mathvocabulary

MATHMATHVOCABULARYVOCABULARY

MATHMATHVOCABULARYVOCABULARY

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

calculate• Perform (do) an operation

(+,-,x,÷)


operationDescribes 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 itselfExamples 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 cm3 cm

3 cm

3 cm3 cm

3 cm

3 cm

3 cm

3 cm


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

15 18

+3

-37/12/2012 Source: teachers.rmcity.org

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

factors• The numbers we multiply together.

3·4 = 123 and 4 are factors of 12

7·(6+4) = 707 and (6+4) are factors


product • The result of multiplication.

3 · 4 = 1212 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 · m3 · 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 = 0n · 0 = 0


One (Identity) Property of Multiplication

• The product of any number and 1 is that number…

4 · 1 = 1+1+1+1 = 4n · 1 = n1 · 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 = 2 R 1…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

(x, y)(Over, Up)

*walk the ladder OVER to the spot, then

climb UP the ladder*

ordered pair


bar graph

Single bar Double bar

- Shows data that tells how many or how much


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 9List the first 9 multiples of each number:

6: 6, 12, 18, 24, 30, 36, 42, 48, 549: 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. 34

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.34

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: 0.30.670.258


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


mathvocabulary

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