numerator how many pieces out of the whole top #
TRANSCRIPT
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