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expanded form

A number written as the sum of the place values of its digits.

exponential form

A way of writing repeated multiplication of a number using exponents.

base (in numeration)

A number multiplied by itself the number of times shown by an exponent.


The number that tells how many times the base is being multiplied by itself.


The number of times a number is multiplied by itself.


A number that is multiplied by itself two times.


A number that is multiplied by itself three times.

expanded form using exponents

A number written in expanded form with the place values written in exponential form.


To give an approximation for a number to the nearest one, ten, hundred, thousand, and so on.


To find a number that is close to an exact answer.

front-end estimation

A method of estimation using the first digits of each addend that have the same place value.

front-end estimation with adjusting

A method of front-end estimation that adjusts the result based on the remaining digits of each addend.

front-end estimation

An estimation method where numbers that are approximately equal are treated as if they were equal.

compatible numbers

Numbers that are easy to compute mentally.


The difference between the greatest and the least numbers in a set of data.

order of operations

A set of rules mathematicians use to determine the order in which operations are performed.

Commutative Properties

The properties that state the order of the addends or factors does not affect the sum of the products.

Associative Properties

Properties that state the way in which addends or factors are grouped does not affect the sum or product.

Identity Properties

The properties that state the sum of any number and zero is that number and the product of any number and one is that number.

Multiplication Property of Zero

Property that states the product of any number and zero is zero.

Distributive Property

Multiplying a sum by a number produces the same result as multiplying each addend by the number and adding the products.

break apart

Using the Distributive Property to compute mentally.


Choosing numbers close to the numbers in a problem, and then adjusting the answer to compensate for the numbers chosen.

equal additions

Adding the same number to two numbers in a subtraction problem does not affect the difference.


A quantity that can change or vary, often represented by a letter.


To find the number that an algebraic expression names by replacing a variable with a given number.

properties of equality

Properties that state performing the same operation to both sides of an equation keeps the equation balanced.

inverse operations

Operations that "undo" each other, such as addition and subtraction, or multiplication and division (except multiplication by zero).


A mathematical sentence stating that two expressions are equal.

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