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Introduction to Numbers
Warm-UpYesterday we discussed using the PLEASE
method to solve problems. On a sheet of notebook paper, please tell me which step you think is most important and why. (Or, write about the one you most remember.)
Hint: P - ______________________________________
L - ______________________________________
E - _______________________________________
A - ______________________________________
S - ______________________________________
E - ______________________________________
Hierarchy of Numbers“The way numbers are organized”
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
Natural Numbers•Also called the counting numbers, natural numbers include all of the whole numbers except zero (1, 2, 3, ....)
•Examples: __________ __________
__________ __________
Números Naturales – También se llama los números de cuenta, números naturales
incluyen todos los números enteros excepto cero.
Whole Numbers•Zero and the positive integers are the whole numbers. •Examples: __________ __________
__________ __________
Números Enteros – El cero y los números enteros positivos
Integers•The counting numbers (1, 2, 3, ...), their opposites (-1, -2, -3, ...), and zero are integers.
•A common error for students is to assume that the integers account for all (or only) negative numbers. •Examples: __________ __________
__________ __________
Enteros – el conjunto de los numeros enteros y sus opuestos.
Rational Numbers•Any number that can be written in fraction form is a rational number.
•This includes integers, terminating decimals, and repeating decimals as well as fractions.
•Examples: __________ __________
__________ __________
Numero racional – Cualquier número que puede escribirse en forma de fracción
Irrational Numbers• Any real number that cannot be written in fraction form is an irrational number.
•These numbers include the non-terminating, non-repeating decimals (pi, 0.454455444555...).
•Any square root that is not a perfect root is an irrational number.
Numbero irracionales – Cualquier número real que no se pueden escribir en forma de fracción
Real Numbers•Any number that can name a position on a number line is a real number.
•An important property of real numbers is the Density Property. It says that between any two real numbers, there is always another real number
•Examples: __________ __________
__________ __________
Numero real – el conjunto de numberos racionales junto con el conjunto de
numberos irracionales.
Where would 0 be categorized?
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Zero and the positive integers are the
whole numbers.
Natural Numbers
Where would ½ be categorized?
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Any number thatcan be written in fraction form
is a rational number.
Natural Numbers
Where would 10 be categorized?
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
Also called the counting numbers,
natural numbers include all of the whole numbers
except zero (1, 2, 3, ....).
Where would √3 be categorized?
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Any real number that cannot be
written in fraction form is an
irrational number.
Natural Numbers
Where would -26 be categorized?
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
The counting numbers (1, 2, 3, ...), their
opposites (-1, -2, -3, ...), and zero are integers.
Natural Numbers
Your Turn!Create your own version of the number hierarchy in your math journal including 5 examples of each (HINT: Do not use circles.)
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
