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### expanded form using exponents

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

### 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.

### 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.

### Distributive Property

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

### compensation

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.

### evaluate

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).