Intersection, Union, Venn Diagram and Number System

Group A Group B A B A B{Apple, Banana, Grape, Kiwi}

{Apple, Coconut, Egg, Kiwi}

{Apple, Banana, Coconut, Egg, Grape, Kiwi}

{Apple, Kiwi}

{1,2,3,4,5,6,7,8,9} {5,6,7}

Even Numbers Odd Numbers All Numbers

Males in this room

People older than 16 in this room

The males or those older than 16 in this room

1 5 82 6 93 7

1. Explain in your own words what , , and mean.

2. Mentally fill in the chart

3. Sally looked at the following diagram and said that A B = . Is she right? Explain your answer..

Group A Group B A B A B

{Tom, Sally, Henry} {Jackson, Paul}

Even Numbers Numbers from 1-11

Mt. Tabor

Kittens Cats

A B

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-5

Classifying Rational and Irrational NumbersRational Numbers

Irrational Numbers

Not enough info.

Terminating decimal

Non-terminating repeating decimal

Non-terminating non-repeating decimal

P-6

7/8.123(8 + 2)(8- 2)8/ 22* 8

2/322/70.1230.123.9

3/482 + 8

0.123...0.123 rounded to three decimal places

Instructions for Always, Sometimes or Never True

P-8

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.

Always, Sometimes or Never True?

The sum of a rational number and an irrational number is irrational.

True for: False for:

P-9

Always True!!!!3 + 2 = Irrational

Always, Sometimes or Never True?

The circumference of a circle is irrational. True for: False for:

P-10

SOMETIMESr= 3 2(3) r=3/ 2(3/ ) 6 6

Always, Sometimes or Never True?

The diagonal of a square is irrational. True for: False for:

P-11

SOMETIMES32 + 32 =18 (8)2 + ( 8)2 = 16 =18 = 16 = 4

Always, Sometimes or Never True?

The sum of two rational numbers is rational. True for: False for:

P-12

Always True!!!!

Always, Sometimes or Never True?

The product of a rational number and an irrational number is irrational.

True for: False for:

P-13

SOMETIMES3*5= 15 3 * 0 = 0

Always, Sometimes or Never True?

The sum of two irrational numbers is irrational. True for: False for:

P-14

SOMETIMES3+5= 3+5 3 + - 3 = 0

Always, Sometimes or Never True?

The product of two rational numbers is irrational.

True for: False for:

P-15

NEVER True!!!!¾*2/3 = ½

Always, Sometimes or Never True?

The product of two irrational numbers is irrational.

True for: False for:

P-16

SOMETIMES3*5= 15 3* 3 = 9 = 3

NNatural Numbers

1,2,3,4 …

W Whole Numbers

0,1,2,3,…

ZIntegers

-2,-1,0,1,2 …

Q Rational Numbers -3, 2/3, ½,4

IIrrational Numbers

5,

R Real Numbers