Intersection Union Venn Diagram and Number System Group

Intersection, Union, Venn Diagram and Number System

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 Numbers 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. Mentally fill in the chart Group A Group B A B {Tom, Sally, Henry} {Jackson, Sally, Paul} {Sally} {Even Numbers} {Numbers from 1 -11} {Tom, Sally, Henry, Jackson, Paul} {1, 3, 5, 7, 9, 11 & Even Numbers} {High schools & Businesses on Petree} Mt. Tabor {Cats} {Kittens} {High Schools} {Kittens} {Businesses with Petree Address} {Cats} 3. Sally looked at the following diagram and said that A B = . Is she right? Explain your answer. . {2, 4, 6, 8, 10} A B

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

Great Youtube Video and Songs for the 4 basic types of numbers: https: //www. youtube. com/watch? v=m 94 WTZ P 14 SA

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

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 5. What is Integers Rationals? Integers is a subgroup of Rationals so Integers 6. What is Irrational U Rationals? Real numbers

= rational 9. a=4 c b= 5 Determine if the following are true or false: a. a + b is a natural number =9 so it’s natural True b. b+ c is a rational number c. c 2 – b 2 is an integer d. c*a is rational

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 500 5. A natural number greater than 15 6. 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 Numbers Terminating decimal Nonterminating repeating decimal Nonterminating non-repeating decimal P-13 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-14

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-15 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-16

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-17

Always, Sometimes or Never True? The sum of two rational numbers is rational. True for: Always True!!!! P-18 False for:

Always, Sometimes or Never True? The product of a rational number and an irrational number is irrational. True for: P-19 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-20

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

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