Download Classification Warm-Up

PreCalculus
Period:
Unit 1, Lesson 1: ReTeach: Warm-up
Name:
Classification Warm-Up
Directions:
Use the Venn Diagram to determine if each statement is true or false. If it is false, explain why.
Venn Diagram #1: Overlapping Circles
1) It is possible to be both Alpha and Omega at
the same time.
Omegas
2) All Omegas are Alphas.
B
Alphas
C
3) If you’re not an Alpha, you must be an
Omega.
A
D
4) Some Alphas are not Omegas.
Venn Diagram #2: Subsets
Clydes
1) All Clydes are Inkies.
Blinkies
2) All Inkies are Clydes.
Inkies
3) No Blinkies are Inkies.
A
B
D
C
4) If you’re not a Blinky, you’re a Clyde.
Numeracy Skill Builder:
Write each number as a fraction.
1) 0.5
2) 3.871
3) 6
4) -2
5) 0.333333...
6) 5¾
Bonus neat-o numeracy trick!
You can write any repeating decimal as a fraction by putting 9’s in the denominator. Count the
number of digits that repeat, and use that many 9’s in the denominator.
For example:
0.323232...
0.530530...
32
.
99
530
Three digits repeat, so this decimal equals
.
999
Two digits repeat, so this decimal equals
Don’t believe me? Grab a calculator and try it!
If you want to know why it works, come during lunch and ask!
PreCalculus
Period:
Unit 1, Lesson 1: ReTeach: Classwork
Name:
Classifying Real Numbers
Directions:
Write each number in the correct location on the Venn Diagram of the real number system. Each number
should be written only once.
#
3
%$ −6, 2.73, 7 ,
2,
9, −100, 0, π , 1, −
&
1
, − 3.8, 5.42, 8.293017...(
2
'
Real Numbers
Rational Numbers
Irrational
Numbers
Integers
Whole Numbers
True or false? If false, explain why.
1) All whole numbers are integers.
3) Some rational numbers are integers.
2) All integers are whole numbers.
4) Some whole numbers are irrational numbers.
Understanding Real Numbers
1
1) List the numbers in the set # 4 , −18, 0,
5, − , − 2.01, 5,
%$ 5
2
Whole numbers: (Ordinary Counting {1, 2, 3, ….} + 0)
&
π , 2.513, 5.1823159...( that are:
'
Integers: (Whole Numbers + Opposites (Negatives))
Rational numbers: (Numbers written as simple fractions/decimals that terminate or repeat)
Irrational numbers: (Numbers where the decimal does not end)
Real numbers: (Whole, Integer, Rational, & Irrational)
2) Put a check mark for each set that the number is a part of:
Whole
Numbers
Integers
Rational
Numbers
Irrational
Numbers
-7
¾
2
5
0.398
3) True or false? If false, explain why.
a.
All integers are rational.
b. If a number is rational, then it must be a whole number.
c.
Some irrational numbers are integers.
d. All irrational numbers are real numbers.
e. No whole numbers are integers.
Real
Numbers
PreCalculus
Homework # 3
Period:
Name:
Mastering the Real Number System
1) Write each number in the correct location on the Venn Diagram of the real number system. Each number
should be written only once. # 3, 2.09824...,
%$
25,
24,
2
,
5
2
2&
−100, − 7, π , − , 6.5, − 3.01, 3 (
5
7'
Real Numbers
Rational Numbers
Irrational
Numbers
Integers
Whole Numbers
2) List the numbers in the set
Whole numbers
Integers
Rational numbers
Irrational numbers
Real numbers
#
%$ −17, 0,
1 5
3, − ,
, 7.99, 8,
6 7
&
π , 0.03986..., 0.53( that are:
'
3) True or false? If false, explain why.
Some irrational numbers are integers.
a.
b. All rational numbers are whole numbers.
If a number is not an integer, then it is not a whole number.
c.
d. If a number is not an integer, then it is not a rational number.
e. Some irrational numbers are not real numbers.
No rational numbers are integers.
f.
4) Put a check mark for each set that the number is a part of:
Whole
Numbers
Integers
Rational
Numbers
Irrational
Numbers
Real
Numbers
0
2.07
-35
7
7
3
5) Write each number in fraction form.
-25
3
5
7
7
0.002
0.25
8
1
9
2.913
0.5555...
0, 1, 2, 3...
Whole
Numbers
Positive and negative
whole numbers
Integers
Numbers that can be written in
p
the form q where p and q are
integers and q ≠ 0
Rationals
Numbers that cannot be
p
written in the form q where p
and q are integers and q ≠ 0
Irrationals
7
-5
0.222...
3
4
0
-1
0.45
7.02189...
0.5
2
5
9
π
3.21
11
5
12
199
-32