Logistics and Supply Chain Management Operations' Process Control, Assignment

Logistics and Supply Chain Management Operations' Process Control, Optimization, and Sustainability in Seaport Container Termina - Assignment Example This is to say that the result of a productive port container terminal over a relatively longer period of time yields sustainability (Clark, Dollar and Micco, 2004). But for productivity to be optimized, a couple of operational management needs have to be fulfilled. These are logistics and supply chain management. The reason why these two phenomena should be incorporated and used hand-in-hand is that productivity and for that matter sustainability of container terminal is measured partly by the discharge and loading of container onto vessel as well as the reception and delivery operations, which involves transferring containers in and out of trucks (Kim and Park, 2003). These means of measurement directly require logistics to control the flow of container demands as well as supply chain management, which would determine the activities of individuals and organizations, which ensure the upstream and downstream flow of products and goods in vessel operations (De Monie, 1987). Problem St atement Vessel operators have recently adapted several methodologies and strategies in achieving sustainability in seaport container terminal including the use of concessions and the privisation of ports but not much of results seem to have been achieved even with these (Drewry Consultants Ltd. 2003). In the midst of the major failures being recorded therefore, there is the need for there to be a paradigm shift that looks at an unorthodox and radical strategy that can promise an unprecedented result. Interestingly, there have been a couple of research works already undertaken by a number of researchers who have looked at the impact of logistics and supply chain management towards process control, optimization and sustainability in seaport container terminal. For the present study, a number of those studies that made use of qualitative research approach shall be critically analysed. This implies that the proposed research shall be made to follow the qualitative research approach. By this study, some of the major forms of qualitative research approach shall be reviewed according to their weaknesses and strengths and an eventual decision on the best form or type of qualitative research approach for the proposed study shall be selected. Aims and Objectives Generally, the present study is structured around and aim, which is the overall goal that the researcher wants to achieve for the study. But the aim is wide and cannot be achieved without breaking it down into divisible parts. To this end, a number of specific objectives are set to help accomplish the research aim. The aim of the study is to determine which qualitative methods in the academic literature have been most effectively used in addressing the issue of how logistics and supply chain management aids in accelerating process control, optimization and sustainability in seaport container terminal. The specific objectives that need to be achieved independently to consolidate the achievement of the overall aim are given as follows. 1. To identify the two commonest forms of qualitative methods used in addressing the issue of logistics and supply chain management in seaport container terminal. 2. To evaluate the two types of approaches independently on the basis of The type of research questions addressed The value of the results presented The methods and instruments employed in achieving results 3. To evaluate the

Text Set-Literacy Curriculum Research Paper Example | Topics and Well Written Essays - 500 words

Text Set-Literacy Curriculum - Research Paper Example This leaves no room for ambiguity for students at the same time in understanding the subject matter. It is rather suggested that teachers should undertake activities in class where students will have to select short text as per their choice. However, a limitation is there in this regard i.e. teacher’s obligation for reading each and every story that the students pick as a short text. For this, it can be said that short text is much manageable in reading (Fletcher & Portalupi, 2001). It immediately finishes up in one sitting rather than longer novels that are continued for some days. Looking at the real life examples of reading habits of general public, short text such as tweets, how-to articles, cookbooks, announcements, online forums are read more than longer books. Therefore, there is an avid need of making reading interesting for peers that is possible with the help of short text selection (Cohen,

Rook Polynomials and Chess

Rook Polynomials and Chess Introduction Chess is a complex strategical board game. The board on which the game is played is an eight by eight grid. Each player begins the game with 16 pieces: eight pawns, two knights, two bishops , two rooks, one queen, and a single king. Each of the six piece types move differently, and each are able to attack, or remove a certain piece, in different directions. The objective of chess is to checkmate the opposing king by placing ones own pieces around the king where it is being attacked no matter what action it takes.. While chess is primarily a recreational activity, the complexity of the movement of the pieces has resulted in it having significant mathematical properties. Chess analysis is complicated because of the multitude of movement options open to both players at every single move. Many mathematical chess problems involve discovering how specific placement of pieces can result in none of the pieces attacking each other, I.e. None of the pieces are within the same line of sight. One particular variation of these problems is the rook polynomial. The rook piece is able to move horizontally or vertically up to a max of eight squares. In combinatorial mathematics, a rook polynomial generates the combinations of non-attacking rooks; no two rooks are in the same row or column. A board is any layout of squares of a rectangular board with (y) rows and (z) columns. While there are, numerous formulas determining rook placement for rook polynomials, this investigation will look into the method of classifying all quadratic polynomials which are the rook polynomial for some generalized board G. Rook Movement and Application As stated, in chess, rooks are able to attack   any square in its line of sight,( i.e. its row or column)   exhibited below If a rook were to fall in the line of sight of another rook, they would be attacking. Rook polynomials focus on nonattacking rooks. The board of a rook polynomial is defined as a square n x n chessboard, but can also include any subset of a board. For instance, on a 2 x 3 chess board, or an L shaped chessboard would be subset of a regular board. To denote the patterns in which multiple nonattacking rooks can be placed on a generalized board, the variable S can represent the ways to place a number of non-attacking rooks. R will represent the rook, and (G) the size of the generalized board, creating the formula rs(G). rs(G) will be stated as rs when the size of the board (G) as the size of the board will be apparent. For all boards, r0 will always be equal to one, because it is impossible to set 0 rooks in differing combinations. R1 will always be the number of squares on the board because rook can be placed anywhere as no other rooks are on the board to attack. Rs = 0 when k is greate r than the number of rows or columns on the board, as there will be no way to place all the nonattacking rooks. The following generalized board provides an example of the equation: According to our determined parameters, for this particular subset r0 would again be equal to 1, and r1 would be equal to the number of squares, in this case six. For r2 there are 8 ways to place 2 non attacking rooks, demonstrated below. x x x x x x x x x X X x x x x x Three rooks placed on the board only allow for 3 different non-attacking combinations, meaning r3 equals 3 x x X X x X X x x Since there are only 3 rows for this particular generalized board any rs>3 as being equal to 0. Using this general principle it is possible to create a polynomial that tracks all of the potential rook combinations on a generalized board. The rss would be the coefficients of xs, resulting in the formula: r0 + r1x + r2x2 + à ¢Ã¢â€š ¬Ã‚ ¦+rs-1xs-1+ rsxk The rook placement numbers from the previous generalized board: r0 = 1, r1 = 6, r2 = 8, r3 = 3, r4 = 0, r5, r6,à ¢Ã¢â€š ¬Ã‚ ¦ = 0 Resulting in the following polynomial: 1+ 6x + 8x2 + 3x3 However it is important to understand that rook polynomials are not unique to a single generalized board. Any board with a similar 3 column lay out would have the same polynomial formula. This leads to the purpose of this mathematics investigation which is to classify all quadratic polynomials which are the rook combinations for a generalized board G. Determining the Quadratic Polynomial Since r0= 1 will always be true, and   r1 = number of squares of (g) the root of the quadratic is: 1 + r1x + r2x2 r1 is determined by board size, therefore it is necessary to discover any r2s where r3 is equal to 0.   If r3 is greater than zero, the rook polynomial could potentially be a cubic, or even quartic. As demonstrated in the previous example, generalized boards with 3 rows will result in polynomials where r4=0 When examining the requirements of r4 = 0, the generalized board must contain two rows of a board and contain squares that are consecutive in each row. As determined preciously, r1 is equal to the number of squares on the generalized board. With that information, we can summarize each row of the board as variables (y) and (z). In this case r1= y+z. With this methodology, (y) and (z) will be placed in a way that the spaces in row (y) are consecutive, and (z) squares are consecutive in the next row. Another important aspect is the number of columns created by (y) and (z). The overlap of the rows will be labeled (p). Using the number of squares in the example, consider r1 to be equal to 12. The possible pairs for (y) and (z) are: 1,11; 2,10; 3,9; 4,8; 5,7; 6,6 To create a formula outlining all the potential quadratic equations of a rook polynomial, any of these numbered pairs will work. In the case of 4,8, if none of the rows overlapped, r2 would be equal to 48. To determine r2 when squares are overlapping, it is necessary to multiply the number of squares in row (y) which are not overlapping by (z), and that to the product of the number of squares overlapping between the two of them and the number of squares not overlapping in row (z). Each square overlap should reduce r2 by 1. To demonstrate: 28+27 18+37 47 If a closer look is taken at each of these equations, it is possible to expand it to and relabel the numbers with variables to create a formula. To demonstrate (38) + (17) = (4-1)8 + 1(8-1) (28) + (27) = (4-2)8 + 2(8-1) (18) + (37) = (4-3)8 +3(8-1) The numerals in these expanded equations can be replaced to reform the formula: r2= (y-i)(z) + (p)(z-1) Simplifying into r2 = yz -pz + pz -   p r2 = yz -p We can insert this equation into the rook polynomial already established to create a formula which can calculate all potential rook polynomial combinations. For example if a generalized board contains row (y) with 6 squares, and row (z) contains 9 squares, with an overlap of p=4, the quadratic polynomial would appear as: 1+(y+z)x +(yz-p)x2 1+(6+9)x +((69)-4)x2 1+15x +((54)-4)x2 1+ 15x + 50x2 Therefore the formula to calculate all potential rook polynomial combinations is 1 + (y+z)x + (yz-p)x2 Discussion and Conclusion Rook polynomials, despite appearing as only a theoretical chess puzzle, actually have a number of practical applications. Various organization problems and layouts can be modeled by the rook problem by equating the objects involved to acting as rooks. A practical application stems from company scheduling. Management may require a specifc number of employees to work their jobs at specific times. However there maybe scheduling issues to ensure no two workers are performing the same job at the same time. A rook polynomial calculation could give insight into the number of combinations of how the workers could be scheduled. The number of workers could represent row (z), and the times available row (y). Each worker must be be at the job and only one time, which is similar to the concept of a rook being at a specific spot that is not attacking any other rook. Depending on the overlap of times and workers available schedule, the formula produce in this investigation could be used to determin e the number of combinations. Another example is if a company desires to hire a certain (y)number of employees on a number (z) different jobs. Each job can only be held by only one employee. By putting both employee number and job number on the rows of a generalized chessboard chessboard, the result is similar to that of a rooks dilemma. When worker A is appointed to job B, it is like a rook is placed on the square where row (y)overlaps row (z). Every occupation will be performed by a single worker, and every worker is assigned to a single job. Therefore all rows and columns in the pattern will contain only one rook, signifying that the rooks will not be attacking one another. The rook polynomial formula could be used to calculate the number of ways the assignments can be executed. However, the investigation in creating a quadratic rook polynomial formula did have limitations. I was unable to expand the formula to examine greater sized generalized boards, requiring that it not reach cubic or quartic levels. I had initially attempted this, but found that I could not find a generalized rule for each and every combination of a generalized board. For this reason, the application to general life problems is limited. My process could have been improved by investigating further into complex rook polynomials such as the Lagueree polynomial.   Ultimately the complexity of chess allow for both simple and complex mathematical analysis, which can produce formulas which have real life application. Having chess as a visual and interactive tool to explore various concepts of math was a helpful resource when performing this investigation. Not only this, but my own enthusiasm for playing chess and studying the intricacies of the math behind the pieces pushed me to write the investigation.

Essay --

Memories from July â€Å"He threw with all his might, but the third stone came skipping back.† Fifty years later. â€Å"Running through the stormy weather, he ran to the spot where he meets the love of his life every afternoon during July. Ever since they were eight, they would meet through the forest at an enormous pond to chat and skip rocks. They decided early on that the amount of rocks they skipped would represent the number of things that they need to get off of their chest. Once he reached the water’s edge, the boy bent over and picked up a pearl colored stone and skipped it, releasing all of his bottled up emotions. After the stone was swallowed by the vast pond, he immediately picked up another and gently tossed it.† â€Å"Making her way down to stand next to him, the girl asked, ‘Why only two?’† â€Å"‘No reason. I’ve just had a lot of things on my mind lately.’ the boy grinned, motioning for the girl to pick up a stone.† â€Å"Did they love each other?† a small child anxiously asked her grandmother. â€Å"Slow down dearie.† said the old woman, smiling. â€Å"You wouldn’t want to skip any parts, now would you?† The young girl eagerly shook her head and looked up at her grandmother’s green eyes once again. â€Å"When the sun began to set,† the grandmother spoke, â€Å"the boy and girl decided that it was time for them to go home. The boy was from a wealthy family, and had messy, golden hair that came just above his eyes. His eyes were as golden as the honey from a honeybee. The girl, however, came from a poor family and had jade green eyes, and dark red, curly hair that she wore in a French braid. The boy’s mother absolutely hated the girl, and forbid him from ever seeing her again.† â€Å"But why?† whined the tiny child. â€Å"What did he do?!† The grandmother chuckled... ...the rest of the year, and when July finally came around again, they waited for the other at the rock. They grew closer to each other with every passing day and never went a day without skipping stones.† â€Å"So they fell in love and got married?† asked the smiling toddler. â€Å"Not exactly,† her grandmother said. â€Å"The end of July neared once again, and they were feeling blue, knowing that their days together were coming to an end. It stormed on the last day of July, but they didn’t think anything of it. The young couple said their heartfelt goodbyes and went their own separate ways.† â€Å"Nick stopped replying to Katalina’s letters around Christmas time. He would send a letter a few times here and there, but never explained why he didn’t write to her as often. Katalina felt as if things weren’t the same anymore so she asked him to meet her at their spot, but he never showed up.

Fast Food Nation Essay

Of all non-profit organizations involved in the improvement of food handling, S. T. O. P or Safe Tables Our Priority deserved to be supported by the government as it had effectively acted as public health organization dedicated to preventing illness and death from food-borne pathogens. Since 1993, S. T. O. P had advocated changes in US public policy, widely educated and had done massive outreach, provided assistance to the victims of food-borne diseases, and implemented in-depth studies based on victims’ experience and listed them in the organizations’ registry so as for them to study the long-term consequences of food-borne disease. Historically, the organization was borne out of united anguish of parents of E. coli O157:H7 victims brought about the mishandling of foods by Jack in the Box hamburgers. Given its substantial numbers of victims, it has reached a nationwide attention of the public and the media. The group has presented itself with a clear mission of propagating food safety rules and regulations that would safeguard and inform the American populace on the seriousness of the illness. And since there was no existing organization as such, S. T. O. P. ’s membership had radically increased. Now everyone worries about the nutritional implications of excessive dining at fast-food restaurants and food safety issues. Moreover, their national visibility has soared as they were frequently contacted by media sources. Since then, new programs across the nation had run five different shows discussing meat, seafood, poultry, produce and even fruit juice safety guidelines for the sake of public education. Because of the mass media channel, food industry and legislative officials had taken action and highlighted the issue of food safety whereas before none had done at all. Through the media mileage S. T. O. P. ’s mission had a pivotal momentum as media had effectively assisted its advocacy and legislative efforts that had resulted to reform of food safety in the United States. Current food safety strategy followed by both the government and industry places far too much emphasis on consumer behavior. This over-emphasis on consumer education fosters the misleading impression that it is the consumers’ responsibility to make sure their food is safe, and if people get sick, it is their own fault. Furthermore, through their research they had found out that there were government agencies that lacked efficient communication when the said outbreak happened. They also found out that there were agencies of the government that are aware of the emerging food-borne pathogens however they lacked propagation of the knowledge nor do they have any comprehensive plan to resolve it. According to their study, the USDA (Department of Agriculture), the Congress and the media had failed to inspect these food products and aren’t aware of the massive growth in numbers of its victims. Moreover, S. T. O. P. had joined Safe Food Coalition, an organization with twelve consumer groups that advocated food safety. After several, extensive communication with USDA S. T. O. P. had became a catalyst for change as they were invited to join at policy making table and became a key player in assisting and promoting the launching of food handling inspection after ninety years. They endorsed microbial testing for animal fecal contamination like Salmonella and E. coli. They implored government agencies to reform their policies and address improved food handling. They implored that medical professional for humans and not just veterinarians to work at USDA. They implored for USDA to eradicate conflict of interest in view of the fact that both the marketing and the inspection of food handling is under the same department. In addition, the organization had promptly become the shelter of food-borne victims. They had received frequent telephone calls inquiring about the disease and S. T. O. P. had distributed packets of information from consumers to households. Members had helped try save victims and their families through anchoring various lectures for those struggling with the medical and emotional repercussions of the disease. Then in 2003, S. T. O. P. had launched a groundbreaking report entitled, â€Å"Why Are People Still Dying from Contaminated Food. † It reports the food safety challenges and their recommendations. They advocated that everyone should address the problem from the start of food handling fro instance by keeping pathogens out of the food supply. Also, they had distributed this information through mailings, newsletters and currently through E-alerts. These medium had discussed numerous food-borne diseases such as Pathogens 101, E. coli 0157:H7 bacteria, viruses like Hepatitis A and Norovirus among others, parasites from foods such as Cryptosporidium and others, other syndromes and conditions like Hemolytic Uremic Syndrome (HUS), nvCJD (Mad Cow Disease) and reactive Arthritis/Reiter’s among others, numerous miscellaneous illnesses from digested metals, toxins, prions or wasting diseases and even plastics. Suffice it to say in its endeavor to combat food-borne bacteria S. T. O. P. has had many successes as they focus on advocacy, victim support, outreach, and safe food education. For more than fifteen years they already had worked with both national and local media, responsive food industry trade groups and firms, government agencies such as the Congress, USDA, Food and Drug Administration (FDA), Health and Human Services (HHS), and the Centers for Disease Control (CDC). Through various television segments such as S. T. O. P. in the News, numerous newsletters, teleseminars and podcasts, press releases, media kits, special events and reports, speaking engagements, and online educational resources, the organization had brought about a drastic change in the eating lifestyle of Americans. Thus, the government should be supporting such agencies that clearly promote safety on its constituents.

Effects of Overpopulation in China Essay

This literature review discusses the impacts of overpopulation on the environment in China through four main studies. Each study directed its research on one consequence: the water issue and the aquatic ecosystem, the overexploitation of land and resources as well as the extinction of green land, climate change, GHG emission and desertification of land1. Several methods and sources were used such as Pressure–State–Response (PSR), urban-rural population model or other research papers written previously2. The results of these studies clearly show that the overpopulation has multiple negative impacts on the Chinese environment and that strategies and policies regarding these issues should be established. The population of China is growing exponentially and it is a serious issue because of its impact on the environment. The water deficiency is growing and as it is presented, the expectations of the Chinese people exceed the capacity of the land3. Since the population of China is increasing fast, the urbanization of land and the agricultural development increase at the same rhythm4. As it is presented, human activity and human density are the main explanation for climate change5. According to Shijie Wang’s study, the southwest of China is experiencing a desertification, in other words the land becomes like a desert left with no resources6. Each article presents a different way of conducting its research to prove its point. In Qian Hong et al. research, the methods used to pursue the study are Pressure–State–Response (PSR), the landscape ecology method and Remote Sensing – Global Positioning System (RS-GPS) 7. According to the authors, there are three types of indicators: Pressure indicators, State indicators and Response indicators7. The indicators either presented a high or a low number. If the number is high, it means that the region suffered from important water degradation; if the number is low, it means the opposite7. The analysis of the research is made through a process called Analytical hierarchy process (AHP) that has four specific indicators7. Jianfa Shen’s study uses urban-rural population model to do predictions about the density of the population and is also represented as spatial demographic-economic model 8, whereas Shijie Wang conducted its research by investigating the studied region and by using indicators such as aerial photos and satellite images. He then compares and analyses the results with previous images and researches from the land 9. The only piece of work that did not use any kind of Research method was written by Hung Ming-Te et al. who preferred to write the paper in reference to researches and studies made and scientific predictions 10. One of the most important consequences of overpopulation is the expanding deficiency in water resources. Investigators processed in six districts of China which are part of one region (Jinan) that was recognized for its important source of water, aquatic ecosystem and surface. Due to industrial development and human actions the water condition became polluted and rarer 11. Researchers found that water deficiency and erosion, rainy climate, poor land vegetation, climate change, loss and decrease of agricultural production, which all lead to desertification of land, are all consequences of the activities of the overpopulation 12. Ming-Te et al.’s study presented that the GHG level increased rapidly and the national security is at risk. GHG growing production would also make the lack of water and air pollution worse than it actually is; also they stated that climate change, in addition to being caused by overpopulation, is influenced by poor sustainable development, poor resources management and over-use of energy. This study shows that such changes have impact such as poor water resource and low agricultural production. These consequences engender other concerns such as the lack of food, the decrease in water resources and the desertification of land 13. The conclusions are clear regarding this area, the exceeding use of natural resources is a threat for the environment’s protection and conservation 14. Hong et al. are from the same opinion when they wrote that water condition is getting worse and it affects China’s population’s lifestyle as well as the aquatic ecosystem 15. 10 Hung Ming-Te et al., 363-366 11 Qian Hong et al., 321 12 Shijie Wang et al., 127-129 13 Hung Ming-Te et al., 363-364 14 Jianfa Shen, 39 15 Qian Hong et al., 319 In the field of environment, every single factor is closely related to another one. Each of the four studies shows how the desertification of land, the migration, the exceeding use of resources and the poverty of population are linked. In Wang et al.’s research, poverty is shown to be one of the most devastating causes of desertification because farmers, in order to survive and feed their families, have to increase the production of grains. The overexploitation of the land then leads the land to become rocky 16. According to Shen’s study, agriculture is over-used and China has to import grains to meet the population’s needs 17. The deterioration of the environment and the growth of the land desertification are strongly correlated with the increasing population of this region as well as their activities 18. In reference to Wang et al., Shen and Ming-Te et al.’s studies, since the land is experiencing a phenomenon of desertification because of the exceeding use of agriculture and the high density of population in rural zones, populations are migrating to cities that have already exceeded their capacity in supporting people19. Basically, what Shen is trying to explain is that the construction of urban areas and the overexploitation of lands lead to a decreasing number of green land which causes the environment to deteriorate, because the more people there is, the more resources needed 20. The biggest problem China is facing is the lack of policing and measures adopted regarding the protection of the environment. According to Ming-Te et al., 16 Shijie Wang et al., 131 17 Jianfa Shen, 36 18 Shijie Wang et al., 124 19 Shijie Wang et al., 124-131; Jianfa Shen, 36-39; Hung Ming-Te et al., 363-364 20 Jianfa Shen, 35-36 China’s way of ‘fighting’ against climate change is to invest in the development of sustainable technologies as well as establishing measures and policies regarding the environment 21. Qian Hong et al. specified that the conservation and the protection of water are essential to the survival of the land and aquatic ecosystem 22. The researchers from the two other articles did not write about the policies that should be established to preserve the environment. Studies show that the impacts of overpopulation are multiple and they do affect the ecosystem in China. Shijie Wang et al.’s study proved that the land is overloaded with population growth and has met its capacity. This forced farmers to deforest the land of the Liupanshui district in order for them to increase agricultural production. Also, even though the environment is favorable in this region for such phenomenon to happen, restricted natural resources, overpopulation activities, rapid population growth and social instability make the process happen faster. The consequence of overpopulation’s production of sulfur dioxide in the atmosphere exceeds the national average for smelting sulfur by over 13.8 times in some regions such as Bijie and Zunyi which causes air pollution and desertification of land 23. The results of the study conducted in the region of Jinan by Qian Hong et al. clearly showed that this region has the best water condition because of its good conservation of environment, poor population density and important vegetation 24. Hung Ming-Te et al. proved that overpopulation, causing in many ways the change in climate would increase the frequency and strength of natural weather disasters 25. Jianfa Shen suggested that the exceeding use of natural resources due to the increasing density of population is a threat for the environment’s protection and conservation and that people’s lifestyle influences the environment negatively 26.   Bibliography Shen, J. â€Å"China’s Future Population and Development Challenges†. The Geographical Journal 164 no. 1 (1998): 32-40 Hung, M., et al. â€Å"China’s Response to Climate Change: A Policy Analysis.† Journal Of Alternative Perspectives In The Social Sciences 3 no. 2 (2011): 362-375. Wang, S., et al. â€Å"Mechanism of Rocky Desertification in the Karst Mountain Areas of Guizhou Province, Southwest China.† International Review For Environmental Strategies 3 no. 1 (2002): 123-135 Hong, Q., et al. â€Å"Regional aquatic ecological security assessment in Jinan, China†. Aquatic Ecosystem Health & Management 13 no. 3 (2010): 319-327

Ordinal Number Definition and Examples

Ordinal Number Definition and Examples An ordinal number is a number that indicates position or order in relation to other numbers: first, second, third, and so on. Contrast these types of numbers with cardinal numbers  (in math theyre also called natural numbers and integers), those numbers that represent countable quantity.   Ordinal numbers  do not represent quantity, notes Mark Andrew Lim, but rather indicate rank and position, such as the fifth car, the twenty†fourth bar, the second highest marks, and so on(The Handbook of Technical Analysis, 2012). Learning Ordinals If you are teaching ordinals to English language learners, introduce the concept by reviewing cardinal numbers. Then continue with the ordinals to contrast the concepts. Also, introduce the term last as a position vocabulary word. Examples of Ordinals All ordinal numbers carry a suffix: -nd, -rd, -st, or -th.  Ordinal numbers can be written as words (second, third) or as numerals followed by abbreviations  (2nd, 3rd). first (1st)second (2nd)third (3rd)fourth (4th)fifth (5th)sixth (6th)seventh (7th)eighth (8th)ninth (9th)tenth (10th)eleventh (11th)twelfth (12th)twentieth (20th)twenty-first (21st)twenty-second (22nd)twenty-third (23rd)twenty-fourth (24th)thirtieth (30th)one hundredth (100th)one thousandth (1,000th)one millionth (1,000,000th)one billionth (1,000,000,000th) Using Ordinal Numbers and Cardinal Numbers Together When a cardinal number and an ordinal number modify the same noun, the ordinal number always precedes the cardinal number: The first two operations were the most difficult to watch. The second three innings were quite dull. In the first example, the ordinal number first precedes the cardinal number two. Both first and two are determiners. In the second example, the ordinal number second precedes the cardinal number three. Both second and three are determiners. Try reading the sentences with the ordinal and cardinal numbers reversed. They simply sound wrong.(Michael Strumpf and Auriel Douglas, The Grammar Bible. Owl Books, 2004) More Tips on Using Ordinal Numbers Spell out ordinal numbers- first, second, third, fourth- except when quoting from another source. In the interests of saving space, they may also be expressed in numerals in notes and references. ... Use words for  ordinal numbers in names, and for numerical street names ... : the Third Reich the Fourth Estate a fifth columnist Sixth Avenue a Seventh-Day Adventist ... Use figures for ages expressed in cardinal numbers, and words for ages expressed as ordinal numbers or decades: a girl of 15 a 33-year-old man between her teens and twenties in his 33rd year (R. M. Ritter, New Harts Rules: The Handbook of Style for Writers and Editors. Oxford University Press, 2005) Do not use the ordinal (th, st, rd, nd) form of numbers when writing the complete date: January 15 is the date for the examination. However, you may use the ordinal suffixes if you use only the day: The 15th is the date for the examination. ... Write out ordinal numbers when they contain just one word: third prize, tenth in line, sixtieth anniversary, fifteenth birthday. Use numerals for the others: the 52nd state, the 21st Amendment.(Val Dumond, Grammar for Grownups. HarperCollins, 1993)