Reflection

Whatever you do, work at it with all your heart, as working for the Lord, not for

men, since you know that you will receive an inheritance from the Lord as a reward. It is the

Lord Christ you are serving.

Colossians 3:23-24

Today

Natural numbers

Puzzles

Patterns

Reasoning

Don’t Forget

Pick up

» Course outline

» Practice 1.1

Quiz Every Thursday

POOR ATTENDANCE =

OF

Don’t Forget

You NEED a scientific

calculator for this course

(needs log key and yx key,

key will really help also).

Get a phone #

Semester Overview

Thinking

Sets

Logic

Buying a house

Graph theory (not what it sounds like)

Voting

Friends don’t let friends take College Algebra Natural Numbers

The set of natural numbers is also called the set of counting numbers.

N = {1, 2, 3, 4, 5, 6, 7, 8, …}

The three dots, called an ellipsis, mean that 8 is not the last number but that the numbers continue in the same manner.

1.1-8

Practice: Vote with your thumbs

Is it a natural number? 13

295.27

-6

½

256

p

Practice Exercise #1

Divisibility

If a ÷ b has a remainder of zero, then a is divisible by b.

The even counting numbers are divisible by 2. They are 2, 4, 6, 8,… .

The odd counting numbers are not divisible by 2. They are 1, 3, 5, 7,… .

1.1-11

Inductive Reasoning

The process of reasoning to a general

conclusion through observations of

specific cases.

Also called induction.

Often used by mathematicians and

scientists to predict answers to

complicated problems.

1.1-12

Puzzles

What comes next?

2,5,8,11,...

,,,, ,,,...

Puzzles

What comes next?

2,5,8,11,...

,,,, ,,,...

, , , ,…

1,0,-1,0,1,0,-1,…

3/2, 9/4, 81/16,…

27,9,3,1,1/3,...

Practice Exercise #2 Deductive Reasoning

A second type of reasoning process is

called deductive reasoning.

Also called deduction.

Deductive reasoning is the process of

reasoning to a specific conclusion from a

general statement.

1.1-16

Find a Pattern

Pick any number, and add 2 to the

number. Multiply the sum by 3, then

subtract 6 from the product. Finally,

divide the difference by 3.

Pick a Number, Any Number

Pick any number, multiply the number by 4, add 2 to the product, divide the sum by 2, and subtract 1 from the quotient. Repeat this procedure for several different numbers and then make a conjecture about the relationship between the original number and the final number.

1.1-18

Practice Exercise #3 Pick a Number, Any Number

Pick any number, multiply the number by 4, add 2 to the product, divide the sum by 2, and subtract 1 from the quotient. Repeat this procedure for several different numbers and then make a conjecture about the relationship between the original number and the final number.

1.1-20

Practice Exercise #3 Counterexample

In testing a conjecture, if a special case is found that satisfies the conditions of the conjecture but produces a different result, that case is called a counterexample.

» Only one exception is necessary to prove a conjecture false.

» If a counterexample cannot be found, the conjecture is neither proven nor disproven.

1.1-22

Find a counterexample

All professional football players weigh

over 300 pounds.

Any counting number added to 3 is

even.

The quotient of any two natural

numbers is even.

Find a Pattern

Multiply any odd counting number by 5.

Multiply another odd number by 5. Try

a few more. Can you describe a

pattern?

Scientific Method

Inductive reasoning is a part of the

scientific method.

When we make a prediction based on

specific observations, it is called a

hypothesis or conjecture.

1.1-25

Not-so-trivial Trivia

What’s the difference between conjecture

and hypothesis?

A Dot Puzzle Your Opinion

What kind of reasoning

did we use?

Challenge

Can we make a

deductive argument?

The End of Section 1.1

Finish homework from

section 1.1 and read

section 1.2 for next time.

Reflection

Peacemakers who sow in peace raise a

harvest of righteousness..

James 3:18

Warm up: Is it a natural number?

139

5679

1

0

¾

2

25

Give a Counterexample

Every UIW student is in a sorority.

The product of any natural number and 5

ends in zero.

Today

Warm up

Homework Stumpers

Rounding for Estimation

Estimating Arithmetic

Estimating Map Distance

Estimation from Pictures

Problem Solving and Puzzles

Quiz 1

Don’t Forget

Pick up

» Practice 1.2

Turn in

» HW 1.1

Stumper Rules

If I go over a problem before hand in, I expect you to correct your solution.

If I want to see what you had first, I won’t go over it before hand in.

Solutions will be posted on the course web site.

Homework Stumpers Discomfort

Rounding Decisions

8%1 .4

87.3 .3

.690 .2

3184 .1

Addition Estimation

2.3912.5886

Practice Exercise #1 Multiplication Estimation

097.02134

Practice Exercise #2 Division Estimation

0.000421

0812.0

Practice Exercise #3 Percent Estimation

$1987 of 1%1

Practice Exercise #4 Estimate the Tree’s Height

True Story: House hunting Reflection

Peacemakers who sow in peace raise a

harvest of righteousness..

James 3:18

Warm up: Why you are taking this course

Express-News:

“His sudden downfall came just days after

the university said it could not ‘condone’

recent statements Agnese made at a

luncheon that resulted in a written

complaint to the university by ‘very

concerned students’.”

Today

Warm up

Estimation from a picture

Estimating map distance

Area estimation

Stumpers

Solving (word) problems

Don’t Forget

Pick up

» Practice 1.3

Turn in

» HW 1.1

Sampling Sampling

Your Turn

1.2-59

Practice Exercise #5

Estimating Map Distances

Mayberry

Mt. Pilot

Scale (Miles)

0 1/2 1 2

Practice Exercise #6

Estimate the number that fit Practice Exercise #7

The End of Section 1.2

Finish homework from

section 1.2 and read

section 1.3 for next time.

Homework Stumpers

Quiz 2 Content

Practice §1.1

Practice §1.2

Ratio & Proportion

The instructions on the Ortho Weed-B-Gon lawn weed killer indicate that to cover 1000 square feet (ft2) of lawn, 20 teaspoons (tsp) of the weed killer should be mixed in 5 gallons (gal) of water. Ron Haines wishes to spray his lawn with the weed killer using his pressurized sprayer.

a) How much weed killer should be mixed with 8 gal of water to get a solution of the proper strength?

1.3-69

Ratio & Proportion

1.3-70

The instructions on the Ortho Weed-B-Gon lawn weed killer indicate that to cover 1000 square feet (ft2) of lawn, 20 teaspoons (tsp) of the weed killer should be mixed in 5 gallons (gal) of water. Ron Haines wishes to spray his lawn with the weed killer using his pressurized sprayer.

b) How much weed killer is needed to cover an area of 2820 ft2 of lawn?

Practice Exercise #1 Unit Analysis

A Toyota Corolla gets 40 mpg on the

highway, and it’s about 300 miles to

Port Isabel. Estimate the cost of gas for

a round trip drive to South Padre.

Practice Exercise #2 Averages

Ralph got a 75, a 54, and a 62 on his first

three tests. What score does he need

on his next test to have a 70 average?

Practice Exercise #3 Puzzlers

30 drivers in a traffic jam, no passengers.

No trucks, just Harleys and cars. I

count 104 tires on the road. How many

cars and how many hogs?

The End of Section 1.3

Finish homework from

section 1.3 and read

section 2.1 for next time.

Who Cares About Sets?

Sets

You use sets any

time you sort or

organize.

Practical Examples of Sets

Kitchen

Music

Films & shows

Dmitri Mendeleev KPCOFGS

Phylogenetic Heirarchy Think about it...

The periodic table

was organized before

the atomic theory was

developed.

The phylogenetic

classification system

preceded Darwin’s

theory of evolution.

e=mc2?

Counting numbers

Vote with your thumbs:

True

False

True False

5 N

6.75 N

-29 N

8 {x|x N and x is between 1 and 8}

8 {x|x N and x is between 1 and 8,

inclusive}

10 {1,2,3,…,16}

Cardinal and Ordinal #s

Reflection

Do not be anxious about anything, but in every situation, by prayer and petition, with thanksgiving, present your requests to God.

Philippians 4:6

Warm up

Last time, we described how you use sets

in your kitchen. Describe another

example from real life where you use sets

(probably without thinking about sets).

Write a complete sentence or two.

Today

Warm up

Defining a set

Subsets

The Power Set

Don’t Forget

Pick up

» Graded HW 1.1 & 1.2

» Graded Quiz 2

Turn in

» HW 1.3

Scores on

mccarronsite.net

Homework Stumpers Numbers

Cardinal

One

Two

Three

Four

Five

…

Ordinal

First

Second

Third

Fourth

Fifth

…

Cardinal or Ordinal?

He is the third idiot who has tried that

line on Brenda tonight.

Cody bought drinks for three different

ladies tonight.

The Senator has been caught alone

with an intern twenty times.

This is the eleventh time the

Congressman has been indicted on

bribery charges.

How many ways can you define a set?

Description

Set builder

Roster

Examples

Well defined

roster

set builder

cardinality

ordinal #

equality

equivalence

N

•A is the set of students in

this class who drove a Ford

today.

•B is the set of students in

this class who are smart.

•C is the set of students in

this class who own a pet

fish.

Well defined set?

The set of US citizens who turned 21 on

9/5/2016

The set of UIW students who are tall

The set of UIW students whose height

is greater than 6 feet

The set of horses that have won the

Kentucky Derby

The set of fast horses

Finite set?

The set of counties in the US

The set of girlfriends Thomas Bazan

has had.

The set of fractions

The set of ants in the US at precisely

1:00 AM EDT on July 4, 2016.

Finite set?

{4,8,12,16,…}

{n|n and 3<n<10 }

{n|n and 3<n }

Express in Roster Form

The set of odd natural numbers less than 11

The set of high schools in Boerne ISD

The set of actors who have played Batman

in a movie

The set of people in this class who have a

pet cat

Write using set builder

{12, 13, 14, 15,…, 32}

{5, 6, 7, 8, …}

Write a description of the set

S={Curly, Moe, Larry}

O={Atlantic, Pacific, Indian, Arctic, Southern*}

Find the set’s Cardinal # (cardinality)

A = {1,2,3,…45}

B = {3,6,9,…81}

S is the set of states in the United

States

P is the set of United States Senators

J is the set of United States Supreme

Court Justices

Equal, equivalent, both, neither?

A is the set of state governors.

B is the set of states.

A is the set of odd numbers less than 15.

B = {1,3,5,…,13}

A is the set of United States Senators.

B is the set of States in the United States.

The End of Section 2.1

Finish homework from

section 2.1 and read

section 2.2 for next time.

Homework: Exercises Section 2.1

(p. 47-51), #3-16, 18-25,28-31, 34,

36, 37, 43, 44, 50, 53, 54, 57, 59,

60, 67-70, 72, 79-83, 87, 89-92

Estimated time: 1:48