– 6 – MATME/PF/M11/N11/M12/N12
For final assessment in 2011 and 2012
STELLAR NUMBERS SL TYPE I
Aim: In this task you will consider geometric shapes which lead to special numbers. The simplest example of these are square numbers, 1, 4, 9, 16, which can be represented by squares of side 1, 2, 3 and 4. The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular numbers (1,3,6,)…. 1 3 6 10 15

Complete the triangular numbers sequence with three more terms. Find a general statement that represents the nth triangular number in terms of n. Consider stellar (star) shapes with p vertices, leading to p-stellar numbers. The first four representations for a star with six vertices are shown in the four stages S1–S4 below. The 6-stellar number at each stage is the total number of dots in the diagram. S1 S2 S3 S4

Find the number of dots (i.e. the stellar number) in each stage up to S6. Organize the data so that you can recognize and describe any patterns. Find an expression for the 6-stellar number at stage S7.

Find a general statement for the 6-stellar number at stage Sn in terms of n. Now repeat the steps above for other values of p.
Hence, produce the general statement, in terms of p and n, that generates the sequence of p-stellar numbers for any value of p at stage Sn. Test the validity of the general statement.
Discuss the scope or limitations of the general statement.
Explain how you arrived at the general statement.

...
StellarNumbers
Results
1. Triangular Numbers
Observation of the number pattern of polynomial type or different pattern needed.
Identifying the order of the general term by using the difference between the succeeding numbers.
Students are expected to use mathematical way of deriving the general term for the sequence.
Students are expected use technology GDC to generate the 7th and 8th terms also can use other graphic packages to find the general pattern to support their result
The general term in this stage is
2. 6- stellarnumbers
Stage
No of dots
1
1
2
13
3
37
4
73
5
121
6
181
Students are expected to make the stellar shape for the next to stages and count the no of dots to get the 6-stellarnumber in 5th and 6th stage
Diagrams can be hand made or using technology
Communication or observation of the number pattern has to be given
From the observation, the expression of the terms of this sequence has to be identified
Expression for the 7th term
General expression 6 – stellar shape
or
p n (n-1) +1
Other stellar shapes – based on the no of vertices the students choose...

...The aim of this task is to investigate geometric shapes, which lead to special numbers. The simplest example of these are square numbers, such as 1, 4, 9, 16, which can be represented by squares of side 1, 2, 3, and 4.
Triangular numbers are defined as “the number of dots in an equilateral triangle uniformly filled with dots”. The sequence of triangular numbers are derived from all natural numbers and zero, if the following number is always added to the previous as shown below, a triangular number will always be the outcome:
1 = 1
2 + 1 = 3
3 + (2 + 1) = 6
4 + (1 + 2 + 3) = 10
5 + (1 + 2 + 3 + 4) = 15
Moreover, triangular numbers can be seen in other mathematical theories, such as Pascal’s triangle, as shown in the diagram below. The triangular numbers are found in the third diagonal, as highlighted in red.
The first diagrams to be considered show a triangular pattern of evenly spaced dots, and the number of dots within each diagram represents a triangular number.
Thereafter, the sequence was to be developed into the next three terms as shown below.
The information from the diagrams above is represented in the table below.
Term Number (n) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Triangular Number (Tn) | 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 |
Establishing...

...think everybody knows. It are the following 10 things:
1. If you want to scroll down on the internet, don’t go with your mouse on the slider, a waste of time. Use the spacebar. With the spacebar you will scroll down one page.
2. If you enter an address form on the internet. In the pop-up menu to fill in your province, don’t open it, its a waste of time. Type the first letter of your province and you will find it in 1 second.
3. Also on the Internet if the text is too small, use the CTRL + plus button.
4. If you type something on your iPhone, don’t go to your text keys to the number keys to enter the space and then the capital. Press two times just into the spacebar. The phone will then keep the point or capital self.
5. If you want to repeat your last call, push the call button and the most recently number is coming on your screen. And if you push again, the number is calling.
6. Bij ? leaving a massage on a voicemail. After: “leave a massage”. There coming fifteen other difficult (verrekte) instructions. There is one button, waarmee je direct nar de piep kunt springen. He is telling that’s in the most of time hash on your mobile, but you have to fin it out for yourself.
7. With Google you could find more than only a website. It’s a dictionary, flight database and also a calculator.
8. If you want to select a word in your word document, ga niet als een groentje (nubie) met je muis erover slepen....

...The numbers are overwhelming: Over the next 17 years, 350 million rural residents (more than the entire U.S. population today) will leave the farm and move to China’s cities. That will bring the Chinese urban population from just under 600 million today to close to 1 billion, changing China into a country where more than two-thirds of its people are city dwellers, says Jonathan Woetzel, a director in McKinsey’s Shanghai office. The change will reverse China’s centuries-old identity as a largely rural country. Thirty years ago, when China started modernizing its economy, more than 80% of Chinese lived in the countryside. And just six years ago it still was about 60%. Today China is just under 50% urban.
The newly urbanized population will live in eight megacities, those with a population of more than 10 million, as well 15 big cities with populations between 5 million and 10 million. In addition, by 2025 China will probably have at least 221 cities with a population over 1 million, estimates Woetzel. That compares with 35 cities of that scale across all of Europe today. These new urbanites are expected to be a powerful booster of growth: Urban consumption as a share of gross domestic product will most likely rise from 25% today to roughly 33% by 2025. “Urbanization is the engine of the Chinese economy—it is what has driven productivity growth over the last 20 years,” says Woetzel. “And China has the potential to keep doing this for the next 20 years.”...

...patterns evolve, such as the square numbers, triangular numbers, and much more. The StellarNumbers are mostly used in astronomy and astrology. StellarNumbers are figurate numbers based on the number of dots that can fit into a midpoint to form a star shape. The points of the star determine the number of points plotted around the midpoint.
Triangularnumbers is a figurate number system that can be represented in the form of a triangular grid of points where the first row contains a single element and each subsequent row contains one more element than the previous one. The triangular numbers from that pattern are 1 followed by 1+2 followed by 1+2+3 and so on. From the pattern of the triangular numbers, this infinite serious starts with 1, 3, 6, 10, 15… With this pattern, calculated by counting, the next three terms would be 21, 28, and 36. To derive a formula from this pattern, we can see that x is repeated and the number goes up each time by one. After using the rules of the sequences and a few checks, the final formula results inx(x+1)2 where x is any natural number. I found this formula with the calculator with steps show below. To prove this formula, there is the typical guess and check formula where the number of dots in the next triangle is...

...
Portfolio Assignment
SUS1501 – Sustainability and Greed
Student Name: Shitlhangu Mercy Tsakani
Student Number: 40525007
Date: 2014.05.06
Teaching Assistant Name: S GEORGE
Declaration:
By submitting this portfolio, I implicitly declare that this is my own work except for the “Introduction” which was kindly written for me by my lecturer.
Introduction
My aim in compiling this portfolio was to reflect on the things that have struck me throughout this crazy module.
My starting point for doing this was to revisit my opinions to the multiple choice questions which were presented in the Crossroads assignment. I present these current opinions, together with my original opinions, and some brief notes in the section entitled: “Back at the Crossroads!”
Once I have done this, I draw some key conclusions about this crazy module and about the things that did indeed strike me.
Back at the Crossroads!
1. “The assets of the three richest people in the world match the combined annual GDP’s of the 48 poorest countries.” My personal opinion on this statement is most closely described by:
a. Good for them – they worked hard to get their wealth
b. The only problem I have with this is that this money is in their bank account and not in mine
c. No problem with this – many of these people give huge amounts to charities
d. I think that it is morally wrong for anyone to have that...

...Republic of the Philippines
LAGUNA STATE POLYTECHNIC UNIVERSITY
Siniloan (Host) Campus
Siniloan, Laguna
College of Hospitality Management and Tourism
PORTFOLIO
In Partial Fulfillment of the requirements
For the degree of
Bachelor of Science in Tourism
Submitted to:
MR. FRITZ S. CALLANTA
Practicum Coordinator
Submitted by:
DARYL MAY B. SARMIENTO
BS Tourism
S.Y. 2013 – 2014
DARYL MAY B. SARMIENTO
177 L. De Leon St.,Brgy. Acevida, Siniloan, Laguna
+639056221736
bagieewagiee_09@yahoo.com
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Objective:
I personally would like to apply in this institution that will enhance my knowledge about new trends in tourism services as well as develop my skills in tourism practice and also, have a good attitude towards work and co-workers.
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PERSONAL INFORMATION:
Full Name: Daryl May Barbacena Sarmiento
Nickname: Din-Din
Age: 20
Birthday: October 3, 1993
Place of Birth: Pio Duran, Albay, Bicol
Nationality: Filipino
Civil Status: Single
Religion: Roman Catholic
Father: Dariel Sarmiento
Occupation: Dressmaker
Mother: Belinda Sarmiento
Occupation: Housekeeper...

...Associate in Arts degree in Nursing. I also didn’t know it would take me 5 years to have a Bachelor in Arts degree in Nursing. I need to have special qualities to be a nurse like having good time management skills, concentration skills, good computer skills, etc. There are many things I will learn throughout my journey at Durham Tech.
I learned how to use resources while working on my portfolio assignment. I learned how to use the Occupational Outlook Handbook. I already knew how to use the CFNC site because I used it throughout high school. These websites helped me to research how many years it will take me to be a nurse, what qualities a nurse must have, the amount of money they will earn, etc. It’s awesome that there are websites to help you to research about your career.
I can use my portfolio as a tool as I complete my studies at Durham Tech. I can use my portfolio to see what classes I’m going to take in the next two and a half years. I’m going to see if I really did achieve my SMART goals when I graduate from Durham Tech. After these 3 years I should know which kind of nurse I want to be. This portfolio assignment made me realize that I was going to take the wrong path through the wrong plan of study.
I understood many things through the CFNC Assessments ‘Interest Profiler’ and ‘Work Value Sorter.’ According to the Interest Profiler on CFNC, Social and Investigative are two of my top interest areas. Nurses...