Intersection, Union, Venn Diagram and Number System

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 Numbers 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 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:

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 AGroup B A  BA  B {Tom, Sally, Henry}{Jackson, Sally, Paul} {Even Numbers}{Numbers from 1-11} Mt. Tabor {Kittens}{Cats} A B {Tom, Sally, Henry, Jackson, Paul} {Sally} {1,3,5,7,9, 11 & Even Numbers} {2,4,6,8,10} {High Schools} {Businesses with Petree Address} {High schools & Businesses on Petree} {Cats} {Kittens}

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

Great Youtube Video and Songs for the 4 basic types of numbers: P14SA

NumberNaturalWholeIntegerRationalIrrationalReal -3 0/7 7/0 π /

5. What is Integers Rationals?  6. What is Irrational U Rationals? 11 so it’s Natural, Whole, Integer, Rational, and Real 11 so only Irrational ε Rational, Real so: Natural, Whole, Integer, Irrational ε Irrational, Real so: Natural, Whole, Integer, Rational Integers is a subgroup of Rationals so Integers Real numbers

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 = rational =9 so it’s natural  True

Math Madlib Write down the following items: 1. A rational number less than 4 2. A whole number 3. A real number 4. An irrational number greater than A natural number greater than Name of a person of the opposite gender 7. An integer My future I will graduate from college with a grade average of rational number. I will get a job working whole number hours a week. I will walk real number miles to the job everyday. My house will be irrational number square feet. When I become natural number years old, I will marry person of opposite gender and we will have integer children.

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-12

Classifying Rational and Irrational Numbers Rational NumbersIrrational NumbersNot enough info. Terminating decimal Non- terminating repeating decimal Non- terminating non-repeating decimal P-13 7/8.123 (8 +  2)(8-  2)  8/  2  2*  8 2/3 22/   3/4  8  2 +  rounded to three decimal places

Instructions for Always, Sometimes or Never True P-14 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-15 Always True!!!!  = Irrational

Always, Sometimes or Never True? The circumference of a circle is irrational. True for:False for: P-16 SOMETIMES r= 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-17 SOMETIMES =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-18 Always True!!!!

Always, Sometimes or Never True? The product of a rational number and an irrational number is irrational. True for:False for: P-19 SOMETIMES  3*  5=  15  3 * 0 = 0

Always, Sometimes or Never True? The sum of two irrational numbers is irrational. True for:False for: P-20 SOMETIMES  3+  5=  3+  5   3 = 0

Always, Sometimes or Never True? The product of two rational numbers is irrational. True for:False for: P-21 NEVER True!!!! ¾*2/3 = ½

Always, Sometimes or Never True? The product of two irrational numbers is irrational. True for:False for: P-22 SOMETIMES  3*  5=  15  3*  3 =  9 = 3