CLASSIFYING NUMBERS

DUFF’S MATH STUFF…

MAKING SENSE OF NUMBER SENSE

LESSON 1

WHAT IS CLASSIFICATION ???

IN SCIENCE CLASS, WE LEARN ABOUT DIFFERENT ANIMAL SPECIES AND HOW THEY ARE CLASSIFIED

ACCORDING TO THEIR PHYSICAL FEATURES, HABITATS, AND SURVIVAL TRAITS…

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

TOGROUPS FOR CLASSIFYING NUMBERS ARE

CALLED NUMBER SYSTEMS OR

NUMBER SETS

THE REAL NUMBER SYSTEM

REAL NUMBERS

IRRATIONAL

NUMBER

S

RATIONAL NUMBERS

INTEGERSWHOLE NUMBERSCOUNTING

NUMBERS

RATIONAL VS IRRATIONAL

ALL THE NUMBERS WE USE IN MIDDLE SCHOOL MATH ARE IN THE REAL NUMBER SYSTEM AND

EITHER RATIONAL OR IRRATIONAL…

NEVER BOTH!!!!RATIONAL NUMBERS

IRRATIONAL NUMBERS

• ANY NUMBERS THAT CAN BE EXPRESSED AS FRACTIONS

• MAY BE NEGATIVE, POSITIVE, OR NEUTRAL

• MAY BE WHOLE NUMBERS, MIXED NUMBERS, DECIMALS, OR FRACTIONS

EXAMPLES: 25, -4, ½, 1.676767

• ANY NON-REPEATING, NON-TERMINATING DECIMAL NUMBERS

• 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 ∏

-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

-4-3-2-1012

NEGATIVE INTEGERS ¤ POSITIVE INTEGERS

WHOLE AND COUNTING 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 CONTAIN THE SAME NUMBERS, EXCEPT ZERO

(IMAGINE HOW YOU COUNT WHEN PLAYING HIDE-AND-SEEK)

THIS IS THE SMALLEST SET OF RATIONAL NUMBERS1, 2, 3, 4, 5, 6, 7 … ON INFINITELY

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**

LESSON 1 VOCABULARY REVIEWTERM DEFINITION

CLASSIFYTO 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

RATIONALTHE 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)

IRRATIONALANY 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….)

INTEGERTHE 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