Math Grade 1

Teresa Bomba

1Get Ready!FOR STANDARDIZED TESTS

MATH, GRADE ONE

Other Books in the Get Ready! Series:

Get Ready! for Standardized Tests: Grade 1 by Joseph Harris, Ph.D.

Get Ready! for Standardized Tests: Grade 2 by Joseph Harris, Ph. D.

Get Ready! for Standardized Tests: Grade 3 by Karen Mersky, Ph.D.

Get Ready! for Standardized Tests: Grade 4 by Joseph Harris, Ph.D.

Get Ready! for Standardized Tests: Grade 5 by Leslie E. Talbott, Ph.D.

Get Ready! for Standardized Tests: Grade 6 by Shirley Vickery, Ph.D.

Get Ready! for Standardized Tests: Math, Grade 2 by Kristin Swanson

Get Ready! for Standardized Tests: Math, Grade 3 by Susan Osborne

Get Ready! for Standardized Tests: Math, Grade 4 by June Heller

Get Ready! for Standardized Tests: Reading, Grade 1 by Molly Maack

Get Ready! for Standardized Tests: Reading, Grade 2 by Louise Ulrich

Get Ready! for Standardized Tests: Reading, Grade 3 by Joanne Baker

Get Ready! for Standardized Tests: Reading, Grade 4 by Kris Callahan

1T E S T P R E P A R A T I O N S E R I E S

Get Ready!FOR STANDARDIZED TESTS

MATH, GRADE ONE

Sandy McConnell

Carol TurkingtonSeries Editor

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Skills Checklist ix

Introduction 1Types of Standardized Tests 1The Major Standardized Tests 2How States Use Standardized Tests 2Valid Uses of Standardized Test Scores 3Inappropriate Use of Standardized

Test Scores 3Two Basic Assumptions 4A Word about Coaching 4How to Raise Test Scores 4Test Questions 5

Chapter 1. Test-Taking Basics 7What This Book Can Do 7How to Use This Book 8Basic Test-Taking Strategies 8On to the Second Chapter 10

Chapter 2. Understanding Numbers and Patterns 11

What First Graders Should Know 11What You and Your Child Can Do 12What Tests May Ask 14Practice Skill: Understanding

Numbers and Patterns 14

Chapter 3. Addition 23What First Graders Should Know 23

Equal Sign 23

Sets 23Zero Property of Addition 24One Plus Rule 24Communitive Property of Addition 24Grouping Addition Facts 24Doubles Addition Facts 24Doubles Plus One Facts 25The Nine Plus Rule 25Counting On 25Adding Three Numbers 25Adding a Two-Digit Number to a

Two-Digit Number 25What You and Your Child Can Do 26What Tests May Ask 27Practice Skill: Addition 27

Chapter 4. Subtraction 33What First Graders Should Know 33

Subtracting from a Two-Digit Number 33What You and Your Child Can Do 34What Tests May Ask 36Practice Skill: Subtraction 36

Chapter 5. Time: Clocks andCalendars 39

Telling Time 39What First Graders Should Know 39What You and Your Child Can Do 40What Tests May Ask 40Practice Skill: Telling Time 40

Calendars 42

vii

M A T H , G R A D E O N E

ContentsFor more information about this title, click here.

Copyright 2001 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.

What First Graders Should Know 42What You and Your Child Can Do 42What Tests May Ask 42Practice Skill: Calendars 42

Chapter 6. Money 45What First Graders Should Know 45

Counting Money 45What You and Your Child Can Do 46What Tests May Ask 46Practice Skill: Money 46

Chapter 7. Geometry 51What First Graders Should Know 51What You and Your Child Can Do 51

Two-Dimensional Shapes 51Three-Dimensional Shapes 52Symmetry 53Graphs 53

What Tests May Ask 54Practice Skill: Geometry 54

Chapter 8. Fractions 57What First Graders Should Know 57What You and Your Child Can Do 57What Tests May Ask 58Practice Skill: Fractions 58

Chapter 9. Measurement 61What First Graders Should Know 61What You and Your Child Can Do 62

Measuring Length and Capacity 62Measuring Mass (Weight) 63

What Tests May Ask 63Practice Skill: Measuring 64

Chapter 10. Solving WordProblems 69

What First Graders Should Know 69What You and Your Child Can Do 70What Tests May Ask 70Practice Skill: Solving Word Problems 70

Appendix A: Web Sites andResources for More Information 75

Appendix B: Read More about It 79

Appendix C: What Your Childs Test Scores Mean 81

Appendix D: Which States Require Which Tests 89

Appendix E: TestingAccommodations 99

Glossary 101

Answer Keys for Practice Skills 103

Sample Practice Test 105

Answer Key for SamplePractice Test 127

M A T H , G R A D E O N E : G E T R E A D Y !

viii

ix


S K I L L S C H E C K L I S T

MY CHILD HAS LEARNED IS WORKING ON

NUMBERS AND PATTERNS

ADDITION

EQUAL SIGN

SETS

FACT FAMILIES

PLACE VALUE

SKIP COUNTING

SUBTRACTION

TELLING TIME

CALENDARS

NAMES AND VALUE OF COINS

COUNTING MONEY

CIRCLE

SQUARE

RECTANGLE

TRIANGLE

SYMMETRY

FRACTIONS: 1/2

FRACTIONS: 1/3 AND 2/3

FRACTIONS: 1/4, 2/4, 3/4

NONSTANDARD UNITS OFMEASUREMENT

WEIGHING POUNDS

WORD PROBLEMS


1Almost all of us have taken standardized testsin school. We spent several days bubbling-inanswers, shifting in our seats. No one ever toldus why we took the tests or what they would dowith the results. We just took them and neverheard about them again.

Today many parents arent aware they areentitled to see their childrens permanentrecords and, at a reasonable cost, to obtaincopies of any information not protected by copy-right, including testing scores. Late in the schoolyear, most parents receive standardized testresults with confusing bar charts and detailedexplanations of scores that few people seem tounderstand.

In response to a series of negative reports onthe state of education in this country, Americanshave begun to demand that something be doneto improve our schools. We have come to expecthigher levels of accountability as schools facethe competing pressures of rising educationalexpectations and declining school budgets.High-stakes standardized tests are rapidlybecoming the main tool of accountability for stu-dents, teachers, and school administrators. Ifstudents test scores dont continually rise,teachers and principals face the potential loss ofschool funding and, ultimately, their jobs.Summer school and private after-school tutorialprogram enrollments are swelling with studentswho have not met score standards or who, every-one agrees, could score higher.

While there is a great deal of controversyabout whether it is appropriate for schools touse standardized tests to make major decisionsabout individual students, it appears likely thatstandardized tests are here to stay. They will beused to evaluate students, teachers, and theschools; schools are sure to continue to use stu-dents test scores to demonstrate their account-ability to the community.

The purposes of this guide are to acquaint youwith the types of standardized tests your chil-dren may take; to help you understand the testresults; and to help you work with your childrenin skill areas that are measured by standardizedtests so they can perform as well as possible.

Types of Standardized TestsThe two major types of group standardized testsare criterion-referenced tests and norm-refer-enced tests. Think back to when you learned totie your shoes. First Mom or Dad showed youhow to loosen the laces on your shoe so that youcould insert your foot; then they showed youhow to tighten the lacesbut not too tight. Theyshowed you how to make bows and how to tie aknot. All the steps we just described constitutewhat is called a skills hierarchy: a list of skillsfrom easiest to most difficult that are related tosome goal, such as tying a shoelace.

Criterion-referenced tests are designed todetermine at what level students are perform-


Introduction


ing on various skills hierarchies. These testsassume that development of skills follows asequence of steps. For example, if you wereteaching shoelace tying, the skills hierarchymight appear this way:

1. Loosen laces.

2. Insert foot.

3. Tighten laces.

4. Make loops with both lace ends.

5. Tie a square knot.

Criterion-referenced tests try to identify howfar along the skills hierarchy the student hasprogressed. There is no comparison against any-one elses score, only against an expected skilllevel. The main question criterion-referencedtests ask is: Where is this child in the develop-ment of this group of skills?

Norm-referenced tests, in contrast, are typi-cally constructed to compare children in theirabilities as to different skills areas. Althoughthe experts who design test items may be awareof skills hierarchies, they are more concernedwith how much of some skill the child has mas-tered, rather than at what level on the skillshierarchy the child is.

Ideally, the questions on these tests rangefrom very easy items to those that are impossi-bly difficult. The essential feature of norm-ref-erenced tests is that scores on these measurescan be compared to scores of children in similargroups. They answer this question: How doesthe child compare with other children of thesame age or grade placement in the develop-ment of this skill?

This book provides strategies for increasingyour childs scores on both standardized norm-referenced and criterion-referenced tests.

The Major Standardized TestsMany criterion-referenced tests currently in useare created locally or (at best) on a state level,

and there are far too many of them to go intodetail here about specific tests. However, chil-dren prepare for them in basically the same waythey do for norm-referenced tests.

A very small pool of norm-referenced tests isused throughout the country, consisting primar-ily of the Big Five:

California Achievement Tests (CTB/McGraw-Hill)

Iowa Tests of Basic Skills (Riverside)

Metropolitan Achievement Test (Harcourt-Brace & Company)

Stanford Achievement Test (PsychologicalCorporation)

TerraNova [formerly Comprehensive Test ofBasic Skills] (McGraw-Hill)

These tests use various terms for the academ-ic skills areas they assess, but they generallytest several types of reading, language, andmathematics skills, along with social studies andscience. They may include additional assess-ments, such as of study and reference skills.

How States Use Standardized TestsDespite widespread belief and practice to thecontrary, group standardized tests are designedto assess and compare the achievement ofgroups. They are not designed to providedetailed diagnostic assessments of individualstudents. (For detailed individual assessments,children should be given individual diagnostictests by properly qualified professionals, includ-ing trained guidance counselors, speech andlanguage therapists, and school psychologists.)Here are examples of the types of questionsgroup standardized tests are designed toanswer:

How did the reading achievement of studentsat Valley Elementary School this year com-pare with their reading achievement lastyear?


2

How did math scores at Wonderland MiddleSchool compare with those of students atParkside Middle School this year?

As a group, how did Hilltop High School stu-dents compare with the national averages inthe achievement areas tested?

How did the districts first graders mathscores compare with the districts fifthgraders math scores?

The fact that these tests are designed primar-ily to test and compare groups doesnt meanthat test data on individual students isnt use-ful. It does mean that when we use these teststo diagnose individual students, we are usingthem for a purpose for which they were notdesigned.

Think of group standardized tests as beingsimilar to health fairs at the local mall. Ratherthan check into your local hospital and spendthousands of dollars on full, individual tests fora wide range of conditions, you can go from sta-tion to station and take part in different healthscreenings. Of course, one would never diagnoseheart disease or cancer on the basis of thescreening done at the mall. At most, suspiciousresults on the screening would suggest that youneed to visit a doctor for a more complete exam-ination.

In the same way, group standardized testsprovide a way of screening the achievement ofmany students quickly. Although you shouldntdiagnose learning problems solely based on theresults of these tests, the results can tell youthat you should think about referring a child fora more definitive, individual assessment.

An individual students group test datashould be considered only a point of informa-tion. Teachers and school administrators mayuse standardized test results to support or ques-tion hypotheses they have made about students;but these scores must be used alongside otherinformation, such as teacher comments, dailywork, homework, class test grades, parentobservations, medical needs, and social history.

Valid Uses of Standardized TestScoresHere are examples of appropriate uses of testscores for individual students:

Mr. Cone thinks that Samantha, a third grad-er, is struggling in math. He reviews her fileand finds that her first- and second-gradestandardized test math scores were very low.Her first- and second-grade teachers recallepisodes in which Samantha cried becauseshe couldnt understand certain math con-cepts, and mention that she was teased byother children, who called her Dummy. Mr.Cone decides to refer Samantha to the schoolassistance team to determine whether sheshould be referred for individual testing for alearning disability related to math.

The local college wants to set up a tutoringprogram for elementary school children whoare struggling academically. In decidingwhich youngsters to nominate for the pro-gram, the teachers consider the studentsaverages in different subjects, the degree towhich students seem to be struggling, par-ents reports, and standardized test scores.

For the second year in a row, Gene has per-formed poorly on the latest round of stan-dardized tests. His teachers all agree thatGene seems to have some serious learningproblems. They had hoped that Gene wasimmature for his class and that he would dobetter this year; but his dismal grades contin-ue. Gene is referred to the school assistanceteam to determine whether he should be sentto the school psychologist for assessment of apossible learning handicap.

Inappropriate Use of StandardizedTest ScoresHere are examples of how schools have some-times used standardized test results inappropri-ately:

I N T R O D U C T I O N

3

Mr. Johnson groups his students into readinggroups solely on the basis of their standard-ized test scores.

Ms. Henry recommends that Susie be heldback a year because she performed poorly onthe standardized tests, despite strong gradeson daily assignments, homework, and classtests.

Geralds teacher refers him for considerationin the districts gifted program, which acceptsstudents using a combination of intelligencetest scores, achievement test scores, andteacher recommendations. Geralds intelli-gence test scores were very high.Unfortunately, he had a bad cold during theweek of the standardized group achievementtests and was taking powerful antihista-mines, which made him feel sleepy. As aresult, he scored too low on the achievementtests to qualify.

The public has come to demand increasinglyhigh levels of accountability for public schools.We demand that schools test so that we havehard data with which to hold the schoolsaccountable. But too often, politicians and thepublic place more faith in the test results thanis justified. Regardless of whether its appropri-ate to do so and regardless of the reasonsschools use standardized test results as they do,many schools base crucial programming and eli-gibility decisions on scores from group stan-dardized tests. Its to your childs advantage,then, to perform as well as possible on thesetests.

Two Basic AssumptionsThe strategies we present in this book comefrom two basic assumptions:

1. Most students can raise their standardizedtest scores.

2. Parents can help their children becomestronger in the skills the tests assess.

This book provides the information you need

to learn what skill areas the tests measure,what general skills your child is being taught ina particular grade, how to prepare your child totake the tests, and what to do with the results.In the appendices you will find information tohelp you decipher test interpretations; a listingof which states currently require what tests;and additional resources to help you help yourchild to do better in school and to prepare for thetests.

A Word about CoachingThis guide is not about coaching your child.When we use the term coaching in referring tostandardized testing, we mean trying to givesomeone an unfair advantage, either by reveal-ing beforehand what exact items will be on thetest or by teaching tricks that will supposedlyallow a student to take advantage of some detailin how the tests are constructed.

Some people try to coach students in shrewdtest-taking strategies that take advantage ofhow the tests are supposedly constructed ratherthan strengthening the students skills in theareas tested. Over the years, for example, manyrumors have been floated about secret formu-las that test companies use.

This type of coaching emphasizes ways to helpstudents obtain scores they didnt earnto getsomething for nothing. Stories have appeared inthe press about teachers who have coached theirstudents on specific questions, parents whohave tried to obtain advance copies of tests, andstudents who have written down test questionsafter taking standardized tests and sold them toothers. Because of the importance of test securi-ty, test companies and states aggressively pros-ecute those who attempt to violate test securi-tyand they should do so.

How to Raise Test ScoresFactors that are unrelated to how strong stu-dents are but that might artificially lower testscores include anything that prevents students


4

from making scores that accurately describetheir actual abilities. Some of those factors are:

giving the tests in uncomfortably cold or hotrooms;

allowing outside noises to interfere with testtaking; and

reproducing test booklets in such small printor with such faint ink that students cant readthe questions.

Such problems require administrative atten-tion from both the test publishers, who mustmake sure that they obtain their norms for thetests under the same conditions students facewhen they take the tests; and school adminis-trators, who must ensure that conditions underwhich their students take the tests are as closeas possible to those specified by the test pub-lishers.

Individual students also face problems thatcan artificially lower their test scores, and par-ents can do something about many of theseproblems. Stomach aches, headaches, sleepdeprivation, colds and flu, and emotional upsetsdue to a recent tragedy are problems that mightcall for the student to take the tests duringmake-up sessions. Some students have physicalconditions such as muscle-control problems,palsies, or difficulty paying attention thatrequire work over many months or even yearsbefore students can obtain accurate test scoreson standardized tests. And, of course, some stu-dents just dont take the testing seriously ormay even intentionally perform poorly. Parentscan help their children overcome many of theseobstacles to obtaining accurate scores.

Finally, with this book parents are able tohelp their children raise their scores by:

increasing their familiarity (and their comfortlevel) with the types of questions on stan-dardized tests;

drills and practice exercises to increase theirskill in handling the kinds of questions theywill meet; and

providing lots of fun ways for parents to helptheir children work on the skill areas that willbe tested.

Test QuestionsThe favorite type of question for standardizedtests is the multiple-choice question. For exam-ple:

1. The first President of the United Stateswas:

A Abraham Lincoln

B Martin Luther King, Jr.

C George Washington

D Thomas Jefferson

The main advantage of multiple-choice ques-tions is that it is easy to score them quickly andaccurately. They lend themselves to opticalscanning test forms, on which students fill inbubbles or squares and the forms are scored bymachine. Increasingly, companies are movingfrom paper-based testing to computer-basedtesting, using multiple-choice questions.

The main disadvantage of multiple-choicequestions is that they restrict test items to thosethat can be put in that form. Many educatorsand civil rights advocates have noted that themultiple-choice format only reveals a superficialunderstanding of the subject. Its not possiblewith multiple-choice questions to test a stu-dents ability to construct a detailed, logicalargument on some issue or to explain a detailedprocess. Although some of the major tests arebeginning to incorporate more subjectivelyscored items, such as short answer or essayquestions, the vast majority of test items con-tinue to be in multiple-choice format.

In the past, some people believed there werespecial formulas or tricks to help test-takersdetermine which multiple-choice answer wasthe correct one. There may have been sometruth to some claims for past tests. Computeranalyses of some past tests revealed certain

I N T R O D U C T I O N

5

biases in how tests were constructed. For exam-ple, the old advice to pick D when in doubtappears to have been valid for some past tests.However, test publishers have become sosophisticated in their ability to detect patternsof bias in the formulation of test questions andanswers that they now guard against it aggres-sively.

In Chapter 1, we provide information aboutgeneral test-taking considerations, with adviceon how parents can help students overcometesting obstacles. The rest of the book providesinformation to help parents help their childrenstrengthen skills in the tested areas.

Joseph Harris, Ph.D.


6

7At some point during the 12 years that yourchildren spend in school, theyll face a stan-dardized testing situation. Some schools testevery year, some test every other yearbuteventually your child will be assessed. How wellyour child does on such a test can be related tomany thingsDid he get plenty of rest the nightbefore? Is she anxious in testing situations? Didhe get confused when filling in the answersheets and make a mechanical mistake? Thatswhy educators emphasize that a childs score ona standardized test shouldnt be used as the solejudge of how that child is learning and develop-ing. Instead, the scores should be evaluated asonly one part of the educational picture, togeth-er with the childs classroom performance andoverall areas of strength and weakness. Yourchild wont pass or fail a standardized test, butoften you can see a general pattern of strengthsand weaknesses.

Although most states dont require standard-ized testing in first grade, it is important forchildren to become familiar with the testing sit-uation as early as possible in order to build con-fidence for required testing in later grades.

Keep in mind, however, that the format forstandardized tests may differ slightly from onetest to another. While this book offers your childexposure to typical sample questions that mayappear on the tests, its difficult to provide sam-ples common to all. Keep this in mind, and dontmake your children practice too muchor theymay become alarmed when the real test is notexactly like the questions they have seen in this

book. Guiding is the key hereif your childunderstands the basic concepts, she will be suc-cessful regardless of the format.

What This Book Can DoThis book is not designed to help your child arti-ficially inflate scores on a standardized test.Instead, its intended to help you understand thetypical kinds of skills taught in a first-gradeclass and what a typical first grader can beexpected to know by the end of the first year. Italso presents lots of fun activities that you canuse at home to work with your child in particu-lar skill areas that may be a bit weak.

Of course, this book should not be used toreplace your childs teacher. It should be used asa guide to help you work together with theschool as a team to help your child succeed.Keep in mind, however, that endless drilling isnot the best way to help your child improve.While most children want to do well and pleasetheir teachers and parents, they already spendabout 7 hours a day in school. Extracurricularactivities, homework, music, and play take upmore time. Try to use the activities in this bookto stimulate and support your childrens work atschool, not to overwhelm them.

Most children entering the first grade areeager to learn. One of the most serious mistakesthat many parents of children this age make isto try to get their children to master skills forwhich they arent developmentally ready. Forexample, while most children this age are ready

C H A P T E R 1

Test-Taking Basics


to read, some arent, and no amount of drill willmake them ready to read.

Theres certainly nothing wrong with workingwith your child, but if youre trying to teach thesame skill over and over and your child just isntgetting it, you may be trying to teach some-thing that your child just isnt ready for.

You may notice that your child still seems abit clumsy and still has problems coloring with-in the lines. Symbolic reasoning begins toappear in first grade, as children start to learnthat printed numbers stand for numeralsthat5 means five. As the year progresses, your firstgrader will become more and more able to rec-ognize abstract qualities and to consider morethan one characteristic at one time.

Remember, however, that not all childrenlearn things at the same rate. What may be typ-ical for one first grader is certainly not typicalfor another. You should use the information pre-sented in this book in conjunction with schoolwork to help develop your childs essential skillsin mathematics and number skills.

How to Use This BookThere are many different ways to use this book.Some children are quite strong in certain mathareas but need a bit of help in other areas.Perhaps your child is a whiz at adding but hasmore trouble with telling time. Focus yourattention on those skills which need some work,and spend more time on those areas. Youll seein each chapter an introductory explanation ofthe material in the chapter, followed by a sum-mary of what a typical child in first gradeshould be expected to know about that skill bythe end of the year. This is followed in eachchapter by an extensive section featuring inter-esting, fun, or unusual activities you can do withyour child to reinforce the skills presented inthe chapter. Most use only inexpensive itemsfound around the home, and many are suitablefor car trips, waiting rooms, and restaurants.

Next, youll find an explanation of how typicalstandardized tests may assess that skill and

what your child might expect to see on a typicaltest.

Weve included sample questions at the end ofeach section that are designed to help familiar-ize your child with the types of questions foundon a typical standardized test. These questionsdo not measure your childs proficiency in anygiven content areabut if you notice that yourchild is having trouble with a particular ques-tion, you can use the information to figure outwhat skills you need to focus on.

Basic Test-Taking StrategiesSometimes children score lower on standardizedtests because they approach testing in an ineffi-cient way. There are things you can do before thetestand that your child can do during thetestto make sure that he does as well as hecan. There are a few things you might want toremember about standardized tests. One is thatthey can only ask a limited number of questionsdealing with each skill before they run out ofpaper. On most tests, the total math componentis made up of about 60 items and takes about 90minutes. In some cases, your child mayencounter only one exercise evaluating a partic-ular skill. An important practice area that isoften overlooked is the listening element of thetests. Most of the math questions are done as agroup and are read to the students by the proc-tor of the test, who is almost always the class-room teacher.

You can practice listening skills by readingthe directions to each question to your child.Sometimes the instructions are so brief and tothe point that they are almost too simple. Insome cases, teachers are not permitted toreword or explain; they may read only what iswritten in the test manual. Usually, questionsand directions or instructions may be repeatedonly one time. Read the directions as they havebeen given on the practice pages and then haveyour child explain to you what they mean. Thenyoull both be clear about what the tests actual-ly require.


8

Before the Test

Perhaps the most effective thing you can do toprepare your child for standardized tests is to bepatient and positive. Remember that no matterhow much pressure you put on your children,they wont learn certain skills until they arephysically, mentally, and emotionally ready todo so. Youve got to walk a delicate line betweenchallenging and pressuring your children. Ifchildren view testing as a big, bad wolf, thenthey may develop negative attitudes that couldaffect their performance. If you see that yourchild isnt making progress or is getting frus-trated, it may be time to lighten up.

Dont Change the Routine. Many experts offermistaken advice about how to prepare childrenfor a test, such as recommending that childrengo to bed early the night before or eat a high-protein breakfast on the morning of the test. Itsa better idea not to alter your childs routine atall right before the test.

If your child isnt used to going to bed early,then sending him off at 7:30 p.m. the nightbefore a test will only make it harder for him toget to sleep by the normal time. If he is used toeating an orange or a piece of toast for breakfast,forcing him to down a platter of fried eggs andbacon will only make him feel sleepy or uncom-fortable.

Neatness. There is an incorrect way to fill in ananswer sheet on a standardized test, and if thishappens to your child, it can really make a dif-

ference on the final results. It pays to give yourchild some practice on filling in answer sheets.Watch how neatly your child can fill in the bub-bles, squares, and rectangles below. If he over-laps the lines, makes a lot of erase marks, orpresses the pencil too hard, try having him prac-tice with pages of bubbles. You can easily createsheets of capital Os, squares, and rectanglesthat your child can practice filling in. If he getsbored doing that, have him color in detailed pic-tures in coloring books or complete connect-the-dots pages.

During the Test

There are some approaches to standardized test-ing that have been shown to make some degreeof improvement in a score. Discuss the followingstrategies with your child from time to time.

Bring Extra Pencils. You dont want your childspending valuable testing time jumping up tosharpen a pencil. Send along plenty of extra,well-sharpened pencils, and your child will havemore time to work on test questions.

Listen Carefully. You wouldnt believe howmany errors kids make by not listening toinstructions or not paying attention to demon-strations. Some children mark the wrong form,fill in the bubbles incorrectly, or skip to thewrong section. Others simply forget to includetheir names. Many make a mark without realiz-ing whether they are marking the right bubble.

T E S T - T A K I N G B A S I C S

9

Read the Entire Question First. Some childrenget so excited about the test that they begin fill-ing in the bubble before they finish reading theentire question. The last few words in a questionsometimes give the most important clues to thecorrect answer.

Read Carefully. In their desire to finish first,many children tend to select the first answerthat seems right to them without thoroughlyreading all the responses and choosing the verybest answer. Make sure your child understandsthe importance of evaluating all the answersbefore choosing one.

Write It Down. Most standardized tests allowchildren to use scratch paper for the math por-tion or to work directly in their test booklet.Encourage your child to write it down and workit out whenever appropriate. This would includecomputation for word problems given horizon-tally

53 + 24 = ___that can be solved easier if rewritten vertically

53+ 24____

Skip Difficult Items; Return Later. Many chil-dren will sit and worry about a hard question,

spending so much time on one problem thatthey never get to problems that they would beable to answer correctly if they only had leftenough time. Explain to your child that he canalways come back to a knotty question once hefinishes the section.

Refer to Pictures for Clues. Tell your child notto overlook the pictures in the test booklets,which may reveal valuable clues that he can useto help him find the correct answers. Studentsalso can find clues to correct answers by lookingat descriptions, wording, and other informationin the questions.

Use Key Words. Have your child look at thequestions and try to figure out the parts thatare important and those that arent.

Eliminate Answer Choices. Just like in thewildly successful TV show Who Wants to Be aMillionaire, remind your child that its a goodidea to narrow down his choices among multiple-choice options by eliminating answers he knowscant possibly be true. Emphasize that thereshould be only one answer marked for eachquestion.

On to the Second ChapterNow that youve learned a bit about the test-taking basics, its time to turn your attention tothe first of the math skillsunderstandingnumbers and patterns.


10

11

Whether its age, number of brothers or sisters,or how many days until a holiday, your childhas been exposed to numbers at a very earlyage. A child sees numerals on televisions, mail-boxes, clocks, and phones. When numerals areassociated with real-life experiences or concreteobjects, a child sees the relevanceand under-standing begins to develop. You want to be surethat this continues, so surround your child withnumbers and involve her in their everyday func-tions.

Mathematics is the science of patterns, andyou can train your child to be a pattern detec-tor. Through guided experiences, your child candiscover the patterns in the world around her(especially the base 10 number system). Thiswill build a good foundation and allow her tounderstand future math concepts. The ability tocontinue a pattern requires a child to analyzeand sort information and make generalizations.Based on these generalizations, she makes pre-dictions about how to continue a pattern. Forexample, when presented with the numbers 2, 2,3, 2, 2, 3, your child should look at all the num-bers given and try to discover what pattern isformed in order to arrive at the number thatshould appear next. After sorting the informa-tion, she should see that the pattern 2, 2, 3 isrepeated and be able to make the generalizationthat 2, 2, 3 is going to be repeated over and overand that the numbers should continue to appearin that order. A child can learn the skillsinvolved in patterning by using objects in herenvironment. Patterns can be found all around

us in areas other than math, such as nature, art,music, and reading. Learning to see and under-stand patterns helps children to see relation-ships between information in our world, andthis, in turn, produces logical thinkers. Childrenwho look for patterns are usually more persis-tent and are less prone to frustration as mathstudents.

What First Graders Should KnowFirst-grade children are expected to rote count(count by memory) from 1 to 100 and to be ableto recognize and write the numerals from 1 to100. Dont worry if your child reverses thenumerals 2, 5, 7, or 9. With increased practice,these reversals usually occur less frequentlyand eventually are eliminated.

Children are expected to be able to count setsof up to 20 objects and write the numeral repre-senting the number of objects in the set. Theyshould be able to skip count by twos, fives, andtens to 100 (2, 4, 6; 5, 10, 15; or 10, 20, 30; and soon). Understanding the patterns in our base 10number system and seeing the relationshipsbetween the numbers will enable them to beable to perform skip counting and also enablethem to complete a sequence of skip countingbackwards, such as 25, 20, 15, . Given a set ofnumbers or objects, children should be able toextend a pattern.

Children also should be familiar with ordinalnumbers from first to twentieth. (An ordinalnumber is the number listing the order in which

C H A P T E R 2

Understanding Numbersand Patterns


an object appears in a series, such as first,second, and so on.) For example, when showna picture of eight dogs in a line, your childshould be able to identify the third dog.

Comprehending place value of the ones, tens,and hundreds is also a concept that should begrasped in mid-first grade. When a child seesthe numeral 27, she should be able to under-stand that the 2 represents two tens and the7 represents seven ones. Finally, your childshould understand the concepts of greaterthan and less than and be able to state thoserelationships between any two numbers from 1to 100.

What You and Your Child Can Do

Rote Counting. Expose your child to as manycounting experiences as possible through theuse of finger plays, counting songs, and nurseryrhymes. These provide excitement and fun whilelearning to count forward and backward. TenLittle Indians, This Old Man, One, Two,Buckle My Shoe, Five Little Ducks, and RollOver, Roll Over all help a child learn how torote count.

Counting Objects. To learn how to countobjects, your child first needs to know how torote count. In addition to rote counting, shemust incorporate the concept of one-to-one cor-respondence. This means that every time shesays a number, she should point to only oneobject. The number of objects in the set is thelast number she states. Encourage your child tocount her toy cars, crayons, snacks, or books.Completing a household chore such as settingthe table helps to enhance her understanding ofone-to-one correspondence.

Counting Books. Help your child check outcounting books such as Ten Black Dots byDonald Crews or Fish Eyes by Lois Ehlert in thelibrary, and read them together.

Games. Many beginner board games, such asChutes and Ladders or Uncle Wiggly, willprovide excellent practice counting and helpyour child become familiar with numbers.

Create a Book. Cut out pictures from a maga-zine, and create your own counting book. Thefirst page should contain the numeral 1 and apicture of one object. The second page shouldcontain the numeral 2 and a picture of twoobjects. Continue the pattern.

Play and Write. Write numerals in pudding,powdered Jell-O, sand, colored glue, paint,chalk, or glue and glitter.

Dough Numerals. Create numerals using Play-Doh or bread dough, and bake your number!Help your child pour out pancake batter intonumbers and eat her handiwork.

Base 10 Patterns. The Hundred Board, a 10 10 grid of numbers from 1 to 100, is a valuabletool to help your child understand the numbersystem. You can buy one or make your ownyoucan easily draw a 10 10 grid. The first lineshould contain the numbers from 1 to 10; thesecond line should include 11 through 20, and soon to 100. It is well worth the effort to constructone; it will allow your child to discover for her-self the patterns inherent in the number sys-tem. Complete the activities below using yourHundred Board, and use M&Ms, Cheerios,Smarties, or corn kernels to serve as markers.Have fun!

1. Mark the numbers 6, 16, 26, 36, 46, and 56.Do you see a pattern? What do all the num-bers end with? What pattern do you see onthe number board? (All the numbers thatend the same are in the same column.)

2. Mark the numbers 21, 22, 23, 24, 25, 26,and 27. Do you see a pattern? What do allthe numbers begin with? Do you see a pat-tern? Is there a number in the row thatdoes not fit the pattern?


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3. Mark the number 8. What number is oneless than 8? Mark the number 42. Whatnumber is one less than 42? Mark the num-ber 85. What number is one less than 85?Do you see a pattern?

4. Mark the number 36. What number is onemore than 36? Mark the number 9. Whatnumber is one more than 9? Mark thenumber 93. What number is one more than93? Do you see a pattern?

5. Play Guess My Number. Using theHundred Board, ask the following ques-tions: Im thinking of a number that is oneless than 12. What is my number? Imthinking of a number that is between 15and 17. What is my number? Im thinkingof a number that is two more than 76.What is my number?

6. Take a piece of paper and cover all thenumbers except the numbers that end with0. Read all the uncovered numbers. You arecounting by tens!

7. Find the number 20. What is 10 more than20? Find the number 15. What is 10 morethan 15? Find the number 78. What is 10more than 78? Your child may need tocount 10 places after the given number inorder to find the answer, but after severalrepetitions, she should discover that byadding 10 to a number, she just needs tofind the number on the Hundred Boardthat is directly below the original number.This is the pattern. This generalization willcome in very handy when your child learnsto add tens to a number that ends with afive.

8. Cut two pieces of paper to a length andwidth that only covers the first fourcolumns (the numbers that end with 1, 2, 3,and 4) and the sixth column through theninth column (the numbers that end with6, 7, 8, and 9). Practice reading them. Yourchild is counting by fives!

9. Cut strips of paper and cover the first,third, fifth, seventh, and ninth columns.Read the numbers. Practice counting bytwos. Another way to practice skip count-ing is through the use of a calculator. Tocount by fives, have your child tap in 0 +5 = = = = = =. Allow her to guess the num-ber first and then tap the equal sign. If shecant guess, have her read the numbers asthey appear each time the equal sign istapped. This repetition will help her learnhow to skip count by fives. To count bytwos, tap in 0 + 2 (your constant) = = = = .Each time the equal sign is tapped, twowill be added to the preceding number. Tryto skip count by tens.

100 Hungry Ants. Read this book by ElinorPinczes, and have your child arrange raisins orminimarshmallows in the same formationsmade by the ants in the book. She can explorethe number 100 by arranging 100 items in dif-ferent groups. She will group them into equallines: one line, two lines, four lines, five lines,and finally, ten lines.

Hundreds of Things. Find objects such as cot-ton balls, stickers, stars, pennies, or toothpicksand arrange them on poster board in 10 groupsof tens. Count by tens to 100. Your child will beable to visualize what 100 items looks like.

Learning to Write to 100. Help your child dis-cover the pattern that when she counts to 100,the numbers 0 to 9 are repeated over and over,first by themselves and then preceded by a one,then a two, then a three, and so on. She shouldbegin writing the numerals on a 10 10 grid inorder for her to be able to correct her work bychecking that all the numbers in the first col-umn end with a zero and that each number in arow (except the first row) begins with the samenumeral.

Place Value. Emphasize to your child that themagic number in the number system is 10. You

U N D E R S T A N D I N G N U M B E R S A N D P A T T E R N S

13

can buy base 10 blocks or make your ownmanipulatives. Explain that counting is madeeasier by grouping things into tens. Take ahandful of about 35 straws (or any similar objectthat can be bundled), and ask your child tocount by ones to find out how many objects yougave her. Now have her group the straws inbundles of 10 by banding them together. If shedoesnt have enough to make a group of 10,those are considered ones.

Now ask her to count the objects. Count thebundles by 10, and add on the ones left over toarrive at the correct number, counting 30, 31,32, 33, 34, 35.

Have her write the number, pointing out thetens column and the ones column. The 3 repre-sents three bundles or three tens, and the 5 rep-resents five singles or five ones. Writing thenumber helps her link her experience with thestraws to the written number.

Discover how grouping objects makes count-ing much easier. Make ten bundles and leavenine unbundled or in ones. Count the bundles bycounting by tens. Ask your child to find 62. Sheshould select six bundles and two ones. Practicewriting each number after she makes that num-ber with the straws. Have her find 50, 28, 18,and 37 and practice until she feels comfortablewith this concept.

Show her the numeral 52, and have her selectthe straws she needs to make a match. Sheshould select five bundles and two singles.Connect this learning with the HundredBoard, and play Guess My Number: Imthinking of a number that is 2 tens and 4 ones.Mark my number. Im thinking of a number thatis 5 tens and 0 ones. Mark my number.

Patterns Using Objects. Children can learnthe skills involved in patterning by using

objects in their environment. Use objects thatdiffer by one attribute such as color, shape, orsize, such as M&Ms, Legos, or any item that dif-fers by color only, or buy pattern blocks. Begin apattern, and have your child continue it: red,brown, brown, red, brown, brown, _____. Remindher to use every part of information she wasgiven. Point to every item from the beginning ofthe pattern, and state the important attributethat makes it different, and then continue thepattern. The attribute of shape can be used bycutting three different shapes out of paper andmaking a pattern: circle, triangle, square, circle,triangle, square, circle, _____.

What Tests May AskA standardized test may ask any number ofquestions dealing with basic facts, but time andspace on the test limit the number of items per-taining to one particular concept. Your childshould be prepared to

count objects and choose the matchingnumeral.

compare sets of objects.

list numbers in order.

skip count by twos, fives, and tens.

Practice Skill: UnderstandingNumbers and Patterns

Directions: Look at the pictureand listen carefully to the question.Darken in the bubble beside youranswer.


14


15

Example:

How many cars are there here?A 3B 5C 7D 6

Answer:B 5

1 How many dogs are therehere?A 7B 9C 8D 10

2 How many pencils are therehere?A 15B 12C 16D 13

3 Which picture has the samenumber of balls as there arebats?

A

B

C

D


16

4 Which set of cars is two lessthan the number of houses? A

B

C

D

5 How many more stars areneeded to make the sets equal? A 1B 2C 3D 4

6 How many more balls areneeded to make the sets equal? A 1B 2C 3D 4

7 Fill in the missing number: 36,37, 38, 39, __, 41.A 30B 40C 42D 93


17

8 Fill in the missing number: 66,67, __, 69.A 65B 70C 76D 68

9 What number is between 28and 30?A 31B 27C 40D 29

10 What number is closest to 84?A 48B 90C 82D 87

11 What number is more than 46and less than 51?A 45B 52C 48D 64

12 What number comes justbefore 80?A 79B 81C 70D 69

13 What number comes rightafter 12 when counting byones?A 21B 13C 11D 18

14 What number is between 16and 20?A 18B 61C 21D 14

15 Count by tens. Which numberis missing? 20, __, 40, 50, 60A 70B 30C 25D 10


18

16 Count by twos. What numberis missing? 2, 4, 6, __, 10A 8B 7C 9D 12

17 Count by fives. What numberis missing? 5, 10, __, 20, 25A 30B 15C 13D 52

18 Count by tens backward. Whatcomes after 60?A 70B 10C 50D 55

19 Count by twos backward. Whatnumber comes next? 8, 6, 4, __A 6B 3C 10D 2

20 Continue the pattern.4, 2, 2, 4, 2, 2, 4, __,___.A 2, 2B 4, 4C 2, 4D 4, 2

21 Look at the picture above.Continue the pattern.

A

B

C

D


19

22 Look at the picture above. Continue the pattern.

A B

C D

23 What number has a 6 in thetens place?A 63B 26C 33D 635

24 How many tens are in 83?A 11 tensB 8 tensC 3 tensD 5 tens

25 Which number is equal to 4tens?A 4B 400C 40D 44

26 How many ones are in thenumber 32?A 5 onesB 1 onesC 3 onesD 2 ones


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27 What number has 1 ten and 2ones?A 3B 12C 21D 11

28 What number has 5 tens and 9ones?A 50B 59C 95D 14

29 Look at the picture above. Howmany are there in all? A 10B 27C 37D 73

32 Which object is fifth?

A B

C D

30 Which is the greatest number?A 24B 42C 8D 40

31 Which is the smallest number?A 64B 46C 40D 60

(See page 103 for answer key.)


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33 To which ball does the arrowpoint? A sixthB secondC thirdD fourth

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Addition builds on the skill of counting objectsin a set. Addition is the joining of two sets anddiscovering how many objects are altogether inboth sets. Using concrete objects to demonstratethis is an important step in visualizing theprocess and understanding addition. To connector link this visual representation of addition tothe mathematic symbols, children should writethe addition sentence that matches the picturemade with the concrete objects.

What First Graders Should KnowFirst graders are expected to state the numbersentences represented by pictures of two setsbeing joined together. For example, when a pic-ture of three objects and a picture of two objectsare shown, a child should be able to read the pic-ture and state the number sentence as 3 + 2 = 5.

Learning addition facts is an important partof the first grade curriculum, and knowing whenand how to apply the addition facts is just asimportant. First graders are expected to learnall the addition facts up to the sum of 18. Theyshould be able to add three numbers together (2+ 3 + 5 = 10), add a two-digit number to a two-digit number where no regrouping or carryingis required (36 + 12 = 48), and determine a miss-ing addend (the numbers that are added togeth-er in an addition problem). They also should beable to write a number sentence horizontallyand vertically.

Equal Sign

Explain that the equal sign (=) means that theamount on one side of the sign must be thesame as the amount on the other side.Demonstrate this concept by drawing the equalsign on an index card and having your child puthis hands on either side of the card. Put anythree objects in one of his hands, and ask him tomake the number of objects in both hands or onboth sides of the equal sign the same by addingmore objects. He should select three objects withhis empty hand. Increase the degree of difficultyby putting an unequal number of objects in hishands and having him select enough objectswith one hand so that both sides are equal.

Sets

Make two sets with a different number ofobjects in each set. Read the picture made bythe objects, and write an addition problem thatmatches it in horizontal form. For example,make a set with five objects and a set of twoobjects, read it as 5 + 2 = 7, emphasizing theplus sign (+) and the equal sign (=), and explainthat the plus sign means added to. Arrange thesets of objects so that one is above the other, andwrite the same number sentence in verticalform. Point out that the numbers are writtenone on top of the other, the addition sign is to theleft of the bottom number, and the answer doesnot change. The equal sign is not written as it is

C H A P T E R 3

Addition


in the horizontal form (=), but instead, the equalsign is the line below the bottom number.

Zero Property of Addition

Using objects found in your home to make sets,demonstrate that zero plus any number willequal that number. Use word problems andhave your child make the sets and join them.Example: Stephanie has three toys in one boxand no toys in another box. How many toys doesshe have in all? Have your child make a set withthree objects in it and a set with no objects.Have him count how many there are altogether.Lead him to discover that zero plus any numberis equal to the number other than zero.

One Plus Rule

State word problems involving two sets, whereone set always contains one object, and allowyour child to discover that one plus any numberis equal to the next higher number when count-ing by ones. Have your child make sets thatmatch the numbers in a word problem andarrive at the answer by counting how manyobjects there are in all. Using a number line (ahorizontal line with the numbers in countingorder) also allows your child to explore thissame concept. Describe a word problem, andhave your child point to the number on the num-ber line as it appears in the story. The wordproblem should include a set with one object,and your child should be adding one to the firstnumber by pointing to the following number onthe line. Example: Neil has three dinosaurs(your child should point to the number 3 on thenumber line), and his father gives him one more(the child should move his finger to the nexthigher number on the line, which is the 4). Howmany dinosaurs does Neil have now? Yourchilds finger should be pointing to the answerbecause it moved to the next higher numberwhen a 1 was added.

Communitive Property of Addition

The communitive property of addition (orderrule) states that the order in which the addendsappear in an addition problem can be reversedwithout affecting the sum. Your child needs tounderstand this rule. In order to comprehendthis concept, have him join two sets of objectsand record the number sentence represented bythe groups. Have him switch the order of the setsand record the new number sentence. For exam-ple, your child can make a set of four toys and aset of three toys and record the number sentence4 + 3 = 7. Then he reverses the groups and has aset of three toys first and then a set of four toysand records the number sentence as 3 + 4 = 7.Since no toys were added or taken away, theanswer (sum) will stay the same. After practice,have your child discover that the first addendplus the second addend will equal the secondaddend plus the first addend: 3 + 4 = 4 + 3.

Grouping Addition Facts

Its easier to break addition facts into smallgroups, which can be referred to as the threeplus facts or the four plus facts:

2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+

2+2 3+3 4+4 5+5 6+6 7+7 8+8 9+9

2+3 3+4 4+5 5+6 6+7 7+8 8+9

2+4 3+5 4+6 5+7 6+8 7+9

2+5 3+6 4+7 5+8 6+9

2+6 3+7 4+8 5+9

2+7 3+8 4+9

2+8 3+9

2+9

Doubles Addition Facts

The doubles (any number plus itself) is thefirst row of the preceding chart. Children usual-ly grasp these eight addition facts quickly.


24

Adding little clues like I ate it and ate it andgot sickteen may help to learn that 8 + 8 = 16.

Doubles Plus One Facts

Embellish the knowledge that your child hasacquired by teaching the doubles plus one. Useconcrete objects to represent the doubles fact;for example, a set of three objects and anotherset of three objects would show 3 + 3. A doublesplus one fact would be 3 + 4 or [3 + (3 + 1)]. Yourchild should add one object to one of the sets ofthree in order to represent the new problem.The sum would be one more than the originalproblems sum because only one object wasadded. Your child should verbally explain theconcept by stating that since 3 + 3 = 6, 3 + 4must equal 7 because 4 is one more than 3 and7 is one more than 6. Understanding this con-cept enables your child to learn the second rowof the preceding chart, leaving only 21 facts tolearn.

The Nine Plus Rule

Teaching the nine plus rule through the use ofobjects and making sets of 10 will allow yourchild to learn the nine plus number facts with-out memorizing them. In order to teach 9 + 5,make a set of 9 objects and another set of 5objects. Take one object from the set of 5 leav-ing 4, and move it to the set of 9 to make it aset of 10. Now you have 1 ten and 4 ones, or 14.Try another problem: 9 + 7. Make a set of 9objects and a set of 7 objects. Take one objectfrom the set of 7, leaving 6, and move it to theset of 9 to make it a set of 10. Now you have 1ten and 6 ones, or 16. Lead to the generaliza-tion that the sum of a nine plus addition factwill have a one in the tens place, and the num-ber in the ones place will be one less than theaddend other than the nine. After your childunderstands this concept, he will only need tomemorize 15 facts!

Counting On

In order to add two sets of objects using thecounting on method, your child needs to selectthe higher number in a given addition numbersentence and count from that number as manytimes as the other addend states. For example, inthe number sentence 5 + 2, your child shouldselect the higher number (obviously, 5), state it(5), and count up two numbers (6, 7). This strat-egy is very useful learning the remaining plustwo facts. If your child is using this strategy toadd greater numbers, he can state the highernumber in the addition sentence and then drawdots on a piece of paper to match the lesseraddend. He should count as he points to each ofthe dots. For example, in the number sentence 3+ 5, your child should state 5 and make 3 dots.He should count 5, 6, 7, 8. If your child can graspthe aforementioned addition strategies, he onlyneeds to memorize 10 addition facts. These 10facts are underlined in the preceding chart thatshows how to group the addition facts. Strategiesshould be learned using concrete objects linkingmeaning to the number facts. You can help yourchild memorize the remaining facts by attachingclues to them; for example, singing four plus se-ven is e-le-ven helps to remember 4 + 7 = 11.

Adding Three Numbers

Using three sets of objects, write the numbersrepresented by these sets, and choose two of thenumbers to add together first. Draw lines thatmeet from these two numbers, and write theirsum next to them. Now add that sum to the thirdaddend. Count the objects, and check to see ifthat number matches the sum that was written.

Adding a Two-Digit Numberto a Two-Digit Number

Even though these problems do not requireregrouping or carrying in first grade, empha-

A D D I T I O N

25

size to your child that the ones column willalways be the starting point in any additionproblem. Then he is to add the numbers in thetens column. This approach to addition willinstill good math habits.

Have your child use bundles of straws andsingle straws to show the addition problem.When your child adds, say, 27 + 52, he shouldshow the number 27 with 2 bundles of ten and 7ones, and he should show the number 52 with 5bundles of ten and 2 ones. When he adds themor joins them together, he will have 7 bundles often and 9 ones, or 79. This should match thesum he has in written form.

What You and Your Child Can DoIn order for your child to connect meaning to theaddition facts and explore the process of addition,you should relate the process to objects in yourchilds environment. Children have already beenexposed to addition informally in various situa-tions. Children are natural collectors; whether itis dolls, figurines, stamps, coins, or butterflies,when they engage in collecting things, they arereally joining sets or adding when they realizehow many they have in total. Children need toconnect this knowledge with the mathematicsymbols. Here are some ways to help your childlearn about the concept of addition:

Using brief stories or word problems, haveyour child use concrete objects and make sets tomatch the numbers in your story. For example,your story may state that Nancy has four bal-loons and Larry has three, how many do theyhave in all? Your child may use any objects torepresent the balloons and make a set of fourand a set of three using those objects. Then heshould count the total number of objects toarrive at the answer. Practice telling many dif-ferent story problems that involve joining twosets together.

Missing Addend. Show a particular number ofpennies, stones, or other small items. Start witha low number of items, and add more as your

child gains confidence with this activity. Haveyour child hide his eyes while you divide theitems into two sets, one in each hand. Open onehand and display the number of items in it.Have your child write the number sentenceusing a blank where the missing addend wouldappear and determine how many items are inyour closed hand.

Your child must decide how many moreitemsin addition to the ones he sees in theopen handare needed to equal the total hesaw before he closed his eyes. Have him verifyhis answer by checking the hidden items andthen filling in the blank in the number sentence.Example: Put six pennies on the table. Haveyour child look at the six pennies and then hidehis eyes. Pick up two pennies in one hand andfour in the other. Have your child open his eyes,and then show him the four pennies in your oneopened hand. Keep your other hand closed. Heshould write the number sentence as 4 + __ = 6to match the information he knows. Now heneeds to determine how many pennies must bein the closed hand to equal a total of six pennies.He can use the counting on method to discoverthe answer and then write it in the blank as 4 +2 = 6.

High or Low. Play High or Low with a reg-ular deck of playing cards minus the tens andface cards. Deal each player two cards that areplaced face down and one card that is face up;the dealer also takes three cards but doesntshow them. Take turns being the dealer. Theplayers predict if the sum of their cards will behigher or lower than the dealers three cards.Turn over the cards and add all three cardstogether. If the prediction is correct, the playergets a point. If the prediction is incorrect, thedealer gets the point. If it is a tie, the dealer getsthe point. The one with the most points is thewinner.

War with Dice. This game is played with twoplayers, using two dice and a paper plate foreach player and markers such as beans,Cheerios, or minimarshmallows. When the word


26

war is said, both players roll their dice on theirplates and add up the numbers on the dice.Whoever has the higher sum gets a marker.Continue playing until one player reaches 10markers. You may use regular dice, but polyhe-dra (many sided) dice are available at educationstores. There are dice with the numbers fromone to nine, and these are the ideal dice to usewhen practicing all the addition facts.

Come My Way. Create a playing board bydrawing a center starting space and 10 blankspaces on both sides of the center. Have oneplayer sit with the 10 blank spaces facingtoward him and the opponent sit with the other10 blank spaces facing him. Place one marker onthe center space, and use addition flashcardsshowing addition facts that need to be practiced.Decide who goes first. The first player turnsover a flashcard, answers the problem, andmoves the marker toward him the number ofspaces that are in the ones column of the sum.Take turns turning over a flashcard, answeringthe problem, and moving the same markertoward the player who is answering the additionproblem. The marker will move back and forthalong the board. The first one to move the mark-er off his side of the board is declared the win-ner of Come My Way!

Guess My Number. Three players and a reg-ular deck of playing cards (minus the face cardsand the tens) are needed to play this game. Ofthe three people, one person is designated thedealer and the sum caller, and this person is notdealt any cards. The dealer gives one card toeach player. Without looking, the two playersplace their card to their foreheads so that theycannot see their own card but are able to seetheir opponents card. The dealer looks at thecards of both players and calls out the sum ofthe two numbers on the cards. The first playerto guess his own number gets the point. In orderto guess it, the player must determine what themissing addend is. He must think: What (mynumber) plus my opponents number equals thesum that the dealer called out?

Make an Addition Book. Read Keith BakersQuack and Count book that shows all the differ-ent combinations of numbers that have the sumof seven. This cute, short book uses ducks toillustrate different addition number sentences.Help your child make your own Quack andCount book illustrating all the different waysto make the sum of another number.

What Tests May AskOne- and two-digit addition is a math computa-tion skill and is included in that portion of thetest. Your child will be asked simply to solve theproblems in a certain amount of time and prob-ably to solve some word problems involving one-and two-digit numerals. Children may beexpected to choose correct number sentences tomatch pictures, choose correct math signs, fill inthe missing addends, and correctly solve one-,two-, and three-digit addition problems (bothvertically and horizontally) with no regrouping.

Practice Skill: AdditionDirections: Listen carefully to thefollowing questions, and darken inthe bubble beside the correctanswer.

A D D I T I O N

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Example:What number sentencematches this picture?A 2 + 1 = 3 B 3 + 5 = 8C 2 + 5 = 7 D 3 + 3 = 6

Answer:B 3 + 5 = 8

Directions: Look at these mathproblems and select the correctanswers.

5 5 + 2 = __A 5B 52C 3D 7

Example:

3 + 3 = __A 3B 6C 5D 0

Answer:

B 6

4 Fill in the blank. 9 __ 6 = 15A +B

C =D /


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1 Which sign means plus?A =B +C

D /

2 What number sentence match-es this picture? A 3 + 3 = 6B 6 3 = 3C 6 + 3 = 9D 6 + 4 = 10

3 What number sentence match-es this picture?A 8 + 7 = 15B 9 7 = 2C 9 + 6 = 15D 9 + 7 = 16

12 3+ 9___A 12B 13C 10D 6

11 6+ 6___A 60B 0C 12D 14

10 8+ 4___A 13B 3C 12D 15

9 5+ 4___A 6B 1C 9D 8

8 7 + 9 = __A 79B 2C 16D 18

7 0 + 7 = __A 70B 7C 0D 8

6 6 + 5 = __A 9B 1C 11D 65

A D D I T I O N

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19 34

+ 1___A 7B 6C 5D 8

18 21+ 35____A 12B 55C 58D 56

17 44+ 23____A 21B 67C 76D 27

16 0 + 4 + 6 =__A 8B 9C 10D 11

15 5 + 1 + 3 = __A 12B 9C 7D 10

14 Fill in the missing addend:2 + __ = 5.A 2B 4C 3D 7

13 Fill in the missing addend:7 + __ = 12.A 5B 19C 9D 4


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25 12 + 6 = __A 6B 17C 24D 18

24 34+ 5____A 39B 30C 31D 89

23 57+ 2____A 79B 55C 59D 50

22 3 + 1 + 4 = __A 5B 6C 7D 8

21 4 + 2 + 5 = __A 10B 11C 12D 9

20 52

+ 7___A 14B 12C 13D 10

A D D I T I O N

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Subtraction is the inverse of addition. It is tak-ing away some objects from a set and discov-ering how many objects remain. Subtraction isalso used to compare two sets to determine thedifference in the number of objects between thesets. In order to do this, the number of objects inthe smaller set (the number where the sets areequal) is subtracted from the number of objectsin the larger set. The objects remaining will bethe difference between the two sets.

What First Graders Should KnowSubtraction is harder for children to masterthan addition. First graders are expected to beable to translate into mathematic symbols a pic-ture showing a subtraction story. They arelearning how to relate their knowledge aboutaddition to subtraction through a conceptreferred to as the family of facts.

This concept relates four number sentences,two subtraction and two addition. An example ofthe family of facts is as follows: Since 4 + 3 = 7and 3 + 4 = 7, then 7 3 = 4 and 7 4 = 3.Children are expected to use strategies for sub-traction to answer problems.

In addition to the family-of-facts strategy,they learn how to draw circles to represent thenumbers in the number sentence, and they crossoff the number of circles that are to be subtract-ed in the problem. The pattern of minus 0 andminus 1 and the count back strategies are alsoused to help children learn to subtract. First

graders are also expected to be able to subtracta one-digit number or a two-digit number from atwo-digit number when no regrouping, or bor-rowing, is required. Writing a subtraction prob-lem in vertical and horizontal form is also a firstgrade skill.

Subtracting from a Two-Digit Number

Showing your child objects that represent a two-digit number, ask her to subtract a specific num-ber of objects. Make sure that no regrouping, orborrowing, is required; borrowing is intro-duced in second grade. Have your child recordthe number sentence in vertical form and sub-tract in the ones column first and then proceedto the tens column. Remind her that this is thesame procedure that is used in addition, but thistime you subtract the numbers in both columns.Emphasize that the bottom number is subtract-ed from the top number, and if the top is notgreater, the bottom number must be subtractedfrom the whole number. For example, in theproblem

14 6____

you cant say 4 minus 6, you must say 14minus 6.

A very common mistake is made soon after achild learns to subtract a two-digit number from

C H A P T E R 4

Subtraction


a two-digit number. Incorrect answers such asthe following are made often: 14 5 = 11. Thechild has attempted to subtract 5 from 4 in theones column and has arrived at the incorrectanswer of 1, when in reality, 5 from 4 requiresthe child to use the whole number, 14. Remindyour child to check to make sure that the topnumber is greater than the bottom number sothat she can accurately subtract. Use concreteobjects to demonstrate that she cant take 5ones away from the 4 ones. She must use theentire top number. Explain that in the process ofaddition, the addends may be changed aroundwithout affecting the answer; however, in sub-traction, the greater number must be first.

What You and Your Child Can DoThe Snack Muncher. Begin the concept of sub-traction using concrete objects. Tell stories thatwill translate into a subtraction problem.Eating snacks creates a wonderful opportunityto relate real objects to subtraction. If your childhas five pieces of candy and eats three, makethe appropriate subtraction number sentenceand write it for your child, emphasizing theminus sign (). Explain that it means minusor take away. After repeated practice, allowyour child to write the subtraction number sen-tence independently.

Read My Picture. Draw pictures of subtractionstories. You may want to draw four ducks in thewater and two waddling away. Relate this to thenumber sentence 6 (total number of ducks) 2(2 going away) = (equals) 4 (ducks left in thewater).

Minus Zero. Using concrete objects, demon-strate that taking zero items away from any setdoes not change the original set.

Minus One. Explain that whenever one is takenaway from any given number, the answer simplywill be one less than that original number. Useconcrete objects to demonstrate this concept,

and allow your child to verify her answer bycounting the objects left in the set after oneobject has been removed. Writing the numbersentence after she has been given a chance tovisualize it is helpful in relating the concretestage (manipulating the objects) to the abstractstage (using the mathematical symbols).

Count Back. Starting with about ten objects,arrange them in a horizontal line. Have yourchild count the number of objects aloud. Coverthe last one with a piece of paper, and have yourchild discover how many are left. Cover anotherobject, and have your child count back anothernumber every time another object is covered.You may practice again using fewer or moreobjects, depending on how difficult this activityis for your child. If she reaches a point wherebyshe isnt able to count backwards from memory,allow her to count the objects and start again.Practice using the number line (a piece of paperwith the numbers 1 to 20 written on it) is also avaluable tool when using the count backmethod. Given a subtraction number sentence,find the first number in the number sentence onthe number line, and count backwards the num-ber of spaces equaling the number being sub-tracted. The answer will be the number onwhich you land after counting backwards.

Crossing Out. Use word problems and allowyour child to draw circles to represent theobjects in the story. After you have told her howmany objects are leaving or being taken away,have her cross out that many objects andcount the remaining objects to arrive at theanswer. Record her answer in a complete num-ber sentence.

Family of Facts. Have your child draw a housewith two windows and two doors. On the win-dows show two related addition number sen-tences (addition sentences with the numbers indifferent order, for example, 6 + 7 = 13 and 7 + 6= 13), and on the doors show the two subtractionnumber sentences (13 7 = 6 and 13 6 = 7).


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Lead your child to relate subtraction and addi-tion when presented with a subtraction problemsuch as 13 6, by asking herself the question:What number plus the 6 equals 13?

Candy Blocks. Using two different coloredblocks or pieces of candy also can help your childto see how addition and subtraction are related.Arrange six red blocks and three blue blockstogether. Your child should be able to describethe addition number sentences related to thispicture as 6 + 3 = 9 and 3 + 6 = 9. Ask her tostate the subtraction number sentence of thispicture if, for instance, the six red blocks wereremoved. She should be able to state 9 (alto-gether) 6 = 3. Now ask her to describe the sub-traction number sentence when the three blueblocks are separated from the set.

She should state 9 (altogether) 3 = 6.Repeated practice with objects will help yourchild grasp the family of facts concept.

Whats the Difference? Using a deck of regularplaying cards, remove the tens and face cards,and deal four cards to each player. Each playerlooks at her cards and arranges them so that thetwo highest cards are on top and the two lowestcards are underneath them, making two two-digit numbers. Each player subtracts the num-ber she has made with the bottom cards from thenumber she has made with the top cards.Whoever has the highest difference is the win-ner. For example, if a 2, 4, 7, and 6 were dealt,they should be arranged in the following order:

76 42____

The difference is 34You may increase the level of difficulty of this

game and really challenge your child by chang-ing the rules. For example, you may arrange thecards in the order that you think will allow youto have the greatest difference. The same cards

that were dealt above could be arranged inmany ways:

74 76 67 7662 24 24 42____ ____ ____ ____

You may use the same game to find the lowestdifference. Games such as this are as entertain-ing as they are challenging!

Cover Up. Using two dice, plus items to mark aspace and two pieces of paper with the numer-als 1 through 12 on them, give each player oneof the papers. The object of the game is to havethe most numbers covered. Take turns rollingthe dice. The player who rolls the dice mayeither add the numbers on the dice or subtractthem and then cover the sum or difference. Forexample, if a 3 and a 4 are rolled, the player cancover either a 1 or a 7. If both numbers are cov-ered, she is not able to cover any number, andpossession of the dice goes to her opponent.When the playing time is over, the player whohas the lowest sum when all the uncoverednumbers are added together is the winner.

Subtraction Race. Make a board game with apath of squares to get from a starting point to afinishing point. Using two dodecahedron dice(twelve-sided dice available at educationalstores for a minimal cost), take turns rolling thedice and subtracting the smaller number fromthe higher number. The player may move asmany spaces as the difference between the num-bers she rolled. The first player to the finishpoint is the winner. Six-sided dice may be sub-stituted for the dodecahedron dice when thegame is intended for children who are justlearning to subtract.

Computer Fun. Computer games such asFranklin Learns Math and Number Munchersprovide motivation while practicing subtractionfacts. They are appropriately geared for firstgrade children.

S U B T R A C T I O N

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What Tests May AskStandardized tests in first grade will assess achilds ability to read a subtraction picture andmatch a number sentence with it and subtractvertical and horizontal subtraction problems.These tests also will assess a childs ability tosubtract a one-digit number or a two-digit num-ber from a two-digit number when no regroup-ing, or borrowing, is required.

Practice Skill: Subtraction

Directions: Listen carefully toeach question, and darken in thebubble beside the correct answer.


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Example:Which number sentencematches the picture?

A 5 2 = 3 B 7 2 = 5C 2 7 = 5 D 6 2 = 4

Answer:B 7 2 = 5

1 Which number sentencematches the picture above? A 1 + 4 = 5B 5 1 = 4C 4 1 = 3D 4 3 = 1

2 How many more bats thanballs are there? Find the num-ber sentence that matches thepicture.A 6 + 2 = 8B 5 + 2 = 7C 6 2 = 4D 2 + 2 = 4

9 18 9____A 11B 8C 9D 10

8 24 12____A 36B 12C 16D 11

7 26 10 = __A 36B 9C 16D 61

6 7 4 = __A 2B 3C 4D 1

5 12 __ 5 = 7A +B

C =D /

S U B T R A C T I O N

37

3 How many fewer books arethere than pencils? Find thenumber sentence that matchesthe picture.A 8 3 = 5B 8 + 3 = 11C 7 3 = 4D 8 3 = 6

4 What number sentence doesthe picture show?A 6 + 2 = 8B 8 2 = 6D 8 + 2 = 10D 6 2 = 4


15 16 8 = __A 12B 24C 9D 8

14 10 6 = __A 3B 16C 4D 5

13 14 7 = __A 6B 7C 8D 21

12 49 26_____A 63B 615C 23D 25

11 15 8____A 13B 7C 8D 6

10 12 7____A 19B 15C 5D 8


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Telling Time

Since the use of digital clocks and digitalwatches has become commonplace, childrenhave little opportunity to practice telling timeon an analog clock (a clock with a circular faceand hands). Many homes dont contain anyclocks with hour and minute hands, whichmeans that children arent familiar with thismethod of telling time.

What First Graders Should KnowChildren in first grade are taught how to telltime to the hour and to the half hour. Givenrepeated practice with telling time to the houron an analog clock, and distinguishing the dif-ference between the hour hand and the minutehand, most children this age are able to masterthis concept. Still, even late first graders mayhave some lingering problems with telling time,even if the clocks have very large numbers. Mostchildren this age will be confused with clocksfeaturing Roman numerals.

However, many children have problems tellingtime to the half hour. The most common mistakechildren make is naming the incorrect hour. Youshould be careful to name the hour that the hourhand has passed. Often, children will state thehour that the hour hand is approaching; forexample, when the clock is set at 4:30, a childoften states the incorrect time as 5:30.

A childs first experience with the concept oftime usually involves bedtime, a specific time adaily activity occurs, or a particular time a

favorite TV program starts. Associating the timeshown on the clock with these real-life situa-tions will help your child become familiar withtelling time. It also will help motivate your childto learn to tell time and make the concept oftime become more meaningful. Heres how tohelp:

1. Explain that the minute hand is longerthan the hour hand and that it is used tocalculate minutes. Your child should under-stand that the numbers written on the faceof the clock represent hours and that thehour hand points to the specific hour. Somechildren may confuse the hour and theminute hands.

2. Explain that the markings between thenumbers stand for minutes and that thereare five minutes from one number to thenext.

3. Show how the hands work simultaneously:The hour hand moves from one number tothe next while the minute hand movesfrom the 12 completely around the clockuntil it reaches 12 again.

4. Practice telling time on an analog clockthat is set at different times to the hour.

5. Practice counting by fives as you point toeach number on the clock emphasizing theminutes. Provide lots of practice withtelling time to the half hour.

6. Provide a mixed practice: telling time tothe hour and half hour.

C H A P T E R 5

Time: Clocksand Calendars


7. Practice writing the time in two differentways: in symbol form (12:00 or 12:30) andin written form (12 oclock and 12 thirty, orthirty minutes past 12).

8. Explain that the numbers before the colonon a digital clock represent the hours andthat the numbers after the colon representthe number of minutes it is past the hour.

What You and Your Child Can Do

The Grouchy Ladybug. This book by Eric Carlereinforces the concept of telling time with ananalog clock. Children love it!

Make a Clock. Help your child make a clockusing a bendable brass fastener, two pieces ofconstruction paper for the hour and minutehands, and a paper plate.

1. Trace the hour and minute hands on theconstruction paper.

2. Let your child cut them out.

3. Punch a center hole in the paper plate anda hole at the end of each hand.

4. Let your child print the numbers on thepaper plate clock face.

5. Push the brass fastener through the holesin the ends of the clock hands and throughthe center of the plate; bend the fastenerbehind the plate to fasten.

6. Have your child rotate the hands to makedifferent hour and half-hour times on theclock.

Make a Picture. Let your child pick his favoritetime of the day to the half hour. Have him drawa clock depicting that time. Then, beneath theclock picture, have him draw a picture of whathe is doing at that time.

Just a Minute Ask your child to make upsome activities that take less than a minute to

complete. This helps reinforce how long aminute really is.

TV Times. Have your child come up with a fewfavorite TV programs that are a half hour long.Let him check the clock before and after the pro-gram to see the clock display the hour and half-hour times.

What Tests May AskStandardized tests for this age assess the abili-ty to tell time in two ways. First, they will pre-sent pictures of clocks and ask children tochoose the correct time from a choice of answers.Second, the tests include questions on elapsedtime. The test will give a time when an activitybegins and whe

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Math Grade 1