Math Vocabulary
Account - an arrangement made with a bank whereby one may deposit and withdraw
money and in some cases be paid interest
Acute angle - an angle that has a measure less than a right angle (less than 90° and
greater than 0°)
Example:
Acute triangle - a triangle that has three acute angles
Example:
Addend - a number that is added to another in an addition problem
Example:
Addition (sum) - the process of finding the total number of items when two or more
groups of items are joined; the opposite or inverse of subtraction
Additive pattern – a pattern that has an addition rule that allows the pattern to change
in a predictable manner
Example: AB, ABC, ABCD [adds the next letter in the alphabet]; 2,4,6,8 [adds 2 to
each value]
Adjacent - next to each other, having a common side or point
Example:
Algorithm - a step-by-step process for solving a problem
Analog clock – a clock or watch that has numbers 1 – 12 on its face and two hands to
show the time
Example:
Page 1
Ang
gle - a sha
ape forme
ed by two line segm
ments or ra
ays that share
s
the same
s
endpoint
Example:
Ape
ex - the to
op, the hig
ghest poin
nt, the poiint furthes
st from the base
Example:
App
proximattion - see estimate
Arc
c - a part of
o any currve
Example:
Are
ea – the number of square un
nits that cover
c
a figure – the amount of
o surface that is
contained witthin a bou
undary
Exa
ample: Th
he square has an arrea 25 squ
uare units
Are
ea model – a rectangular grid formed from squa
are units
Arrangemen
nt – a sele
ection of items in which
w
orde
er is important
Array – a sett of items arranged
d in rows and
a
colum
mns
ample: A 4 by 10 arrray is sho
own below
w
Exa
Page 2
Asc
cending Order
O
- go
oing upwa
ard, increa
asing in va
alue
Exa
ample: 2, 3, 4, 5, 6,, . . .
sociative Property
y - a prope
erty of addition or multiplicat
m
tion where
e the grou
uping of
Ass
the addends or factors
s does not change the outcom
me of the operation
o
Exa
ample: (5 + 8) + 4 = 5 + (8 + 4) or (2
2 × 3) × 4 = 2 × (3
3 × 4)
eristic thatt helps de
efine a figu
ure
Attribute – a characte
Ave
erage - on
ne score that
t
represents a whole collection of sc
cores. The average
e is found
by adding
a
all the score
es togethe
er and dividing the answer
a
(sum) by th
he numberr of scores
s
Axis/Axes - the horiz
zontal (x-a
axis) and vertical
v
(y
y-axis) number lines on a coo
ordinate
plan
ne
Exa
ample:
Balance - 1)) an equal distribution of weig
ght 2) the
e amount of money
y in a bank
k account
Barr graph – a graph with
w
horizontal or vertical bars that rep
presents categoric
c
cal data
Exa
ample:
Bas
se (geom
metry) - in
n two dim
mensions, one
o
side of
o a triang
gle or para
allelogram
m that is
used to help find the area. In th
hree dime
ensions, a plane figu
ure, usually a polyg
gon or
circle, by whiich a three
e dimensio
onal figure
e is measured or na
amed
Exa
amples:
Page 3
Base-ten system – a number system based on multiples of 10, where each digit has
ten times the value of the same digit one place to its right and ten times less than the
value of the same digit one place to its left
Basic Facts - operations (adding, subtracting, multiplying and dividing) performed with
one-digit numbers
Benchmark Fractions - common fractions that you can use to judge other numbers
against
Example:
Bi - a prefix that means two or twice
Example: A biplane has two wings
Bisect - to cut or divide something into two equal parts
Example:
Borrower - A person or company that has received money from another party with the
agreement that the money will be repaid
Brackets - see parentheses
Budget - an organized plan for spending and saving money
Benchmark - a familiar number used as a point of reference
Calculate - to work out or find the answer
Capacity – the maximum amount a container will hold when filled
Cardinal Number – counting numbers denoting a quantity
Categorical Data - a set of data is sorted or divided into different categories or groups,
according to the attributes of the data. Bar graphs, pie charts, picture graphs and
frequency tables are used to graph categorical data
Page 4
Cause – a reason for an action
Celsius (˚C) - a metric scale for measuring temperature
Cent “¢” – a symbol used to identify that the total is less than a dollar and represented
in coins
Example: 56¢
Center - a point in the middle of something
Centimeter (cm) - a metric unit used to measure length or distance
(0.01 meter = 1 centimeter)
Certain event – in probability, an event that will always happen
Chance - a likely hood of an event happening (impossible, less likely, equally likely,
most likely, certain)
Chart - a diagram that illustrated or displays information in the form of a table, graph or
picture
Check - an order in writing to a bank asking that a certain sum of money be paid out of
one’s account
Example:
Chronological Order - the arrangement of events by when they happened, with the
earliest coming first
Circle - a two-dimensional closed shape made by drawing a curve that is always the
same distance from a center
Example:
Circumference - the distance around a circle
Classification - organization or collection of items into groups or sets according to
attributes
Page 5
Classify - to organize,, order or sort thing
gs or peop
ple to grou
ups based on attributes or
characteristic
cs
hich the ha
ands of an
n analog clock norm
mally trave
el
Clockwise - the directtion in wh
ample:
Exa
Closed figurre - a figu
ure that be
egins and ends at th
he same point
p
Examples:
Coin value – describe
es what the coin is worth
w
in dollars and
d/or cents
Com
mbination
n – a sele
ection of ittems in wh
hich orderr does nott matter
mmon de
enominator - a com
mmon multiple of tw
wo or morre denominators
Com
ଵ
ହ
Exa
ample: Som
me common denom
minators fo
or and are 12, 24
4, and 36
ସ
଺
Com
mmon fac
ctor(s) – a factor or
o set of fa
actors sha
ared by tw
wo or more
e numbers
Example: 1, 2,
2 3, 4, 6 and 12 arre commo
on factors of 12 and
d 24
Com
mmutativ
ve proper
rty – a pro
operty of addition or
o multiplication wh
here the su
um or
prod
duct stays
s the same
e when th
he order of the adde
ends or factors is ch
hanged
Example: 3+4 = 4+3 or
o 2x6 = 6x2
6
mpare - lo
ook for diffferences or similarrities
Com
Com
mparative
e statement – a sttatement that describes whether numbers are equal
e
to,
less
s than, or greater th
han each other
o
Examples: 5 < 6, 6 > 5, 6 ≠ 5, 5 = 5
Com
mpatible Numbers
s – numbe
ers that are easy to
o compute
e mentally
y
Com
mplemen
nt - sometthing that completes or fills up
u a whole
e
Com
mpose – to
t combin
ne decomp
posed num
mbers toge
ether to fo
orm a num
mber
Exa
ample: 30
00 + 40 + 9 compos
sed is 349
9
Com
mposite number
n
– a whole number with
w
more than two factors
Exa
ample: 4 is
s composite becaus
se it has 1, 2, and 4 as factorrs
Page 6
Con
ne - a 3-dimensiona
al shape with
w
a circular base,, a curved
d surface and
a
one vertex
Exa
ample:
Con
ngruent – two figures that are exactly
y the same
e size and
d same shape
Con
nsecutive
e multiple
es – see skip
s
countting
nservatio
on of num
mber – the
e understa
anding tha
at the num
mber of ob
bjects rem
mains the
Con
sam
me when the objects
s are rearranged sp
patially
Example:
ntext – th
he story sc
cenario that provide
es clarity to
t the mo
odel, proce
ess, and/o
or
Con
ope
eration nee
eded to so
olve the siituation
Con
nvert - a change in the form of a measurement, differentt units, without a ch
hange in
the size or am
mount
Exa
ample:
Coo
ordinate grid
g
- a grid
g
formed by a horizontal lin
ne called the
t
x-axis
s and a ve
ertical line
calle
ed the y-a
axis
Exa
ample:
ordinates
s - a set of numbers
s or letterrs that sho
ows the po
osition of a point on
na
Coo
coordinate grrid. The fiirst number in the pair
p
is the
e x-coordin
nate, the second
s
nu
umber is
the y-coordin
nate – see
e example for Axis
Con
ngruence
e Marks - marks on
n a geome
etric shape
e that indicate cong
gruence
Exa
amples: None of the sides
Oppo
osite sides
s are
or angles are
cong
gruent, all angles
congruent
are congruent
c
t
Page 7
Constant - a number that always remains the same value in an equation, opposite of
variable
Converging lines - two or more lines that meet at the same point
Credit card - an identification card issued by a bank that allows a user to buy items and
services immediately and pay the cost at a later time. The bank might charge the user
interest in exchange for the use of the money
Cube - a three-dimensional figure with six congruent square faces
Example:
Cubic unit - a unit used to measure volume such as cubic foot or cubic meter
Example:
Cup (c) - a customary unit used to measure capacity (8 ounces = 1 cup)
Example:
Curved surface – a surface with no edges
Customary measurement – the system of measurement used in the United States
Examples: Inches, Feet, Yards, Miles, Ounces, Pints Quarts, Gallons, Pounds
Cylinder - a 3-dimensional shape with 1 curved surface and 2 circular bases that are
parallel and congruent
Example:
Data – numbers or information that are/is collected from a survey or experiment –
information that is collected about people, events, or objects often to draw conclusions
about them
Page 8
Deb
bit card - an identification ca
ard issued
d by a ban
nk that allo
ows a use
er to imme
ediately
rem
move mone
ey from an accountt
c - a prefix
x that me
eans 10
Dec
Dec
cagon - a polygon with ten sides
s
and ten angles
s
Exa
amples:
Des
scending order -going down
nward, de
ecreasing in
i order
Exa
ample: 9, 8,
8 7, 6, . . .
Dec
cimal – an
nother name for a decimal
d
frraction, wh
hich is a fractional number
n
w
with
a
den
nominator of ten or a power of
o ten
Dec
cimal point - A sym
mbol used
d to separa
ate dollars
s from cen
nts in mon
ney, and to
t
separate the ones plac
ce from the tenths place
p
in a decimal
Dec
compose – the pro
ocess of se
eparating numbers into their place valu
ue components
Exa
ample: 349
9 decomposed is 30
00 + 40 + 9
Dec
crease - to
t get sma
aller in siz
ze or number
Ded
duce - to come up with an answer by logic or by
y putting pieces of informatio
on
toge
ether
Ded
duct - to take
t
away
y, anotherr word for subtract
gree - a unit
u
used for
f measu
uring angle
es and tem
mperature
e
Deg
nominato
or - the nu
umber bellow the ba
ar in a frac
ction that tells how many equal parts
Den
are in the wh
hole or in the
t
group
Exa
ample:
posit -to put money
y into a bank accou
unt
Dep
Diagonal - a straight line joinin
ng two opp
posite corn
ners of a square,
s
re
ectangle, or
o other
stra
aight-sided
d shape
Exa
ample:
Page 9
Diffference (subtract
(
tion) – the
e answer to a subtrraction pro
oblem
Dig
git – any numeral
n
frrom 0 – 9 used to write
w
numbers
Dig
gital clock
k – a clock
k or watch
h that sho
ows time by
b numberrs; it has no clock hands
h
Exa
ample:
ect mode
eling – the use of objects,
o
m
manipulativ
ves, and/o
or illustrations to represent
Dire
dire
ectly the solving pro
ocess of a problem
Dim
mension - a measure in one direction:: one dime
ension objjects only have a le
ength, two
o
dim
mension ob
bjects have a length
h and a wiidth and three dime
ension objects have
e a length,,
widtth and height
Exa
amples:
Distributive
e Property
y - the pro
operty tha
at states that
t
multip
plying a sum by a number
n
is
ng each ad
ddend in the sum by
y the num
mber and then
t
addin
ng the
the same as multiplyin
prod
ducts
Exa
ample: 3 × (4 + 2)
2 = (3 × 4)
4 + (3 × 2)
3 × 6 = 12 + 6
18
8 = 18
vide - to separate in
nto equal groups; th
he opposite or inverse operation of
Div
mulltiplication
n
Div
vidend - the numbe
er that is to
t be divid
ded in a division pro
oblem
Exa
ample:
Div
visibility – the ability for a nu
umber to be divided
d withoutt a remain
nder
Page 10
Divisibility rules - patterns used to determine whether a number divides evenly into
another number
Divisible by
The Rule
2
last digit is 0, 2, 4, 6, 8
3
the sum of the digits is
divisible by 3
5
last digit is 0 or 5
Example
1502 is divisible by 2 because the
last digit is 2
1401 is divisible by 3 because
1+4+0+1 = 6
which is divisible by 3
1,246,735 is divisible by 5
because the last digit is a 5
Division (quotient)– The process of sharing a number of items to find how many equal
groups can be made or how many items will be in each equal group; the opposite or
inverse operation of multiplication
Divisor - the number by which the dividend is divided
Example:
Dot plot - a graph that records each piece of numerical data along a number line
Example:
Dozen - a group or set of 12
Duration – the amount of time something takes
Each - used to refer to every member of a group of people or things
Edge – the line segment where two faces meet on a three-dimensional figure
Example:
Effect – a result of an action
Page 11
Elapsed time - the tim
me that pa
asses betw
ween the start of an
n activity and the end
e
of thatt
activity
ual (=) – same amount or sa
ame size
Equ
Equ
ual to – a symbol (=) used to compare
e two num
mbers, witth the sam
me value
Exa
ample: 5 = 5
Equ
uality - be
eing equal
Equ
ually likely– all pos
ssible outc
comes hav
ve the sam
me probab
bility of oc
ccurring
Equ
uation – a statement showin
ng the equ
uality of tw
wo express
sions joine
ed by an equal
e
sign
n
Equ
uilateral triangle
t
- a trianglle with thrree congru
uent sides
s
Exa
ample:
Equ
uivalent - having th
he same value
v
or amount
Equ
uivalent fractions
f
– fraction
ns with diffferent names that representt the same
e value
Exa
ample:
Estimate – an
a answerr close to, or to app
proximate an exact answer - to make a well
info
ormed gue
ess (also called
c
approximation
n)
panded fo
orm – the
e represen
ntation of a numberr as a sum
m of place values
Exp
example:
985
5,156,789.782 as 90
00,000,00
00 + 80,000,000 + 5,000,000 + 100,0
000 +
50,0
000 + 6,0
000 + 700
0 + 80 + 9 + 0.7 + 0.08 + 0..002 or as
s 900,000,000 + 80
0,000,000
0
଻
଼
ଶ
+ 5,000,000 + 100,00
00 + 50,00
00 + 6,00
00 + 700 + 80 + 9 +
+
+
ଵ଴
ଵ଴଴
ଵ଴଴଴
Exp
panded notation – the repre
esentation
n of a num
mber as a sum of place values where
each term is shown as a digit tim
mes its pla
ace value
example:
985
5,156,789.782 as 9((100,000,,000) + 8((10,000,0
000) + 5(1
1,000,000
0) + 1(100
0,000) +
5(10,000) +6
6(1,000) + 7(100) + 8(10) + 9 + 7(0..1) + 8(0.01) + 2 (0.001) orr as
00) + 8(10,000,000
0) + 5(1,0
000,000) + 1(100,0
000) + 5(1
10,000) +6(1,000)
+
9(100,000,00
ଵ
ଵ
ଵ
8
+ 9 + 7 ( ) + 8(
)+2(
)
))
+ 7(100) + 8(10)
ଵ଴
ଵ଴଴
ଵ଴଴଴
pense - th
he amount of mone
ey that is needed
n
to pay for or
o buy som
mething
Exp
Page 12
Exp
pression – a mathe
ematical phrase
p
tha
at can contain ordinary numb
bers, unkn
nowns
(suc
ch as x orr y) and op
perators (such as add, subtra
act, multip
ply and/orr divide), but does
s
nott have an
n equal sign
Eva
aluate - to
o find the value of
Exa
ample: the
e value of 21 x 3 is 63
en - a who
ole numbe
er that has
s a 0, 2, 4,
4 6, or 8 in the one
es place
Eve
Eve
en pattern – a num
mber string
g or numb
ber sequence that only
o
conta
ains even numbers
n
ce – A poly
ygon that is a flat surface
s
of a solid fig
gure
Fac
Exa
ample:
ct families – A set of related
d multiplication and division, or addition and sub
btraction,
Fac
equ
uations; also called related facts
Exa
amples:
ctor – a number mu
ultiplied by
y another number to
t find a product
p
Fac
Fac
ctor tree - a diagra
am showin
ng the prim
me factors
s
Example:
hrenheit (°F)
(
- a customary
c
y scale for measurin
ng temperature
Fah
vorable Outcome
O
– the outc
come of in
nterest
Fav
ancial - relating
r
to
o money matters
m
Fina
Page 13
3
Finite - anything that has boundaries or can be counted
Fluency - is the ability to recall the answers to basic math facts automatically and
without hesitation
Fluid ounce (fl oz) - A customary unit used to measure liquid capacity
(1 cup = 8 fluid ounces)
Foot (ft) - a customary unit used to measure length or distance (1 foot = 12 inches)
Formula - a set of symbols that expresses a mathematical rule
Example: A = b × h (area = base x height)
Fraction – a number in the form
௔
௕
where a and b are whole numbers and b is not zero.
A fraction can be used to name part of an object, part of a set of objects, to compare
two quantities or to represent division.
Fraction Strip/Bar - a model to help students visualize (see) fractions
Example:
Frequency - the number of times an event occurs
Frequency table - a table that uses numbers to record data about how often something
happens
Example:
Front end estimation - keep the front digit the number make the remaining digits zero
Example: 349
300
Fundamental Counting Principle – an algebraic method to determine the number of
all possible outcomes in a sample space by multiplying the number of ways each event
can occur
Gallon (gal) - a customary unit used to measure capacity (4 quarts = 1 gallon)
Page 14
Generate - to produce a set or sequence by the application of defined rules or the
performance of defined operations
Geometry - the part of mathematics that deals with solids, surfaces, lines, angles and
space
Gram (g) - a metric unit used to measure mass (1,000 grams = 1 kilogram)
Greater than – a symbol (>) used to compare two numbers, with the larger number of
value given first
Example: 6 > 5 - spoken as "six is greater than five"
Greatest - most, largest
Greatest common factor (GCF) - the largest factor that two or more numbers have in
common
Example: 6 is the greatest common factor of 18 and 30
Graph - 1) a diagram used to indicate relationships between two or more variable
quantities, 2) to add data to a graph
Grid - evenly divided and equally spaced squares on a figure or flat surface
Example:
Gross income - income or pay before any taxes are taken out of it
Half (Halves) – two equal parts of a whole
Heft – to lift something in order to estimate its weight
Height - the length of a perpendicular from the base to the top of a two-dimensional or
three-dimensional figure
Examples:
Hept - a prefix meaning seven
Page 15
Heptagon - a polygon with seven sides and seven angles
Example:
Hex - a prefix meaning six
Hexagon - a polygon with six sides and six angles
Examples:
Horizontal - extending left and right, parallel with the horizon (the line at which the
earth's surface and the sky appear to meet)
Hour (h)- a unit used to measure time (1 hour = 60 minutes)
Hundredths - one of 100 equal parts, the second digit to the right of a decimal point
ହ଺
Examples: 0.56,
, fifty-six hundredths
ଵ଴଴
Identical - exactly alike
Identity Property of Addition - the property that states that when you add zero to a
number, the result is that number
Example: 5 + 0 = 5
Identity Property of Multiplication - the property that states that the product of any
number and 1 is that number
Example: 5 x 1 = 5
Impossible event – an event that will never happen
Improper fraction – a fraction with a numerator that is greater than or equal to the
denominator and whose value is equal to or greater than one
Example:
Inch (in.) - a customary unit used to measure length or distance (12 inches = 1 foot)
Increase - to get larger in size or number
Income - money earned, pay, salary
Page 16
Inc
come tax - money paid to a city, town
n, or state government or to the U.S.
gov
vernment based
b
on income
equality - a mathem
matical se
entence th
hat contain
ns the sym
mbol <, >, ≤, ≥, orr ≠, but
Ine
nott =
Infe
er - Come
e to a conclusion orr make a guess
g
based on obs
servation or
o logic
Infiinite - witthout bounds of size or numb
ber; unlim
mited, endless
Inte
erest (ra
ate) - the additional money paid
p
by a borrower
b
t a lende
to
er in excha
ange for
the use of the
e lender’s money. For
F examp
ple, you ea
arn interest from a bank if yo
ou have a
savings accou
unt and yo
ou pay intterest to a lender if you have
e a loan
Inp
put/outpu
ut machine or tab
ble – takes a numbe
er called the
t
input and
a
performs one
or more
m
operrations on it to prod
duce a new
w value ca
alled the output
o
Exa
ample:
Inte
egers - positive
p
or negative whole numbers inc
cluding 0
Exa
amples: -3
3, -2, -1, 0,
0 1, 2, 3
Inte
ersecting
g lines - lines that cross each other att exactly one
o
point
Exa
ample:
ersection
n - the point where two lines intersect
Inte
Exa
ample: Se
ee picture above
erval – The difference betwe
een one number and the nex
xt on the scale
s
of a graph
Inte
Inv
verse ope
erations - opposite operation
ns, or ope
erations th
hat undo each
e
otherr, such as
addition and subtractio
on or multtiplication and division
vest - to put
p valuab
ble resourc
ces into so
omething that you expect
e
will give you
ua
Inv
pers
sonal or fiinancial ga
ain
Exa
ample:
Page 17
7
Isosceles triangle - a triangle with two congruent sides
Example:
Joining – addition
Key - the part of a map or graph that explains the symbols
Kilo - a prefix meaning 1000
Kilogram (kg) - a metric unit used to measure mass (1,000 grams = 1 kilogram)
Kilometer (km) - a metric unit used to measure length or distance (1,000 meters = 1
kilometer)
Label - the horizontal title across the bottom and the vertical title along the side tells us
what kinds of facts are listed in a graph
Leading Zeroes - any 0 digit that comes before the first nonzero digit in a number
string in positional notation
Example: James Bond's famous identifier, 007, has two leading zeros
Least - smallest
Least common denominator - the smallest common multiple of two or more
denominators
ଵ
ହ
Example: The least common denominator for and is 12
ସ
଺
Least common multiple - the smallest number that is a common product of two or
more numbers
Example: The least common multiple of 3 and 5 is 15
Lend - to give (money) on condition that it is returned and that interest is paid for its
temporary use
Length – how long something is from end to end
Less likely – not expected to happen or a small chance to be true
Less than (<) - a symbol used to compare two numbers or two quantities, with the
lesser number given first
Example: 4 < 6, spoken, "four is less than six"
Page 18
Leveling – the process of adding a specific amount to one addend in order to make that
addend a multiple of ten and subtracting that same specific amount from the other
addend to find the total (e.g., 37 + 34, make one addend a multiple of ten, so in this
case, 3 is added to 37 and then you level the other addend by subtracting 3 from 34, so,
40 + 31 = 71)
Line - a straight path in a plane, extending in both directions with no endpoints
Example:
Line graph - a graph in which points are connected by line segments to show changes
in data over time
Example:
Line of symmetry (reflection) – an imaginary line on a two-dimensional figure that,
when folded, produces two halves that match identically
Example:
Line segment - a part of a line that includes two points called endpoints and all the
points between them
Example:
Linear unit - a one-dimensional measure of length, width, height, or distance
Liquid volume - the amount of liquid in a container
Liter (L) - a metric unit used to measure volume or capacity (1 liter = 1,000 milliliter)
Magnitude - the 'size' or 'quantity' of an object
Mass - the amount of matter in an object
Maximum - the greatest or biggest value
Mean - see average
Page 19
Measure - to find the size or amount of something
Median – the middle number of a set of data that has been arranged in order from
greatest to least or least to greatest
Meter (m) - a metric unit used to measure length or distance (1 meter = 100
centimeters)
Metric measurement – the system of international measure (SI) based on the decimal
systems and base units of tens
Midpoint - a point in the middle of an interval
Example:
Mile (mi) - a customary unit used to measure length or distance (5,280 feet = 1 mile)
Mileage - the distance in miles a vehicle travels on a certain amount of fuel. Mileage is
measured in miles per gallon (MPG)
Milligram (mg) - a metric unit used to measure mass (1,000 milligrams = 1 gram)
Milliliter (mL) - a metric unit used to measure capacity (1,000 milliliters = 1 liter)
Millimeter (mm) - a metric unit used to measure length or distance (1,000 millimeters
= 1 meter)
Million - 1,000 thousands; written as 1,000,000
Minimum - the smallest or least value
Minute - a unit used to measure time (60 minutes = 1 hour)
Mixed number – a number that has a whole number part and a fractional part
Example:
Mode – the most frequent piece of data in the set - there can be one, more than one or
no mode
Month - a period of time. A month has 28, 29, 30 or 31 days
Page 20
More - greater in amount
More likely – an event that has the greatest chance of happening
Most - the greatest amount
Multi - a prefix meaning "more than one"
Multi-step equation – an equation that requires two or more steps and/or operations
to solve
Multiple - the product of two counting numbers is a multiple of each of those numbers
Example: 15 is the multiple of 3 and 5
Multiplication (product) - a process to find the total number of items made up of
equal-sized groups, or to find the total number of items in a given number of groups. It
is the inverse operation of division
Multiplicative Pattern - a pattern that has a multiplication rule that allows the pattern
to change in a predictable manner
Example: 2, 4, 8, 16, 32, . . . (each number is multiplied by 2)
Multiply - when you combine equal groups, you can multiply to find how many in all;
the opposite operation of division
Net income - income that is left after payroll taxes are taken out of the gross income
Non - a prefix meaning nine
Nonagon - a polygon with nine sides and nine angles
Not equal to (≠) - a symbol that indicates one quantity is not equal to another
Example: 5 ≠ 6
Number - represents the quantity or size of a set
Number line – a line on which numbers can be located
Example:
Number Sentence – a statement about numbers, usually in symbols rather than words
Number string or number sequence – a grouping of numbers that are arranged so
there is a pattern, usually written with the numbers separated by commas (e.g., 2, 7, 4,
9…)
Numeral – a symbol used to name a number
Page 21
Num
merator - the num
mber above
e the bar in a fraction that te
ells how many
m
equal parts of
the whole or group are
e being considered
Exa
ample:
Num
merical data
d
- valu
ues or obs
servations
s that can be measu
ured. Sca
atter plots, stem
and
d leaf and line graph
hs are use
ed to graph numeric
cal data
Num
merical expressio
e
on - a matthematical phrase that
t
uses only
o
numb
bers and operation
o
sign
ns
Obttuse anglle - an an
ngle whose
e measure
e is greate
er than 90
0° and less
s than 180
0°
Exa
ample:
Octt - a prefix
x meaning
g eight
Octtagon - a polygon with
w
eight sides and
d eight angles
Exa
amples:
Odd
d - a wholle numberr that has a 1, 3, 5,, 7, or 9 in
n the ones
s place
Odd
d pattern
n – a number string or numbe
er sequen
nce that on
nly contains odd nu
umbers
One
e-dimens
sional figure – a figure, such as a line
e or the siide of a tw
wo-dimens
sional
figu
ure, that has
h one ba
asic unit of measure
ement – le
ength
One
e-to-one correspo
ondence – the ability to coun
nt objects
s so that each
e
objec
ct counted
d
is matched
m
w
with
one nu
umber wo
ord
Example:
Ope
en figure
e - a figure
e that doe
es not begin and end at the same pointt
Exa
ample:
Page 22
Open number line – a number line representation that may or may not use equivalent
intervals to demonstrate a solution process for an equation or mathematical problem
(e.g., for the number sentence 34 + 28, an open number line could represent a solution
strategy of decomposing the second number into tens and one, then adding the tens
onto the first number, and then add the ones. See example below).
Operations - there are four mathematic operations: addition, subtraction, multiplication
and division
Order - to arrange in a pattern or sequence according to size, value, etc.
Order of operations - a special set of rules which gives the order in which calculations
are done in an expression
Ordered Pair - a pair of numbers used to locate a point on a grid. The first number
tells the horizontal (left-right) position and the second number tells the vertical (updown) position - see example for Axis
Ordinal number - a number that indicates a position
Examples: 1st, 2nd, 3rd . . .
Origin - the point where the two axes of a coordinate plane intersect (0, 0) - see
example for Axis
Page 23
Outcome – the result of an action or event
Outlier - part of a set of data that stands out from the rest
Ounce (oz) - a customary unit used to measure weight (16 ounces = 1 pound)
Overdraft - the result of removing more money out of a bank account than you
actually have in it
Overestimate - an estimate that is greater than the exact answer
Parallel lines – lines that lie in the same plane, never intersect, and are the same
distance apart
Example:
Parallelogram - a quadrilateral whose opposite sides are parallel and have the same
length, or are congruent
Example:
Parentheses - the symbols used to show which operation or operations in an
expression should be done first
Example:
Partial product – a method of multiplying in which the ones, tens, hundreds, and so on
are multiplied separately and then the products are added together
Example:
Page 24
Partial quotient - a method of dividing in which multiples of the divisor are subtracted
from the dividend and then the quotients are added together
Example:
Partial sums – addends that are separated into parts (tens and ones). Each part is
combined separately, and then the sums of the parts are combined for the total sum
Example:
Pattern - An ordered set of numbers or objects; the order helps you predict what will
come next
Examples: 2, 4, 6, 8, 10
Pattern core or Pattern Rule – the shortest string of elements that repeat – the
repeating section within a pattern
Example:
is the pattern core/rule of the pattern above
Page 25
Payroll tax - money an employer withholds from an employee’s earnings
Example:
Pent - a prefix meaning five
Pentagon - a polygon with five sides and five angles
Examples:
Percent (%) - the ratio of a number to 100
଼଴
Example:
= 80%
ଵ଴଴
Perfect Square - a number made by squaring a whole number
Example: 16 is a perfect square because 42 = 16
Perimeter – the distance around the outer edge of a figure
Period – a three-digit group of whole numbers separated by commas where each
grouping consists of ones, tens, and hundreds
Example:
Units
Period
Units
Page 26
Perpendicular lines – lines that intersect at right angles to each other to form square
corners
Example:
Pictograph – a graph composed of pictures where each picture may represent one or
more than one unit of data
Example:
Pint (pt) - a customary unit used to measure capacity (2 cups = 1 pint)
Pip – the dot on a domino or die
Place value – the value of a digit as determined by its position in a number, such as
units, tens, hundreds, etc.
Plane - a flat surface that extends without end in all directions
Example:
Plot - to draw on a graph or map
Example: Plot the point (12, 5) on the coordinate plane
Point – a specific location on a number line or coordinate plane representing a value
Poly - a prefix meaning many
Page 27
Polygon – a flat, closed figure that has three or more straight sides
Examples:
Position – describes the location of something
Possible outcome – the possible result of an experiment
Pound (lb) - a customary unit used to measure weight (1 pound = 16 ounces)
Prediction – a statement about an event in the future based on an experiment or an
experience
Prime number – a number with exactly two factors, 1 and the number itself
Examples: 2, 3, 5, 7, 11, 13, 17, and 19 are prime numbers; 1 is not a prime number
Prime Factorization - a composite number expressed as the product of its prime
factors
Example:
Principal - the amount of money borrowed or invested
Prism - a solid figure that has two congruent, polygon-shaped bases, and other faces
that are all rectangles
Examples:
Probability – the number of favorable outcomes divided by the number of possible
outcomes – the likelihood of an event occurring
Problem-solving model – a flexible framework to think about the processes involved
in mathematics (e.g., Poyla’s stages: understanding the problem, making a plan,
carrying out the plan, and looking back; etc.)
Page 28
Pro
oblem-sollving stra
ategy – a plan or strategy
s
to
o solve wo
ord problems (e.g., acting it
out,, drawing a picture or graph, using log
gical reaso
oning, look
king for a pattern, using
u
a
proc
cess of eliimination, creating an organized chart or list, so
olving a simpler butt related
prob
blem, usin
ng trial an
nd error (s
systematic
c guessing
g and chec
cking), wo
orking bac
ckwards,
etc.)
Pro
oduct (mu
ultiplication)– the
e solution to a multiplication problem
p
Pro
ofit - the amount
a
left after all the expe
enses are subtracted from the
e amount of money
y
rece
eived from
m selling an
a item or service
oper Fraction - a frraction with a nume
erator tha
at is less th
han the de
enominato
or and
Pro
who
ose value is less tha
an one
Exa
amples:
Pro
operty - a characteristic of an object, such
s
as le
ength, weiight, faces
s, vertices
s, etc.
operty tax
x - a portiion of the value of items
i
thatt is paid to
o a city orr state gov
vernment.
Pro
Prop
perty tax can be ch
harged on things such as cars
s, houses, boats, orr land
Pro
oportion - part of a whole wrritten as a fraction, percentage or deciimal
ଵ
ଷ
Exa
ample: The
e drink is or 0.25 or 25% sy
yrup and 0r 0.75 or 75% water
w
ସ
ସ
otractor - a tool used for me
easuring or drawing angles
Pro
Example:
ove - show
w the correctness off a calcula
ation
Pro
Pyrramid - a 3-dimens
sional shape whose base is a polygon; all other faces are triangles
Examples:
Page 29
9
Quad - a prefix meaning four
Quadrilateral -a polygon with four sides and four angles
Example:
Quadruple - increase the amount four times
Example: Quadruple 20 means 4 x 20 or 80
Quantity – the number or amount represented in a set – the amount of something
Quart (qt) - a customary unit used to measure capacity (2 pints = 1 quart)
Quarter - One of four equal parts or
ଵ
ସ
or 0.25 or 25%
Quotient (division) - the number, not including the remainder, that results from
dividing
Example:
Random event – an event that does not have a determined outcome
Range – the difference between the greatest number and least number in a set of data
Rate – when one amount (quantity) is compared to another
Ratio – a way of comparing amounts (quantities) where one quantity is expressed as
part of another
Rational Numbers - a number that can be made by dividing two integers (Note:
integers have no fractions), the word comes from "ratio"
Ray - a part of a line; it has one endpoint and continues without end in one direction
Example:
Real-object graph – a graph where concrete objects are placed in individual cells to
represent one piece of data
Page 30
Rec
ciprocal - the recip
procal of a number is
i one divided by th
hat numbe
er
Exa
ample:
Rec
ctangle - a parallelogram with four rig
ght angles
s
Exa
ample:
Rec
ctangularr prism - a three-d
dimension
nal figure in
i which all
a six face
es are recttangles
Exa
ample:
duce - to simplify or
o make sm
maller
Red
Exa
ample:
ver a line to make a mirror im
mage of th
hat figure
Refflection – a flip of a figure ov
Exa
ample:
Reg
group - to
o exchang
ge amountts of equal value to rename a number
Exa
ample: 5 + 8 = 13 ones
o
or 1 ten 3 one
es
Reg
gular poly
ygon - a polygon in
n which alll sides are
e congrue
ent and alll angles arre
congruent
Exa
ample:
Related factts - a set of related addition and subtrraction, orr multiplica
ation and division,
num
mber sente
ences
Exa
amples: 4 × 7 = 28,, 28 ÷ 4 = 7, 7 × 4 = 28, 28
8÷7=4
p - a signiificant con
nnection or
o similaritty between two or more
m
thing
gs
Relationship
Page 31
1
Remainder - the amount left over when a number cannot be divided equally
Remaining - still left, left over, left behind
Rename - two names for the same amount
ଶ
ସ
Example: =
ଷ
଺
Repeating pattern – a pattern where the core repeats (e.g., AB, AB, AB, etc.) – a
repeated arrangement using shapes, colors, numbers, etc.
Represent - 1) to express or explain what is happening or what people think, 2) to be
equivalent of something
Rhombus - a parallelogram with four equal, or congruent, sides
Example:
Right angle - an angle that forms a square corner and has a measure of 90˚
Example:
Right triangle - a triangle that has a right angle
Example:
Rotation – a turn of a figure that moves the figure around a point
Example:
Rounding – to replace a number with one that is simpler and is approximately the same
size as the original number
Example: 114.6 rounded to the nearest ten is 110 and to the nearest one is 115
Rule - a mathematical process for performing an operation or solving a problem
Sales tax - money added to the cost of items or services. Sales tax amounts vary from
state to state and from city to city
Page 32
Sample space – the set of all possible outcomes of an experiment
Savings - the portion of one's income not spent on expenses, usually put aside for later
use
Scale – an arrangement of numbers at regular intervals
Scalene triangle - a triangle with no congruent sides
Example:
Scatter plot - a graph that shows a relationship between two sets of data
Example:
Second (sec) - a small unit of time (60 seconds = 1 minute)
Semicircle - a half circle, formed by cutting a whole circle along a diameter line
Example:
Sequence - a set of numbers or a pattern following an order or rule
Example:
Set – a collection or group of objects or items
Page 33
Share - divide an object into equal parts
Side – a line segment of a two-dimensional figure
Simplify – To write something in the simplest, shortest form
Example:
Skip counting pattern – automatized rhythmic interval counting by a number other
than one
Solution - a value that makes an equation true
Solve - 1) to find the answer to a question or puzzle, 2) to work out the solution to an
equation or other mathematical problem
Spend - To use your money to buy or pay for things
Square - a polygon with four equal, or congruent, sides and four right angles
Square unit - a unit used to measure area such as square foot, square meter, and so
on
Standard form – a way of writing numbers using digits (e.g., 789)
Standard unit – a unit of measure that has been defined by a recognized authority,
such as a government or standards organization. For example, inches, meters, seconds,
liters, pounds, and grams are all standard units
Statement - a sentence that is either true or false
Stem-and-leaf plot - a graph that shows groups of data arranged by place value
Example:
Page 34
Straight angle - an angle whose measure is 180°
Example:
Strategies - a carefully devised plan or method of solving a problem
Subset - a set of which all the elements are contained in another set
Substitute - putting numbers in place of the variables (letters) in an equation
Subtraction (difference)- the process of finding how many are left when a number of
items are taken away from a group of items; the process of finding the difference when
two groups are compared; the opposite of addition
Sum (addition) – the answer to an addition problem
Supplementary Angles - two angles that together make 180 degrees
Example:
Symbol - a printed mark used to represent an operation or idea
Examples: +, -, X, ÷, <, >
Symmetry - having the same size and shape across a dividing line
Example:
Table - information organized in columns and rows
Tablespoon (tbsp) - a customary unit used to measure capacity (3 teaspoons = 1
tablespoon)
Tax - money paid to the government in exchange for services, such as road
maintenance and police protection
Tally mark - used to keep track of data being counted
Example:
Page 35
Teaspoon (tsp) - a customary unit used to measure capacity (1 tablespoon = 3
teaspoons)
Tenths - one of ten equal parts, the first number to the right of a decimal point
Example: 0.7 = seven tenths
Temperature – refers to how “hot” or “cold” an object may be
Term – Each of the two amounts in a ratio
Example:
or each of the quantities connected by a + or – in an algebraic expression or equation
Example:
Tessellation - a pattern of repeating shapes covering a surface without gaps or
overlaps
Example:
Thousandths - one of one thousand equal parts, the third number to the right of a
decimal point
Example: 0.006 = six thousandths
Three-dimensional figure – a figure that has three basic units of measurement
(usually length, width, and height/depth) – a solid figure
Example:
Ton (T) - a customary unit used to measure weight (2,000 pounds = 1 ton)
Trailing zeros – a sequence of zeros in the decimal part of a number that follow the
last nonzero digit, and whether recorded or deleted, does not change the value of the
number
Example: 0.5 = 0.500
Page 36
Transaction - the act of buying or selling something
Transformation – a change of position of a geometric figure, see Reflection, Rotation
and Translation
Transitive reasoning – a logical relationship between terms, events, or situations
(e.g., If freezer pop A is colder than freezer pop B, and freezer pop C is colder than
freezer pop A, then freezer pop C is the coldest freezer pop.)
Translation – a slide that moves a figure horizontally, vertically, or diagonally from one
location to another along a straight line
Example:
Trapezoid - a quadrilateral with exactly one pair of parallel sides
Examples:
Trend - A line on a graph showing the general direction that a group of points seem to
be heading
Example:
Triangle - a polygon with three sides and three angles
Examples:
Page 37
Two-dimensional figure – a figure that has two basic units of measurement (usually
length and width) – a flat figure
Underestimate - an estimate that is less than the exact answer
Unit – a quantity or amount used as a standard of measurement
Example: Units of time are second, minute, hour, day, week, month, year and decade
Unit cube - a cube that has a length, width, and height of 1 unit
Example:
Unit fraction - a fraction that has 1 as a numerator
ଵ ଵ ଵ
Examples: , ,
ଷ
ସ
଺଴
Unitize – the foundation of our base-ten system which involves counting and grouping
of 1s to 10s and 10s to 100s
Unit of Measure – the object or unit used to measure an attribute (e.g., 14 color tiles,
14 cm cubes)
Unknown - is the number we do not know in a problem, often represented by a
variable
Unlike denominators - fractions that have different denominators
Example: Both fractions show the same amount with different names
Use - to apply or rely on math skills to solve a problem
Value - how much something is worth
Variable - a letter or symbol that stands for an unknown number or numbers
Venn diagram - a diagram that shows relationships among sets of things
Example:
Page 38
Vertex (vertices) – a point or corner where two or more sides meet
Example:
Vertical - extending up and down
Volume - the measure of the space a solid figure occupies
Week - a period of seven days
Weight - how heavy an object is
Whole - all of the parts of a shape or group
Whole number - one of the numbers 0, 1, 2, 3, 4, . . . ; the set of whole numbers goes
on without end
Width - The measurement of something from side to side
Withdrawal - to take money out of a bank account
Word form - a way to write numbers in standard English
Example: 4,829 = four thousand, eight hundred twenty-nine
x-axis - the horizontal number line on a coordinate plane
Example:
x-coordinate - the first number in an ordered pair; tells the distance to move right or
left from (0, 0)
Yard (yd) - a customary unit used to measure length or distance (3 feet = 1 yard)
y-axis - the vertical number line on a coordinate plane
Example: See x-axis above
y-coordinate - the second number in an ordered pair; tells the distance to move up or
down from (0, 0)
Page 39
Year - 1) the time taken by a planet to make one revolution around the sun, 2) a period
of 365 days
Zero - the number that indicates no quantity, size or magnitude
Zero Property of Multiplication - the property that states that when you multiply by
zero, the product is zero
Example: 5 x 0 = 0
10-long – a base ten block that represents a value of 10
100-flat – a base ten block that represents a value of 100 units or ten 10longs
Page 40