1. Introduction to Numbers

2. Warm-Up Yesterday 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 - ______________________________________

3. Hierarchy of Numbers “The way numbers are organized” Real Numbers Irrational Numbers Rational Numbers Integers Whole Numbers Natural Numbers

4. 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.

5. Whole Numbers Zero and the positive integers are the whole numbers. Examples: ____________________ __________ Números Enteros – El cero y los números enteros positivos

6. 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.

7. 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

8. 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

9. 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.

10. 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

11. Where would ½ be categorized? Real Numbers Irrational Numbers Rational Numbers Integers Whole Numbers Any number that can be written in fraction form is a rational number. Natural Numbers

12. 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,....).

13. 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

14. 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

15. BrainPOP Movie

16. Your Turn!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