1. Group AGroup B A  B (union; list all members) A  B Intersections (in common) {Apple, Banana, Grape, Kiwi} {Apple, Coconut, Egg, Kiwi} {Apple, Banana, Coconut, Egg, Grape, Kiwi} {Apple, Kiwi} {1,2,3,5,6,7,8,9}{5,6,7} A ε {Even Numbers}B ε {Odd Numbers} All integers but 0  (no solution) Males in this room People older than 18 in this room The males or those older than 18 in this room 1 5 8 2 6 9 3 7 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} For Subgroups:

2. 1. Explain in your own words what , , and  mean. 2. 3. Sally looked at the following diagram and said that A  B = . Is she right? Explain your answer.. Group AGroup B A  BA  B {Tom, Sally, Henry}{Jackson, Sally, Paul} {Even Numbers}{Numbers from 1-11} {Mt. Tabor} {Kittens}{Cats} A B

3. N Natural Numbers 1,2,3,4 … W Whole Numbers 0,1,2,3,… Z Integers -2,-1,0,1,2 … R Real Numbers Q Rational Numbers -3, 2/3, ½,  4 I Irrational Numbers  5,  Types of Numbers Does not exist Imaginary

4. NumberNaturalWholeIntegerRationalIrrationalReal -3 0/7 7/0 π 3.4523415.. 2/3 3.4523415

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

6. 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

7. 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

8. Classifying Rational and Irrational Numbers Rational NumbersIrrational NumbersNot enough info. Terminating decimal Non- terminating repeating decimal Non- terminating non-repeating decimal P-8 7/8.123 (8 +  2)(8-  2)  8/  2  2*  8 2/3 22/7 0.123.9   3/4  8  2 +  8 0.123... 0.123 rounded to three decimal places

9. Instructions for Always, Sometimes or Never True P-9 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.

10. Always, Sometimes or Never True? The sum of a rational number and an irrational number is irrational. True for:False for: P-10 Always True!!!!  3 + 2 = Irrational

11. Always, Sometimes or Never True? The circumference of a circle is irrational. True for:False for: P-11 SOMETIMES r= 3  2  (3) r=3/   2  (3/  ) 6  6

12. Always, Sometimes or Never True? The diagonal of a square is irrational. True for:False for: P-12 SOMETIMES 3 2 + 3 2 =18 (  8) 2 + (  8) 2 = 16 =  18 =  16 = 4

13. Always, Sometimes or Never True? The sum of two rational numbers is rational. True for:False for: P-13 Always True!!!!

14. Always, Sometimes or Never True? The product of a rational number and an irrational number is irrational. True for:False for: P-14 SOMETIMES  3*  5=  15  3 * 0 = 0

15. Always, Sometimes or Never True? The sum of two irrational numbers is irrational. True for:False for: P-15 SOMETIMES  3+  5=  3+  5  3 + -  3 = 0

16. Always, Sometimes or Never True? The product of two rational numbers is irrational. True for:False for: P-16 NEVER True!!!! ¾*2/3 = ½

17. Always, Sometimes or Never True? The product of two irrational numbers is irrational. True for:False for: P-17 SOMETIMES  3*  5=  15  3*  3 =  9 = 3