Group A
Group B
{Apple, Banana,
Grape, Kiwi}
1
2
3
AB
AB
(union; list all members)
Intersections
(in common)
{Apple, Coconut, Egg, {Apple, Banana,
Kiwi}
Coconut, Egg, Grape,
Kiwi}
5
6
7
{Apple, Kiwi}
{1,2,3,5,6,7,8,9}
{5,6,7}
All integers but 0
(no solution)
8
9
A ε {Even Numbers}
B ε {Odd Numbers}
Males in this
room
People older than The males or those
18 in this room
older than 18 in this
room
For Subgroups:
A small group U Larger group = Large Group
A small group  Larger group = Small Group
Ex: {Boys} U {Males} = {Males}
Ex: {Boys} n {Males} = {Boys}
1. Explain in your own words what , , and 
mean.
2.
Group A
Group B
{Tom, Sally, Henry}
{Jackson, Sally, Paul}
{Even Numbers}
{Numbers from 1-11}
AB
AB
{Mt. Tabor}
{Kittens}
{Cats}
3. Sally looked at the following diagram and
said that A  B = . Is she right? Explain your A
answer..
B
Types of Numbers
R Real Numbers
Does not
exist
W
Whole Numbers
0,1,2,3,…
N
Natural Numbers
1,2,3,4 …
Z
Integers
-2,-1,0,1,2 …
Q Rational Numbers -3, 2/3, ½,4
I
Irrational
Numbers
5, 
7
0
Imaginary
4
Number
-3
0/7
7/0
π
23
81
3.4523415..
3.45
2/3
3.4523415
9
4
Natural
Whole
Integer
Rational
Irrational
Real
1. What group of numbers does 121 belong to?
2. What group of numbers does 121 not belong to?
3. What group of numbers does -3/4 not belong to?
4. What group of numbers does 𝜋 not belong to?
5. What is Integers  Rationals?
6. What is Irrational U Rationals?
7. A ε {-2, 1/3, 0, 7, 3 , 25, (-2)3 , (-2)2, -22, 0/7, 18/(9-32)
List all the whole numbers of A
8. x = 2 𝑎𝑛𝑑 𝑦 = 3 2. Determine if the following are rational:
X+y
X–y
X*y
x/y
9.a=4
c
b= 5
Determine if the following are true or false:
a. a + b is a natural number
b. b+ c is a rational number
c. c2 – b2 is an integer
d. c*a is rational
•
Instructions for Placing Number
Cards
Take turns to choose a number card.
•
When it is your turn:
–
Decide where your number card fits on the poster.
–
Does it fit in just one place, or in more than one place?
–
Give reasons for your decisions.
•
When it is your partner’s turn:
–
If you agree with your partner’s decision, explain her reasons in your own words.
–
If you disagree with your partner’s decision, explain why. Then together, figure out
where to put the card.
•
When you have reached an agreement:
–
Write reasons for your decision on the number card.
–
If the number card fits in just one place on the poster, place it on the poster.
–
If not, put it to one side.
P-7
Classifying Rational and Irrational Numbers
Rational Numbers
Terminating
decimal
Nonterminating
repeating
decimal
Nonterminating
non-repeating
decimal
P-8
Irrational Numbers
7/8
.123
(8 + 2)(8- 2)
8/ 2
2* 8
Not enough info.
0.123...
0.123 rounded
to three
decimal places
2/3
22/7
0.123
0.123
.9

3/4
8
2 + 8
Instructions for Always, Sometimes or Never True
1. Choose a statement.
• Try out different numbers.
• Write your examples on the statement card.
2. Conjecture: decide whether you think each statement is
always, sometimes or never true.
• Always true: explain why on the poster.
• Sometimes true: write an example for which it
is true and an example for which it is false.
• Never true: explain why on the poster.
P-9
Always, Sometimes or Never True?
The sum of a rational number and an irrational
number is irrational.
True for:
Always True!!!!
3 + 2 = Irrational
P-10
False for:
Always, Sometimes or Never True?
The circumference of a circle is irrational.
True for:
False for:
SOMETIMES
r= 3  2(3)
r=3/  2(3/ )
6
6
P-11
Always, Sometimes or Never True?
The diagonal of a square is irrational.
True for:
False for:
SOMETIMES
32 + 32 =18
(8)2 + ( 8)2 = 16
= 16 = 4
=18
P-12
Always, Sometimes or Never True?
The sum of two rational numbers is rational.
True for:
Always True!!!!
P-13
False for:
Always, Sometimes or Never True?
The product of a rational number and an
irrational number is irrational.
True for:
P-14
False for:
SOMETIMES
3*5= 15
3 * 0 = 0
Always, Sometimes or Never True?
The sum of two irrational numbers is irrational.
True for:
False for:
SOMETIMES
3+5= 3+5
3 + - 3 = 0
P-15
Always, Sometimes or Never True?
The product of two rational numbers is
irrational.
True for:
False for:
NEVER True!!!!
¾*2/3 = ½
P-16
Always, Sometimes or Never True?
The product of two irrational numbers
is irrational.
True for:
False for:
SOMETIMES
3*5= 15
3* 3 = 9 = 3
P-17