quiz, quiz, frade - indiana university...
TRANSCRIPT
Quiz,Quiz,fradeStudents quiz a partner, get quizzed
by a partner, then trade cards to
repeat the process with a new
partner.
1 Stand up, card up, pair up.
2 PartnerA quizzes.
3 Partner B answers
4 Partner A coaches and/or praises.
5 Switch roles.
6 Partners trade cards.
7 Repeat Steps 1-6 a number of times.
I
I
Laurie & Spencer Kagan: Structures for SuccessKagan Publishing . 1(800) 933-.2667 .www.KaganOnline.com
28 - -
IDE A !S
for my class!
I.
· Worksheetsthat label items· Sciencequestions· Idioms
· Fact/opinionor True/False· MathFacts
· Vocabulary· Practicespelling words· Parts of speech· HistoryFacts· Mathoperations· Typesof simple machines· Beginningsounds..
. . . . . . . . . . . . . . . . . . . . . .
oTeambuildingoClassbuilding
oMasteryoThinking SkillsoCommunication Skills
o Information Sharing
Review Rules
1. Walking only2. Raise hand if need a partner
3. Visit each person only once* AskseveralstudentshowmanyQQTtheythinkthey'll do during _ minutes.
$ Laurie & Spencer Kagan: Structures for Success~agan Publishing. 1(800) 933-2667 . www.KaganOnline.com
29
Math VocabularyWord ListsK-6
KindergartenAfternoonAllBetweenCalendarClock
DayEqualEveningInsideLeastLess
ManyMonthMore
MorningMostNumberOutsidePatternProblemSet
Shape (Cir,Sq,Rec,Tri)SizeSome
TodayTomorrowWeekYear
YesterdayZero
First GradeAdditionBalanceCentimeterCoinCubeDime
Dimensional (2-D, 3-D)Direction
Fact FamilyFraction
GraphHalf-hourHourInch
LengthMeasure
MoneyNickelNon-standard UnitNumber LineNumber SentenceOnes
PennyPlace ValuePlaneSolutionStandardSubtractionTensWhole Number
I
Second GradeAM/PM
Bar GraphCongruentDifferenceDollar
Elapsed TimeFaceFewestFootGreatestHalf-DollarHundredsMeterMinuteNearestNumeralOdd/Even
QuarterQuarter HourRectangular PrismRegroupSecond (Time)SumTable
Tally ChartTemperature (OC,OF)ThermometerVertex/Vertices
Weight (Cup,Pint)Yard
Third GradeAssociative PropertyCapacity(Qt,Gal,Liter)Commutative PropertyCone
CylinderDecimalDenominator
Equivalent fractionsExpanded formFactorsGramHalf. InchHundredths
Kilograms vs. PoundsLine
Line segmentMetric SystemNumeratorPerimeterPoint
PolygonProduct
PyramidQuadrilateralRight AngleSphereSymmetryTenthsThousandsVolume
Fourth Grade Fifth Grade Sixth GradeAccuracy Axis AcreAcute Angles Composite Adjacent AnglesAlgorithms Coordinate Plots/Maps CircumferenceArea Data Set Complementary AngleCommon Denomina'Diameter ConjectureComputation Equilateral Coordinate PlaneDistributive Propert~Function CumulativeDividend Greatest Common Factor Distribution
Equation Input/Output ExpressionsFonnula Isosceles Exterior AnglesImproper Fraction Least Common Multiple Frequency TableInverse Linear Equations HistogramsLine Graph Mean Interest (Money)Number System Median Interior AnglesOblique Mixed Numbers InteryalObtuse Angle Mode Negative IntegerOrder of Operation Multiple NotationsParallel Lines Ordered pairs PiParallelogram Percent Positive IntegerPerpendicular Line Prime ProportionalPrism Probability QuadrantQuotient Protractor RatioRay Radius RelativeRemainder Range RepresentationRepeated Addition Rational Number SignificantRhombus Reflectional Symmetry Stem/Leaf PlotStraight Angle Rotational Symmetry Supplementary AngleTrapezoids Scalene TranslationVariables SubstitUtion ValidityWidth Surface Area Vertical Angles
,'echnical VocabularyWord ListsK-6
KindergartenBeginningBrainsto11Tl
CircleColorConnect
CopyCountDescribeDraw a PictureEndFindFollowListListenMakeMatchMiddleNameOrderPredictPrintShareShowSolveSort
SpellTell/RetellTraCtUnderlmeWrite
First GradeAdd
AlphabetizeBlend
CapitalizeCategorizeChangeClassifyCollect
CompareContrastCreateDecodeDemonstrateDiscussEstimate
ExplainFlag ItGraphHighlightIllustrateInferLabelMeasureObservePlaceReadReread
SegmentStudySubtract
Second GradeAssemble
ClarifyComprehendComputeConsequenceConstructDecideDefine
DesignDetermineEvidenceFalse.
IdentifyIncludeLocateMonitor
OrganizePlan
QuestionReasonRecall
RecognizeRecordRelate
RespondRestate
SequenceShadeStateTrue.
Third GradeAbbreviate
ArrangeAssessCalculateConcludeConsiderConstructConvertDivideExtend
InterpretOpaquePlot
PromptRankReflect
RephraseReportRepresentReviewRoundScanSelect
SimplifySketchSkim
SpecifySuggestTranslucent
Transparent
Fourth GradeAccuracyAssumeAttributeCharacterizeCite
CompleteConfirm
ConveyDebate
DevelopDisplayEvaluate
ExploreFormulate
ImplyIndicateInterfereIntroduce
JudgeModelPersuadeProve
QuoteReciteReduceRelateResearch
SupportSurveyTranslate
Fifth GradeAbstractAdmirable
AdvantageApplyCompileConcreteContradictContribute
CooperativeDefend
DepictDisadvantageDiscard
DistinguishExamineExhibit
FalsifyGeneralize
HypothesizeIncorporateJustifyManipulativeOutline
PlagiarizePreventProduceRecommend
SpeculateSymbolizeVoice
Sixth GradeAddress
AdjustAnalyzeAnticipateConsult
CritiqueDetectDifferentiateDisassemble
EmphasizeEvaluate
ExpressExtract
GroupInfluence
InquireInspectInterpersonalIntrapersonalInvestigateModifyNote
ParaphrasePortrayPresumeRationalizeReassembleSubstituteTheorizeUnderstand
Hit The Target!The target number is
Make today's target in each of the following ways.
Activity adapted from Number Sense by McIntosh, Reys, Reys, Hope and published byDale SeymourPublications.
1. Add two numbers
2. Find the difference of two numbers
3. Multiply two numbers
4. Divide one number by another
5. Add three numbers
6. Multiply three numbers
7. Multiply and subtract
9. Do it a different way
MULTI PL. ~A VI 0 N TAB LE'S
I ,
1 2 3 4 S 6IX 1= 1 2 X 1=2 3 X 1=3 4 X 1=4 5 X 1=5 6 X 1-=61 X 2=2 2 X 2=4 3 X ,2= 6 4 X 2=8 5 X 2= 10 6X 2= 121 X 3=3 2X 3=6 3 X 3=9 '4 X 3"" 12 5 X 3 = 15 6X 3= 11 X 4=4 2 X 4-8 ' 3 X 4=12 4 X 4=16 5 X 4=20 6 X 4 = 2.41 X 5=5 2X 5=10 3X 5",,15 .4 X 5 =20 5'X 5=25 6X 5=30 '
1 X 6=6 2X 6=12 3X 6=18 4 X 6=24 5 X 6=30 6X 6=361 X 7=7 2X 7=1.4 3 X 7=21 4 X 7 = 28 5 X 7= 35 6 X 7=42IX 8=8 2X 8= 16 3 X 8 = 24 4 X 8 =32 5X 8-40 6 X 8=481 X 9=9 2X 9-18 3 X 9 = 27 4 X 9=36 5X 9=45 6 X 9=54I X 10= 10 2 X 10 = 20 3X10=30 4 X 1E)"" 40 5 X 10... 50 6 X 10 = 601 X 11"" 11 2 X 11 = 22 3X1t=33 4 X 11 = 44 5 X 11 = 55 6 X 11= 661 X 12= 12 2 X 12 :::::24 3X12=36 4X12=48 5 X 12 = 60 6XI2=72
7 8 9 10 11 127X 1=7 8 X 1=8 9X 1=9 10 X 1= 10 11 X 1=11 12 X 1= 127X 2= 14 8 X 2 = 16 9 X 2 = 18 10 X 2 =20 11 X 2 = 22 12 X 2=2.47X 3=21 8 X 3 = 24 9X 3= 27 10 X 3 =30 11 X 3 =3,3 12 X 3 ==367X 4 =28 8 X 4 = 32 9X 4=36 10 X 4 =40 11 X 4 =44 12 X 4 =487 X 5 = 35 8 X 5 = 40 9 X 5 = 45 10 X 5 =50 11 X 5=55 12 X 5=607 X 6=42 8 X 6 = 48 9 X 6 = 54 10 X 6=60 11 X 6=66 12 X '6=727 X 7 = 49 8 X 7=:=56 9 X 7 = 63 10 X 7=70 11 X 7=77 12 X 7-847 X 8 =56 8 X 8 =64 '9 X 8 =72 10 X 8 =80 11 X 8 =88 12 X 8 =967 X 9= 63 8 X 9=72 9 X 9=81 10 X 9=90 11 X 9=99 12 X 9= 1087 X 10 = 70 8 X 10=80 9 X 10 = 90 lOX ! 0 = 100 11 X 10= 110 12 X 10"" 120
- 7 XII = 77 8Xll=88' 9 XII = 99 10 X 11 = 110 11 X 11 = 121 12 X 11 ==1327X12=84 8 X 12=96 9 x 12= 108 lOX 12 = 120 11 X 12=132 12 X 12= 144
RULES OF DIVISIBiliTY
A natural number is divisibleby:...
.2If and only If the units digit of its decimal numeraIs O. 2. 4. 6 or 8. then it Is <Ineven number,
3 if and only If the sum of the digits of Its decimalnumeral is a multiple of 3,
4 If and only if the last two digits of its decimalnumeral are divisible by 4.
5 Ii and only If the units digit of Its decimalnumeral is 0 or 5.
6 If and only if the decimal numeral is divisibleby both 2 and 3.
9 if and only if the sum at the digits of its decimalnumeral is a multiple of 9.
10 if and only if the 'Iast digit of Its decimalnumeral Is :lero,
..I ..
.
~
..
o::I<IIen
",A_ ..~..
0":>..
-I:r:J:o t:t: :>..a.III..:> coe--I:rg-lOJ<IIII):::::Ia.IO
-I:r0s::..III::Ia.
::ct::>51-0a.01-
:>..
r.I
1. -1-.
P\I.) /
,jJr,C~\\
-tee e.:'\.-h ~. t~.J
U 6l -h-......
o()l f\
,~~Cern bl (\0
G-l1
3. *-..I
P 1'DCluQ.'1.'---¥t VII e.. ')
b'j
Inu l+lple..)
rnu \+ pLj
\Q+-ft e:..E
0- crc.I!..1
~eo..-k..c{~'-
'< ,"., '"
.01:"
2. -
c\l ,\~+tV""C-i"-{'
R- ~ Q'-LC'-'-j
rn c. r~ '-\--hc~ ;')
/' .::- "'<', _Ljr'.'":.n, ,_ T t \-
4." =f,<.. -,
f e 11-' G i \1 cl e. ~
L() jrJCt..-fs { e.J-t-
~-o
7-'U0h E...i~{dt vlde.
rD..+-~OJ
~(D-C-+l~ 'l .)
d eCl rnc,. (
V'n C c."C
l e)
VI :'~ ~'-ll
t,.
,
.~I '-- ," ,~ . '_:~:---
, ,
1-~~j\;:,~-.. " .
I. .
."..
.
,"".; ~-y")\"../ I (V'-'
/
Review of Place Value Name Date
Answer BoxUse with 1-3.
3,955 26,801 4,129
1. Use digits to writetwenty-six thousand, eight hundred one
2. Use digits (numbers) to writefour thousand, one hundred twenty-nine
3. Use digits to writethree thousand, nine hundred fifty-five
ExampleUse the number 4,321
a.Which digit is in the tens place?2
b. What is the value of the digit 3?300
c. How many thousands are there?4
4. Use the number 25,678.
a. Which digit is in theten thousands place?
b. What is the value of the digit 6?
c. How many thousands are there?
5. Use the number 35,267.
a. Which digit is in the tens place?
b. What is the value of the digit 2?
c. How many thousandsare there?
..
5'
Assessment Tips
EDM assessment is different than traditional assessment. It relies on teachersusing three types of assessment to get an accurate picture of how the students areprogressing. Ongoing, Product, and Periodic assessments:
Teachers should be monitoring these types of work throughout the teaching ofthe unit. All of these observations and collections of work should be taken into
conSideration when reporting stUdent progress to parents.
Teachers need to be sure they know to which level of mastery they are teachinga particUUtr skill. Refer to the "Learning Goals iu Perspective" page of the Unitovervie'l'\' for quick references.
The End if the Unit Assessment are not a "TEST", When a-teacher "tests" s/he
is usually checking for mastery. Because this program spirals and tcachesBeginning, Developing, and Secure skills in _ one Unit, questions will reflect allthree learning goals.
The Assessment is designed to be used with Individual Profile of Progress sheetsincluded in the Math Master[.book (and as seen in the Assessment Handbook),
If a "grade" is necessary on the End of Unit Assessment, cOJlsiderweighing thequestions as follows-3points for a Secure skill, 2 points for a developing sldU,
. The first page of the Uuit Assessment lessonwill teU which questions are B, D, S.
It is important for there to be consistency among the teachers when decidinghow to report student grades.
-l::::..
Alternative Assessment Tips
Major changes in the way mathematics is taught has led to the increased changes inhow teachers assess their students. When changing your assessment plan consideJ"these suggestions:
Keep your plan manageable Do not try everything at once. Try oneor two new ways to assess each grading period.
Trv to include some anecdotals frGm observations especially whenassessing problem solving, group work, and other areas that are hardto assess on a test.
Use some opep,-ended QUestionsto assess problem solving and toconvey the message that mathematics is more than solving short -oneanswer. one method problems.
- Trv to includeyour students in the IIssessmentprocess. Usestndentsamples of excellent work, allow students to explain concepts to peersand create rubrics, tlse student chosen portfolio work and writtenassessment of individual progress, etc.
Ask the followinfl auestions of your assessment plan:Row is tbe class doing as a whole?How are individunl students doing?How do I need to adjust instruction to meet students' needs?How can I communicate to students, parents, and others theprogress being made?
**Remembcr that End of Uuit Assessments, Checldng Progress and Math Boxes areto inform you about your teaching as much as they are to give you valuableinformation about an individual student. They may not be valid instruments fordetcnnining student grades in isolation fr()D1other sources of infonnatioD.
GETTING TO ONE GAME
Grade Level: Thirej'andhigher
Number of Players: 2
Object of the Game:
One player chooses a mystery number. The other player tries to guess the number inas few tries as possible. Players then trade roles. The player who guessedthemystery number in fewer tries wins the round.
How to Play:
1. Player A chooses a mystery number less than 100.
2. Player A then secretly enters the number in the calculator and divides itby itself. 'For Example,if the mystery'numberis 65,PlayerA enters65In 65 [=].
3. Player B guesses the' mystery number and, without clearing thecalculator, enters the guess and [=] in the calculator.
. If the calculator shows a number less than 1, then the guess was too low,
. If it shows a number greater than 1, then the guess was too large.
~ If it shows a 1, then Player B guessed the mystery number,
Player B enters 'guesses until the result is 1. Player A keeps track of th~,numberofguesses. Do not clear the calculator until the number has been guessed.
Example: Mystery number =65
Player B enters: Calculator shows:
55 [=]70 [=)67 [=)65 I;']
0.8461538 too small1 .076923 too big1.0307692 too big, but closer1 Just rlghtl '
It took Player B four tries to guess the mystery number.
., For a harder version of the game allow numbers up to 1000.
-W
- -
Game 1TriedTried
'TriedTriedTried
Game 2TriedTriedTriedTriedTried
Game 3TriedTriedTriedTriedTried
Gettingto ONEGoal- 1.0
gotgotgotgotgot
Game 4'
Tried
TriedTriedTriedTried
gotgotgotgotgot
Game 5TriedTriedTriedTriedTried
gotgotgotgotgot
Game 6TriedTriedTriedTriedTried
gotgotgotgotgot
gotgotgotgotgot
gotgot~ot~otgot
---......
Name # Date
Rewrite to Make It RiQht!l
Problem #
1. Here's what I did wrong...
2. This is what I should've done...
3. This is how I reworked the problem to find the correct solution...
Everyday Math Game Rubric
C()
J
4 ...., 2 1.)
Student actively Student usually Student Student is unwilling to
Partcipationparticipates during the pal1icipates during the sometimes/occasionall pal1icipate during thegame. game. y pm1icipates during game.
the game.Student consistently Student usually solves Student Student seldom solves
Solutions solves the problems the problems sometimes/occasionall the problemspresented. presented. y solves the problems presented.
presented.Student us.es a variety Student uses Student uses strategies Student is unable to se
Strategyof appropriate appropriate strategies to reach a solution. strategies, but guessesstrategies to reach a to reach a solution. solutions.solution.
Student consistently Student usually "plays Student Student seldom "plays
Fair Play"plays fair" with fair" with his/her sometimes/occasionall fair" with his/herhis/her classmates. classmates. y "plays fair" with classmates.
his/her classmates.
A POWERFULREFERENCETOOL
Ihave taught EverydaylHathernaLicsto students with
teaming and other disa~ilitiesfor the last five years. Often, thestudents I teach have cognitivedeficits that make it difficult forthem to memorize facts andfactors. As a result, the studentshave used references, such asfact tables, to compensate fal'their deficits. I, as the teacher,have attempted to modity thecurriculum to help the studentsmeet with success and I havefound that the fact tables
provide limited support for thestudenl~. Yet, modifying thecurriculum can take away fromi"tstrue grade level intentions. Inan effort to meet my students'needs and maintain grade levelconcepts, I use a common factstable that has been a moreelaborate and illustrative
instmment. This chart goesbeyond the traditional factstables, and allows the students todo more in the regutarcurriculum and feel good abouttheir success. My fifth gtadersused the chart in an inclusion
setting, and had great successwith it.
The chart is a 100s chart withthe factors for each number
By Mark Ramsay
Fifth Grade Special Education
WillowRidge Elementary, Amherst, NY
written within the box far eachnumber. The factors are
arranged so that the top factorsdirectly below the bottom factorsmake factor pairs. Squarenumbers have square boxesaround them, and primenumbers have circles around
them. In my fjfth gradecurriculum, the chart has been averYvaluable tool in so many of
I ,the lessons. The chart has
assisted my students in workingwith a variety of concepts suchas number theory, counting,fractions, division, and algebra.In particular, I've found the charthelps target the following skills:
· Identifying factors· Making factor strings
· Using divisibility rules
· Prime and compositenumbers
· Squal;ng numbers/unsquaring numbers
· Finding prime tactorizatiun
· Changing improperfractions to mixed numbers
· Finding equivalent fractions
· Reducing fractions·Finding commondenominators
· Finding a fractional partof the whole/finding thewhole given a fractional part
· Division and algebraicexpressions
· NumberIine skip countingwith missing values
The chart enables studbusto see the "big pictllre" of manyaspects of numeratio~. Just bylooking at the ch~trt, studentscan quickly see that somenumbers have many factors andare very divisible, while othernumbers have few fadars andare not very divisible.
I am not aware of any teacherusing a chart like this, thoughthere very well may be othersjust like it oUt there. TeachersI have talked with in my districthave shown interest in it, and Irecently attended a conferencewith an Everyday Alathematicsconsultant at ""hich this chart
appeared to be of great interestto fellow teachers from other
districts. I encourage you to trythis chart in your classroom sothat other students and teachers
can achieve greater success inthe RlIcrydayiHathematicsprogram.
.\d:tprerl hy i\hrk Ramsay fro III nf,m(/r.r Number (;amt'.
0..
OJ @ @ 28] @2
(j)2 3 2
6 8 102 3 Lf 3 5-
2,3
@)2 3 2,Lf
@2,3 2.Lf
@ 12 14 15 [§J 18 @ 206,Lf 7 5 &.Lf 9.6 10,S
3 2
@2.3.Lf 5 2 3 2.Lf
@2,3,S
21 22 24 26 27 28 307 I I 12.&.6 S 13 9 1Lf:7 15JQ6
@2,lf 3 2 S 2.3.Lf:6
@2 3 2.Lf:S
32 33 34 35 38 39 4016.0 /I 17 7 1&.12.9.6 19 13 2Q IQ fS
@ 42 @2.Lf 3.5 2
@ 2'48
7 2.S44 45 46 50
i 2ULf.7 22. II 15,9 ,23 i 2Lf:16.12.fS 7 2510
3 12.lf I 2.3. 6 S 12.lf.7 3 12
@2.3.lf.S,6
51 i 52 I @ I 54 ! 55 I 56 57 i 58 6017 26./3 I 27/fS,91/ 2fS.llf;fS 19 29 3Q2Q/5./2.IO
@)2 13.7 2;lf.fS 5 2,3.6
@ ,2'8
3 2.5.7
62 I 63 I J 64] I 65 66 69 7031 .21,9 i32./6.& 1/3 33,22.11 13Lf,17 23 35.1lf.lO
6)2.3.lf,6.fS 12 3,5 2.lf 7
'2781 @2.lf,S.3
72 @ 74 75 I 76 77 8036.2'1./8.12.'1 37 25.15 13&./9 /I 39,26./3 '10.20./6./0
3.f2 2,3,lf,6,7 5 '2 3 2,lf.fS
@2,3,S,6,9
821@ 84 85 86 87 I 88 90!
27 9 '+/ i '12.28.21.1 'f./ 2 17 lf3 29 If'+.22, /I 'f 5.30.18.1 5.10
72.'+ \3
2 5 2,3.Lf,6.fS
@2.7 3.9 2,Lf.5./0
91 92 . 93 94 95 96 98 99 11001/3 Lf6,23 31 Lf7 19 'f 1..32. 2 'f.i6.1 2 Lf9, Ilf 33.1/ 50.25,20,/0
Student Reference Folder
The Student Reference Folder is a quick resource tor math vocabulary and'concepts that encourage multiple exposures over time (with understanding), to go to longterm memory.
These masters have been supplied as samples of the options that can be used tocreate Student Reference Folders. They are only samples and you the teacher are thebest judge ()fwhat would best benefit your students.No matter what math program youuse, many of these samples are helpful references. Specific examples can be pulled fromyour program to bridge the gap for your child. Within a class the folders may lookdifferent according to the needs of the child. (blow up items, group sides by operation orfunction, add or delete items) Try to make the outside look the same to protect a child'sself-esteem. Fill in the samples for folders on levels appropriate for each child. In mostcases the students can make their own folders from your sample. In tact, they take pridein their work.
Instructions: Take two file folders and glue long sides together so that short sides fold in.Cut apart samples you wish to use and glue to a blank sheet. Six sheets may be filled tocover all sides. Have the students complete the samples in color then glue and laminate.Makes a great 3 sided carol for students to work behind.
OPTIONS: Use a small photo album with samples cut and inserted. Use page protectorswith items inserted to keep in their notebooks. They can easily be updated as needed.Older students prefer this.
CAUTION: Allowing only the struggling students to have SRF's would create unwantedstigmas for struggling learners. In reality there are many students who would benetitfrom these folders that are not identified as struggling. By having all students make aSRF, the stigma is gone. Those who don't need it will extinguish it on their own. For theother students, the teacher will need to monitor the students progress and begin toextinguish it's use over time. Some of the more severe students may need it much longerthan others.
Createstudycarolsbygluingresourcefolderstogetherandlaminatingresourcesto them.
rMULTIPL;lCAT10N TAB'LES
ro
>- ro. :>.. Q) E ro... f= EI- ..c g...: ~ ro 0
Q)"O E Q) OJ
. <1>.a 0 .a"U--' _ ro E If) OJ E 'iI; U)_ ..c E::J .~ "U E ro._ 0 C > .- E
en ~n Q) '+- U) 0 ....v, 0 '+- .-. ._"U c: ._ Q) 0 0_ > Q) VI
'U en <1>
en _ - "U,. ,.. ._ > 0 VI VIV, ..., .- OJ..." ......_ .VU ._ ro 'bi> VI~ _c: ~ 11) L.. .......> <n Oro : .~ 15 E 'U :._ V) .c 'U ::1 <1> 0_ b.O .- C :5 .......~ ('f) 0 bJ) .'-
~ 'U ~ '0 ~ ~ 'U ,ro _ C1I b.,()
(1) UJC: '6 >. E 0_ -0.c Q) E .a en 0u E .......
LL. E § :5 ~ Q) ;. Q) c: Q) :3 ~ ~a. -:0 :3 'U VI C-
O ::J <1> 00 <1> ~ Q) .- Q) to <1> Q) <1>
I::..c ..c ::J .L: .~ ..c .L: ('f) .c ::i .i::.::; E > 0 E 0_ ~ _'U _ _"0 _ -~
ro lO ro .- Q) .- 0 .- ~ .- ro .- Nen ~ >. . - >-. U) >-. L.. :::;. UJ :::;. :::;. U) » U)
LLI. ::J c: ;q- t: .- c: ro c .- C N C .- c: .-
~ 0 0 0_ 0_ 0..c 0_ 0'" N ro ro ro ro roII ,v -0 'U 'U ~ 'U J.,;, '0 0 '"0 L.. '1:1, ~
___ _ c: c: <1> c: \1) C <1> c: .a c: Q) c:: \1)~ _ roO roE roE roE ro roE cu'E'--' U) _::J _:3 ::J >. _::J :3
0:: ex:: .- C .- c: c: .- .a .- C c:. N ("I') q- LO (.0 (j') 0......
'"
1. .2 3' 4 5 6I X I = I 2X 1=2. '3X 1=3 4X 1";'4 5X 1=5 6X 1=6I.X 2 = 2 . 2 X 2'= 4 3X 2 .,;.6 .4X 2=8 5X 2= 10 6 X 2=.12I X 3=3 ' 2 X 3';"'6 3X 3=9 ,. o4X 3=12 5X 3:::;15 6X 3= 18,I X 4::;4' 2 X 4=:-8 3 X 4 = 12 .o4X 4=16 5 X '4=20 6 X 4=2.41 X 5=5 2 X 5':;=J0 . 3 X 5= 15 .4 X 5;=20 5 X 5= 25 6X 5=30IX 66 2X 6= 11 3X.6=d8 o4X6=24 5 X 6=30 6X 6=36I X 7=7 2 X 7.;= 1-4 3 X 7='21 4 X 7=2.8 5 X 7 = 35 6 X 7=421 X 8::;8 2X8=16 3X 824 4 X 8 = 32 5X 8=40 6 X 8=48IX 9=9 2X 9=18 3X 9=27 4 X' 9=36 5X 9=45 6 X 9::; 54IXIO=IO 2 X 10=20 3XI0=30 -4 X 1EJ= 40 5 X 10=50 6 X 10 = 60i X II = I I 2X1122 3 X 11 = 33 4X 11=44 5 X I I =55 6 X 1I = 66I X 12=12 2 X 12=24 3. X 12 = 36 o4X12=48 'S X 12 = 60 6.X 12=72
7 B, 9. 10 11 127X 1=:=7 8 X 1=8 9X 1=9 10 X... 1=10 .11 X r= I I 12 X I = I 27X 2.=14 8X 2=16 ?X 2= 18 10 X 2=20 II X: 2=22 .12X 2=2-'7X 3=21 8X 3';"24. . 9 X 3=27 1b X 3 = 30 I I X j=33 12 X 3=367X 4=28 8 X 4=32 9X 4=36 10 X .. ==40 II X 4=44 . 12 X 4=467X 5=35 8.X 5=40 9 X 5=45' 10 X 5=50 11 5 = 55 12 X 5=607 X .6=42 8X- 6=48 9X 6=54 10 X 6=60 11 X 6=66 12 X 6=727X 7=49 8 X 7=56 9 X 7 ==63 lOX 7=70 11 X 7=77 12X 7=847 X '8=56 8X 8.=64 9)( 8=72 10 X 8=80 J1 X 8= 88 .12 X' 8=967X 9=.63 8X 9=72 9X 9=81 lOX. 9.= 90 I 1 X 9 = 99 . . 12 X 9::;1087 X 10=70 a X 10=80 9 X 10=90 lOX 10= 100 11 X 10::; 110 I 2 X '10::; 1207. x- ) I :;=77 ax 1)::;88 9 X I I = 99 IO,X.lJ=110 11 X 11::z'121 12 X 1.1=1327X 12=84 8 ?<12 ='96 9 X, I 2";' 108 10 X J2= 120 J 1 X 12=132 12 X'12= 144
-- - - - - - -
Thefactorsof a numberare the numbers thatcan be multiplied by whole numbers'to get thatnumber or the numbers that a number can bedivided by.without having remainders.
"-;::'~'f;~.~~~~~~~~~~~~~:~~~g~~~'i~~~~'~1~'!1c:::\~...:~::\., ~ ;':_......-._.. ".'..'
Example Factors of 16: 1, G, II, 8, illFactors'of 16: 1,2, 4, 8,16
t. Factors of 7: T, 7
I. Factors of 18: 1'121 3I ~t qI 18
. Factors of 36: 1, 2., ?J, 41 &!, 9, J?.,18',36
Factors of 50: \) 2, 5, JOi,25,50
PD /Vq (/ /15
Triangles
L6 ""/ ~Quadrangles (Quadrilaterals)
/hombU'; BG>
\ rectangle J
Other polygons,
8exagon 8. octagon
e 8
------
t?IU
~-~
c:gJ~~. lE5JlQ Q
l([j)trian~Jular prisms rectangular prisms hexagonal prism
Lh4 4t~QVI
triangularpyramids
pentagonalpyramid
t 1< CD.CD 0..~ coCD CD><
hexagonalpyramid
rectangularpyramids
8@iJ(jjj Yspheres cylinders cone
Five Regular PolyhedronsThe faces that make each shape are identical.
.~u@tetrahedron cube
(pyramid) (prism)4 faces" 6 faces
octahedron dodecahedron icosahedron
8 faces 12faces 20 faces
... .. ...-..."rI.,
".
I 01<0
DI01.... olw ol <XII.... <XII(.71 <XIIW <XII CJ)I (.711.1>-<.nIW U'lIN U'l1.... .l>-IW .l>-I WIN WI 'N\- " DI
!:!...0'<='
i VI
,eI
I
ID9 9 9 0 0 0 9 0 0 0 0 0 0 0 0 0 0 nCD -..J W .... Co a, W - 0)1Co a, N '-I N 0:11 WI 0, 3"0 0 0 0 -..J I\) -..J I\) 0 0 0 0 (J\ (J\ 0
(J\ <.n <.n (J1 DI.;;;-
"aCD OJ c..J - Q) W ID-..J I\) -..J I\) Q) Q) W "'I
CD -..J W ....NI- NI- NI.... NI- WIN
OJ (j) .j:>. I\) -..J I\) WIN WI (J1 1'\0 0 0 0 0 0 0 0 <.11 (J\ 0 tD
::!! ::!! ::!! ::!! ::!! ::!! '?fl :I0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 !!
0:> I
10)t\)
<<D
<D;:!.
Cl.CO
o. <D <D<D (/) enen
Example' Number model: 3 x 4 = 12
Area = 12 square units
Example Add the lengths of the sides together:
2 ern 2 em + 3 em + 2 em + 3 em = 10 emI
Perimeter = 10 em
3 em I 13em
2em ------- ~The diameter is given. Find the circumference byusing the "about 3 times" Circle Rule.
1 in.
parallel lines
intersecting lines
3cm 2em
><Xintersecting line segments
parallel rays..
cry«)M
1\
-I('()
II
1I,I,
~I'rs,. I
QtrO
II.,,-.1N
II
1\
('()I;:r-
II
I
(/)(/)Q) Q)
..c ..c, 0 0
Q) C Cill -- .--CONC'J (f) r-
\I \I \I-0'-0 ,'- '- 0<tl (1j 0>.>.- r-
(/)'- (/)
(/) Q) '- (/)L.~Q)1-Q)Q) ,Q)1DEQ)1DE.~ .~ E._ c .......o Q) CQ) 0 Q)
E-000'0000
I~ ~ ~ ~
LOLn0 I N
- N .II II 1\
_1° -lbO -I::t"
II II 1\
. ,OO@ E9
. ;
." We~gh.t...
kilogram: 1,000 9pound: 16 ozton: 2,000 lb
1 ounce is about 30 g
< is less than> is more than
;s equal" to- is the same as
Prefixes
{ L~'n9th
kilometer: 1,000 mmeter: 100 cm or
10 dm
foot:
yard:mile:
12 in.3 ft or 36 in.
5,280 ft or1,760 yd
10 cm is about A in.
uni- one
bi- Iwolri- Ihree
quad- . . . . . fourpenta- fivehexa- six
he pla- sevenocla- eighlnon a- ninedeca- tendodeca- ... twelve
icosa- . . . , . twenty
lera- . . . . trillion (10'2)
giga- . . . . billion (109)
mega- . . . million (106)kilo- Ihousand (103)heclo- . . . hundred (102)
deca- ... len (10')uni- . . . . . one (10°)deci- . . . . lenlh (10-1)cenli- _.. hundredlh (10-2)milli. . . . _Ihousandth (10-3)
micro- _ . . millionlh (10-6)nano- " _pillionth (10-9)
flI
III
Time
year: 365 or 366 daysyear:. about 52 weeksyear: 12 months
.month: 28,29, .30, or
_ 31 daysweek: 7 daysday: 24 hourshour: 60 minutesminute: 60 seconds
--5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
-1 o 21 3 4 5 6 7 8 9 10 11 12
Abbreviations
kilometers kmmeters mcentimeters em
miles mifeet ft
yards _ ydinches in.
tons. T
pounds Ib
ounces 02
kilograms kg
grams 9
Units of Volume1 cubic meter (m3) 1000 cubic decimeters (dm3)
1,000,000 cubiccentimeters (cm3)
= 1000 cubic centimeters1 cubic decimeter
.Units of Capacity1 kiloliter (kL)1 liter
= 1000 liters (L)= 1000 milliliters (mL)
Units of Mass
1 metric ton (t)
1 kilogram.1 gram
1000 kilograms (kg)1000 grams (g)1000 milligrams (mg)
Units of Time
1 century1 decade1 year (yr)
= 1no \fo~rc::J ...,...........
1a years12 months
52 weeks (plus one or two days)365 days (366 days in a leap year)
= 28, 29, 30, or 31 days7 days24 hours60 minutes
= 60 seconds (see)
1 month (mo)1 week (wk)1 day (d)1 hour (hr)1 minute (min)
System Equivalents
1 inch is about 2.5 em (2.54)
1 kilometer is about 0.6 mile (0.621)
1 mile is about 1.6 kilometers (1.609)
1 meter-is about 39 inches (39.37)
1 liter is about 1.1 quarts (1.057)
1 ounce is about 28 grams (28.350)
1 kilogram is about 2.2 pounds (2.205)
1 hectare is about 2.5 acres (2.47)
1760 yards (yd)= 52801eet (ft)= 3 feet
= 36 inches (in.)= J2inches
11I
I,
I
I
I
I
Units of Length1 mile (m!) .
1 yard
1 foot
Units of Area
1 square yard (yd2)
1 square foot1 acre
1 square mile (mi2)
Units of Volume1 cubicyard (yd3)1 cubicfoot
Units of Capacity1 g.allon (gal)1 quart1 pint1 cup1 fluid ounce1 tablespoon
Units of Weight
. 1 ton (T)1 pound
= 9 square feet (ft2)= 1296'square inches (in. 2)= 144 square inches= 43,560 square feet= 640 acres
= 27 cubic feet (ft3)= 1728 cubic inches (in.3)
= 4 quarts (qt)= 2 pints (pt)= 2 cups (c)= 8 fluid ounces (ft oz)= 2 tablaspoons (tbs)= 3 teaspoons (tsp)
= 2000 pounds (Ib)= 16 ounces (oz)
Meridians(longitude)
Parallets(latitude)
. .South Pole
900S
Point A is located at 300N latitude arid
300E longitude.
Reference
.,___,- - _" ____n
Units of Length1 kilometer (km) = 1000 meters (m)1 meter = 10 d.ec/meters(dm)
= 100 centimeters (em)= 1000 millimeters (mm)
1 decimeter = 10 centimeters1 centimeter = 10 millimeters
Units of Area
1 square meter (m2) = 100 square decimeters (dm2)= 10,000 square
centimeters (cm2)1 square decimeter = 100 square centimeters1 are (a) = 100 square meters1 hectare (ha) = 100 ares
1 square kilometer (km2) = 100 hectares
.'
Pictures of Math
EXPONEN T ,
,~~~/!~ ,-~,. ~',,~-=- -~l\"ll.--",..\~~_____
GRAPH., ~III).;\';.~.I,.t:~ ~
)~i:'I"/f/l'("~ ''':--4~
., ;;t~_. ., I" "\
__,__,-~ ~'~;;ZroJ---'-""-IU!. TIP/. Y
/V/UL TIPt.. y/f//ULTlPL Y
/11ULTIPL Y/I/1ULT/PL Y
/1/IULTIPLY'
Metric Conversions Fifth Grade
King Henry Died Before Drinking Chocolate Milk~-_...--.-._---
01 VIDE \ l 5UBTRACi
--==".-- ---~--I\~~--, . . ~--- r-~
ELwJ;IDIIVIDE__ L__-
i--' ::::;----/ C' l.
~dn you )
FR.
AC~_" \\1 +hinkof, ).. ' ~ some.TION € ~\ more)
~'~.
'...J....-......-.
'J_.' ._ J:s:' .-",
To convert, just .countthe number of places you m~veonthe chart, and the direction in whichyou move.
Example: 17 kilometers = decimeters
Movethe decimal4 places to the rIght, So the answerIs 170,000.
Example: 342.5 milliliter = dekaliters
Movethe decimal 4 places to the left. So the answerIs 0.03425
EA .
EN L
G
- - - - I
Aoo
Movethe decimal 2 places to the right., So the answerts 8600. In this one think: you're going frcHnmeters to!=cnrl!T'et.~r.$.' so you moveright"
Example " centimeters = 86 meters
- - ,
leilo He.cto Deka BASE Deei Centi Milli
1000 100 10, 1 0.1 0.01 0,001
Note: Baseunitsare liter(masur capacity),meter(meQSureslength), and grom (measures mass),