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3 9 NUMERATOR TOP #

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3 9 NUMERATOR TOP #
NUMERATOR
TOP
#
HOW MANY PIECES
OUT OF THE WHOLE
3
9
BOTTOM #
DENOMINATOR
HOW MANY TOTAL
PARTS MAKE 1 WHOLE
1
3
2
4
6
5
8
7
9
#
9
IMPROPER
MORE THAN 1 WHOLE
14
9
PROPER
LESS THAN 1 WHOLE
5
9
MIXED
MORE THAN 1 WHOLE
WHOLE # AND A FRACTION
5
9
WHOLE #
9

1
9
WHOLE #

3
9
27
EQUIVALENT
EQUAL PART OF 1
WHOLE
18
24
3
4
FRACTIONS
COMMON DENOMINATOR
4
3
1 2
9
5
2
20
27
47
1
2
3
 4
45
EQUIVALENT
3
4
9
12
EQUIVALENT
3
12
1
4
FRACTION N2A DECIMAL
DIVIDE!!
0

.625
5
 8 5.000
8
TOP DOG IN THE HOUSE
IMPROPER FRACTIONS
1
2
15
7
 7 15
7
TOP DOG IN THE HOUSE
PROPER FRACTIONS
.4
6
7
 15 7.000
15
TOP DOG IN THE HOUSE
PLACE VALUE
THE NAME OF A DIGIT’S LOCATION AND VALUE
DECIMALS / FRACTIONS
LESS THAN 1 WHOLE
WHOLE NUMBERS
DECIMAL BACK TO A FRACTION
HUNDRED MILLIONS
TEN MILLIONS
MILLIONS
HUNDRED THOUSANDS
TEN THOUSANDS
THOUSANDS
HUNDREDS
TENS
UNITS OR ONES
.
TENTHS
HUNDREDTHS
THOUSANDTHS
TEN THOUSANDTHS
HUNDRED THOUSANDTHS
MILLIONTHS
102,102,102 102102
PLACEVALUE
USE TO CHANGE A
DECIMAL INTO A FRACTION
.125
.08
5.6
125
THOUSANDTHS
8 HUNDREDTHS
5 AND
6 TENTHS
125
5
1


1000 40 8
8
2

100 25
6
3
5 5
10
5
.05
is NOT
.5
DECIMAL OUT OF SIGHT
7060
TO THE RIGHT
7060.0
OR
DECIMALS
LINE THEM UP!!
67  4.8 
67.0
- 4.8
DECIMALS
1.5 6.0
MOVE DECIMAL TO
MAKE THE DIVISOR
A WHOLE NUMBER
DECIMALS
.15 6.00
MOVE DECIMAL TO
MAKE THE DIVISOR
A WHOLE NUMBER
DECIMALS
1.5 .06
MOVE DECIMAL TO
MAKE THE DIVISOR
A WHOLE NUMBER
DECIMALS
DON’T LINE THEM UP!!
COUNT ….
TOTAL DECIMAL PLACES!!
6.04
X2.5
15.100
3020
+1208
15100
A NUMBER BY
10, 100, 1000, 10000
COUNT ZEROS
MOVE DECIMAL TO
THE
A NUMBER BY
10, 100, 1000, 10000
COUNT ZEROS
MOVE DECIMAL TO THE
CONVERSION
BIG
TO SMALL
X BY 16
X BY 100
X BY 36
CONVERSION
BIG
SMALL TO
÷BY 16
÷BY 100
÷BY 60
PERCENT
PER HUNDRED
PERCENT
OF A NUMBER
25
25
USE FOR TIPS, TAX, AND SALES!
DECIMAL TO
DECIMAL 2 TO THE
RIGHT
1.85
TO
DECIMAL
DECIMAL 2 TO THE
LEFT.
.285
FRACTIONTO
1.TOP DOG IN THE HOUSE
17
 .85
20
2.DECIMAL TO
0.85
85%
TO
1.
2.
FRACTION
TO DECIMAL
28.5%
.285
PLACE VALUE AS FRACTION
& SIMPLIFY
285
57

1000
200
TAX
MULTIPLY
ADD
• BYABOUT 8 CENTS OR $0.08
FOR DENTON TEXAS.
• BACKONTO THE TOTAL COST.
TOTAL WITH
X .08 =
TAX
TOTAL COST= $3.6296 OR 45.37 + 3.63 =
$3.63
$45.37
$49.00
HALF
X BY .5
1
X BY 2

BY
2
61
NUMBERS
.5
122
THAT EQUAL
HALF
1
17
00.5000
.50 0.500
2 0.5 0.50 .500 34
HALF OF HALF
HALF
HALF OF
HALF
1 1
1
 
2 2
4
1
4
OR
.25
DIVISIBILITY
SIMPLIFY
FRACTIONS
27
57
SIMPLIFY
27 X

PROPORTIONS 57 38
27  3
9

57  3 19
9
X

19 38
SIMPLIFY RATIOS
SIMPLIFY RATES
4 OUT OF 28
FREE THROWS
1 OUT OF 7
FREE THROWS
2 FOR $1.50
1 FOR $0.75
FACTORS
WHAT 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
GCF
GREATEST COMMON FACTOR
GCF OF
36 AND 90
1 36
2 18
3 12
4
9
6
6
1 90
2 45
3 30
5 18
6 15
10 9
GCF =18
DIVISIBILITY
BY “ ”
27 27  9 3

45 45  9 5
SUM OF THE DIGITS is
DIVISIBILITY
BY “ ”
3942
SUM OF THE DIGITS is
DIVISIBILITY
BY “ ”
9
27 27  3

57 57  3 19
SUM OF THE DIGITS is , ,
DIVISIBILITY
BY “ ”
7341
SUM OF THE DIGITS is , ,
DIVISIBILITY
BY “ ”
28 28  4 7
108 108  4 27
EVEN AND
ARE
04, 08, 12, 16, 20, 24, 28, 32, …..
DIVISIBILITY
BY “ ”
136
EVEN AND
ARE
04, 08, 12, 16, 20, 24, 28, 32, …..
DIVISIBILITY
BY “ ”
18 18  6 3
48

6
8
48
EVEN AND SUM OF DIGITS IS
DIVISIBILITY
BY “ ”
978
EVEN AND SUM OF DIGITS is
DIVISIBILITY
BY “ ”
3.5 3.5  5 .7

10 10  5
2
LAST DIGIT IS A “ ” OR “ ”
DIVISIBILITY
BY “ ”
3.75
LAST DIGIT IS A “ ” OR “ ”
DIVISIBILITY
BY “
50
330
50  10

330  10
”
5
33
LAST DIGIT IS A “ ”
Move decimal once to the left
DIVISIBILITY
BY “
”
3170
LAST DIGIT IS A “ ”
Move decimal once to the left
DIVISIBILITY
BY “ ”
3.178
LAST DIGIT IS A
“
”
CHECKIE
THINGY
7 39
4 
8 8
OR
FRACTIONS
FRACTIONS
AINT NO PROBLEM
TOP TOP AND
BOTTOM BOTTOM
2 3 27 3
5  

5 4
5 4
81
1

4
20 20
FRACTION
A
#
⅔ OF 84
2 84 168


3
1
3
FRACTIONS
DON’T CRY!!
FLIP THE Right & MULTIPLY
3 1 28 1
5  

5 3 5
3
28 3 84


5 1
5
4
 16
5
RECIPROCAL
FLIP THE
2 5 2 1
  
3 1 3 5
MULTIPLES
A NUMBER’S MULTIPLICATION FACTS
MULTIPLES OF 72:
72, 144, 216, 288,
360, 432, 504, 576,
648, 720, 792, 864…
LCM
LEAST COMMON MULTIPLE
LCM OF
36
AND
90
36 2=72
90 2=180
X
X
36X3=108
36X4=144
36X5=180
90X3=270
90X4=360
LCM =180
PERIMETER
TOTAL DISTANCE AROUND
THE OUTER EDGES
JUST ADD!
FENCE, BORDER, TAPE, CUT
AROUND, FRINGE, LACE, CUFF,
OUTLINE, FRAME, EDGE,
TRACE,
AREA
TOTAL INSIDE FLAT SPACE
MEASURED IN SQUARE UNITS
USES MULTIPLICATION!!
FLAT SPACE, INSIDE, PAINT,
CARPET, COVER, SPREAD,
ROOM, TILE, MOW LAWN,
VACUUM, ….
MEASURES OF CENTRAL
TENDENCY
MEAN MODE
MEDIAN
CONCLUSION OF THE
DATA
Average
+, ÷
MEDIAN
Middle #
MODE
MOST
RANGE
Highest
– lowest
WHOLE NUMBERS
ARE
ARE NOT
•RATIONAL
•IRRATIONAL
•IMPROPER
•PROPER
•LESS THAN
•EQUAL TO OR
ONE
MORE THAN 1
DECIMAL OUT OF SIGHT
TO THE RIGHT!!
RATIONAL
ARE NOT
π
CAN BE MADE INTO A
FRACTION
1 4
67, …
-8 -38 -101…..
⅔ ⅓ ½
.833333333…… 6 
1.625
2.4494897....
16  4
IRRATIONAL
CAN NOT BE MADE
INTO A FRACTION
π
6
2.4494897....
DECIMAL GOES ON
FOREVER WITH NO
REPEATING PATTERN
INEQUALITIES
READ LEFT TO RIGHT
=
EQUAL
TO
INEQUALITIES
READ LEFT TO RIGHT
5
2.83 = 2
6
IS EQUAL
TO
INEQUALITIES
READ LEFT TO RIGHT
-4 2
INEQUALITIES
READ LEFT TO RIGHT
2 -4
CONSECUTIVE
ONE AFTER THE OTHER
CONSECUTIVE PRIME
NUMBERS
1, 3, 5, 7, 11, 13, 17, 19, 23..
PRIME NUMBERS
ONLY TWO FACTORS
ONE AND ITSELF
3 = 1X3
5 = 1X5
7 = 1X7
19 = 1 X 19
11 = 1 X 11
13 = 1 X 13
17 = 1 X 17
23 = 1 X 23
COMPOSITE
NUMBERS THAT HAVE MORE THAN 2
FACTORS
UNPOPULAR
COMPOSITE NUMBERS:
THEYLOOKPRIME,BUTAREACTUALLYCOMPOSITE!
39, 51, 57, 87,
91, 117,
119,
133, 203
AND
5.007
FIVE AND SEVEN THOUSDANDTHS
1¾
ONE AND THREE FOURTHS
INTERVALS
SKIP COUNTING
EXAMPLE: AN INTERVAL OF
1
8
.125 .25 .375 .5 .625…
FREQUENCY TABLE
SHOWS THE NUMBER OF TIMES AN EVENT
OCCURS
BAR GRAPH
DISPLAY, REPRESENT,
COMPARE DATA
90
80
70
60
50
40
30
20
10
0
GIRLS
BOYS
PERIODPERIOD
1
PERIOD
2
PERIOD
3
4
LINE PLOT
A NUMBER LINE THAT USES “X” MARKS
TO SHOW THE FREQUENCY OF AN EVENT
X
X
X
X
XX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
M
L
XL
XXL
XS
# OF TEAM UNIFORMS
S
LINE GRAPH
SHOW A CHANGE OF DATA OVER
VERTICAL AXIS
100
90
80
70
60
50
40
30
20
10
0
TIME
East
West
North
2005
2006
2007
2008
HORIZONTAL AXIS
CIRCLE GRAPH
PARTS OF THE WHOLE 100%
REPRESENTS DATA parts AS A
FRACTION, DECIMAL, OR PERCENT
.25 ¼
OR 25%
ELECTRIC
GAS
.2, 1/5,
OR 20%
PHONE
WATER
CAR
HOUSE
VENN DIAGRAM
USES OVERLAPPING SHAPES TO
SHOW HOW DATA IS RELATED
WHOLE NUMBERS FROM 1 TO 10
PRIME
EVEN
NUMBERS
NUMBERS
1,3,5
7
9
2
4, 6, 8,
10
STEM AND LEAF PLOT
11, 13, 14, 15, 21, 24,
27, 27, 34, 35, 34, 36
STEMS
1 1,3,4,5
2 1,4,7,7
3 4,4,5,6
LEAF(S)
HISTOGRAM
A GRAPH THAT DISPLAYS DATA FROM A
STEM AND LEAF PLOT.
Groups information together!!
PATTERN
SHAPES, SYMBOLS OR
NUMBERS THAT OCCUR IN
A PREDICTABLE ORDER.
3, 9, 27, 81, 243…..
POSITION
THE NUMBER THAT TELLS WHERE
SOMETHING OCCURS IN A PATTERN
POSITION
1
2
3
4
5
3, 9, 27, 81, 243…..
TERM
THE ACTUAL NUMBERS IN A
PATTERN OR
ANSWERS IN A SEQUENCE
POSITION
1
2
3
TERMS
3
9
27
4
5
81 243
SEQUENCE
A PATTERN WHERE A RULE SHOWS
THE RELATIONSHIP BETWEEN THE
POSITION AND THE TERM
POSITION
1 2 3
4
TERMS 3 9 27 81
10
N
3
3
10
N
3
3 TO THE POWER OF THE POSITION
RULE :
n
RULE
An expression that describes the
relationship between the
POSITION and TERM
.5n
ORDER OF OPERATIONS
2
3
P
6(7)
6y
6 7
6 7
5y
42
7
7 42
42  7
DIVISION
DIVISION
INTEGERS
POSITIVE AND
NEGATIVE WHOLE
NUMBERS
+
1
-72
-1001
29
INTEGER EXPRESSION
NUMBER LINE
1+3+3-8
ABSOLUTE VALUE
8=8
-13=13
DISTANCE FROM 0
OR
INTEGERS
MOVE ON A NUMBER LINE
1+3+3-8
INTEGERS
MOVE
ON A
NUMBER LINE
MOVE RIGHT 7
MOVE RIGHT 6
+(6)
+7
-(-3)
MOVE RIGHT 3
DOUBLE
NEGATIVE!
INTEGERS
MOVE
ON A
NUMBER LINE
MOVE LEFT 9
MOVE LEFT 9
-(9)
-1
+(-3)
MOVE LEFT 3
SUBTRACTING INTEGERS
IT’S ADDING A NEGATIVE!!
-7-8
-15 IS
THE
ANSWER
-7+(-8)
MOVE LEFT 8
SUBTRACTING INTEGERS
IT’S ADDING A NEGATIVE!!
7-8
-1 IS THE
ANSWER
7+(-8)
MOVE LEFT 8
T CHART
EVALUATING INTEGER EXPRESSIONS
14-24+2+(-12)
20 More negatives, so a
negative answer
DOUBLE NEGATIVES
Become
PUNCH
EM
OUT!
or
INTEGERS
 24  3  72
 72
 3
 24
or
INTEGERS
24  3  72
72

 3
24
$120 FOR 15 HOURS
$120
15h
UNIT RATE
DENOMINATOR OF 1
$8
1h
RATIO
45 STUDENTS 18 GIRLS
GIRLS TO STUDENTS
18
2
OR
45
5
BOYS TO GIRLS
27
3
OR
18
2
PROPORTION
$8 $150

1h
?h
CROSS PRODUCTS
ARE EQUAL
$8 $150

1h
?h
8h  150
CONGRUENT
SAME SIZE
SIMILAR
DIFFERENT SIZE
SAME SHAPE
CORRESPONDING
SAME LOCATION
~
SIMILAR
SAME SHAPE DIFFERENT SIZE
A
B
~
a b
SCALE
1: 3
ON A MAP, 1 CM
REPRESENTS 3 KM
1CM
3KM
ACUTE ANGLES
LESS THAN 90˚
50 ˚
89.5 ˚
22 ˚
OBTUSE ANGLES
MORE THAN 90˚
91 ˚
RIGHT ANGLES
90˚
90 ˚
90 ˚
STRAIGHT ANGLES
180 ˚
COMPLEMENTARY
ANGLES
ADD TO 90 ˚
31˚
59˚
31 + 59 = 90
SUPPLEMENTARY
ANGLES
ADD TO 180 ˚
133˚
47˚
47 + 133 = 180
ADJACENT ANGLES
SHARE A
VERTEX AND SIDE
VERTICAL ANGLES
SHARE A VERTEX
OPPOSITES
ARE EQUAL!
115˚
65˚
65˚
115˚
CORRESPONDING
ANGLES
SAME LOCATION
ARE EQUAL!
75˚
75˚
CONGRUENT
ANGLES
ARE EQUAL!
47˚
47˚
PLANE
INTERSECTING
LINES
PARALLELL
LINES
NEVER
INTERSECT
PERPINDICULAR
LINES
INTERSECT
TO FORM 90˚
RIGHT
ANLGES
A CLOSED FIGURE
WITH STRAIGHT SIDES
4 SIDES
QUADRILATERAL
QUADRILATERAL
TOP AND BOTTOM II AND
RIGHT AND LEFT II AND
OPPOSITE ANGLES

SQUARE
RHOMBUS
RECTANGLE

PARALLELOGRAM
QUADRILATERAL
RIGHT & LEFT TOP CORNERS
SUPPLEMENTARY ∠
RIGHT & LEFT BOTTOM CORNERS
SUPPLEMENTARY ∠
=180°
SQUARE
RHOMBUS
=180°
RECTANGLE
PARALLELOGRAM
QUADRILATERAL
TRAPEZOID
KITE
TRAPEZIUM
QUADRILATERAL
ANGLES ADD TO
360˚
40 ˚
100 ˚
40 ˚
90˚
80 ˚
90˚
90 ˚ + 90 ˚ + 100 ˚+80 ˚ = 360 ˚
3 SIDES
TRIANGLE
ACUTE
OBTUSE
RIGHT
ISOSCELES
ISOSCELES
EQUILATERAL
ACUTE
OBTUSE
ACUTE
RIGHT
SCALENE
SCALENE
SCALENE
ISOSCELES
TRIANGLE ANGLES
ADD TO 180˚
110 ˚
40 ˚
30 ˚
110 ˚+ 40 + 30 = 180
30˚
75˚
75˚
45˚
45˚
90˚
ISOSCELES
2 = SIDES
2 = ANGLES
REGULAR
POLYGON ALL SIDES EQUAL
REGULAR
OCTAGON
5 CM
5 CM
5 CM
5 CM
IRREGULAR
OCTAGON
3.141592….

PI

THE CIRCUMFERENCE THE
DIAMETER OF A CIRCLE
A LITTLE MORE
THAN 3!
DIAMETER

CIRCUMFERENCE
THE PERIMETER OF A CIRCLE
MULTIPLY PI x d
C  πd
DIAMETER
MULTIPLY PI x 2r

C 2 r
RADIUS
CIRCUMFERENCE
PERIMETER , DISTANCE
AROUND, EDGE, RIM, FENCE,
BORDER…
AREA
INSIDE SPACE, INSIDE FLAT SQUARES,
COVER, OVERLAY, CARPET, FLOOR, ….
RADIUS
RADIUS
HALFWAY ACROSS A CIRCLE
FROM THE CENTER
2r=d
DIAMETER
DIAMETER
ALL THE WAY ACROSS A CIRCLE
THROUGH THE CENTER
d
d
r
2
EQUALS
EVALUATE
SIMPLIFY OR SOLVE
GET AN ANSWER!
EXPRESSION
A MATH
SENTENCE
NO EQUAL SIGN
NUMERICAL
EXPRESSION
HAS ONLY NUMBERS
3  (3  3 )
3
3 3
3
2
EVALUATE THEM!
VARIABLE
EXPRESSION
HASNUMBERS
ANDVARIABLES
3X
2Y+4
SUBSTiTUTION
VARIABLE OUT
NUMBER IN
VARIABLE
A LETTER
REPRSENTS AN AMOUNT OR QUANTITY
EQUATION
MATH SENTENCE
WITH = SIGN
(b1  b 2 )h
A
2
SOLVE FOR THE
VARIABLE
3X - 4 = 5
X = ????
THE
TO THE
OF
POWERS
EXPONENTS
POWER OR
EXPONENT
BASE
=
CUBED
RD
3
POWER
VOLUME of CUBE
V=SxSxS
S
S
S
S³
SQUARED
ND
2
POWER
AREA of SQUARE
A=SxS
S
S
S²
SQUARE ROOT
SQUARE ROOT
SQUARE ROOT
DIVISION
3 ways
BABY ADULT TEEN
BABY ÷
REMAINDER
r1
5
3 16
15
ADULT ÷
REMAINDER
AS FRACTION
1
5
3
3 16
15
1
TEEN ÷
DECIMAL
KEEP DIVIDING!
5.
3 16.
15
1
1
TESSELATIONS
RELFECTIONS
TRANSLATIONS
ROTATIONS
TESSELATIONS
RELFECTIONS
REFLECT
ACROSS Y AXIS
Y STAYS THE SAME
REFLECT
ACROSS X AXIS
X STAYS THE SAME
TRANSLATION
SLIDE`
ROTATION
TURN
COORDINATE PLANE
QUADRANT
QUADRANT
(+X,+Y)
(-X,+Y)
POINTOFORIGIN
START
QUADRANT
QUADRANT
(-X,-Y)
(+X,-Y)
ORDERED PAIR
-LEFT OR
+RIGHT
FIRST
-DOWN OR
+UP NEXT
LOCATION OF A COORDINATE POINT
COORDINATE POINT
(-4, 3)
+3
(-X, Y)
-4
AXIS
X AXIS
HORIZONTAL
Y AXIS
VERTICAL
EVEN
LAST DIGIT 0, 2, 4, 6, 8
ODD
LAST DIGIT 1, 3, 5, 7, 9
SYMMETRY
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