Base Ten and Fractions

Expanded Form / Expanded Notation

break apart each digit in the number and show the digits' true value

Real Numbers

numbers that have a specific value

Whole Numbers

infinite set of natural numbers and zero

Denominator

the bottom term of a fraction

Common Denominator

when 2 fractions share the same total parts of whatever item or items are being represented

Additive Identity Property

a number that, when added to any element xx in a set, always yields xx. zero itself is sometimes referred to as the additive identity.

Multiplicative Identity Property

a number that, when multiplied by xx, yields xx. These are one or forms of one such as x/x

Multiplier

a number that multiplies another number (multiplicand)

Multiplicand

a number that is multiplied by another number (multiplier)

Associative Property

a property of an operation in which the way the terms are grouped (regrouped) does not change the result; applies to addition and multiplication only

Rounding

A number is simplified to its closest multiple of 10, 100, 1,000, etc

Proportional Manipulatives

objects that are proportional to each other with respect to shape and size

Dividend

A number that is divided by another number (divisor) to find the quotient

Addend

a number that is added to another number

Concrete Operational Stage

the third stage of Piaget's Theory of Cognitive development, occurring from 7 years old to adolescence, in which children begin to think logically and use inductive reasoning

Difference

the result of subtracting one number from another

Factors

Values that are multiplied to get another number.

Fraction Composition

Adding fractions to come up with a larger one

Order of Operations

PEMDAS: the set order in which multi-step equations must be solved: Parenthesis, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)

Fraction Decomposition

Breaking down a fraction into smaller fractions that total to the original

Distributive Property

a number in front of a group of terms will multiply all terms in the grouping individually

Reciprocal Fraction

the inverse or "flip" of a fraction in which the numerator and denominator switch places

Number Line

a straight line where each number is equal distance from the next one

Mixed Number

A whole number with a fraction

Least Common Multiple (LCM)

the smallest number that is a multiple of two or more numbers; the smallest number two or more numbers will divide into evenly

Commutative Property

An operation is commutative if changing the order of terms does not change the outcome

Numerator

the top term of a fraction

Scientific Notation

numbers expressed as the product of a base-10 number and a number between 1 and 10

Non-proportional Manipulatives

objects that are not proportional to each other with respect to shape and size. Often all of the items are the same size.

Zero Product Property

When a real number is multiplied by 0, the result is 0.

Manipulatives

objects used by students to illustrate and explore mathematical concepts, such as to represent numbers in an equation

Sum

the result of adding two or more numbers, a total

Benchmark Fraction

an easily remembered fraction that can be used to make problems simpler

Quotient

the result of dividing two numbers

Natural Numbers

set of counting numbers starting at 1 and increasing by 1s up to infinity; sometimes called "counting numbers"

Integers

infinite set of positive and negative countin

Base 10 Number System

Our number system. Each place location for a number has a value that is a power of 10

Divisor

A number that divides another number (dividend) to find the quotient

Greatest Common Factor (GCF) / Greatest Common Divisor (GCD)

the greatest factor that is common to two or more numbers; the largest number that will divide evenly into two or more numbers

Product

the result of multiplying two or more numbers

Unit Fraction

a fraction composed of 1 over any rational number; the inverse of a whole number

Irrational Numbers

real numbers that CANNOT be represented exactly; they can not be shown as a ratio of two integers nor placed on a number line

Closure Property

The sum of two real numbers is a real number. The product of two real numbers is a real number.

Improper Fraction

A fraction where the numerator is larger than the denominator