Number concepts & Operations

division

mathematical operation involving two numbers that tells how many groups there are or how many are in each group, the inverse of multiplication, indicated by a / or ÷

simplification or simplify

when a fraction is in simplest form when both the numerator and denominator can't be any smaller while still being whole numbers

Difference

when one number is subtracted by another number the result is called the difference--minuend - subtrahend

rounding

Can be used to estimate a sum/difference or product and to make a Mental approximation rules: digits 0-4 leave the digit the way it is digits 5...9 round up 5-->6 all digits after the rounded digit become zero

rational number

A number that can be expressed as a ratio or quotient of two non-zero integers, they can be expressed as common fractions Or decimals such as 3/5 or 0.6 for example

irrational number

A number that can't be represented as an exact ratio of two integers, and the decimal form of the number never ends and never repeats--square root of 2 & Pi (3.14)

repeated decimal

A number that repeats infinite times, indicated by a bar above the repeating digit; 0.3 (bar over the 3)

natural number

A positive integer or non-negative integer, non-negative integers also include zero ex: 1. 2, 3, 4, 5...∞

real number

Describe any number that is positive, negative or zero and can be used to measure continuous quantities, includes numbers that have decimal representation, even those with infinite decimal sequences such as Pi (3.14)

Absolute value

Distance of a number from zero on the number line; it ignores the + and - signs,Two vertical lines represent absolute value; |X| EX: |5| or |-5| both = 5

prime factorization

Every composite number can be written as a product of a prime number; use a factorization tree to do the factoring of a composite number

scientific notation

Form of writing numbers as the product of a power of 10 and a decimal number greater or equal to one or less than 10 Ex: 2,400,000 = 2.4 x 10^6

Property of zero

In addition the number plus zero is the number itself, in multiplication the Number times zero is zero EX: 8 + 0 = 8 and 8 x 0 = 0

estimation

Is used to make an approximation that is still close enough to be useful, when using an estimation use the Leading or left-most digit to make an estimate EX: 532 + 385 + 57 = 500 + 400 + 60 = 960

expanded notation

Like expanded form but shows place value by multiplying each digit in a number by the Appropriate power of 10 EX: 523 = 5*10^2 + 2*10 + 3*1 or 5*10^2 + 2*10^1 + 3*10^0

subtraction

is the process/operation of removing objects from a larger group or finding parts of a whole, opposite of addition, it's indicated by a - (minus sign)

prime number

Natural number greater than 1 that are divisible only by themselves and 1 such as: 2/3/5/7/11/13/17/19

composite number

Natural numbers greater than zero that are divisible by at least one other number Besides 1 and themselves, have at least three factors such as: 9 = 1/3/9

place value

The basic foundation for understanding mathematics computation (ones, tens, hundreds, thousands, ect)

addition

The mathematical operation of combining two or more quantities into a sum, the quantity is often a number with One or more digits, indicated by a + (plus sign)

Competency 002 number concepts & operations

The teacher understands concepts related to numbers, operations, algorithms, and the Properties of numbers

greatest common divisor (factor) = GCD/GCF

Two or more non-zero integers is the largest positive integer that divides into the numbers without producing a remainder, (divided evenly) it's used to simplify fractions into lowest terms to find the GCF of two numbers use a factorization tree to factor the composite numbers and see what the largest factor that both composite numbers share

front-ended estimation

Uses the leading left-most digit to make an estimate quickly (is less precise than doing the actual addition)

common multiple

Whole number that is a multiple of two or more given numbers, the times tables of The number EX: multiples of 3 = 3/6/9/12/15 (product of a multiplication expression)

improper fraction

a fraction with the numerator greater than the denominator, ex: 11/4

common denominator

a number that is a multiple of the original denominator ex: 2/3 + 1/2, CD: 6

fraction

a number that represents part of a whole , part of a set, or a quotient in the form of a/b, it's read as a divided by b

exponential notation

a symbolic way of showing how many times a number or variable is used as a factor EX: 5^3 = five is a factor three times; 5*5*5 = 125 Neg exponent is reciprocal = -5^3 = 1/5*5*5 = 125

integer

a whole number that includes all positive and negative numbers, including zero ex: -6, -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6

Associative property

adding or multiplying the order of the addends or factors don't change the sum or product EX: (a + b) + c = a + (b + c) or (a*b) * c = a * (b * c) (2 +3) +4 = 2 + (3 +4) or (2 x 3) x 4 = 2 x (3 x 4)

Order of Operations (PEMDAS)

an arithmetic expression is evaluated by following ordered steps, PEMDAS-stands for Parenthesis/Exponents/multiplication/division/addition/subtraction and the pneumonic that is taught for remembering the steps is please excuse my dear aunt sally, multiplication/division/addition and subtraction is done left to right sequence Ex: 3 + 2 x 6 = n --> 6 x 2 + 3 = 15

Algorithm

an established and well-defined step-by-step problem-solving method used to achieve a desired mathematical result

quotient

answer to a division problem

Percentage of a quantity

change percent to a fraction or decimal then multiply the fraction or the decimal by the quantity EX: 15% of 200 = 0.15 * 200 = 30

decimal number

fractional numbers that are written using basic ten, mixed decimal number has a whole number part as well, decimal number denominators are power of ten (10,100,1000) ex: 0.28 = decimal number, 3.9 = mixed decimal number, 0.098 = 98/1000

equivalent fraction

fractions with different numerator or denominator that represents the same value or proportion of the whole

expanded form

in Numbers they show the place value of each digit EX: 263 = 200 + 60 + 3; 2 hundreds, 6 tens, and 3 ones

digit

in mathematics, it's a number symbol (1,2,3) used in numerals to represent numbers or integers in positional numeral systems

reciprocal

is a fraction with the numerator and denominator is switched, ex: 2/3 --> 3/2

multiplication

is a mathematical operation of combining groups of equal amounts, might be described as repeated addition and the inverse of division, indicated by a x (multiplication sign)

percent

is another way of expressing a fractional number in terms 1/100 or 0.01, it's indicated by the % (percent sign)

numerator

number above the fraction bar

dividend

number being divided

denominator

number below the fraction bar

divisor

number doing the dividing

mixed number

number with a whole number part and a fractional part ex: 2 2/4

factor

portion of a quantity usually an integer or called a multiplier

product

refers to the result of one or more digits being multiplied together

Distributive property

says that everything in the parenthesis needs to be multiplied by the number on the outside; you can multiply first then add and vice versa Ex: a (b + c) = a * (b + C) or a (b + c) = (a * b) + (a * c) 8 (5 +2) = 8 * 7 = 56 or 8 (5 + 2) = (8 * 5) + (8 * 2) = 56

Commutative property

the order of addends or factors; addition & multiplication don't change the answer EX: a + b = b + a or aXb = bXa 4 + 5 = 5 + 4 or 4x5 = 5x4