numerator how many pieces out of the whole top #

NUMERATORHOW MANY PIECES OUT OF THE WHOLE

TOP #

93

DENOMINATORHOW MANY TOTAL PARTS

MAKE 1 WHOLE

BOTTOM #

9#

1

2

3

4

5

6

7

8

9

IMPROPERMORE THAN 1 WHOLE

149

PROPERLESS THAN 1 WHOLE

59

MIXEDMORE THAN 1 WHOLE

591

WHOLE # AND A FRACTION

WHOLE #

99 1

WHOLE #279 3

EQUIVALENTEQUAL PART OF 1 WHOLE

1824 = 3

4

4547

34527

24520

1

ADDORSUBTRACT

FRACTIONSCOMMON

DENOMINATOR

452

4

53

294

1 X5

X5

X9

X9

20 27

45 45

MULTIPLY

EQUIVALENTRAISE

34 = 9

12

X3

X3

SIMPLIFY

EQUIVALENTDIVIDE

312 = 1

4

÷3

÷3

85

58 0.625

.000

FRACTION N2A DECIMALDIVIDE!!

TOP DOG IN THE HOUSE

1577

15

IMPROPER FRACTIONS

71

2

TOP DOG IN THE HOUSE

7.00015157

6.4

PROPER FRACTIONS

TOP DOG IN THE HOUSE

MIL

LIO

NT

HS

HU

ND

RE

D T

HO

US

AN

DT

HS

TE

N T

HO

US

AN

DT

HS

TH

OU

SA

ND

TH

S

HU

ND

RE

DT

HS

TE

NT

HS

HU

ND

RE

D M

ILL

ION

S

TE

N M

ILL

ION

S

MIL

LIO

NS

HU

ND

RE

D T

HO

US

AN

DS

TE

N T

HO

US

AN

DS

TH

OU

SA

ND

S

HU

ND

RE

DS

TE

NS

UN

ITS

OR

ON

ES

PLACE VALUETHE NAME OF A DIGIT’S LOCATION AND VALUE

102,102,102.102102WHOLE NUMBERS

DECIMALS / FRACTIONS

LESS THAN 1 WHOLE

DECIMAL BACK TO A FRACTION

106

5

.125 1000125

PLACEVALUEUSE TO CHANGE A

DECIMAL INTO A FRACTION

1008

.08

5.6

252

53

5

405

81

5 AND 6 TENTHS

8 HUNDREDTHS

125 THOUSANDTHS

.05is NOT .5

DECIMAL OUT OF SIGHT

TO THE RIGHT

7060

7060.0

+ OR – DECIMALS

LINE THEM UP!! 4.867

67.0- 4.8

÷ DECIMALS

6.01.5

MOVE DECIMAL TO MAKE THE DIVISOR

A WHOLE NUMBER

÷ DECIMALS

6.00.15

MOVE DECIMAL TO MAKE THE DIVISOR

A WHOLE NUMBER

÷ DECIMALS

.061.5

MOVE DECIMAL TO MAKE THE DIVISOR

A WHOLE NUMBER

X DECIMALSDON’T LINE THEM UP!!

COUNT …. TOTAL DECIMAL PLACES!!

6.04X2.53020

+120815100

15.100

MULTIPLY A NUMBER BY10, 100, 1000, 10000

COUNT ZEROS

MOVE DECIMAL TO

THERIGHT

DIVIDE A NUMBER BY10, 100, 1000,

10000COUNT ZEROS

MOVE DECIMAL TO

THE LEFT

!

CONVERSION

BIG TO SMALLMULTIPLYX BY 16

X BY 100X BY 36

GALLONS TO CUPSM TO CM

YARDS TO INCHES

CONVERSIONSMALL TOBIG

DIVIDE÷BY 16

÷BY 100

÷BY 60

CUPS TO QUARTSCM TO M

SECONDS TO MINUTES

PERCENTPER HUNDRED

%15%

.15HUNDREDTHS

15100

PERCENT OF A NUMBER

MULTIPLY!!43% OF 25

.43 X 25USE FOR TIPS, TAX, AND SALES!

%

DECIMAL TO

DECIMAL 2 TO THE

RIGHT1.85 185%

%MULTIPLY BY 100

DECIMAL 2 TO THE

LEFT.

TO DECIMALDIVIDE BY 100

28.5% .285

%

FRACTIONTO

.852017

0.85

1.TOP DOG IN THE HOUSE

2.DECIMAL TO

85%%

%

1. % TO DECIMAL

20057

1000285

TO FRACTION

28.5% .285

%

2. PLACE VALUE AS FRACTION & SIMPLIFY

TAX• BY ABOUT 8 CENTS OR $0.08 FOR DENTON TEXAS.

TOTAL COST=

$45.37

X .08 =$3.6296 OR

$3.63

TOTAL WITH TAX

45.37 + 3.63 =

$49.00

MULTIPLYADD

• BACK ONTO THE TOTAL COST.

HALFX BY .5

BY 2

X BY 21

NUMBERS THAT EQUAL

HALF00.5000

.5000.50.50

2

1

34

17

122

61.5

0.50.500

HALF OF HALF

41

OR .25

HALF

HALF OF HALF

4

1

2

1

2

1

DIVISIBILITYSIMPLIFY FRACTIONS SIMPLIFY

PROPORTIONS

SIMPLIFY RATIOS SIMPLIFY RATES

4 OUT OF 28

FREE THROWS

1 OUT OF 7

FREE THROWS

5727

199

357327

38X

5727

38X

199

$1.50FOR 2

$0.75FOR 1

FACTORSWHAT YOU CAN DIVIDE A NUMBER BY (DIVISIBILITY) WITHOUT A REMAINDER

FACTORS OF 72:

1, 72, 2, 36, 3, 24, 4, 18, 6, 12, 8, 9

GCFGREATEST COMMON FACTOR

GCF OF 36 AND 90

1 362 183 124 96 6

1 902 453 305 186 1510 9

GCF =18

DIVISIBILITY

4527

99

45

27BY “9”

SUM OF THE DIGITS is 9

53

2+7=9

4+5=9

DIVISIBILITYBY “9”

39423+9+4+2=

18

1+8= 9

SUM OF THE DIGITS is 9

DIVISIBILITY

5727

357327

BY “3”

199

2+7=9

5+7=12

SUM OF THE DIGITS is 3, 6, 9,12

DIVISIBILITYBY “3”

73417+3+4+1=

15

1+5= 6

SUM OF THE DIGITS is 3, 6, 9,12

4108

428

DIVISIBILITY

10828

EVEN AND LAST TWO DIGITS ARE 04, 08, 12, 16, 20, 24, 28, 32, …..

277

BY “4”

DIVISIBILITY

EVEN AND LAST TWO DIGITS ARE 04, 08, 12, 16, 20, 24, 28, 32, …..

BY “4”

136

648

618

DIVISIBILITY

4818

EVEN AND SUM OF DIGITS IS 3,6,9…

83

BY “6” 1+8=9

4+8=12

978

DIVISIBILITY

EVEN AND SUM OF DIGITS is 3, 6, 9

BY “6”

9+7+8=24

2+4=6

DIVISIBILITY

103.5

51053.5

BY “5”

LAST DIGIT IS A “5” OR “0”

2.7

DIVISIBILITY

3.75BY “5”

LAST DIGIT IS A “5” OR “0”

335

DIVISIBILITY

33050

103301050

BY “10”

LAST DIGIT IS A “0”Move decimal once to the left.

DIVISIBILITY

3170BY “10”

LAST DIGIT IS A “0”Move decimal once to the left.

DIVISIBILITY

3.178BY “2”

EVEN! LAST DIGIT IS A

“0, 2, 4, 6, or 8”

MIXED TO IMPROPER

CHECKIE THINGY

87

4

839

X OR ÷ FRACTIONSMIXED NUMBERS

MUST DO CHECKIE THINGY!

X FRACTIONS

43

52

543

527

AINT NO PROBLEM TOP X TOP AND

BOTTOM X BOTTOM

2081

201

4

MULTIPLYFRACTION OF A #

⅔ OF 84

3168

1

8432

÷FRACTIONSDON’T CRY!!

FLIP THE Right & MULTIPLY!

13

528

31

528

5

84

31

53

5

54

16

RECIPROCAL÷FRACTIONS

FLIP THE right

51

32

32

1

5

MULTIPLESA NUMBER’S MULTIPLICATION FACTS

MULTIPLES OF 72:

72, 144, 216, 288, 360, 432, 504, 576,

648, 720, 792, 864…

36X2=7236X3=10836X4=14436X5=180

LCMLEAST COMMON MULTIPLE

LCM OF 36 AND 90

90X2=18090X3=27090X4=360

LCM =180

PERIMETERTOTAL DISTANCE AROUND

THE OUTER EDGES

FENCE, BORDER, TAPE, CUT AROUND, FRINGE, LACE, CUFF,

OUTLINE, FRAME, EDGE, TRACE,

JUST ADD!

AREATOTAL INSIDE FLAT SPACE

MEASURED IN SQUARE UNITS

FLAT SPACE, INSIDE, PAINT, CARPET, COVER, SPREAD, ROOM, TILE, MOW LAWN,

VACUUM, ….

USES MULTIPLICATION!!

MEASURES OF CENTRAL TENDENCY

CONCLUSION OF THE DATA

MEANMEDIAN

MODE

MEANMEDIAN

Average+, ÷

Middle #

MODEMOST

RANGE

Highest – lowest

•IRRATIONAL

•PROPER

•LESS THAN ONE

WHOLE NUMBERSARE ARE NOT

•RATIONAL

•IMPROPER

•EQUAL TO OR MORE THAN 1DECIMAL OUT OF SIGHT

TO THE RIGHT!!

RATIONAL ARE NOT CAN BE MADE INTO A

FRACTION1 4 67, …

-8 -38 -101…..

⅔ ⅓ ½.833333333…

…1.625416

π6

....2.4494897

IRRATIONAL

CAN NOT BE MADE INTO A FRACTION

DECIMAL GOES ON FOREVER

WITH NO REPEATING PATTERN

π6

....2.4494897

INEQUALITIES

> < =

READ LEFT TO RIGHT

GREATER THAN

LESSTHAN

EQUAL TO

INEQUALITIES

=

READ LEFT TO RIGHT

IS EQUAL TO

32.865

2

INEQUALITIES

< READ LEFT TO RIGHT

IS LESSTHAN

-4 2

INEQUALITIES

> READ LEFT TO RIGHT

IS GREATER

THAN

2 -4

CONSECUTIVEONE AFTER THE OTHER

CONSECUTIVE PRIME NUMBERS

1, 3, 5, 7, 11, 13, 17, 19, 23..

PRIME NUMBERSONLY TWO FACTORS

ONE AND ITSELF3 = 1 X 3 11 = 1 X 11

5 = 1 X 5 13 = 1 X 13

7 = 1 X 7 17 = 1 X 17

19 = 1 X 19 23 = 1 X 23

UNPOPULAR COMPOSITE NUMBERS:

THEY LOOK PRIME, BUT ARE ACTUALLY COMPOSITE!

COMPOSITE NUMBERS THAT HAVE MORE THAN 2

FACTORS

39, 51, 57, 87, 91, 117, 119,

133, 203

AND5.007

FIVE AND SEVEN THOUSDANDTHS

1 ¾ONE AND THREE FOURTHS

INTERVALSSKIP COUNTING

.125 .25 .375 .5 .625…

EXAMPLE: AN INTERVAL OF

81

FREQUENCY TABLESHOWS THE NUMBER OF TIMES AN EVENT

OCCURS

BAR GRAPHDISPLAY, REPRESENT,

COMPARE DATA

PERIOD 1

PERIOD 2

PERIOD 3

PERIOD 4

0102030405060708090

GIRLS

BOYS

LINE PLOTA NUMBER LINE THAT USES “X” MARKS

TO SHOW THE FREQUENCY OF AN EVENT

XS S M L XL XXL

# OF TEAM UNIFORMS

X

X

X

X

X

X

X

X

X

X

X

X

X X

X

X

X

X

X

X

X

X

X

X

LINE GRAPHSHOW A CHANGE OF DATA OVER TIME

2005 2006 2007 20080

102030405060708090

100

East

West

North

VE

RT

ICA

L A

XIS

HORIZONTAL AXIS

CIRCLE GRAPHPARTS OF THE WHOLE 100%

REPRESENTS DATA parts AS A FRACTION, DECIMAL, OR PERCENT

ELECTRIC

GAS

PHONE

WATER

CAR

HOUSE

.25 ¼ OR 25%

.2, 1/5, OR 20%

VENN DIAGRAMUSES OVERLAPPING SHAPES TO SHOW HOW DATA IS RELATED

WHOLE NUMBERS FROM 1 TO 10

PRIME

NUMBERS

EVEN NUMBERS

24, 6, 8,

101,3,5

7

9

STEM AND LEAF PLOT11, 13, 14, 15, 21, 24, 27, 27, 34, 35, 34, 36

1 1,3,4,5

2 1,4,7,7

3 4,4,5,6

STEM

SLEAF(S)

HISTOGRAMA GRAPH THAT DISPLAYS DATA FROM A

STEM AND LEAF PLOT. Groups information together!!

PATTERNSHAPES, SYMBOLS OR

NUMBERS THAT OCCUR IN A PREDICTABLE ORDER.

3, 9, 27, 81, 243…..

POSITION

3, 9, 27, 81, 243…..

THE NUMBER THAT TELLS WHERE SOMETHING OCCURS IN A PATTERN

POSITION

1 2 3 4 5

TERMTHE ACTUAL NUMBERS IN A

PATTERN OR ANSWERS IN A SEQUENCE

POSITION 1 2 3 4 5

TERMS 3 9 27 81 243

SEQUENCEA PATTERN WHERE A RULE SHOWS THE RELATIONSHIP BETWEEN THE

POSITION AND THE TERMPOSITION 1 2 3 4 10 NTERMS 3 9 27 81 3103

RULE : 3 TO THE POWER OF THE POSITION

N

n3

1 2 3 4 5

RULEAn expression that describes the relationship between the POSITION and TERM

.5, 1, 1.5, 2, 2.5….

.5n

ORDER OF OPERATIONS

PEMDAS INSIDE

PARENTHASIS

³ 1 2 3 LAST

WORK LEFT TO RIGHT

WORK LEFT TO RIGHT

X÷ - +

PRODUCT

X

INCREASEDTIMESTRIPLE

DOUBLETWICE

OF

PRODUCT6(7) 6y

76 76

TWICE OR MULTIPLY BY 2

Divide by .5!!

DOUBLE

TRIPLEMULTIPLY BY 3

5yy5

multiply

QUOTIENT

÷

DECREASEDSHARED EQUALLY

DIVIDEDSPLIT EVENLY

CUT OFFSEPARATED

FIT INTOEACH

QUOTIENT

742 427

742

DIVISIONQUOTIENT

DIVISOR DIVIDEND

DIVISIONQUOTIENT

NUMERATORRDENOMINATO

DIFFERENCE

SUBTRACTMINUSLESS

NEGATIVECUT OFF

TAKE AWAYDECREASE

SUM+

ADDPLUS

POSITIVEALL TOGETHER

DOUBLE NEGATIVECOMBINED

WITHTOTAL

AND ANOTHER

INTEGERSPOSITIVE AND

NEGATIVE WHOLE NUMBERS+ --72 1

299

-1001

INTEGER EXPRESSION

NUMBER LINE

1 + 3 + 3 - 8

ABSOLUTE VALUE

DISTANCE FROM 0

8=8-13=13

ADD OR SUBTRACT

1 + 3 + 3 - 8

MOVE ON A NUMBER LINEINTEGERS

MOVE RIGHT 7

ADD

+(6)

MOVE RIGHT ON A NUMBER LINE

INTEGERS

+7 -(-3)MOVE RIGHT 6

MOVE RIGHT 3DOUBLE

NEGATIVE!

MOVE LEFT 9

MOVE LEFT 9

SUBTRACT

-(9)

MOVE LEFT ON A NUMBER LINE

INTEGERS

-1 +(-3)MOVE LEFT 3

MOVE LEFT 8

SUBTRACTING INTEGERSIT’S ADDING A

NEGATIVE!!-7-8-7+(-8)

-15 IS THE

ANSWER

SUBTRACTING INTEGERSIT’S ADDING A

NEGATIVE!!7-87+(-8)

-1 IS THE ANSWER

MOVE LEFT 8

T CHARTEVALUATING INTEGER EXPRESSIONS

14-24+2+(-12)

2412

142

36 1620 More negatives, so a

negative answer

Answer = -20

DOUBLE NEGATIVESBecome POSITIVE

PUNCH EM

OUT!

2 NEGATIVES

POSITIVE

X or ÷ INTEGERS

32472

72324

1 NEGATIVE

NEGATIVE

X or ÷INTEGERS

72324 3

2472

RATE$120 FOR 15 HOURS

15h$120

UNIT RATE DENOMINATOR OF 1

1h$8

RATIO45 STUDENTS 18 GIRLS

GIRLS TO STUDENTS

BOYS TO GIRLS52

OR4518

23

OR1827

PROPORTION

?h$150

1h$8

CROSS PRODUCTS

?h$150

1h$8

ARE EQUAL

1508h

CONGRUENTSAME SIZE

=~

~SIMILAR

DIFFERENT SIZESAME SHAPE

CORRESPONDING

a bA B

SAME LOCATION

~

SIMILAR

CORRESPONDING SIDES PROPORTIONAL

CORRESPONDING ANGLES CONGURENT =

SAME SHAPE DIFFERENT SIZEA B

a b

~

~

SCALE3:1

ON A MAP, 1 CM REPRESENTS 3 KM

3KM1CM

ACUTE ANGLESLESS THAN 90˚

50 ˚89.5 ˚

22 ˚

OBTUSE ANGLESMORE THAN 90˚

91 ˚

113˚

RIGHT ANGLES

90˚

90 ˚

90 ˚

90 ˚

STRAIGHT ANGLES

180 ˚

180 ˚

COMPLEMENTARY

ANGLESADD TO 90 ˚

31˚ 59˚31 + 59 = 90

SUPPLEMENTARY

ANGLESADD TO 180 ˚

47˚133˚

47 + 133 = 180

ADJACENT ANGLESSHARE A

VERTEX AND SIDE

115˚

115˚

65˚ 65˚

VERTICAL ANGLESSHARE A VERTEX

OPPOSITESARE EQUAL!

CORRESPONDING ANGLES

SAME LOCATIONARE EQUAL!

75˚

75˚

CONGRUENT ANGLES

ARE EQUAL!47˚

47˚

PLANE

INTERSECTING

LINES

PARALLELL LINES

NEVER INTERSECT

PERPINDICULAR

LINESINTERSECT TO

FORM 90˚ RIGHT

ANLGES

POLYGONA CLOSED FIGURE WITH

STRAIGHT SIDES

TRIANGLE

QUADRILATERALPARALLELOGRAMS:

SQUARE, RECTANGLE, RHOMBUS

PENTAGON HEXAGON

HEPTAGON DECAGONDODECAGON

TRAPEZOID

OCTAGON

POLYGON 4 SIDES

QUADRILATERAL

PARALLELOGRAMQUADRILATERAL

TOP AND BOTTOM II AND RIGHT AND LEFT II ANDOPPOSITE ANGLES

SQUARE RECTANGLERHOMBUS PARALLELOGRAM

PARALLELOGRAMQUADRILATERAL

SQUARE RECTANGLERHOMBUS PARALLELOGRAM

RIGHT & LEFT TOP CORNERS SUPPLEMENTARY ∠

RIGHT & LEFT BOTTOM CORNERS SUPPLEMENTARY ∠

=180°

=180°

PARALLELOGRAM

QUADRILATERAL

NOT A

TRAPEZOID

TRAPEZIUMKITE

QUADRILATERALANGLES ADD TO

360˚40 ˚

40 ˚

140

˚

140 ˚

90˚ 90˚

100 ˚80 ˚

90 ˚ + 90 ˚ + 100 ˚+80 ˚ = 360 ˚

POLYGON 3 SIDES TRIANGLE

RIGHT

ISOSCELES

RIGHT

SCALENE

OBTUSE

ISOSCELES

OBTUSE

SCALENE

ACUTE

EQUILATERAL ACUTE ACUTE

SCALENE ISOSCELES

TRIANGLE ANGLESADD TO 180˚

110 ˚

30 ˚40 ˚110 ˚+ 40 + 30 =

18030˚

75˚ 75˚90˚

45˚

45˚

ISOSCELES2 = SIDES

2 = ANGLES

REGULARPOLYGON ALL SIDES EQUAL

REGULAR

OCTAGON

5 CM5 CM

5 C

M5 CM

5 CM

5 CM

5 C

M5

CM

IRREGULAR

OCTAGON

AREA = s²

SQUAREQuadrilateralParallelogram

RectangleRhombus

PERIMETER = 4s

s s

s

s

RECTANGLEQuadrilateral

Parallelogram

has 4 right angles

PERIMETER =2L + 2W

AREA =LW OR bh

PERIMETER =ADD 3 SIDES

AREA =bh2

TRIANGLE

heig

ht

base

heig

ht

PERIMETER ADD 4 SIDES

AREA = (b+b)h

2

QuadrilateralTRAPEZOID

base

base

THE CIRCUMFERENCE THE DIAMETER OF A CIRCLE

PI

DIAMETER

A LITTLE MORE THAN 3!

3.141592….

3.1415927

NCECIRCUMFEREDIAMETER

CIRCUMFERENCE

πdC

THE PERIMETER OF A CIRCLE

MULTIPLY PI x d MULTIPLY PI x 2r

DIAMETER RADIUS

r2C

CIRCUMFERENCEPERIMETER , DISTANCE AROUND,

EDGE, RIM, FENCE, BORDER…

πd

AREAINSIDE SPACE, INSIDE FLAT SQUARES, COVER, OVERLAY, CARPET, FLOOR, ….

πr²

RADIUS

RADIUSHALFWAY ACROSS A CIRCLE

FROM THE CENTER

r

2r=d

2πradius

Circumference ÷2π=

c

DIAMETER

DIAMETERALL THE WAY ACROSS A CIRCLE

THROUGH THE CENTER

d r2d

πdiameter

Circumference ÷π=

c

“IS”

EQUALS

EVALUATESIMPLIFY OR SOLVE

GET AN ANSWER!

5(12)-4EVALUATED IS 56

EXPRESSION

A MATH SENTENCE NO EQUAL SIGN

NUMERICAL EXPRESSIONHAS ONLY NUMBERS

33)3(33

3

23

EVALUATE THEM!

VARIABLE EXPRESSIONHAS NUMBERS AND VARIABLES

3X 2Y+4

SUBSTiTUTIONVARIABLE OUT

NUMBER IN

VARIABLE

A LETTERREPRSENTS AN AMOUNT OR QUANTITY

EQUATIONMATH SENTENCE

WITH = SIGN

2)hb(b

A 21

SOLVE FOR THE

VARIABLE3X - 4 = 5

X = ????

THE PRODUCT OF THREE AND THREE

3³=273(3) = 9

THREE TO THE POWER OF THREE

POWERSEXPONENTS

BASE

POWER OR EXPONENT

53

= 125

CUBED

3RD POWERVOLUME of CUBE

S

SS S³

V=SxSxS

SQUARED2ND POWER

AREA of SQUARE

S

S

S²A=SxS

AREA OF SQUARE =

ONE SIDE LENGTH

SQUARE ROOT

SQUARE ROOT

=

SQUARE ROOT

9 =3

DIVISION3 ways

BABY ADULT TEEN

BABY ÷REMAINDER

516315

1

r 1

ADULT ÷REMAINDER

AS FRACTION5

163151

31

5163151

TEEN ÷DECIMAL

KEEP DIVIDING!.0.

0 91

0

0

3.3

TRANSFORMATIONSTESSELATIONS

RELFECTIONS

TRANSLATIONS

ROTATIONS

TRANSFORMATIONSTESSELATIONS

TRANSFORMATIONSRELFECTIONS

REFLECT ACROSS Y AXIS

Y STAYS THE SAME

REFLECT ACROSS X AXIS

X STAYS THE SAME

TRANSFORMATIONSTRANSLATION

SLIDE`

TRANSFORMATIONSROTATION

TURN

COORDINATE PLANE

QUADRANT

QUADRANT

QUADRANT

QUADRANT

POINT OF ORIGINSTART

(+X,+Y)

(+X,-Y)(-X,-Y)

(-X,+Y)

LOCATION OF A COORDINATE POINT

(X,Y)-LEFT OR +RIGHT FIRST

-DOWN OR +UP NEXT

ORDERED PAIR

COORDINATE POINT

-4+3

(-4, 3)(-X, Y)

AXIS

X AXISHORIZONTAL

Y AXISVERTICAL

EVENLAST DIGIT 0, 2, 4, 6, 8

ODDLAST DIGIT 1, 3, 5, 7, 9

SYMMETRY