quick reference guides
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NUMBER &
OPERATIONS IN
BASE 10
OPERATIONS &
ALGEBRAIC
THINKING
NUMBER AND
OPERATIONS
FRACTIONS
SKILL
PAGE NUMBERS
Place Value
Standard Form, Expanded Form, Word Form
Comparing Numbers
Rounding Numbers
Whole Numbers (Adding, Subtracting, Multiplying &
Dividing – How to)
Decimals (Adding, Subtracting, Multiplying & Dividing
– How to)
1-2
•
•
•
•
•
•
•
•
Multiplication Traditional Algorithm
Division Traditional Algorithm
Fact Families
Properties of Multiplication
Patterns
Order of Operations
Prime & Composite
Multiples & Factors
3
•
Vocabulary: Numerator, Denominator, Mixed
Number, Improper Fraction, Simplest Form,
Equivalent
Fractions (Adding, Subtracting, Multiplying & Dividing
– How to)
4
•
•
•
•
•
•
•
MEASUREMENT
& DATA
•
•
•
•
•
•
•
Units of Measure
Measurement Conversions
Liquid Measurement
Types of Angles
Types of Lines
Line Plot
Area, Perimeter & Volume
GEOMETRY
•
•
•
•
Polygons Hierarchy
Types of Lines
Lines of Symmetry
Coordinate Grids
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5-6
7
MaTH
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VALUE
,
,
1
ONES
TENS
HUNDREDS
ONE
THOUSANDs
TEN
THOUSANDs
HUNDRED
THOUSANDs
The
How much
location of a digit is
a digit.
worth.
2 7 5 6 4 3
ONE MILLION
PLACE
STANDARD FORM
24,613
WORD FORM
Twenty-four thousand, six hundred thirteen
Using base ten blocks to represent the number.
20,000 + 4,000 + 600 + 10 + 3
BASE TEN FORM
EXPANDED FORM
less than
Nearest
hundreds
AD
IO
T
I
D
greater than
3,452 3,500
N
TIO
C
A
TR
B
SU
ADDEND
ISI
V
I
D
equal to
ADDEND
SUM
TIO
A
LIC
P
I
LT
U
M
ON
DIVIDEND
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DIVISOR
QUOTIENT
N
N
MINUEND
SUBTRAHEND
FACTOR
FACTOR
DIFFERENCE
PRODUCT
VALUE
,
.
THOUSANDTHS
HUNDREDTHS
TENTHS
ONES
TENS
HUNDREDS
ONE
THOUSANDs
The
How much
location of a digit is
a digit.
worth.
TEN
THOUSANDs
9 6 4 3 8 7 2 1 5
HUNDRED
THOUSAND
PLACE
STANDARD FORM
43.284
WORD FORM
Forty-three AND two hundred eighty-four thousandths
EXPANDED FORM
40 + 3 + 0.2 + 0.08 + 0.004
less than
Nearest
tenth
4.38
equal to
greater than
4.4
ADDING DECIMALS
SUBTRACTING DECIMALS
Line up the numbers by their place value
Line up the numbers by their place value
MULTIPLYING DECIMALS
DIVIDING DECIMALS
q Move the decimal out of each factor
q Multiply
q Place the decimal back into the product
q Move the decimal out of the divisor
q Move the decimal the same in dividend
q Move decimal up to quotient
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Grouping Symbols
104
Exponents
Multiplication
Division
Addition
Subtraction
RIGHT
LEFT
PROPERTIES OF MULTIPLICATION
Identity Property
Any number multiplied by one is that number.
Zero Property
Any number multiplied by zero equals zero.
Commutative Property
If you change the order of the factors, the product remains the same.
Associative Property
The factors can be grouped in any way, and the product will remain the same.
Distributive Property
A problem can be broken into smaller facts.
PRIME
COMPOSITE
factors
A
number
that has
exactly
two
factors.
A
number
that has
two or
more
factors.
Numbers A sequence
of
which are
products
multiplied
made by
together to multiplying
get
two
another
numbers
number.
together.
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multiples
Add
2
Subtract Add Subtract
1
2
1
x
y
Multiply by 2
Add 4
2
4
4
8
8
12
16
16
NUMERATOR
PART OF A WHOLE
PARTS SHADED
DENOMINATOR
TOTAL PIECES IN WHOLE
less than
XED R
I
M
E
MB
U
N
ST
E
L
P
SIM RM
FO
A whole
number and
a fraction
equal to
ER
P
RO ON
P
IM CTI
FRA
greater than
When the
numerator
is greater
than the
denominator
NT
E
L
IVA
U
EQ
ADDITION &
SUBTRACTION
If the denominators are different, find the least common
denominator (LCD). When denominators are the same,
add and subtract the numerators only.
MULTIPLICATION
Multiply straight across
Keep – Change - Flip
DIVISION
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UNITS OF MEASURE
LENGTH
WEIGHT
CAPACITY
CUSTOMARY
Inches (in.)
Feet (ft.)
Yards (yd.)
Miles (mi.)
Ounces
(oz.)
Pounds
(lb.)
Tons (T.)
Fluid Ounces
(fl. oz.)
Cup (c.)
Pint (p.)
Quart (qt.)
Gallon (gal.)
METRIC
Meter (m)
Gram (g)
Liter (L)
TYPES OF LINES
RAY
INTERSECTING
LINE
PARALLEL
LINE
SEGMENT
QQ
QQ
PP PP
PP PP
CC
CC
CC
CC
CC
CC
CC
CC
STRAIGHT
ANGLE
RIGHT
ANGLE
ACUTE
ANGLE
OBTUSE
ANGLE
An angle
that
measures
exactly 180
degrees.
An angle
that
measures
exactly 90
degrees.
An angle
that
measures
LESS than 90
degrees.
An angle
that
measures
MORE than
90 degrees
but LESS than
180 degrees.
PERPENDICULAR
Line plots show how frequently something occurs by displaying data on a number line.
The distance, in units, around the outside of a shape.
P = SIDE + SIDE + SIDE …
The measure of space inside a shape, in square units.
A = LENGTH x WIDTH
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MEASUREMENT CONVERSIONS
K
H
D
!
D
KILO-
HECTO-
DECA-
UNIT
DECI-
METRIC
M
CENTI- MILLI-
METER (m)
LITER (L)
GRAM (g)
DIVIDE BY 10
CUSTOMARY
C
MULTIPLY BY 10
LENGTH
WEIGHT
CAPACITY
Inches (in.)
Feet (ft.)
Yards (yd.)
Miles (mi.)
Ounces (oz.)
Pounds (lb.)
Tons (T.)
Fluid Ounces (fl. oz.)
Cup (c.)
Pint (p.)
Quart (qt.)
Gallon (gal.)
Meter (m)
Gram (g)
Liter (L)
Line plots show how frequently something occurs by displaying data on a number line.
The distance around the outside of a shape.
P = SIDE + SIDE + SIDE …
The measure of space inside a shape, in square units.
A = LENGTH x WIDTH
The amount of space a 3-D object occupies.
V = LENGTH x WIDTH x HEIGHT
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TYPES OF LINES
RAY
LINE
LINE SEGMENT
PARALLEL
INTERSECTING
PERPENDICULAR
OTHER
POLYGONS
TRIANGLES
EQUILATERAL
QUADRILATERALS
PENTAGON
ISOSCELES
SCALENE
PARALLELOGRAM
TRAPEZOID
HEXAGON
RIGHT
OCTAGON
RHOMBUS
RECTANGLE
DECAGON
SQUARE
symmetrical
NON SYMMETRICAL
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Y AXIS à VERTICALLY
5
4
X
Y
4
2
3
2
1
1
2
3
4
5
X AXIS à HORIZONTALLY