Download Real Number System

What’s In A
Number?
The Mysterious World of
Number Identity…
Focus 4 - Learning Goal #1: Students will know that there are numbers
that are not rational, and approximate them with rational numbers.
4
3
2
1
0
In addition to
level 3.0 and
above and
beyond what
was taught in
class, students
may:
-Make
connection with
other concepts
in math.
- Make
connection with
other content
areas.
Students will know
that there are
numbers that are
not rational, and
approximate them
with rational
numbers.
- Convert a decimal
expansion that
repeats into a
fraction.
- Approximate the
square root of a
number to the
hundredth & explain
the process.
- For all items listed
as a 2, students can
explain their
process.
Students will
know the subset
of real numbers.
- Know that all
numbers have a
decimal
expansion.
- Compare the
size of irrational
number.
- Locate
approximately
irrational
numbers on a
number line.
With help
from the
teacher, I
have partial
success with
level 2 and 3.
Even with help,
students have no
success with the
unit content.
Categories of Numbers in the
REAL Number System
•
•
•
•
•
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers
Natural Numbers
• Are the counting numbers
• {1, 2, 3, 4, 5, 6, 7, 8, …}
Whole Numbers
• All of the counting numbers and zero.
• {0, 1, 2, 3, 4, 5, 6, 7, …}
Integers
• Are all of the natural numbers, their
opposites and zero.
• {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …}
Rational Numbers
• Numbers that can be expressed as a fraction
(a/b).
• This set includes the integers, terminating
decimals, and repeating decimals.
• Some examples:
• 2 = 2/1
• 3 ¼ = 13/4
• -0.25 = -25/100
• 1/3 = 0.33333333333333333333333
Irrational Numbers
• Numbers that CANNOT be expressed as
a fraction of integers.
• In decimal form, they are the numbers that
go on forever without a repeating pattern.
• Some examples:
• √2 = 1.4142…
• π = 3.1415…
• 45.9492…
Venn Diagram of REAL
Number System
Rational Numbers
Integers
Whole
Natural
Irrational
Numbers
Tree Diagram of
Real Number System
0.5, 1.4, 0.256
0.3, 0.45
1/
-5, -80
1, 2, 3…
5,
4/
11,
12/3
0.6392518…
Π, √2
Classify each number as natural,
whole, integer, rational,
or irrational.
Write as many as apply.
1.
2.
3.
4.
5.
6.
7.4569594…
-5 ¾
-79
3
0
√16