄16, 6⁄8, 10⁄15, etc.). After completing the first problem inStudent Activity One with the student(s), allow them to finish theactivity on their own.

5. Using flannel board materials, have the student(s) find severalratios of a part of a set to the whole set. Then have them find severalratios of the whole set to part of the set. Give assistance only whennecessary as the student(s) complete Student Activity Two.

6. After reviewing the Roman numeral flash cards, the student(s)should be able to complete Student Activity Three alone.

7. Write several sets of two fractions on the chalk board, someequivalent fractions and some not equivalent. Draw the arrows toshow cross multiplication. Next have the student(s) multiply thenumbers at the opposite ends of the arrows. The student(s) shouldbe able to complete Student Activity Four with little help.

8. The student(s) should be able to complete Student Activity Five,Six, and Eight alone.

9. Give the student(s) play money. Ask them to find three differentways they can return change for several given amounts. Theyshould be able to complete Student Activity Seven by themselves.

242

Teaching Tips:1. Be sure that the student(s) label their answers in Student

Activity One.

2. If the student(s) have difficulty completing Student Activity Six,suggest that they write the corresponding Arabic number by theRoman numeral before they make the comparison.

Objectives:1. The student shall be able to write the measurement of a given line

using a centimeter ruler.

2. The student shall be able to write the correct name for a givenshape or solid.

3. The student shall be able to write the value of a variable in amultiplication equation.

4. The student shall be able to write the sum of two double, triple, orfour-digit horizontal numbers rewritten vertically.

5. The student shall be able to write the number of coins needed toequal a given amount of money three ways.

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

7. The student shall be able to write the fraction resulting fromreducing a given fraction.

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

shapes, and solids

2. Centimeter ruler

3. Meter stick

4. Yardstick

Concepts:Metric linear equivalents, centimeters, shapes, solids, equations,addition, money, greater than and less than, Roman numerals, andfractions

Lesson 106

243

Lesson 106

Worksheets:1. Worksheet 52 – Line graph chart

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

2. Using flash cards for multiplication facts, drill 3’s, 6’s, 9’s, 4’s, 8’s,and 7’s 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 2. Be sure to drill the facts aspairs. Drill the facts that have a divisor of 5, 3, or 6 with theanswers showing.

4. Ask the student(s) to begin collecting information for a line graphabout the high and low temperature, of a city of their choice, for fourdays. The information can be found in the newspaper or on the localTV news. Worksheet 52 has a chart they can use to record theirinformation in addition to an example of what to look for in thenewspaper. The graph will be drawn in lesson 110.

5. Have the student(s) look at their centimeter ruler. The numbers onthe ruler are for centimeters. Have them count the little marksbetween the numbers. The little marks are millimeters. Show thestudent(s) how a meter stick is a little bit longer than a yardstick.Let them see the numbers to 100 which represent centimeters.Draw the student(s) attention to the equivalents above StudentActivity One before they complete the activity.

6. Put the flash cards with the names of the shapes and solids inStudent Activity Two on the chalk board rail for spelling referenceas the student(s) complete the activity.

7. Write “8 x n = 40” on the chalk board. Ask the student(s) how to findthe value of “n” (divide 8 into 40). To undo multiplication, theydivide. To find the value of “n,” they must undo the multiplicationby dividing by 8 on both sides of the equation. 8 divided by 8 is 1and 1 times “n” is “n.” 40 divided by 8 is 5. Therefore, the solutionis n = 5. Work as many problems as are necessary for them to beable to successfully complete Student Activity Three.

8. On the chalk board, write horizontally several addition problemswith two addends of two, three, or four digits. Ask the student(s) tocopy them on a sheet of paper vertically and add. Check to see thatthey keep the ones in the ones’ column, tens in the tens’ column, etc.Remind them that the last digit will always be lined up on the righthand side if there are no decimals. Check the student(s) papers asthey complete Student Activity Four.

9. The student(s) should be able to complete Student Activity Fiveand Six alone.

10. Review lesson 105 activity 4 for Student Activity Seven.

244

Teaching Tips:1. If the student(s) have difficulty completing Student Activity Six,

discuss how they are to undo multiplication (dividing both sides ofthe equation by the number being multiplied times the variable).

2. Check to see that the student(s) are lining the digits in the ones’places in a straight column along the right hand side in StudentActivity Eight.

Objectives:1. The student shall be able to write the perimeter of a given shape.

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

3. The student shall be able to write a single-digit quotient with aremainder when the divisor is single digit.

4. The student shall be able to write the measurement of a given linein millimeters using a centimeter ruler.

5. The student shall be able to write the fraction resulting fromreducing a given fraction.

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

7. The student shall be able to write the numbers necessary toillustrate the distributive principle.

8. The student shall be able to write the sum of three single, double,triple, or four-digit horizontal numbers rewritten vertically.

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

2. Centimeter ruler

Concepts:Perimeter, equal and not equal, fractions, division, millimeters,metric linear equivalents, equations, distributive principle,and addition

Lesson 107

245

Lesson 107Activities:1. Drill all subtraction facts with flash cards.

2. Using flash cards for multiplication facts, drill 3’s, 6’s, 9’s, 4’s, 8’s,and 7’s 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 2. Be sure to drill the facts aspairs. Drill the facts that have a divisor of 5, 3, or 6 with theanswers showing.

4. Check to see that the student(s) are recording the high and lowtemperature for the day to use on their line graph in lesson 110.

5. Discuss the meaning of the word “perimeter.” Ask the student(s) ifthey have an idea what the “P” and the “S” stand for in the formulaP = 4 x S in the first problem of Student Activity One (perimeterand side). They can find the perimeter by adding 13 four times butit is shorter to multiply 13 by 4. Discuss each of the other formulasin the activity. They are not ready to use the shorter forms of theformula for the perimeter of a rectangle. Allow the student(s) tocomplete the activity on their own, checking to see that they labeltheir answers.

6. Give assistance only where needed as the student(s) completeStudent Activity Two using cross multiplication.

7. Draw 9 squares on the chalk board. Write “2)9” under the 9 squares.Ask a student to find how many groups of 2’s are in 9 by drawingcircles around sets of 2. Write the number of circles (4) as thequotient of the division problem. The number of squares left is theremainder and is written in the quotient as “4 r 1.” The remaindermay also be found by multiplying the quotient times the divisor andwriting “-8” under the 9. Subtract 9 - 8 and the remainder is thedifference (1). Follow the same steps as you work each problem inStudent Activity Three with the student(s).

8. Have the student(s) count on their centimeter ruler by 10’s to findhow many millimeters in several given numbers of centimeters. Tellthem to point to the second millimeter mark after 3. Ask them howmany millimeters they have at 3 (30) and add 2 more. The length ofa line to the second millimeter after 3 is 32 millimeters. Follow thisprocedure to guide the student(s) as they complete StudentActivity Four. Since their pencil lead has width, accuracy on sucha small unit of measure is difficult. If their answer is one more orone less than the given answer, give them credit.

9. The student(s) should be able to complete Student Activity Five,Six, Seven, and Eight with little help.

246

Materials, Supplies, & Equipment:1. Clock model

2. Flash cards for division facts

3. Centimeter ruler

Teaching Tips:1. When doing activity 6, discuss with the student(s) how many

millimeters are in a meter. Count the centimeter numbers on ameter stick by 10’s. Some student(s) may find the answer bythinking 1 centimeter equals 10 millimeters. 2 centimeters equal20 millimeters (2 x 10). 60 centimeters equal 600 millimeters (60x 10). 100 centimeters equal 1,000 millimeters (100 x 10).

Objectives:1. The student shall be able to write the fraction resulting from

reducing a given fraction.

2. The student shall be able to write the measurement of a given linein millimeters using a centimeter ruler.

3. The student shall be able to write a single-digit quotient with aremainder when the divisor is single digit.

4. The student shall be able to write the area of a given square.

5. The student shall be able to write the numbers necessary toillustrate the distributive principle.

6. The student shall be able to write the sum of four double, triple, orfour-digit horizontal numbers rewritten vertically.

Concepts:Fractions, metric linear equivalents, millimeters, division, area,distributive principle, addition, and word problems

Lesson 108

247

Lesson 108

Worksheets:1. Worksheet 53 – Addition, subtraction, and multiplication drill sheet

Activities:1. Drill the addition facts using Drill #1, Worksheet 53.

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

4. Check to see that the student(s) are recording the high and lowtemperature for the day to use on their line graph in lesson 110.

5. Write several fractions on the chalk board that need to be reduced.To think of a number that will divide into both the numerator andthe denominator, have the student(s) first tell a number that willdivide into the numerator. Then check to see if the same numberwill divide into the denominator. Give the student(s) guidance asthey complete Student Activity One.

6. Give the student(s) several millimeter measurements to locate onthe centimeter ruler. Give assistance where needed as thestudent(s) do the measurements in Student Activity Two. Givecredit if they come within one of the given answer.

7. Write several division problems on the chalk board with a single-digit divisor and a dividend less than twenty. Above each problemdraw shapes to equal the dividend. In a problem such as 6)14 , askthe student(s) how many sets of 6’s they think they will have, beforethey draw the circles, and write the number as the quotient. Theremaining shapes equal the remainder. Then have the student(s)find the remainder by multiplying the quotient times the divisorand subtracting. Allow those who are capable to complete StudentActivity Three alone, helping those who need it.

8. Ask the student(s) to identify the “A” and “S” in the formula inStudent Activity Four (area and side). Instead of counting thesquares, it is much quicker to say they have 2 rows of 2’s or 2 x 2.Notice that the label for area is square (sq.) units. The student(s)should be able to complete the activity with little help.

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

10. Discuss with the student(s) writing the comparison of two numbersor objects as a ratio in three ways. Complete Student ActivitySeven together.

248

Teaching Tips:1. If the student(s) have difficulty subtracting 9 from a number in

Student Activity Two, suggest this: when subtracting 9 from thenumbers 10 through 19, the answer is always the sum of the topnumbers or 1 more than the number above it. Do severalexamples on the chalk board to demonstrate this concept.

2. If the student(s) have difficulty with Student Activity Six, havethem draw 6 boxes and write “10” in each box (6 groups of 10), 9boxes and write “100” in each box (9 groups of 100), and 7 boxesand write “1,000” in each box (7 groups of 1,000). They should beable to find the answer by counting the boxes by 10, 100, or 1,000;by adding; or by using the easiest way of multiplying.

Objectives:1. The student shall be able to write the word numbers for a given

amount on the face of a check.

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

3. The student shall be able to write the area of a given rectangle.

4. The student shall be able to write the measurement of a given linein millimeters using a centimeter ruler.

5. The student shall be able to write a single-digit quotient with aremainder when the divisor is single digit.

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

2. Checkbook and check

3. Multiplication chart

Concepts:Word numbers, subtraction, area, metric linear equivalents,millimeters, division, and word problems

Lesson 109

249

Lesson 109

Worksheets:1. Worksheet 54 – Division with remainder

2. Worksheet 53 – Addition, subtraction, and multiplication drill sheet

Activities:1. Drill the subtraction facts using Drill #2, Worksheet 53.

2. Using flash cards for multiplication facts, drill 3’s, 6’s, 9’s, 4’s, 8’s,and 7’s without the answers showing. Have the student(s) write theanswers in a column on a sheet of paper. After 10 facts, check theiranswers and give them another series of ten facts.

3. Use flash cards for division facts without the answers showing.Drill the facts that have a divisor of 2. Be sure to drill all facts aspairs. Drill the facts that have a divisor of 5, 3, or 6 with theanswers showing.

4. Check to see that the student(s) are recording the high and lowtemperature for the day to use on their line graph in lesson 110.

5. Show the student(s) a checkbook. Pass around a check for them toexamine. Discuss what goes in the blanks on a check. Ask thestudent(s) to find the place to write the date on the first check inStudent Activity One. Write the date on the chalk board for themto copy. Then tell them to write the dollar amount given on the lineas word numbers. Notice the cents is already written. Let themsign their name. They should be able to write the date and dollaramounts in the remainder of the activity by themselves.

6. Write “805 - 257” on the chalk board as a vertical subtractionproblem. When they cannot take 7 from 5 and cannot borrow

1 from 0, they have to borrow 1 from 80 (8 hundreds equal 80 tens).Mark out the 80 and write 79 above it. Add the 10 ones (1 ten) tothe 5 ones and subtract. Let them solve several similar problemsbefore they complete Student Activity Two alone.

7. Ask the student(s) to identify the “A,” “L,” and “W” in the formulaused in Student Activity Three (area, length, and width). Insteadof counting the squares, they need to multiply. Be sure they labelthe answers correctly as they complete the activity.

8. In Student Activity Four, have the student(s) write themeasurement of each line on the line itself.

9. Before the student(s) begin Student Activity Five, discuss howmany times each divisor will go into the dividend. If they still needobjects to circle, allow them to draw pictures. They may also use themultiplication chart.

10. Once the student(s) are finished with Student Activity Six, discussthe solutions to the word problems.

250

Objectives:1. The student shall be able to draw a line graph using the information

collected about temperatures.

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

3. The student shall be able to write the word numbers for a givenamount on the face of a check.

4. The student shall be able to write the volume of a given rectangularprism.

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

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

Teaching Tips:1. If the student(s) feel that they need more space than is available

in Student Activity One to draw the line graph, allow them touse a plain sheet of white paper. Discuss with them the doubleline graph used when comparisons are made.

2. In Student Activity Four, discuss with the student(s) why theythink that the volume of an object is labeled cubic units.

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

2. Blocks

3. Double line graph

Concepts:Line graphs, subtraction, word numbers, volume, greater than andless than, and word problemsDefinition: Volume is the amount of space or cubic units an object

fills or occupies.

Lesson 110

251

Lesson 110

Worksheets:1. Worksheet 53 – Addition, subtraction, and multiplication drill sheet

Activities:1. Administer Test 11.

2. 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.

3. Drill the multiplication facts using Drill #3, Worksheet 53. Allow 3minutes for the drill.

4. 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.

5. To complete Student Activity One, have the student(s) use theinformation they have collected on high and low temperatures.They will need to write the temperatures on the left vertical scale,the days across the bottom, and title the graph. Ask them to plot thehigh temperatures and connect the dots. Then plot the lowtemperatures and connect the dots. Display a double line graph forthem to use for reference.

6. On the chalk board, write several problems similar to those given inStudent Activity Two. Have the student(s) copy the problems ona sheet of paper and solve them. Discuss any difficulty they mayhave. They should be able to complete the activity by themselves.

7. Discuss why checks are written. Tell them what happens to a checkafter it is mailed or given to a store. (It is taken to their bank. Thebank sends it to a clearing house. The clearing house returns it tothe bank on which the check was written). Have them write thedate, fill in the word number for the number of dollars, and signtheir name to each check in Student Activity Three.

8. Take 12 blocks and stack them into 3 layers of 2 x 2. Discuss theword “volume” (the amount of space or cubic units an object fills oroccupies) with the student(s). The volume of a box is how much thebox will hold. To find the volume of the 12 blocks, the student(s)must determine how many blocks are in each layer (length timeswidth) and how many layers (height) there are. In the top layerthere are 2 rows of 2’s or 2 x 2 (L x W) or 4 blocks. There are 3 layersof 2 x 2 or 3 x 2 x 2 which equals 12 cubic units. Follow the sameprocedure for each of the volumes given in Student Activity Four.

9. The student(s) should be able to complete Student Activity Fiveand Six independently.

10. Discuss the missing information for each of the word problems inStudent Activity Seven with the student(s).

366

2¢moremore

$2.08$1.05$1.03

-8 -8n = 3

3 +8 = 11

-4 -4n = 7

7 +4 =11

-4 -4n = 8

8 +4 =12

-3 -3n = 9

9 +3 =12

-7 -7n = 5

5 +7 = 12

-6 -6n = 7

7 +6 =13

-8 -8n = 9

9 +8 =17

-9 -9n = 7

7 +9 =16

163131679

151141569

111011174

161614

11

<>>

<<<

><>

15

multiplicandmultiplierproduct

sumaddends

14 24 3 30 15 16 27 12 18

24 10 9 12 18 20 6 8 21

159 198 159 149 158 178 178 176odd even odd odd even even even even

370420850530950610730260

370410850530940600720260

4 + 7 =117 + 4 =1111 - 7 = 411 - 4 = 7

7 + 3 =103 + 7 =1010 - 3 = 710 - 7 = 3

7 + 8 =158 + 7 =1515 - 8 = 715 - 7 = 8

6 + 4 =104 + 6 =1010 - 4 = 610 - 6 = 4

14

multiplicandmultiplierproduct

-4 -4n = 8

8 +4 =12

-9 -9n = 6

6 +9 = 15

-6 -6n = 8

8 +6 =14

-7 -7n = 6

6 +7 =13

-2 -2n = 7

7 +2 = 9

12 35 27 30 3 45 21 12 6

30 9 18 15 16 24 40 0 10

66 79 87 76 94 86 95 78

><>

>><

<>>

160280520840630370790950

16131612

17141712

1210128

15111512

-5 -5n = 5

5 +5 =10

-8 -8n = 8

8 +8 =16

-3 -3n = 8

8 +3 =11

367

12 30 1816 40 2414 35 21

4 9 012 27 020 45 0

80 800 8,000240 2,400 24,0001,56015,600156,000

15156987

15154112 13

15151 14 69

15151210

-8 -8n = 6

6 +8 =14

-9 -9n = 6

6 +9 =15

-6 -6n = 6

6 +6 = 12

-4 -4n = 5

5 +4 = 9

-2 -2n = 8

8 +2 =10

-3 -3n = 8

8 +3 =11

-7 -7n = 6

6 +7 =13

-5 -5n = 7

7 +5 =12

441 371 673 262 460 84 72 252

Answers may vary.

260520630

290 333 182 90 593 448 575 692

480200810

Answers will vary.

154 156 162 145 124 147 162 155even even even odd even odd even odd

166 175 156 156 147 166 199 147even odd even even odd even odd odd

490300740580150830

480300730580150820

480290730570140820

><<>

<>><

<<>>

product

27 14 15 35 18 21 16 12 10

30 9 25 40 3 45 18 12 0

1212115

14141112

1414148

101095

Answers may vary.

368

30 6,211 416 5,700 142 24

60 12 346145

134 45 21 217

1 3 46 0 4 52 1 2 1 71 4 5 6 01 2 2 0

3 4 6

6 18 30 54 30 18 42 48 12

24 42 12 36 54 48 6 24

––+++

x–++–

896 597 799 688 895

865 984 796 877 785 894 668 796

addendaddendaddendsum

==≠

=≠=

≠≠=

=≠=

$7.00 or 700¢$50.00 or

5000¢

$6.00 or 600¢80¢ or $0.80

60 watermelons

201016

18 12 614

82520

40 15 3510

3051512

21 6 2718

249

–<>$

=+¢x

560 192 462 95 570 348 266 385

73 775 44 261 51 390 481 434

440880750

910170560

840480510

370630260

369

Answers may vary.

sumaddends

2 one dollar bills, 1 nickeland 2 pennies.

$2.07yes$17.93$11.97

18 54 30 24 18 12 20 48 27R E W A R D I N G

20 16I S

30 42 18 15W O R K

21 24 18 12H A R D

66 272 475 676 46 389 425 246

169 174 548 279 185 145 449

one thousand, three hundred eightyfour thousand, seventy-sixeight thousand, one hundred ninetwo thousand, five hundred oneseven thousand, eight hundred thirtythree thousand, four hundred two

parallelogram trapezoid rectangular rhombusprism

LXXXIVXLVXIX

LXXII

LXVIIILXXVXXXVIXLIX

LXXXVIIXXIIIXCVII

LI

XIIXXIV

717

leftdifference

lessmore than

altogethersumin allboth

768 979 949 869 859 439 549 768

855 736 748 838 537 846 957 867

6 8 14 2 12 0 18 10 20 4 169 12 21 3 18 0 27 15 30 6 2418 24 42 6 36 0 54 30 60 12 4815 20 35 5 30 0 45 25 50 10 40

>>>

<><

<<>

><<

1,2083,0756,4309,8065,6402,029

$15.77 $15.96 $15.84 $18.99 $15.97 $13.76 $16.53 $16.54

370

minuendsubtrahenddifference

years old189 years old

18 games

5,000 600 40 7 5,6478,000 400 60 2 8,4621,000 000 30 6 1,036

1,000 100 10 11,000 100 10 11,000 100 10 1

227 548 517 407 236 225 416 546

20150590

140650970

570850420

280390730

1515913

121289

-3 -3n = 9

-6 -6n = 8

-5 -5n = 6

-8 -8n = 5

4:35 10:20 7:00 2:45 4:15

Answers may vary.

Answers will vary.

1510

1812

8

00

26

618

54

927

816

1224

48

1530

206 69 354 173 867 554 346 356

78 127 487 229 467 128

–+

x+ x

=

81582390

39375275

64168448

1,997 1,659 1,748 1,768 1,748 1,449 1,867 1,313

371

numeratordenominator

226 tickets381st

1,200 chickens

===≠

≠==≠

6,387 9,786 9,374 9,497 9,486 8,285 8,478

87,651 94,320 96,520 87,431

86,310 97,542 98,621 75,430

2:29 5:38 11:02 6:49 3:52

1:44 10:37 7:13 3:31 9:16

12:06 8:22 6:51

9

8 17

18 29

1 8

8

15 20

5

5 1 6

9

–+x+

=

=

–+–x

x+–x

=

minuendsubtrahenddifference689 182 278 188 447 465

126 58 265 584 242 458 349 555

6 10,000 60,0007 10,000 70,0008 10,000 80,0005 10,000 50,0003 10,000 30,0009 10,000 90,0002 10,000 20,000

pyramid

diamond

oval

parallelogram

rectangle

octagon

triangle

cone

circle

cylinder

hexagon

square

rhombusrectangular

prismtrapezoid

sphere

pentagon

cube

410

2 7 1 4 88 271,488

7 4 3 1 25 743,125

710 4.14 1

101.551013.73

> > < <

> < < >

216,398 148,876 721,854 356,575 246,432 304,878

yesnoyesyes

nonoyesno

633,672 167,264 109,080 188,472 428,472 489,656

8 9 4 7 51 894,751

3 5 6 2 87 356,287

5 3 7 6 49 537,649

34 58 92 16 20

><

<><

<

2 2 4 4 2 28 4 6 9 5 3

2 2 3 3 1 16 4 8 5 3 4

$144.00 $927.00 $833.00$475.00 $260.00 $516.00$791.00 $684.00 $369.00

924 1

22345 3

41142 3

4

411

Answers mayvary.

4 510

4510

yesyes

How many vases she has.

How many cookies Clara has.

$5,684.49 $2,472.56 $2,145.69 $1,836.81

multiplicandmultiplierproduct

24

43

45

$7.87 $1.36 $3.78 $3.12 $0.68 $1.86 $3.48 $4.58

7,341795294,276561

3 2 23 2 2

3 1 2 1 6 39 3 8 4 10 5

no yes yes no yes no

8 pennies

4 dimes

2 quarters

3 pennies

1 dime

2 nickels

3 quarters

3 pennies

2 dimes

3 quarters

4 nickels1 dime

1 quarter

2 nickels

1 quarter

2 dimes

1 quarter

3210 2.7

2710

71023.2

21034.5

67 183 684 434 56 361 67 176

noyes

632,745 489,640 547,848 215,769

multiplicandmultiplierproduct

3 4 23 4 2

24

25

48

820

34

912

2 3 22 3 2

13

23

26

69

12

24

45

1215

69

1012

613

82

2:3 2 to 3

8:2

1:7

6:9

10:123:114 to 5

12 to 15

1 to 7 3 to 11

6 to 13

412

Answers mayvary.

3 2 74 7 8

2 1 13 3 3

< < >> > >

>

answers will vary

3,462+ 753,537

521+ 9

530

8+ 75

83

346+ 38

384

6 6 5 5 9 9 8 8n = 7 n = 9 n = 4 n = 7

rectangularprism

triangle

oval

pentagon

diamond

cylinder

cone

rectangle

circle

100 1 1 10

6 cm.13 cm.

10 cm.

279 389 177 359 59 353 224 458

5,081744579,228

parallelogram

rhombus trapezoid pyramid

hexagon

squaresphere

octagon

cube

≠ = = ≠3 x 10 = 30 2 x 15 = 30 9 x 4 = 36 3 x 8 = 246 x 4 = 24 5 x 6 = 30 12 x 3 = 36 7 x 4 = 28

= ≠ ≠≠ = =≠ = ≠

6 6 6 29 9 7 9

2 2 55 3 6

3 3 14 4 3

1 quarter

1 dime

2 pennies

1 quarter

2 nickels

2 pennies

3 dimes

1 nickel

2 pennies

3 quarters

1 penny

2 quarters

2 dimes

1 nickel

1 penny

7 dimes

1 nickel

1 penny

2 quarters

1 dime

1 penny

2 quarters

2 nickels

1 penny

6 dimes

1 penny

2 quarters

1 nickel

2 pennies

1 quarter

3 dimes

2 pennies

1 quarter

2 dimes

2 nickels

2 pennies

2 quarters

2 dimes

4 pennies

2 quarters

1 dime

2 nickels

4 pennies

2 quarters

4 nickels

4 pennies

1 quarter

1 dime

1 nickel

2 pennies

1 quarter

3 nickels

2 pennies

4 dimes

2 pennies

413

5 : 102 : 1010

3 : 52 : 3

6472

8,105+ 39

8,793

27359

6+ 4,781

5,173

2,3695

874+ 75

3,323

(2 x 2) + (2 x 1) = 4 + 2 = 6(4 x 5) + (4 x 2) = 20 + 8 = 28(9 x 5) + (9 x 3) = 45 + 27 = 72(5 x 2) + (5 x 2) = 10 + 10 = 20(8 x 5) + (8 x 1) = 40 + 8 = 48

A = 5 x 5A = 25 sq. ft.

A = 6 x 6A = 36 sq. yd.

A = 7 x 7A = 49 sq. m.

7 r 1 2 r 4 2 r 2 3 r 2

2 r 3 3 r 1 5 r 2 3 r 1

100 10

53 mm.

98 mm.

75 mm.

9÷3 3 4 ÷2 2 12÷6 215÷3 5 10÷2 5 18÷6 3

10÷2 5 6÷6 1 6÷3 216÷2 8 12÷6 2 9÷3 3

3,50284

+ 7914,377

48269

+ 7324

59317

+ 6616

7,832460

+ 98,301

(4 x 3) + (4 x 2) = 12 + 8 = 20(6 x 5) + (6 x 3) = 30 + 18 = 48(3 x 3) + (3 x 1) = 9 + 3 = 12

3 3 7 7 4 4 9 9n = 9 n = 9 n = 8 n = 4

1 2 55 5 6

100 1092 mm.

68 mm.

85 mm.

3 r 2 4 r 1 2 r 3 5 r 1

7 r 1 4 r 3 8 r 1

4 x 24 = 96 4 x 25 = 100 3 x 24 = 72 2 x 35 = 708 x 12 = 96 5 x 16 = 80 12 x 6 = 72 7 x 10 = 70

= ≠ = =

52 cm. 28 cm. 30 m. 72 m.

414

$4.59

72 cookies

882515694,273

21 32 32 11 10 24

4.881042.35

103 3

1023.5

<<<<=

991 1,008 1,326 1,500 1,279 948 1,340 1,342

3 3 24 4 3

60

900

7,000

4 r 3 2 r 5 4 r 4 2 r 3

4 r 1 2 r 4 6 r 1 2 r 4

100 10 1

A = 9 x 2A = 18 sq. units

A = 5 x 3A = 15 sq. units

A = 9 x 6A = 54 sq. units

A = 8 x 5 =A = 40 sq. units

316 143 228 465 247 539 307 38

774 203 557 219 238 424 184 275

Answers will vary for date and signature.

Four hundred fifty-six Seventy-eight

Forty-two One hundred sixty-nine

415

249 285 458 273 128 5 119 466

3:32 6:01 9:18 2:36 11:44

5:07 12:23 7:49 9:55 4:14

800,000 40,000 9,000 200 70 5eight hundred forty-nine thousand, two hundred seventy-five

300,000 80,000 4,000 100 50 6three hundred eighty-four thousand, one hundred fifty-six

500,000 20,000 6,000 300 10 7five hundred twenty-six thousand, three hundred seventeen

200,000 90,000 7,000 800 30 4two hundred ninety-seven thousand, eight hundred thirty-four

5 + n = 6 + 85 + n = 14

-5 -5n = 9

8 + n = 7 + 38 + n = 10

-8 -8n = 2

4 + n = 5 + 124 + n = 17

-4 -4n = 13

256,200 462,400 576,000823,500 784,600 358,400

L x W x H4 x 2 x 540 cu. ft.

4 x 4 x 232 cu. in.

L x W x H8 x 2 x 464 cu. cm.

> < >

< > >

< > <

How much Carl is paid per hour.

How many games Jill won.

How much money Bobby gave to the clerk.

> < >< < <

19725 5,1503,476

V = 4 x 2 x 2V = 16 c. cm.

V = 3 x 2 x 5V = 30 cu. ft.

Three hundred seventy-two Sixty

Eighty-two Seven hundred sixty-two

549 868 29 186 255 474 635 308

Answers will vary.

531

14 0 8 614 14

4 10 7 714 14

11 3 2 1214 14

6 2 1 78 8

9 11 13 720 20

4 5 3 69 9

9 8 12 517 17

8 8 1 1516 16

4 11 9 615 15

11 6 3 1417 17

5 9 12 214 14

6 8 4 1014 14

/-5 -5n = 5

/-4 -4n = 8

/-4 -4n = 7

/-7 -7n = 6

/-4 -4n = 9

/-2 -2n =2

/-9 -9n = 8

/-7 -7n = 8

/-3 -3n = 8

/-8 -8n = 7

/-8 -8n = 9

/-9 -9n = 6

/-6 -6n = 6

/-2 -2n = 9

/-5 -5n = 7

/-6 -6n = 8

/-9 -9n = 3

/-9 -9n = 5

/-5 -5n = 6

/-8 -8n = 4

/-7 -7n = 2

/-5 -5n = 3

/-2 -2n = 8

/-4 -4n = 3

4 3 7 4 1 6 9 4 4

4 0 3 3 7 0 9 3 1

1 3 6 7 1 4 1 6 7

14 10 17 10 5 9 6 11 10

9 11 9 7 8 11 14 8 8

13 0 6 13 8 14 5 2 11

9 2 3 9 1 9 0 7 6

5 9 6 4 8 4 5 9 6

7 1 5 2 8 8 3 9 1

5 13 8 17 10 5 14 2 13

9 11 7 11 4 4 11 11 8

7 14 14 7 16 9 11 8 10

532

XX

LVII

LXXV

LIII

VI

V

LXII

LXIV

XXV

III

XXXIV

LXXX

XVII

LII

LXIX

XIV

XXXI

XXXVIII

XLIII

LXXI

XCVIII

XXXIX

XLIX

XII

LXXXVI

XLVIII

XXVII

61

4

47

97

18

82

32

94

65

40

5

13

37

23

19

68

46

2

51

9

70

36

58

15

59

30

24

1 2 4 5 9 5 5 2 2

4 8 2 5 6 8 9 8 6

8 7 1 5 5 2 5 0 2

15 16 4 10 7 10 10 7 12

3 6 16 9 13 10 6 6 12

9 13 8 10 13 9 15 9 6

11:02 10:21 3:40 4:08 6:29

2:33 10:37 7:19 9:58 8:11

1:45 11:37 8:16 5:24 1:56

7:53 12:42 4:44 2:01 5:55

5 3 9 0 8 1 6 9 0

5 9 3 3 7 8 2 6 6

0 3 8 1 4 1 8 9 4

9 15 7 18 4 12 6 11 11

12 17 4 14 8 12 3 8 14

11 2 12 7 12 15 5 7 15

109

541

27

213

4132

13624

813

513

851

532

Answers will vary.

27 18 4 15 6 0 72 72 90

60 27 16 3 40 0 32 54 24

45 8 9 30 0 12 5 8 8

2 2 5 8 8 5 0 0 2

7 8 6 7 8 0 4 5 1

3 6 3 0 1 8 4 5 7

5 3 8 11 11 12 9 4 8

8 7 17 15 15 6 8 12 12

6 14 12 9 15 14 5 18 6

1036

1047

1018 4.71.8

4.9

3.6

2.35.5

107410

811063

1032410

55

<

<

>

>

<

<

>

<

<

>

<

<

>

>

<

>

<

<

>

<

<

=

≠≠≠≠

542

L x W x H4 x 4 x 464 cu. ft.

L x W x H11 x 3 x 266 cu. cm.

4 x 4 x 116 cu. units

L x W x H6 x 4 x 496 cu. in.

L x W x H3 x 2 x 212 cu. units

L x W10 x 330 sq. cm.

L x W7 x 642 sq. ft.

5 x 420 sq. units

34 sq. units23 sq. units20 sq. units

3 r1 5 r3 5 r1 2 r3 4 r1 4 r3

5 r4 3 r1 3 r3 5 r2 7 r1 5 r4

4 r1 9 r1 4 r2 2 r2 4 r2 7 r1

3 r3 6 r1 2 r2 6 r1 5 r3 7 r6

6 r3 4 r6 2 r7 8 r3 8 r1 7 r2

5 x 2 x 550 cu. in.

128 9 236 468 82 289 69 129

455 333 177 174 567 48 338 27

17 219 344 257 206 178 389 537

513 27 605 857 468 155 57 349

265 485 428 216 337 489 645 208

126 504 246 777 48 178 339 17

56 50 24 5 28 18 14 35 8

12 15 6 0 48 48 14 30 36

20 42 21 2 20 9 24 0 20

2 4 7 6 3 9 9 8 6

8 5 1 9 9 1 3 5 9

0 7 8 5 9 2 6 3 6

13 4 2 10 10 14 11 17 3

11 9 9 14 16 14 5 11 6

8 4 11 8 7 5 13 8 7