Unit 1
When we manipulate expressions and equations, we realize that there are basic properties that govern what we can and can't do. One of those properties is the Commutative Property. Let's consider this property in our discussion. Is there a commutative property of subtraction? In other words, does order matter when subtracting? Why or Why not? Please provide an example to explain your reasoning. Please share any trick or mnemonic device to help you recall what this property is or how to use it. There is no Commutative Property in subtraction. Yes order does matter subtracting, you can not subtract a larger number from a smaller number, such as: 3-6 = this subtraction can not be done but if you turn it around and subtract the smaller number from the larger number it will work: 6 -3 = 3. In all the properties you can not use subtraction or division, just addition and multiplication.

Unit 2
As we know, a set is just a collection of objects that are similar in some way, like a gaggle of geese, pride of lions, or an army of ants. To further classify our world, we can create subsets from a larger set. Let's consider the idea of a subset for our discussion.

• Give an example of a subset and a proper subset. Explain the difference between a subset and proper subset.
• Can any set be a proper subset of itself? Give an example of why or why not. A = {Lions, Tigers, Jaguar}
B={Lions, Tigers, Leopard, Cheetah, Jaguar}
*Everything that is in A is in set B therefore it is an example of a subset.
* Example A and B are also a proper subset because everything in A is in B and they are not equal. I will give an example of a subset that is not proper to try to better explain.
C={Dogs, Cats, Horses, Goats}
D={Horses, Dogs, Cats, Goats}
*They are a subset because of everything in C is in D, but they are not a proper subset because they are equal.
*Any set cannot be a proper subset of itself because the sets would be the exact same. Looking at example C, to make it a proper subset the set you were comparing it to would have to have another object listed such as fish. Comparing C to C would just be a subset.
Give an example of a subset and a proper subset. Explain the difference between a subset and proper subset.

Can any set be a proper subset of itself? Give an example of why or why not.

{karina, shanna, vivi} =Set

{karina,vivi} = Subset

It is possible for a set to be a subset of itself. If the subset is missing at least one member of the original set, then you call the subset a "proper" subset.

Unit 3
The order that we use to assemble a cake or build a house is important. The same holds true for evaluating any expression in math. We call this the Order of Operations. In your own words, explain the Order of Operations.

• Give an example of an expression to fit this situation in math and an example in real life.
• Please share any trick or mnemonic device to help you recall this order or how to use it. A mnemonic device is a memory trick such as using “The quick brown fox jumped over the lazy dog” to learn all the keys on the keyboard.
Professor and Class-Good Morning!

The Order of Operations- A set of rules for the order in which to solve mathematical problems.

The order goes: * and /, + and -. If there are parentheses then work inside them first. Example: Correct: 1+2*3=7. Not Correct: 1+2*3=9

Rule 1: First perform any calculations inside parentheses.

Rule 2: Next perform all multiplications and divisions, working from left to right.

Rule 3: Lastly, perform all additions and subtractions, working from left to right.
(http://www.mathgoodies.com/lessons/vol7/order_operations.html)

The Order of Operations is very much like baking a cake, or driving a car, you cant change much in order to have the same outcome.

The Mnemonic Device that i use it this :

Please Excuse My Dear Aunt Sally-- Meaning....
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Unit 4
Linear relationships between two quantities can be described by an equation or a graph. Which do you think is the more informative? Why? A statistical term used to describe the relationship between a variable and a constant. Linear relationships can be expressed in a graphical format where the variable and the constant are connected via a straight line or in a mathematical format where the independent variable is multiplied by the slope coefficient, added by a constant, which determines the dependent variable.

(http://www.investopedia.com/terms/l/linearrelationship.asp)

On the one hand a graph has the advantage, by seeing a graph your seeing the visual representation, making it easier to see information at a simple glance. On the other hand the equation lets you get whatever data points you want for any range. I feel a graph is more informative because it highlights the limited range of actual data. By a graph giving a picture it allows us to see the data, an equation you see a formula and have to substitute the information your looking for into the equation.

Personally i would rather see data, than to plug in data! I feel that graphs make Math Easier and Fun =)

Unit 5
Explain why the conversions in the metric system are easier to make than conversions in the US system of measurements. Please show or explain your reasoning with an example.
In the metric system there is only one type of measurement system for each type of measuring. Examples: Meter does length, Kilogram does mass, Liter measures volume, Celsius does temperature. Through the United States we have several different types of measuring systems for each type of measuring. Examples: In length we can use the mile, the foot, and yards. For mass we have pounds, ounce or ton. In volume we have cup, quart, pint, and gallon. Just by listing, we are already getting the understanding that the Metric system is much easier to deal with. Then we have the problem in the U.S. system of trying to convert one form to another. Example: Gallon to quart. However, since the U.S. is the only country that uses its form of measuring it is important to understand the Metric system and what each measurement is for.

Unit 6
In your own words, explain why perimeter is measured in units and area is measured in square units. Give examples to clarify your explanation. Why would we measure volume in cubic units? Perimeter is measured in the same units as the sides. Example being if the sides are measured in feet then the perimeter is going to be measured in feet. The perimeter of a two dimensional figure is the sum of the lengths of the sides of the figure. (Sum= addition) If a rectangle had a length of 21 and a width of 12, you would take the length times 2 and the width times 2. 21(2) and 12(2). 42+24=66. 66 Is your perimeter.

Area is measured in square units. We are multiplying to find area. To find the area we are multiplying the length times the width. Example being A being area, A= L x W. Area equals length times width to equal an amount squared. In this case to find the area we would take 21 times 12 to equal 252^2.

Volume is the measure to get the capacity of a three-dimensioned figure. You are trying to find how much of a material you can put inside a three-dimensional figure. To find the volume you will use V=lwh. Volume equals length times width times height. If the length is 5 and the width is 2 and the height is 3 then the volume is 30 cubic units.
Unit 7
How well we understand the difference between empirical and theoretical probability is an important part of our ability to apply probability to a real world set of data. What is the difference between empirical and theoretical probability? Give two to three examples of professions where probability could be used. Explain your answer. A simple way to explain the difference between the two is this.

Empirical probability is the likelihood of an event happening that is based on experience and observation rather than on theory.

Theoretical probability is the likelihood of an event happening based on theory rather than on experience and observation.

I would think that any profession that deals with science would find probability to be most useful. In any kind of experiment you have to be able to predict or expect certain results and being able to use the rules of probability would greatly help in that. Another profession that would make use of it would be casino's. They make a living off of taking the probability that certain outcomes will come from certain actions.

Unit 8
In your own words, give an example in detail of how you would obtain a sample from one of the techniques listed below. (Just select one.)
• Random sampling
• Systematic sampling
• Cluster sampling
• Stratified sampling
• Convenience sampling

Professor and Class --

I choose Random Sampling. Each item or element of the Population has an equal chance of being chosen at each draw. A sample is Random if the Method for obtaining the sample meets the criteria of randomness- Meaning Each Element having its own chance at Each Draw. The Composition does not determine whether or not it was a Random Sample.

All Samples have an equal and Independent chance of being selected.

Unit 9
A common error is neglecting to get ranked data for some statistical processes. Why do we have to have ranked data? Give an example of where you would need ranked data.

Professor and Class--

We need to have Ranked Data because there is no way to measure such attributes as sports, dancing, singing, beauty, cooking and many other competitions besides ranking them in statistical data or ranked data.

One example I could think of would be golf. A round of golf consists of 18 holes which each hole is measured in yards. Breaking each hole down to how many shots it would take for one to get to the hole they make shot limits. These limits are called par which range from par three holes, par four holes and par five holes. Now most Golf courses have a total par count of 72 meaning you would add each holes par which would give you a count of 72. Now when counting this on a golf score card 72 would equal 0. Anything under 72 or 0 would count on a score card -1 for 71, -2 for 70 and any thing over 72 would be 73 as 1, 74 as 2 and so on. I added this for people who don't understand how golf is scored and to possibly give a better understanding.

Now say we have 8 golfers in a tournament. Golfer one shoots a 74, golfer 2=72,golfer 3=68, golfer 4=70, golfer 5=72, golfer 6 =67, golfer 7=73 and golfer 8=71. now we would break this down as such: golfer 1= 2, golfer 2= 0, golfer 3= -4, golfer 4= -2, golfer 5= 0, golfer 6= -5, golfer 7= 1, and golfer 8= -1. Now its time to rank the players and find out who one the tournament.
1.golfer 6
2.golfer 3
3.golfer 4
4.golfer 8
5.golfer 2
5.golfer 5
7.golfer 7
8.golfer 1
Notice as they were placed golfer 2 and 5 have the same place which would skip a sixth place due to them having the same score.

http://aolanswers.com/questions/science_mathematics_518913573838606/way_measure_certain_attributes_149233113717759

Yes we need the ranked data when figuring the median. For example if you have five numbers, 42 32 66 54 22. You need to put them in order to be able to figure out the median. They should be 22 32 42 54 66 then you can figure the median which is 42 the number in the middle of the ranked data.

Unit 10
Take a moment to reflect on your progress in this course during the past 10 weeks. When you started the course, you may have known some basic principles, but now you have a solid foundation in college mathematics to tackle many different problems common to real-world situations.
Take a moment to reflect on your progress in this course. Please answer the following questions:

1) Did the course meet your expectations?
2) How do you feel about your progress in the course? Are you surprised with your progress?
3) What is one concept that you wish you understood better?
4) What advice would you give to a student starting the class next term?
5) What would have made the course a better one?
Be sure to comment on your classmates' reflections.
Hey Everyone--

Cannot believe that were done! Week 10 came so quickly! Coming into the course i was petrified because i am terrible in Math, The Course met all of my expectations, and beyond! I like the fact that the Math Labs allowed you to practice until you got the question right, I was surprised at how well i knew Math, Answered the questions right on the first or second try. I wish i could understand Graphing a bit better. To the students starting Math next term -- Dont give up on the Math Labs, If it becomes frustrating save your work, take a break, you can always come back to it! You can get 100 % on every Math Lab, I did no problem, along with other students I am sure, The only thing i did not like was the "flex" Seminar. Other than that everything was great!

I wish all of you the best of luck in your future endeavors!