Group A Group B A B union list

Group A Group B A B (union; list all members) {Apple, Banana, Grape, Kiwi} {Apple, Coconut, Egg, {Apple, Banana, Kiwi} Coconut, Egg, Grape, Kiwi} A B Intersections (in common) {Apple, Kiwi} {1, 2, 3, 5, 6, 7, 8, 9} {5, 6, 7} All integers but 0 (no solution) 1 5 8 2 6 9 3 7 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 {Mt. Tabor} {Kittens} {Cats} 3. Sally looked at the following diagram and said that A B = . Is she right? Explain your A B answer. .

Types of Numbers R Real Numbers 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, Does not exist Imaginary

Number -3 0/7 7/0 π 3. 4523415. . 2/3 3. 4523415 Natural Whole Integer Rational Irrational Real

5. What is Integers Rationals? 6. What is Irrational U Rationals?

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. c 2 – b 2 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. 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 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 = 18 = 16 = 4 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