Mathvocabulary

MATH
VOCABULARY

7/12/2012 Source: teachers.rmcity.org

calculate
• Perform (do) an operation (+,-,x,÷)


operation
Describes any of these:
– ADDITION
– SUBTRACTION
– MULTIPLICATION
– DIVISION


evaluate

• To find the value of something.
– Value is what something is worth.


identical
…exactly the same.
…worth the same amount.
…has equal value.

5+5=6+4


standard form
• A number as we are used to seeing it
in everyday life…
• Examples are:
– 24
– 765
– 8,758,215… etc.


expanded form
• A number written out to show the
place value of each of its digits.
• Examples:
– 20 + 4
– 700 + 60 + 5
– 8,000,000 + 700,000 + 50,000 + 8,000 +
200 + 10 + 5


word form
• A number written out in words.
• Examples:
– twenty-four
– seven hundred sixty-five
– eight million, seven hundred fifty-eight
thousand, two hundred fifteen


natural numbers
• Also called whole numbers.
• These are the numbers we use to
count things.


digit
• One of the TEN symbols that are
used to write numbers.
• 0,1,2,3,4,5,6,7,8 and 9
• “0” is a DIGIT, not a NUMBER!


place value
• The value of a digit that is based on
it’s position in a number.
• Example:
– In the number “674”, the 7 is in the
tens place, so it’s place value is 70.


period
• A number is divided into groups of
three, starting from the right and
each separated by a comma. These
groups are called periods.
• Example:
– The number 127,453,989 has THREE
periods.


inequality
• A statement that one quantity (also
called “amount”) is greater than or
less than another.
• Uses the symbols:
Greater than >
Less than <
**Remember that when you read these symbols
from the left to the right, the open end is
open to the bigger quantity, no matter how
you look at it.

infinite
• Goes on and on FOREVER
• Doesn’t end


line
• A type of curve that is straight.
• It extends INFINITELY in both
directions.


line segment
• The part of a line between two
points, called endpoints.


ray
• A straight curve that has exactly
ONE ENDPOINT.
• Then it extends INFINITELY in one
direction.


round number
• A natural number ending in one or
more zeros.
– Examples include:
• 20
• 300,000
• 100
• 7,000,000


approximate value
• A value that is close to, but not
exactly, the real value.
• Approximate value is easier to work
with than real value.
• Example:
– 750,000 is an approximate value for the
real value of 748,362.


exact
• The actual amount, the real value.
• Example:
– The exact amount of students in this
school is 639.
– What would be the approximate
amount?


estimate
• To find a number that may not be the
exact answer to a question, but is
close enough.
• We say, then, that it is an estimate
of the exact value.
– Which is an example of an estimate?
Exact or approximate value?


polygon
• a shape in the plane with the following
properties:
– the boundary of the shape is a piecewise linear
curve
– the boundary is closed
– the boundary does not intersect itself
Examples include:
triangle, rectangle, pentagon, trapezoid…


vertex
• two meanings:
– Vertex of a POLYGON: the common
POINT of two sides of a polygon.

– Vertex of an angle: the common
ENDPOINT of two rays that form the
sides of an angle.


perimeter
• The length of a boundary of a shape
in a plane.
• The SUM of the sides of a polygon!
• 3cm+3cm+3cm+3cm+3cm+3cm+3cm+3cm= 24 cm
3 cm
3 cm 3 cm

3 cm 3 cm

3 cm 3 cm
7/12/2012
3 cm
Source: teachers.rmcity.org

compatible numbers
• Add together to make a round number (a
number that ends in zero).
• Example:
17 and 3 are compatible because when you add
them, the answer is 20. (20 is a round number)
• Non-Example:
– 24 and 5 are NOTcompatible because when you
add them, the answer is 29. (29 is not round)


Commutative Property
(of Addition)
• When adding numbers, the order of
the addition does not matter.

2 + 3 = 3 + 2

**You can move the numbers around, just
like people commute…


Associative Property
(of Addition)

• When adding numbers, it doesn’t matter
which ones you group together to do the
addition.

(5 + 2) + 8 = 5 + (2 + 8)

**Associates are friends, so think about
groups of friends…


sum
• The answer to an addition problem.

• Example:
5+3=8
8 is the sum.


summand
• The numbers you are adding together
in an addition problem.

5+3=8
5 and 3 are the summands.

*same thing as “addends”


convenient addition
• Convenient means “easy”.
• So, convenient addition is the
process of using compatible numbers,
the Commutative Property and the
Associative Property to make your
addition easier and quicker.


inverse
• Means “opposite”
• Subtraction is the INVERSE
operation to addition
• Division is the INVERSE operation to
multiplication +3

15 18
-3

subtraction
• An operation that means finding a
missing summand, given the sum and
the other summand…

2 + __ = 5 …to solve it, use 5 – 2 = __


difference
• The answer to a subtraction problem.

5–2=3

3 is the difference between 5 and 2


subtrahend and minuend
• minuend – subtrahend = difference
• Minuend is the number you start
with…
• Subtrahend is the number you
subtract…
5–2=3


parentheses
• A set of two symbols that indicate what
operation to do first in a mathematical
expression.
you have to have the opening side ( … & the closing side )
it matters where they are:
7–(5–1)=7–4=3
(7–5)–1=2–1=1
and there can be more than one set in an expression:
8 – (20 – (9 + 6)) = 8 – (20 – 15) = 8 – 5 = 3


numerical expression
• A mathematically meaningful sequence of
numbers, operation signs and parentheses.

5 + (9 – 2)

Numerical expressions tell us what
operations to do FIRST, SECOND… etc.


algebraic expression
• A mathematically meaningful sequence of
numbers, letters that stand for numbers,
operation signs and parentheses.

3 + (a – 4)

We can replace that “a” with any number we
want to… it’s called a VARIABLE because
it can change. Any letter can be a variable.


multiplication
• Multiplication is adding up several summands, each
equal to the same number.
• Example: 3 + 3 + 3 + 3 = 3 · 4
• There are two different ways to show
multiplication of numbers by themselves:
3 X 4 and 3 · 4
two more ways using letters and/or numbers:
3 · a = 3a and a · b = ab
AND a way to show it with parentheses:
3 · (5 + a) = 3(5 + a)
When there is addition or subtraction AND multiplication in the
same expression with NO parentheses… do the multiplication
FIRST!

factors
• The numbers we multiply together.
3·4 = 12
3 and 4 are factors of 12

7·(6+4) = 70
7 and (6+4) are factors


product
• The result of multiplication.

3 · 4 = 12
12 is the product of 3 times 4


Commutative Property of
Multiplication
• The product of two numbers does not
change if we swap (change the order)
of the factors…
m·n=n·m
3·4=4·3


Associative Property of
Multiplication
• Changing the grouping of the factors
does not change the product…
(a · b) · c = a · (b · c)
(3 · 4) · 2 = 3 · (4 · 2)


Zero Property of
Multiplication
• The product of any number and zero
is zero.
0·n=0
n·0=0


One (Identity) Property
of Multiplication
• The product of any number and 1 is
that number…
4 · 1 = 1+1+1+1 = 4
n·1=n
1·n=n


exponent
• The “little” number in the following
expression:
5³
… which means that we need to take 5
and multiply it by itself 3 times
5 x 5 x 5 = 125
…it is also called a “power”


protractor
• An instrument used to measure
angles.


degree
• The unit used to measure angles.
• Usually written as a small circle in
the superscript after a number:
Example: 60°


right angle
• An angle measuring exactly 90°


obtuse angle
• Any angle that is larger than 90°


acute angle
• Any angle that is less than 90°


intersecting lines
• Lines that cross.
• The point where they cross is called
the point of intersection.


parallel lines
• Two lines that will never cross.
• They stay the same distance apart
forever.


perpendicular lines
• Two lines that meet to form right
(90°) angles.


dividend
• The number that is being divided

A÷B=C

A is the dividend


divisor
• The number we are dividing by

A÷B=C

B is the divisor


quotient
• The result of division

A÷B=C

C is the quotient


remainder
• The number left over after the
divisor has gone into the dividend as
many times as it can.

7÷3=2R1
…because 3 goes into 7 two times and
has one leftover


area
• The measure of the total amount of
surface on a plane that an object
takes up.
• We use “square” units to measure
area


vertical
• UP and DOWN
• Goes from top to bottom in a
straight line.


horizontal
• Goes side to side, from left to right
or right to left in a straight line.


coordinate grid

ordered pair
(x, y)
(Over, Up)
*walk the ladder OVER
to the spot, then
climb UP the ladder*


bar graph
- Shows data that tells how many or how much

Single bar Double bar


line graph
• shows change over time


circle graph
• shows a part-whole relationship


pictograph

• Uses pictures or symbols to
represent amounts


prime
• Having EXACTLY two factors
• Those factors are 1 and itself

Examples:
5 7 23 51 113…


composite
• Has MORE THAN two factors…

Examples:
4 12 24 27 56 144 169


Greatest Common Factor
(GCF)
• the GCF of a group of numbers is the
greatest natural number that divides
(is a factor of) each of the numbers
in the group (common).

• The GCF of 8 and 12 is the factor 4 because it is
the biggest number that both of them can be
divided by.


Least Common Multiple
(LCM)
• The smallest number that is divisible by
both numbers in question.
• Example: the LCM of 6 and 9
List the first 9 multiples of each number:
6: 6, 12, 18, 24, 30, 36, 42, 48, 54
9: 9, 18, 27, 36, 45, 54, 63, 72, 81
– Then look for the least number that is listed
under both… so, 18 is the LCM of 6 and 9


fraction
• A collection of several equal parts
into which a whole is divided.
• A fraction always divides a whole into
EQUAL PARTS.


numerator
• The number on top of a fraction…
• Represents the number of equal
parts making up the fraction.
3
4
3 is the NUMERATOR.


denominator
• The number on the bottom of a fraction.
• Represents the TOTAL number of equal
parts into which the whole is divided.
3
4
4 is the DENOMINATOR.


decimal
• A fraction with a denominator that is a
power of 10.
• It is written with a decimal point that
separates the whole part from the
fractional part.
Examples:
0.3
0.67
0.258


equivalent fractions
• When you multiply or divide BOTH
the numerator and denominator of a
fraction by the SAME number, you
generate equivalent fractions.
• They are worth the same amount,
but they appear different.


simplest form of a
fraction
• When the GCF of the numerator and
denominator is 1.
• To find Simplest Form, simply find
the GCF of the numerator and
denominator, then divide them both
by that number.


improper fraction
• A fraction where the numerator is
greater than or equal to the
denominator.
• all improper fractions are greater
than or equal to one whole.


mixed number
• A way of writing numbers that is the
sum of a whole number and a
fraction.


volume


median


mode


range


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