Much was learned during our extensive study in patterns. We were able to come up with new ways to identify and interpret mathematical, as well as pictorial, patterns by using “In and Out” tables. As mentioned before, this unit was rather extensive, not only did we explore “In and Out” tables; we also discovered functions, domain and ranges of data sets, summation notation, consecutive numbers, factorials, arithmetic sequence and order of operations. On top of that, we investigated triangular numbers, finding formulas, the number of diagonals in a polygon, the sum of interior angles in a polygon, measure of angles in regular polygons, exponents, and squaring negative numbers. As you can see, this was a productive unit!

The “In and Out” tables were a vital piece of this unit. Not only were they an effective way to show information, we were also able to solve patterns using them and find missing terms in a sequence with them. In the example “In and Out” table below: “To find the out value, multiply the in value by itself and then subtracts three.” InOut

0-3
1-2
21
“In and Out” tables taught us to look at problems differently and to find multiple ways as to how to address a problem.

When we solved the “In and Out” tables, we came up with functions to express a rule derived from the table that could describe how to find the out value from the in value and would work for all numbers being applied to it. By solving the functions, we were able to come up with formulas. Upon coming up with formulas, we were able to also solve for missing domains and ranges in the tables. Domains are the inputs in data sets and ranges are the outputs.

Another useful way to display data sets is through summation notation. Summation notation uses the “Sigma” sign and can represent data up to a certain specified limit.

Consecutive and triangular numbers seemed to pop up a lot in this unit while investigating patterns. We noticed that with consecutive...

...The in this unit titled "Patterns" we learned and covered a lot of things. Some of the key concepts we went over are In and Out tables, order of operations, summation notation, consecutive sums, conjecture and proof, geometry, recursive functions, positive/negative numbers and algebraic expressions. We used in and out tables to organize data so that we can see patterns.
By organizing it and looking at the in then the out it made it easier to find apattern. Orders of operations were used to correctly find the correct order and answer to a problem that contained many operations. To help us remember the order we used the acronym PEMDAS (Parentheses, Exponentiation, Multiplication/Division, Addition/Subtraction) which was made easier to remember by using "Please Excuse My Dear Aunt Sally". We also learned about summation notations which taught us things such as the sigma. Consecutive sums showed us how we can use consecutive numbers to get a sum such as the 1-2-3-4 pattern. We also learned about geometry and how to measure angles and finding angles on shapes. Proofs are used to make sure your answer is correct and how you know its complete. We also learned how diagonals can affect the sum of the angles of a polygon. We used algebraic expressions and learned about variables and how to find the answer to certain problems.
Math is a very important subject to learn. I believe that math is a subject in which...

...
The Founding Father, the Propagandist, and a Wife
Daniel Boggs
(HST201-1) – (U.S. History I)
Colorado State University – Global Campus
Dr. Bruce Ingram
August 19, 2014
The Founding Father, the Propagandist, and a Wife
Three people walked into a bar. They were a founding father, a propagandist, and a wife of a famous leader. The three introduced themselves as; Thomas Jefferson, Thomas Paine, and Abigail Adams. Ok, so they really did not meet in a bar. If they did they would have plenty of stories to share with each other about their childhood, their contributions to independence, and their influence on the United States. Maybe, they would talk about the legacy each would like to leave behind and how the world was forever changed. Regardless, they would have a lot to talk about. Back in the Revolutionary and Enlightenment era these three people overcame many obstacles in the name of independence. Each individual had a remarkable background that inspired them to be great leaders that contributed to the birth of the United States. The legacies that these three people have left behind still live on today.
Thomas Jefferson
Thomas Jefferson had many accomplishments in his life. Most notably was that he was the one who wrote the Declaration of Independence and also the Statute of Virginia for Religious Freedom. After the American Revolution, Jefferson was elected the third president of the United States. Before he died on July 4, 1826, he also established...

...Portfolio1
Personal and professional development
By
Faiza Nabil Sabita
UOG ID : 00792125
Tutor: Mr. Panchathan
Part A
Table of content
Part A ……………………………………………………………… pp. 2-5
Part B ………………………………………………………………. pp. 7-9
Introduction:
In essence, a team may be defined as two or more people who co-operate together with a common aim. A Team focuses towards common goals and clear purpose (park, 1990). The purpose of this report is to reflect on my experience on working in groups, effectiveness of group work, presentation skills, and reflect on the presentation skills.
Effectiveness of the group work:
The most popular and common model which explains the effectiveness of the team work is Tuckman (1965) the five stages group development model. According to Tuckman (1965) there are five stages of group development and these stages include: forming, storming, norming, preforming, and adjourning.
The first stage of group development is forming stage, under this stage the team members are selected, and get to know each other, objectives are well defined, and tasks are identified. Group members try to identify a group leader and the other roles, and they try to find out what behaviors are acceptable to work in group. The second stage of group development is storming, this stage often characterized as conflict stage, where member tends to disagree on leadership, objectives and the rules. In addition, some members...

...realized there were many steps and ideas that needed to be learned before the unit goal could be reached. Throughout these six weeks, we learned about trigonometry, similarity, patterns, congruency, and using angles to solve problems. These new math ideas were just things we needed to know to find out our bigger goal for the unit.
One of the first activities we did using manipulatives was physically measuring a shadow or Shadow Data Gathering. When measuring a shadow you need to use four variables, L for the height of the light source, D for the distance from the object to the light source, H for the height of the object and S for the shadow length. These four variables would be the ones you use in the formula for how long a shadow is, our unit goal. This activity helped develop my understanding throughout the unit because it was a hands on experience of measuring a shadow, which relates you back to the unit goal. This also helped because instead of just seeing it in pictures or solving it in homework's such as the sun problem and the lamp problem we got a visual, hands on interpretation,
After measuring shadows and finding out what variables were needed to solve the unit problem the next thing we learned was how to create formulas using an In-Out table. In POW 17 making an In-Out table and identifying patterns was key to finding the formula needed and it is the same situation for solving our unit problem. Although formulas do not relate to...

...if that person asked me about trig and inverse trig, I could easily explain each function, inverse or regular. Without prompting, I could head straight into tessellations, surface area, and volume. And then, I’d become the crazy person who knows way to much about math.
This unit really clicked for me. I’m definitely an artsy person; I love looking at this from a different perspective and trying to see a solution. Geometry is a great way for me to ease into math. I, personally, think that geometry might be my favorite unit in math, just because it does have a more artsy vibe. My favorite doodles are three dimensional shapes; cubes, pyramids, and prisms. And that gave me a slight advantage in this unit. It was enjoyable for me.
IMP 2 was a good place for me to start. It really put my thoughts of high school into perspective, and it braced me for all some of the AP classes I would love to take junior and senior year. I really like the class, the content, the teacher (you are, truthfully, the best math teacher I’ve had so far; you really connect with the class and make math exciting. I’m not lying.) I am kind of known in my group of friends for being the one who always has something to say, who’s constantly talking, who has a way with words. A more word-based math program is really helping me enjoy math this yea, contrary to previous years. Thanks, Mrs. G.
“This is for girls who have the tendency to...

...1. To find my conclusions I had to think about each part of the problem. When you know that one thing means you go on to the next part. When you figure out what that means you have to see how the two statements are related. If they are related then you can deduce a conclusion that makes sense.
2. Here are my conclusions for the 6 problems on page 7.
1. a. No medicine is nice
b. Senna is a medicine
Here I deduced that Senna is not a nice medicine. I think this because the first statement says that “no medicine is nice.” That tells me that all medicines are not nice. The second statement says “Senna is a medicine”. That statement is straight forward. When you put them together you can decide that Senna is a medicine and medicines are not nice. So Senna is not nice.
2. a. All shillings are round
b. These coins are round
Here I decided that no now conclusions can be drawn. The first statement says “All shillings are round.” That statement is clear. The second statement says “These coins are round.” This tells you the coin they have are round. When you put these statements together you can see some flaws. They say these coins but you don’t know if any of these coins are shillings. They can be other coins that are round. So you cannot deduce anything.
These coins are
3. a. Some pigs are wild
b. All pigs are fat
Here I decided that there are no conclusions that can be made. The first...

...the quuantity of the number of colors minus one. So the formula would look something like this: M=k*c- (c-1) This formula really works and all you do is just plug in the numbers from the senario.
For example, in senario one I figured out by myself that three cents is the most amount of money that Ms. Hernandez would have to spend on her children. The most amount of money she would have to spend on her children would be three cents if they each wanted the same color. The equation is the work below.
M=k*c- (c-1)
M=2*2 – (2-1)
M=2*2 – (1)
M= 4 – 1
M= 3 cents
The equation for senario two is :
M=k*c – (c-1)
M= 2 * 3 – (3 – 1)
M= 2*3 – (2)
M= 6 – 2
M=4 cents
The equation for senario three is:
M=k*c – ( c- 1 )
M=3*3 – (3-1)
M=3*3 – (2)
M=9 – (2)
M=7 cents
# of kids
# of colors
Maximum amount of money
2
2
3¢
2
3
4¢
3
3
7¢
Extensions:
1. Ms. Hernandez and her twins pass a gumball machine with five different colors. What it the most amount of money it would cost for her to get her twins the same color gumball?
M=k*c – ( c- 1)
M= 2 * 5 – (5 – 1)
M= 2 * 5 – (4)
M= 10 – 4
M=6¢
2. Mr. Hodges and his triplets pass the gumball machine with five different colors the next day. What is the most amount of money he would have to pay in order to get each of...

...Math Portfolio SL TYPE I
LACSAP’S FRACTIONS
Introduction
This assignment requires us to solve patterns in numerators and denominators in LACSAP’S FRACTIONS, and the first five rows look like:
Figure 1: Lacsap’s Fractions
1 1st row
1 3/2 1 2nd row
1 6/4 6/4 1 3rd row1 10/7 10/6 10/7 1 4th row
1 15/11 15/9 15/9 15/11 1 5th row
Then, let’s look at each part of the question.
Part 1: Numerator of the Sixth Row
Describe how to find the numerator of the sixth row.
For the first part of the question, we need to describe how to find the numerator of the sixth row. To begin with, let’s make all the numerators look the same in a row:
Figure 2: Lacsap’s Fractions
1/11/1 1st row
3/3 3/2 3/3 2nd row
6/6 6/4 6/4 6/6 3rd row
10/10 10/7 10/6 10/7 10/10 4th row
15/15 15/11 15/9 15/9 15/11 15/15 5th row
Then, we can take out the denominator and go down by the row and just look at the numerator for this part of question, which will look like:...