3. WHAT IS CLASSIFICATION ??? CLASSIFIED IN SCIENCE CLASS, WE LEARN ABOUT DIFFERENT ANIMAL SPECIES AND HOW THEY ARE CLASSIFIED ACCORDING TO THEIR PHYSICAL FEATURES, HABITATS, AND SURVIVAL TRAITS…

4. CLASSIFICATION IN MATH NUMBERS CAN BE CLASSIFIED THE SAME WAY: THERE ARE NEGATIVE NUMBERS AND POSITIVE NUMBERS, DECIMALS AND FRACTIONS, BIG AND SMALL, AND THESE CHARACTERISTICS DETERMINE WHICH “GROUPS” A NUMBER BELONGS TO NUMBER SYSTEMS NUMBER SETS GROUPS FOR CLASSIFYING NUMBERS ARE CALLED NUMBER SYSTEMS OR NUMBER SETS

5. THE REAL NUMBER SYSTEM REAL NUMBERS IRRATIONAL NUMBERS RATIONAL NUMBERS INTEGERS WHOLE NUMBERS COUNTING NUMBERS

6. RATIONAL VS IRRATIONAL ALL THE NUMBERS WE USE IN MIDDLE SCHOOL MATH ARE IN THE REAL NUMBER SYSTEM AND EITHER RATIONAL OR IRRATIONAL… NEVER NEVER BOTH!!!! RATIONAL NUMBERS IRRATIONAL NUMBERS ANY NUMBERS THAT CAN BE EXPRESSED AS FRACTIONS ANY NUMBERS THAT CAN BE EXPRESSED AS FRACTIONS MAY BE NEGATIVE, POSITIVE, OR NEUTRAL MAY BE NEGATIVE, POSITIVE, OR NEUTRAL MAY BE WHOLE NUMBERS, MIXED NUMBERS, DECIMALS, OR FRACTIONS MAY BE WHOLE NUMBERS, MIXED NUMBERS, DECIMALS, OR FRACTIONS EXAMPLES: 25, -4, ½, 1.676767 ANY NON-REPEATING, NON- TERMINATING DECIMAL NUMBERS ANY NON-REPEATING, NON- TERMINATING DECIMAL NUMBERS OFTEN HAVE 3 DOTS AT THE END TO SIGNIFY CONTINUATION OFTEN HAVE 3 DOTS AT THE END TO SIGNIFY CONTINUATION *IT IS NOT POSSIBLE TO WRITE IRRATIONAL NUMBERS IN FRACTIONAL FORM, AS THEY HAVE NO END EXAMPLES: 17.418654439… AND ∏

7. -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 INTEGERS INTEGERS ARE NON-DECIMAL NUMBERS THAT MAY BE NEGATIVE, POSITIVE OR NEUTRAL. WE CAN RECOGNIZE THEM AS THE NUMBERS WE SEE ON THE NUMBER LINE -4-4 -3-3 -2-2 -1012 NEGATIVE INTEGERS ¤ POSITIVE INTEGERS NEGATIVE INTEGERS ¤ POSITIVE INTEGERS

8. WHOLE AND COUNTING NUMBERS WHOLE NUMBERS POSITIVE, NON-DECIMAL NUMBERS BELONG TO THE SET OF WHOLE NUMBERS. THESE INCLUDE CONSECUTIVE NUMBERS STARTING WITH ZERO: 0, 1, 2, 3, 4, 5, 6, 7,…. ON INFINITELY COUNTING NUMBERS COUNTING NUMBERS CONTAIN THE SAME NUMBERS, EXCEPT ZERO (IMAGINE HOW YOU COUNT WHEN PLAYING HIDE-AND-SEEK) THIS IS THE SMALLEST SET OF RATIONAL NUMBERS 1, 2, 3, 4, 5, 6, 7 … ON INFINITELY

9. CLASSIFYING NUMBERS… GENERAL RULES:  ALL NUMBERS WE USE IN MIDDLE SCHOOL ARE CLASSIFIED AS REAL  ALL REAL NUMBERS ARE CLASSIFIED AS EITHER RATIONAL OR IRRATIONAL  ANY REAL NUMBERS THAT ARE IRRATIONAL WILL ONLY BE CLASSIFIED AS REAL AND IRRATIONAL  NUMBERS THAT ARE RATIONAL ARE ONLY INTEGERS, WHOLE, AND/OR COUNTING NUMBERS IF THEY DO NOT CONTAIN DECIMALS  NEGATIVE INTEGERS ARE NOT CLASSIFIED AS WHOLE OR COUNTING EXAMPLES: -7 REAL, RATIONAL, INTEGER 0 REAL, RATIONAL, INTEGER, WHOLE 2.08114759… REAL, IRRATIONAL 13 REAL, RATIONAL, INTEGER, WHOLE, COUNTING ½ REAL, RATIONAL -9.1 REAL, RATIONAL **ALL NUMBERS WILL BE CLASSIFIED INTO AT LEAST TWO NUMBER SETS**

10. LESSON 1 VOCABULARY REVIEW TERMDEFINITION CLASSIFY TO IDENTIFY THE NUMBER SETS TO WHICH A GIVEN NUMBER BELONGS (EVERY NUMBER BELONGS TO AT LEAST 2 NUMBER SYSTEMS) NUMBER SYSTEM SETS INTO WHICH NUMBERS MAY BE CLASSIFIED ACCORDING TO MATHEMATICAL CHARACTERISTICS REAL THE SET OF ALL RATIONAL AND IRRATIONAL NUMBERS RATIONAL THE SET OF ALL REAL NUMBERS WHICH MAY BE EXPRESSED AS FRACTIONS (1, 0, -9, -21.35, 8.418, 4.676767676767, AND ½ ARE ALL RATIONAL NUMBERS) IRRATIONAL ANY NUMBER THAT CANNOT BE EXPRESSED AS A FRACTION; ANY NON- REPEATING, NON-TERMINATING DECIMAL NUMBER (.0154663985221… IS AN IRRATIONAL NUMBER) WHOLE THE SET OF ALL COUNTING NUMBERS, PLUS 0 (0, 1, 2, 3, 4, 5…) COUNTING THE SET OF NON-DECIMAL NUMBERS BEGINNING WITH 1 (1, 2, 3, 4, 5….) INTEGER THE SET OF ALL WHOLE NUMBERS AND THEIR OPPOSITES (INCLUDES ALL NEGATIVE AND POSITIVE NON-DECIMAL NUMBERS) NUMBER LINE A MATHEMATICAL TOOL USED TO ORGANIZE THE SET OF REAL NUMBERS