Transcript play lesson 1 presentation: classifying numbers

CLASSIFYING NUMBERS
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 TO
GROUPS FOR CLASSIFYING NUMBERS ARE CALLED
NUMBER SYSTEMS OR NUMBER SETS
THE REAL NUMBER SYSTEM
REAL NUMBERS
RATIONAL NUMBERS
INTEGERS
WHOLE NUMBERS
COUNTING NUMBERS
IRRATIONAL
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
• ANY NUMBERS THAT CAN BE
EXPRESSED AS FRACTIONS
IRRATIONAL NUMBERS
• MAY BE NEGATIVE, POSITIVE, OR
NEUTRAL
• ANY NON-REPEATING, NONTERMINATING DECIMAL NUMBERS
• OFTEN HAVE 3 DOTS AT THE END
TO SIGNIFY CONTINUATION
• MAY BE WHOLE NUMBERS, MIXED
NUMBERS, DECIMALS, OR
FRACTIONS
*IT IS NOT POSSIBLE TO WRITE
IRRATIONAL NUMBERS IN FRACTIONAL
FORM, AS THEY HAVE NO END
EXAMPLES: 25, -4, ½, 1.676767
EXAMPLES: 17.418654439… AND ∏
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
1212
0
34
-
-5 -4 -3
-2 -1
0
1
2
3
4
NEGATIVE INTEGERS ¤ POSITIVE INTEGERS
5
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 NUMBERS
1, 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 REVIEW
TERM
CLASSIFY
NUMBER SYSTEM
REAL
RATIONAL
IRRATIONAL
WHOLE
COUNTING
INTEGER
NUMBER LINE
DEFINITION
TO IDENTIFY THE NUMBER SETS TO WHICH A GIVEN NUMBER BELONGS
(EVERY NUMBER BELONGS TO AT LEAST 2 NUMBER SYSTEMS)
SETS INTO WHICH NUMBERS MAY BE CLASSIFIED ACCORDING TO
MATHEMATICAL CHARACTERISTICS
THE SET OF ALL RATIONAL AND IRRATIONAL NUMBERS
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)
ANY NUMBER THAT CANNOT BE EXPRESSED AS A FRACTION; ANY NONREPEATING, NON-TERMINATING DECIMAL NUMBER (.0154663985221… IS
AN IRRATIONAL NUMBER)
THE SET OF ALL COUNTING NUMBERS, PLUS 0 (0, 1, 2, 3, 4, 5…)
THE SET OF NON-DECIMAL NUMBERS BEGINNING WITH 1 (1, 2, 3, 4, 5….)
THE SET OF ALL WHOLE NUMBERS AND THEIR OPPOSITES (INCLUDES
ALL NEGATIVE AND POSITIVE NON-DECIMAL NUMBERS)
A MATHEMATICAL TOOL USED TO ORGANIZE THE SET OF REAL
NUMBERS